Publications

Endocrine glands secrete hormones into the circulation to target distant tissues and regulate their functions. The qualitative relationship between hormone-secreting organs and their target tissues is well established, but a quantitative approach is currently limited. Quantification is important, as it could allow us to study the endocrine system using engineering concepts of optimality and tradeoffs. In this study, we collected literature data on 24 human hormones secreted from dedicated endocrine cells. We find that the number of endocrine cells secreting a hormone is proportional to the number of its target cells. A single endocrine cell serves approximately 2,000 target cells, a relationship that spans 6 orders of magnitude of cell numbers. This suggests an economic principle of cells working near their maximal capacity, and glands that are no bigger than they need to be.

The accumulation of senescent cells promotes ageing and age-related diseases, but molecular mechanisms that senescent cells use to evade immune clearance and accumulate in tissues remain to be elucidated. Here we report that p16-positive senescent cells upregulate the immune checkpoint protein programmed death-ligand 1 (PD-L1) to accumulate in ageing and chronic inflammation. We show that p16-mediated inhibition of cell cycle kinases CDK4/6 induces PD-L1 stability in senescent cells via downregulation of its ubiquitin-dependent degradation. p16-expressing senescent alveolar macrophages elevate PD-L1 to promote an immunosuppressive environment that can contribute to an increased burden of senescent cells. Treatment with activating anti-PD-L1 antibodies engaging Fcγ receptors on effector cells leads to the elimination of PD-L1 and p16-positive cells. Our study uncovers a molecular mechanism of p16-dependent regulation of PD-L1 protein stability in senescent cells and reveals the potential of targeting PD-L1 to improve immunosurveillance of senescent cells and ameliorate senescence-associated inflammation.

Understanding the mechanisms of geroprotective interventions is central to aging research. We compare four prominent interventions: senolysis, caloric restriction, in vivo partial reprogramming, and heterochronic parabiosis. Using published mice transcriptomic data, we juxtapose these interventions against normal aging. We find a gene expression program common to all four interventions, in which inflammation is reduced and several metabolic processes, especially fatty acid metabolism, are increased. Normal aging exhibits the inverse of this signature across multiple organs and tissues. A similar inverse signature arises in three chronic inflammation disease models in a non-aging context, suggesting that the shift in metabolism occurs downstream of inflammation. Chronic inflammation is also shown to accelerate transcriptomic age. We conclude that a core mechanism of geroprotective interventions acts through the reduction of inflammation with downstream effects that restore fatty acid metabolism. This supports the notion of directly targeting genes associated with these pathways to mitigate age-related deterioration.

Summary Bipolar disorder (BD) is marked by fluctuating mood states over months to years, often with elevated cortisol levels. Elevated cortisol can also trigger mood episodes. Here we combine longitudinal hair cortisol and mood measurements with mathematical modeling to provide a potential mechanistic link between cortisol and mood timescales in BD. Using 12 cm hair samples, representing a year of growth, we found enhanced year-scale cortisol fluctuations whose amplitude averaged 4-fold higher in BD (n=26) participants than controls (n=59). The proximal 2 cm of hair correlated with recent mood scores. Depression (n=266) and mania (n=273) scores from a longitudinal study of BD showed similar frequency spectra. These results suggest a mechanism for BD in which high emotional reactivity excites the slow timescales in the HPA axis to generate elevated months-scale cortisol fluctuations, triggering cortisol-induced mood episodes.

Prediabetes, a subclinical state of high glucose, carries a risk of transition to diabetes. One cause of prediabetes is insulin resistance, which impairs the ability of insulin to control blood glucose. However, many individuals with high insulin resistance retain normal glucose due to compensation by enhanced insulin secretion by beta cells. Individuals seem to differ in their maximum compensation level, termed beta cell carrying capacity, such that low carrying capacity is associated with a higher risk of prediabetes and diabetes. Carrying capacity has not been quantified using a mathematical model and cannot be estimated directly from measured glucose and insulin levels in patients, unlike insulin resistance and beta cell function which can be estimated using HOMA-IR and HOMA-B formula.Here we present a mathematical model of beta cell compensation and carrying capacity, and develop a new formula called HOMA-C to estimate it from glucose and insulin measurements. HOMA-C estimates the maximal potential beta cell function of an individual, rather than the current beta cell function. We test this approach using longitudinal cohorts of prediabetic people, finding 10-fold variation in carrying capacity. Low carrying capacity is associated with higher risk of transitioning to diabetes. We estimate the timescales of beta cell compensation and insulin resistance using large datasets, showing that, unlike previous mathematical models, the new model can explain the slow rise in glucose over decades. Our mathematical understanding of beta cell carrying capacity may help to assess the risk of prediabetes in each individual.Competing Interest StatementThe authors have declared no competing interest.

Differentiation is crucial for multicellularity. However, it is inherently susceptible to mutant cells that fail to differentiate. These mutants outcompete normal cells by excessive self-renewal. It remains unclear what mechanisms can resist such mutant expansion. Here, we demonstrate a solution by engineering a synthetic differentiation circuit in Escherichia coli that selects against these mutants via a biphasic fitness strategy. The circuit provides tunable production of synthetic analogs of stem, progenitor, and differentiated cells. It resists mutations by coupling differentiation to the production of an essential enzyme, thereby disadvantaging non-differentiating mutants. The circuit selected for and maintained a positive differentiation rate in long-term evolution. Surprisingly, this rate remained constant across vast changes in growth conditions. We found that transit-amplifying cells (fast-growing progenitors) underlie this environmental robustness. Our results provide insight into the stability of differentiation and demonstrate a powerful method for engineering evolutionarily stable multicellular consortia.

Antibiotic effectiveness depends on a variety of factors. While many mechanistic details of antibiotic action are known, the connection between death rate and bacterial physiology is poorly understood. A common observation is that death rate in antibiotics rises linearly with growth rate; however, it remains unclear how other factors, such as environmental conditions and whole-cell physiological properties, affect bactericidal activity. To address this, we developed a high-throughput assay to precisely measure antibiotic-mediated death. We found that death rate is linear in growth rate, but the slope depends on environmental conditions. Growth under stress lowers death rate compared to nonstressed environments with similar growth rate. To understand stress's role, we developed a mathematical model of bacterial death based on resource allocation that includes a stress-response sector; we identify this sector using RNA-seq. Our model accurately predicts the minimal inhibitory concentration (MIC) with zero free parameters across a wide range of growth conditions. The model also quantitatively predicts death and MIC when sectors are experimentally modulated using cyclic adenosine monophosphate (cAMP), including protection from death at very low cAMP levels. The present study shows that different conditions with equal growth rate can have different death rates and establishes a quantitative relation between growth, death, and MIC that suggests approaches to improve antibiotic efficacy.

Why do we get certain diseases, whereas other diseases do not exist? In this book, Alon, one of the founders of systems biology, builds a foundation for systems medicine. Starting from basic laws, the book derives why physiological circuits are built the way they are. The circuits have fragilities that explain specific diseases and offer new strategies to treat them. By the end, the reader will be able to use simple and powerful mathematical models to describe physiological circuits. The book explores, in three parts, hormone circuits, immune circuits, and aging and age-related disease. It culminates in a periodic table of diseases. Alon writes in a style accessible to a broad range of readers - undergraduates, graduates, or researchers from computational or biological backgrounds. The level of math is friendly and the math can even be bypassed altogether. For instructors and readers who want to go deeper, the book includes dozens of exercises that have been rigorously tested in the classroom.

Genetically identical cells in the same stressful condition die at different times. The origin of this stochasticity is unclear; it may arise from different initial conditions that affect the time of demise, or from a stochastic damage accumulation mechanism that erases the initial conditions and instead amplifies noise to generate different lifespans. To address this requires measuring damage dynamics in individual cells over the lifespan, but this has rarely been achieved. Here, we used a microfluidic device to measure membrane damage in 635 carbon-starved Escherichia coli cells at high temporal resolution. We find that initial conditions of damage, size or cell-cycle phase do not explain most of the lifespan variation. Instead, the data points to a stochastic mechanism in which noise is amplified by a rising production of damage that saturates its own removal. Surprisingly, the relative variation in damage drops with age: cells become more similar to each other in terms of relative damage, indicating increasing determinism with age. Thus, chance erases initial conditions and then gives way to increasingly deterministic dynamics that dominate the lifespan distribution.

Major depressive disorder (MDD) is the most common psychiatric disorder. It has a complex and heterogeneous etiology. Most treatments take weeks to show effects and work well only for a fraction of the patients. Thus, new concepts are needed to understand MDD and its dynamics. One of the strong correlates of MDD is increased activity and dysregulation of the hypothalamic-pituitary-adrenal (HPA) axis which produces the stress hormone cortisol. Existing mathematical models of the HPA axis describe its operation on the scale of hours, and thus are unable to explore the dynamic on the scale of weeks that characterizes many aspects of MDD. Here, we propose a mathematical model of MDD on the scale of weeks, a timescale provided by the growth of the HPA hormone glands under control of HPA hormones. We add to this the mutual inhibition of the HPA axis and the hippocampus and other regions of the central nervous system (CNS) that forms a toggle switch. The model shows bistability between euthymic and depressed states, with a slow timescale of weeks in its dynamics. It explains why prolonged but not acute stress can trigger a self-sustaining depressive episode that persists even after the stress is removed. The model explains the weeks timescale for drugs to take effect, as well as the dysregulation of the HPA axis in MDD, based on gland mass changes. This understanding of MDD dynamics may help to guide strategies for treatment.

Many autoimmune disorders exhibit flares in which symptoms erupt and then decline, as exemplified by multiple sclerosis (MS) in its relapsing-remitting form. Existing mathematical models of autoimmune flares often assume regular oscillations, failing to capture the stochastic and non-periodic nature of flare-ups. We suggest that autoimmune flares are driven by excitable dynamics triggered by stochastic events auch as stress, infection and other factors. Our minimal model, involving autoreactive and regulatory T-cells, demonstrates this concept. Autoimmune response initiates antigen-induced expansion through positive feedback, while regulatory cells counter the autoreactive cells through negative feedback. The model explains the decrease in MS relapses during pregnancy and the subsequent surge postpartum, based on lymphocyte dynamics. Additionally, it identifies potential therapeutic targets, predicting significant reduction in relapse rate from mild adjustments of regulatory T cell activity or production. These findings indicate that excitable dynamics may underlie flare-ups across various autoimmune disorders, potentially informing treatment strategies.

Longevity research aims to enhance the period of healthy life, known as the healthspan, while minimizing the duration of disability and morbidity, known as the sickspan. Various interventions extend lifespan in model organisms, but it is not known which of these are likely to compress the relative sickspan. Here, we present a theory that predicts which interventions effectively compress the sickspan. The theory is based on the shape of the survival curve - the fraction of organisms surviving as a function of age. Interventions that lengthen mean lifespan while preserving the shape of the survival curve, known as scaling, are hypothesized to extend the sickspan proportionally, without compressing it. Such interventions include caloric restriction and most other known longevity interventions. Conversely, a small subset of interventions that extend lifespan and alter the shape of the survival curve, particularly by steepening it, are predicted to compress the sickspan. We provide intuitive explanations for this theory and demonstrate its origin from the saturated removal model, a recent mathematical aging model calibrated in mice. We discuss specific longevity interventions in mice that steepen the survival curves, including senolytics, ketogenic diet, and agents that reduce glucose spikes and protect blood vessels, as potential candidates for compressing the sickspan. This hypothesis offers insights into the potential strategies for achieving compressed morbidity and extending healthspan.Competing Interest StatementThe authors have declared no competing interest.

The tumor microenvironment (TME) is comprised of non-malignant cells that interact with each other and with cancer cells, critically impacting cancer biology. The TME is complex, and understanding it requires simplifying approaches. Here we provide an experimental-mathematical approach to decompose the TME into small circuits of interacting cell types. We find, using female breast cancer single-cell-RNA-sequencing data, a hierarchical network of interactions, with cancer-associated fibroblasts (CAFs) at the top secreting factors primarily to tumor-associated macrophages (TAMs). This network is composed of repeating circuit motifs. We isolate the strongest two-cell circuit motif by culturing fibroblasts and macrophages in-vitro, and analyze their dynamics and transcriptomes. This isolated circuit recapitulates the hierarchy of in-vivo interactions, and enables testing the effect of ligand-receptor interactions on cell dynamics and function, as we demonstrate by identifying a mediator of CAF-TAM interactions - RARRES2, and its receptor CMKLR1. Thus, the complexity of the TME may be simplified by identifying small circuits, facilitating the development of strategies to modulate the TME.

Hormones are regulatory molecules that impact physiological functions. Much is known about individual hormones, but general rules that connect the regulatory logic of different hormone systems are limited. In this study, we analyzed a range of human hormone systems using a mathematical approach to integrate knowledge on endocrine cells, target tissues and regulation, to uncover unifying principles and regulatory circuits. We find that the number of cells in an endocrine gland is proportional to the number of cells in its target tissues, as one single endocrine cell serves approximately 2000 target cells. We identified five classes of regulatory circuits, each has specific regulatory functions such as homeostasis or allostasis. The most complex class includes an intermediate gland, the pituitary, which can otherwise be considered redundant and exposes to fragilities. We suggest a tradeoff: with the price of fragilities comes advantages -amplification, buffering of hypersecreting tumors, and faster response times. By elucidating these unifying principles and circuits, this study deepens our understanding of the control of endocrine processes and builds the foundation for systems endocrinology.

Pregnancy involves dynamic alterations in most physiological systems. Delivery initiates a transition to postpartum recovery, which similarly exhibits widespread dynamic changes. Physiological dynamics during pregnancy and after delivery have not been systematically analyzed at high temporal resolution in a large human population. Here, we present a dynamic atlas of 78 laboratory tests with weekly time resolution, spanning the period from 20 weeks pre-conception until 80 weeks postpartum, totaling 45 million measurements from over half a million pregnancies. Tests exhibited discontinuities and rebound effects after delivery, and showed extended recovery times of up to a year postpartum. The accuracy of the data revealed effects of preconception supplements and intricate temporal responses to changes in blood volume and renal filtration rate. The dynamical data allowed discrimination between distinct mechanistic models of adaptation in the thyroid axis. These results provide a comprehensive dynamic portrait of the systems physiology of pregnancy.Competing Interest StatementThe authors have declared no competing interest.

Graves' disease (GD) and Hashimoto's thyroiditis (HT) are common autoimmune diseases of the thyroid gland, causing hyperthyroidism and hypothyroidism, respectively. Despite their opposing clinical manifestation, they have several enigmatic links. Here, we propose that GD and HT have the same fundamental origin: both diseases are the cost of a beneficial physiological process called autoimmune surveillance of hypersecreting mutants. Autoreactive T cells selectively eliminate mutant cells that hypersecrete the hormones and threaten to become toxic nodules. These T cells can trigger a humoral response in susceptible individuals, leading to the production of antibodies against thyroid antigens. This shared origin can explain similarities in incidence and risk factors between HT and GD, despite their opposite clinical phenotypes.

Dominance hierarchy is a fundamental social phenomenon in a wide range of mammalian species, critically affecting fitness and health. Here, we investigate the role of pheromone signals in the control of social hierarchies and individual personalities within groups of wild mice. For this purpose, we combine high-throughput behavioral phenotyping with computational tools in freely interacting groups of wild house mice, males and females, in an automated, semi-natural system. We show that wild mice form dominance hierarchies in both sexes but use sex-specific strategies, displaying distinct male-typical and female-typical behavioral personalities that were also associated with social ranking. Genetic disabling of VNO-mediated pheromone detection generated opposite behavioral effects within groups, enhancing social interactions in males and reducing them in females. Behavioral personalities in the mutated mice displayed mixtures of male-typical and female-typical behaviors, thus blurring sex differences. In addition, rank-associated personalities were abolished despite the fact that both sexes of mutant mice formed stable hierarchies. These findings suggest that group organization is governed by pheromone-mediated sex-specific neural circuits and pave the way to investigate the mechanisms underlying sexual dimorphism in dominance hierarchies under naturalistic settings.

Interventions to reduce fat are important for human health. However, they can have opposing effects such as exercise that decreases fat but increases food intake, or coherent effects such as leptin resistance which raises both. Furthermore, some interventions show an overshoot in food intake, such as recovery from a diet, whereas others do not. To explain these properties we present a graphical framework called the operating point model, based on leptin control of feeding behavior. Steady-state fat and food intake is given by the intersection of two experimental curves  steady-state fat at a given food intake and ad libitum food intake at a given fat level. Depending on which curve an intervention shifts, it has opposing or coherent effects with or without overshoot, in excellent agreement with rodent data. The model also explains the quadratic relation between leptin and fat in humans. These concepts may guide the understanding of fat regulation disorders.

Advanced hepatic fibrosis, driven by the activation of hepatic stellate cells (HSCs), affects millions worldwide and is the strongest predictor of mortality in nonalcoholic steatohepatitis (NASH); however, there are no approved antifibrotic therapies. To identify antifibrotic drug targets, we integrated progressive transcriptomic and morphological responses that accompany HSC activation in advanced disease using single-nucleus RNA sequencing and tissue clearing in a robust murine NASH model. In advanced fibrosis, we found that an autocrine HSC signaling circuit emerged that was composed of 68 receptor-ligand interactions conserved between murine and human NASH. These predicted interactions were supported by the parallel appearance of markedly increased direct stellate cell-cell contacts in murine NASH. As proof of principle, pharmacological inhibition of one such autocrine interaction, neurotrophic receptor tyrosine kinase 3neurotrophin 3, inhibited human HSC activation in culture and reversed advanced murine NASH fibrosis. In summary, we uncovered a repertoire of antifibrotic drug targets underlying advanced fibrosis in vivo. The findings suggest a therapeutic paradigm in which stage-specific therapies could yield enhanced antifibrotic efficacy in patients with advanced hepatic fibrosis.

Thyroid disorders are common and often require lifelong hormone replacement. Treating thyroid disorders involves a fascinating and troublesome delay, in which it takes many weeks for serum thyroid-stimulating hormone (TSH) concentration to normalize after thyroid hormones return to normal. This delay challenges attempts to stabilize thyroid hormones in millions of patients. Despite its importance, the physiological mechanism for the delay is unclear. Here, we present data on hormone delays from Israeli medical records spanning 46 million life-years and develop a mathematical model for dynamic compensation in the thyroid axis, which explains the delays. The delays are due to a feedback mechanism in which peripheral thyroid hormones and TSH control the growth of the thyroid and pituitary glands; enlarged or atrophied glands take many weeks to recover upon treatment due to the slow turnover of the tissues. The model explains why thyroid disorders such as Hashimoto's thyroiditis and Graves' disease have both subclinical and clinical states and explains the complex inverse relation between TSH and thyroid hormones. The present model may guide approaches to dynamically adjust the treatment of thyroid disorders.

Bipolar disorder (BD) is a complex and dynamic condition with a typical onset in late adolescence or early adulthood followed by an episodic course with intervening periods of subthreshold symptoms or euthymia. It is complicated by the accumulation of comorbid medical and psychiatric disorders. The etiology of BD remains unknown and no reliable biological markers have yet been identified. This is likely due to lack of comprehensive ontological framework and, most importantly, the fact that most studies have been based on small nonrepresentative clinical samples with cross-sectional designs. We propose to establish large, global longitudinal cohorts of BD studied consistently in a multidimensional and multidisciplinary manner to determine etiology and help improve treatment. Herein we propose collection of a broad range of data that reflect the heterogenic phenotypic manifestations of BD that include dimensional and categorical measures of mood, neurocognitive, personality, behavior, sleep and circadian, life-story, and outcomes domains. In combination with genetic and biological information such an approach promotes the integrating and harmonizing of data within and across current ontology systems while supporting a paradigm shift that will facilitate discovery and become the basis for novel hypotheses.

Studying the brain circuits that control behavior is challenging, since in addition to their structural complexity there are continuous feedback interactions between actions and sensed inputs from the environment. It is therefore important to identify mathematical principles that can be used to develop testable hypotheses. In this study, we use ideas and concepts from systems biology to study the dopamine system, which controls learning, motivation, and movement. Using data from neuronal recordings in behavioral experiments, we developed a mathematical model for dopamine responses and the effect of dopamine on movement. We show that the dopamine system shares core functional analogies with bacterial chemotaxis. Just as chemotaxis robustly climbs chemical attractant gradients, the dopamine circuit performs reward-taxis where the attractant is the expected value of reward. The reward-taxis mechanism provides a simple explanation for scale-invariant dopaminergic responses and for matching in free operant settings, and makes testable quantitative predictions. We propose that reward-taxis is a simple and robust navigation strategy that complements other, more goal-directed navigation mechanisms.

Every menstrual cycle, many follicles begin to develop but only a specific number ovulate. This ovulation number determines how many offspring are produced per litter, and differs between species. The physiological mechanism that controls ovulation number is unknown; a class of mathematical models can explain it, but these models have no physiological basis. Here, we suggest a physiological mechanism for ovulation number control, which enables selection of a specific number of follicles out of many, and analyze it in a mathematical model of follicular growth. The mechanism is based on a signal, intra-follicular androgen concentration, that measures follicle size relative to the other follicles. This signal has a biphasic effect, suppressing follicles that are too large or too small compared to others. The ovulation number is determined by the androgen inhibitory thresholds. The model has a scaling symmetry that explains why the dominant follicles grow linearly with time, as observed in human ultrasound data. This approach also explains how chronic hyperandrogenism disrupts ovulation in polycystic ovary syndrome (PCOS), a leading cause of infertility. We propose specific experiments for testing the proposed mechanism.

Understanding the tradeoffs faced by organisms is a major goal of evolutionary biology. One of the main approaches for identifying these tradeoffs is Pareto task inference (ParTI). Two recent papers claim that results obtained in ParTI studies are spurious due to phylogenetic dependence (Mikami T, Iwasaki W. 2021. The flipping t-ratio test: phylogenetically informed assessment of the Pareto theory for phenotypic evolution. Methods Ecol Evol. 12(4):696706) or hypothetical p-hacking and population-structure concerns (Sun M, Zhang J. 2021. Rampant false detection of adaptive phenotypic optimization by ParTI-based Pareto front inference. Mol Biol Evol. 38(4):16531664). Here, we show that these claims are baseless. We present a new method to control for phylogenetic dependence, called SibSwap, and show that published ParTI inference is robust to phylogenetic dependence. We show how researchers avoided p-hacking by testing for the robustness of preprocessing choices. We also provide new methods to control for population structure and detail the experimental tests of ParTI in systems ranging from ammonites to cancer gene expression. The methods presented here may help to improve future ParTI studies.

Single cell biology has the potential to elucidate many critical biological processes and diseases, from development and regeneration to cancer. Single cell analyses are uncovering the molecular diversity of cells, revealing a clearer picture of the variation among and between different cell types. New techniques are beginning to unravel how differences in cell statetranscriptional, epigenetic, and other characteristicscan lead to different cell fates among genetically identical cells, which underlies complex processes such as embryonic development, drug resistance, response to injury, and cellular reprogramming. Single cell technologies also pose significant challenges relating to processing and analyzing vast amounts of data collected. To realize the potential of single cell technologies, new computational approaches are needed. On March 1719, 2021, experts in single cell biology met virtually for the Keystone eSymposium \u201cSingle Cell Biology\u201d to discuss advances both in single cell applications and technologies.

Summary Bacterial chemotaxis is a major testing ground for systems biology, including the role of fluctuations and individual variation. Individual bacteria vary in their tumbling frequency and adaptation time. Recently, large cell-cell variation was also discovered in chemotaxis gain, which determines the sensitivity of the tumbling rate to attractant gradients. Variation in gain is puzzling, because low gain impairs chemotactic velocity. Here, we provide a functional explanation for gain variation by establishing a formal analogy between chemotaxis and algorithms for sampling probability distributions. We show that temporal fluctuations in gain implement simulated tempering, which allows sampling of attractant distributions with many local peaks. Periods of high gain allow bacteria to detect and climb gradients quickly, and periods of low gain allow them to move to new peaks. Gain fluctuations thus allow bacteria to thrive in complex environments, and more generally they may play an important functional role for organism navigation.

Comprehending the meaning of body postures is essential for social organisms such as humans. For example, it is important to understand at a glance whether two people seen at a distance are in a friendly or conflictual interaction. However, it is still unclear what fraction of the possible body configurations carry meaning, and what is the best way to characterize such meaning. Here, we address this by using stick figures as a low-dimensional, yet evocative, representation of body postures. We systematically scanned a set of 1,470 upper-body postures of stick figures in a dyad with a second stick figure with a neutral pose. We asked participants to rate the stick figure in terms of 20 emotion adjectives like sad or triumphant and in terms of eight active verbs that connote intent like to threaten and to comfort. The stick figure configuration space was dense with meaning: people strongly agreed on more than half of the configurations. The meaning was generally smooth in the sense that small changes in posture had a small effect on the meaning, but certain small changes had a large effect. Configurations carried meaning in both emotions and intent, but the intent verbs covered more configurations. The effectiveness of the intent verbs in describing body postures aligns with a theory, originating from the theater, called dramatic action theory. This suggests that, in addition to the well-studied role of emotional states in describing body language, much can be gained by using also dramatic action verbs which signal the effort to change the state of others. We provide a dictionary of stick figure configurations and their perceived meaning. This systematic scan of body configurations might be useful to teaching people and machines to decipher body postures in human interactions.

Consuming addictive drugs is often initially pleasurable, but escalating drug intake eventually recruits physiological anti-reward systems called opponent processes that cause tolerance and withdrawal symptoms. Opponent processes are fundamental for the addiction process, but their physiological basis is not fully characterized. Here, we propose an opponent processes mechanism centered on the endocrine stress response, the hypothalamic-pituitary-adrenal (HPA) axis. We focus on alcohol addiction, where the HPA axis is activated and secretes β-endorphin, causing euphoria and analgesia. Using a mathematical model, we show that slow changes in the functional mass of HPA glands act as an opponent process for β-endorphin secretion. The model explains hormone dynamics in alcohol addiction and experiments on alcohol preference in rodents. The opponent process is based on fold-change detection (FCD) where β-endorphin responses are relative rather than absolute; FCD confers vulnerability to addiction but has adaptive roles for learning. Our model suggests gland mass changes as potential targets for intervention in addiction.

Age-related diseases such as cancer, cardiovascular disease, kidney failure, and osteoarthritis have universal features: Their incidence rises exponentially with age with a slope of 68% per year and decreases at very old ages. There is no conceptual model which explains these features in so many diverse diseases in terms of a single shared biological factor. Here, we develop such a model, and test it using a nationwide medical record dataset on the incidence of nearly 1000 diseases over 50 million life-years, which we provide as a resource. The model explains incidence using the accumulation of senescent cells, damaged cells that cause inflammation and reduce regeneration, whose level rise stochastically with age. The exponential rise and late drop in incidence are captured by two parameters for each disease: the susceptible fraction of the population and the threshold concentration of senescent cells that causes disease onset. We propose a physiological mechanism for the threshold concentration for several disease classes, including an etiology for diseases of unknown origin such as idiopathic pulmonary fibrosis and osteoarthritis. The model can be used to design optimal treatments that remove senescent cells, suggeting that treatment starting at old age can sharply reduce the incidence of all age-related diseases, and thus increase the healthspan.

Hormones control the major biological functions of stress response, growth, metabolism, and reproduction. In animals, these hormones show pronounced seasonality, with different set-points for different seasons. In humans, the seasonality of these hormones remains unclear, due to a lack of datasets large enough to discern common patterns and cover all hormones. Here, we analyze an Israeli health record on 46 million person-years, including millions of hormone blood tests. We find clear seasonal patterns: The effector hormones peak in winter-spring, whereas most of their upstream regulating pituitary hormones peak only months later, in summer. This delay of months is unexpected because known delays in the hormone circuits last hours. We explain the precise delays and amplitudes by proposing and testing a mechanism for the circannual clock: The gland masses grow with a timescale of months due to trophic effects of the hormones, generating a feedback circuit with a natural frequency of about a year that can entrain to the seasons. Thus, humans may show coordinated seasonal set-points with a winter-spring peak in the growth, stress, metabolism, and reproduction axes.

Identification of early processes leading to complex tissue pathologies, such as inflammatory bowel diseases, \u200eposes a major scientific and clinical challenge that is imperative for improved diagnosis and treatment. Most studies of inflammation onset focus on cellular processes and signaling molecules, while overlooking the environment in which they take place, the continuously remodeled extracellular matrix. In this study, we used colitis models for investigating extracellularmatrix dynamics during disease onset, while treating the matrix as a complete and defined entity. Through the analysis of matrix structure, stiffness and composition, we unexpectedly revealed that even prior to the first clinical symptoms, the colon displays its own unique extracellularmatrix signature and found specific markers of clinical potential, which were also validated in human subjects. We also show that the emergence of this pre-symptomatic matrix is mediated by subclinical infiltration of immune cells bearing remodeling enzymes. Remarkably, whether the inflammation is chronic or acute, its matrix signature converges at pre-symptomatic states. We suggest that the existence of a pre-symptomatic extracellularmatrix is general and relevant to a wide range of diseases.

Senescent cells are growth-arrested cells that cause inflammation and play a causal role in aging. They accumulate with age, and preventing this accumulation delays age-related diseases. However, the mechanism for senescent cell accumulation is not fully understood. Accumulation can result from increasing production or decreasing removal of senescent cells with age, or both. To distinguish between these possibilities, we analyze data from parabiosis, the surgical conjoining of two mice so that they share circulation. Parabiosis between a young and old mouse, called heterochronic parabiosis, reduces senescent cell levels in the old mouse, while raising senescent cell levels in the young mouse. We show that parabiosis data can reject mechanisms for senescent cell accumulation in which only production rises with age or only removal decreases with age; both must vary with age. Since removal drops with age, senescent cell half-life rises with age. This matches a recent model for senescent cell accumulation developed from independent data on senescent cell dynamics, called the SR model, in which production rises linearly with age and senescent cells inhibit their own removal. The SR model further explains the timescales and mechanism of rejuvenation in parabiosis, based on transfer of spare removal capacity from the young mouse to the old. The present quantitative understanding can help design optimal treatments that remove senescent cells, by matching the time between treatments to the time it takes senescent cells to re-accumulate.

Cortisol is a major human stress hormone, secreted within minutes of acute stress. Cortisol also has slower patterns of variation: a strong circadian rhythm and a seasonal rhythm. However, longitudinal cortisol dynamics in healthy individuals over timescales of months has rarely been studied. Here, we measured longitudinal cortisol in 55 healthy participants using 12 cm of hair, which provides a retrospective measurement over one year. Individuals showed (non-seasonal) fluctuations averaging about 22% around their baseline. Fourier analysis reveals dominant slow frequencies with periods of months to a year. These frequencies can be explained by a mathematical model of the hormonal cascade that controls cortisol, the HPA axis, when including the slow timescales of tissue turnover of the glands. Measuring these dynamics is important for understanding disorders in which cortisol secretion is impaired over months, such as mood disorders, and to test models of cortisol feedback control.

Stress activates a complex network of hormones known as the hypothalamic-pituitary-adrenal (HPA) axis. The HPA axis is dysregulated in chronic stress and psychiatric disorders, but the origin of this dysregulation is unclear and cannot be explained by current HPA models. To address this, we developed a mathematical model for the HPA axis that incorporates changes in the total functional mass of the HPA hormone-secreting glands. The mass changes are caused by HPA hormones which act as growth factors for the glands in the axis. We find that the HPA axis shows the property of dynamical compensation, where gland masses adjust over weeks to buffer variation in physiological parameters. These mass changes explain the experimental findings on dysregulation of cortisol and ACTH dynamics in alcoholism, anorexia, and postpartum. Dysregulation occurs for a wide range of parameters and is exacerbated by impaired glucocorticoid receptor (GR) feedback, providing an explanation for the implication of GR in mood disorders. These findings suggest that gland-mass dynamics may play an important role in the pathophysiology of stress-related disorders.

Tumors are supported by cancer-associated fibroblasts (CAFs). CAFs are heterogeneous and carry out distinct cancer-associated functions. Understanding the full repertoire of CAFs and their dynamic changes as tumors evolve could improve the precision of cancer treatment. Here we comprehensively analyze CAFs using index and transcriptional single-cell sorting at several time points along breast tumor progression in mice, uncovering distinct subpopulations. Notably, the transcriptional programs of these subpopulations change over time and in metastases, transitioning from an immunoregulatory program to wound-healing and antigen-presentation programs, indicating that CAFs and their functions are dynamic. Two main CAF subpopulations are also found in human breast tumors, where their ratio is associated with disease outcome across subtypes and is particularly correlated with BRCA mutations in triple-negative breast cancer. These findings indicate that the repertoire of CAF changes over time in breast cancer progression, with direct clinical implications.

Some endocrine organs are frequent targets of autoimmune attack. Here, we addressed the origin of autoimmune disease from the viewpoint of feedback control. Endocrine tissues maintain mass through feedback loops that balance cell proliferation and removal according to hormone-driven regulatory signals. We hypothesized the existence of a dedicated mechanism that detects and removes mutant cells that missense the signal and therefore hyperproliferate and hypersecrete with potential to disrupt organismal homeostasis. In this mechanism, hypersecreting cells are preferentially eliminated by autoreactive T cells at the cost of a fragility to autoimmune disease. The "autoimmune surveillance of hypersecreting mutants'' (ASHM) hypothesis predicts the presence of autoreactive T cells in healthy individuals and the nature of self-antigens as peptides from hormone secretion pathway. It explains why some tissues get prevalent autoimmune disease, whereas others do not and instead show prevalent mutant-expansion disease (e.g., hyperparathyroidism). The ASHM hypothesis is testable, and we discuss experimental follow-up.

This Perspective discusses the theory of multi-task evolution in cancer, which can contribute to understanding tumour diversity. It introduces the concept of generalist and specialist tumours in the contexts of driver mutations and discusses the potential applications to interpret intratumour heterogeneity.Tumours vary in gene expression programmes and genetic alterations. Understanding this diversity and its biological meaning requires a theoretical framework, which could in turn guide the development of more accurate prognosis and therapy. Here, we review the theory of multi-task evolution of cancer, which is based upon the premise that tumours evolve in the host and face selection trade-offs between multiple biological functions. This theory can help identify the major biological tasks that cancer cells perform and the trade-offs between these tasks. It introduces the concept of specialist tumours, which focus on one task, and generalist tumours, which perform several tasks. Specialist tumours are suggested to be sensitive to therapy targeting their main task. Driver mutations tune gene expression towards specific tasks in a tissue-dependent manner and thus help to determine whether a tumour is specialist or generalist. We discuss potential applications of the theory of multi-task evolution to interpret the spatial organization of tumours and intratumour heterogeneity.

Tissue repair is a protective response after injury, but repetitive or prolonged injury can lead to fibrosis, a pathological state of excessive scarring. To pinpoint the dynamic mechanisms underlying fibrosis, it is important to understand the principles of the cell circuits that carry out tissue repair. In this study, we establish a cell-circuit framework for the myofibroblast-macrophage circuit in wound healing, including the accumulation of scar-forming extracellular matrix. We find that fibrosis results from multistability between three outcomes, which we term "hot fibrosis" characterized by many macrophages, "cold fibrosis" lacking macrophages, and normal wound healing. This framework clarifies several unexplained phenomena including the paradoxical effect of macrophage depletion, the limited time-window in which removing inflammation leads to healing, and why scar maturation takes months. We define key parameters that control the transition from healing to fibrosis, which may serve as potential targets for therapeutic reduction of fibrosis.

A causal factor in mammalian aging is the accumulation of senescent cells (SnCs). SnCs cause chronic inflammation, and removing SnCs decelerates aging in mice. Despite their importance, turnover rates of SnCs are unknown, and their connection to aging dynamics is unclear. Here we use longitudinal SnC measurements and induction experiments to show that SnCs turn over rapidly in young mice, with a half-life of days, but slow their own removal rate to a half-life of weeks in old mice. This leads to a critical-slowing-down that generates persistent SnC fluctuations. We further demonstrate that a mathematical model, in which death occurs when fluctuating SnCs cross a threshold, quantitatively recapitulates the Gompertz law of mortality in mice and humans. The model can go beyond SnCs to explain the effects of lifespan-modulating interventions in Drosophila and C. elegans, including scaling of survival-curves and rapid effects of dietary shifts on mortality.

Personality traits can offer considerable insight into the biological basis of individual differences. However, existing approaches toward understanding personality across species rely on subjective criteria and limited sets of behavioral readouts, which result in noisy and often inconsistent outcomes. Here we introduce a mathematical framework for describing individual differences along dimensions with maximum consistency and discriminative power. We validate this framework in mice, using data from a system for high-throughput longitudinal monitoring of group-housed male mice that yields a variety of readouts from across the behavioral repertoire of individual animals. We demonstrate a set of stable traits that capture variability in behavior and gene expression in the brain, allowing for better-informed mechanistic investigations into the biology of individual differences.

Recent advances have enabled powerful methods to sort tumors into prognosis and treatment groups. We are still missing, however, a general theoretical framework to understand the vast diversity of tumor gene expression and mutations. Here we present a framework based on multi-task evolution theory, using the fact that tumors need to perform multiple tasks that contribute to their fitness. We find that trade-offs between tasks constrain tumor gene-expression to a continuum bounded by a polyhedron whose vertices are gene-expression profiles, each specializing in one task. We find five universal cancer tasks across tissue-types: cell-division, biomass and energy, lipogenesis, immune-interaction and invasion and tissue-remodeling. Tumors that specialize in a task are sensitive to drugs that interfere with this task. Driver, but not passenger, mutations tune gene-expression towards specialization in specific tasks. This approach can integrate additional types of molecular data into a framework of tumor diversity grounded in evolutionary theory.

Many biological problems involve the response to multiple perturbations. Examples include response to combinations of many drugs, and the effects of combinations of many mutations. Such problems have an exponentially large space of combinations, which makes it infeasible to cover the entire space experimentally. To overcome this problem, several formulae that predict the effect of drug combinations or fitness landscape values have been proposed. These formulae use the effects of single perturbations and pairs of perturbations to predict triplets and higher order combinations. Interestingly, different formulae perform best on different datasets. Here we use Pareto optimality theory to quantitatively explain why no formula is optimal for all datasets, due to an inherent bias-variance (noise-precision) tradeoff. We calculate the Pareto front of log-linear formulae and find that the optimal formula depends on properties of the dataset: the typical interaction strength and the experimental noise. This study provides an approach to choose a suitable prediction formula for a given dataset, in order to best overcome the combinatorial explosion problem.Author summary Sometimes a combination of drugs works much better than each drug alone. Finding such drug cocktails is a pressing challenge in order to combat drug resistance and to improve drug effects. However, it is impossible to test all combinations of multiple drug experimentally. Therefore, researchers are looking for computational rather than experimental approaches to overcome this problem. One approach is to measure the effect of few drugs and plug it into a formula that predicts the effect of many drugs together. Existing prediction formulae typically perform best on the dataset that they were developed on, but less well on other datasets. Here we explain this observation and give a guide for the choice of an optimal prediction formula for a given dataset. The optimal formula depends on two main properties of the dataset: 1) The interaction strength between the drugs and 2) The experimental noise in the data. This study may help researchers discover effective combinations of multiple drugs and multiple perturbations in general.

Steady-state protein abundance is set by four rates: transcription, translation, mRNA decay and protein decay. A given protein abundance can be obtained from infinitely many combinations of these rates. This raises the question of whether the natural rates for each gene result from historical accidents, or are there rules that give certain combinations a selective advantage? We address this question using high-throughput measurements in rapidly growing cells from diverse organisms to find that about half of the rate combinations do not exist: genes that combine high transcription with low translation are strongly depleted. This depletion is due to a trade-off between precision and economy: high transcription decreases stochastic fluctuations but increases transcription costs. Our theory quantitatively explains which rate combinations are missing, and predicts the curvature of the fitness function for each gene. It may guide the design of gene circuits with desired expression levels and noise.

Drug combinations are a promising approach to achieve high efficacy at low doses and to overcome resistance. Drug combinations are especially useful when drugs cannot achieve effectiveness at tolerable doses, as occurs in cancer and tuberculosis (TB). However, discovery of effective drug combinations faces the challenge of combinatorial explosion, in which the number of possible combinations increases exponentially with the number of drugs and doses. A recent advance, called the dose model, uses a mathematical formula to overcome combinatorial explosion by reducing the problem to a feasible quadratic one: using data on drug pairs at a few doses, the dose model accurately predicts the effect of combinations of three and four drugs at all doses. The dose model has not yet been tested on higher-order combinations beyond four drugs. To address this, we measured the effect of combinations of up to ten antibiotics on E. coli growth, and of up to five tuberculosis (TB) drugs on the growth of M. tuberculosis. We find that the dose model accurately predicts the effect of these higher-order combinations, including cases of strong synergy and antagonism. This study supports the view that the interactions between drug pairs carries key information that largely determines higher-order interactions. Therefore, systematic study of pairwise drug interactions is a compelling strategy to prioritize drug regimens in high-dimensional spaces.

Single-cell gene expression reveals the diversity within a differentiated cell type. Often, cells of the same type show a continuum of gene-expression patterns. The origin of such continuum gene-expression patterns is unclear. To address this, we develop a theory to understand how a continuumprovides division of labor in a tissue in which cells collectively contribute to several tasks. We find that a continuum is optimal when there are spatial gradients in the tissue that affect the performance in each task. The continuum is bounded inside a polyhedron whose vertices are expression profiles optimal at each task. We test this using single-cell gene expression for intestinal villi and liver hepatocytes, which form a curved 1D trajectory and a full 3D tetrahedron in gene-expression space, respectively. We infer the tasks for both cell types and characterize the spatial zonation of the task-specialist cells. This approach can be generally applied to other tissues.

Praise for the first edition: superb, beautifully written and organized work that takes an engineering approach to systems biology. Alon provides nicely written appendices to explain the basic mathematical and biological concepts clearly and succinctly without interfering with the main text. He starts with a mathematical description of transcriptional activation and then describes some basic transcription-network motifs (patterns) that can be combined to form larger networks. - Nature [This text deserves] serious attention from any quantitative scientist who hopes to learn about modern biology It assumes no prior knowledge of or even interest in biology One final aspect that must be mentioned is the wonderful set of exercises that accompany each chapter. Alon's book should become a standard part of the training of graduate students. - Physics Today Written for students and researchers, the second edition of this best-selling textbook continues to offer a clear presentation of design principles that govern the structure and behavior of biological systems. It highlights simple, recurring circuit elements that make up the regulation of cells and tissues. Rigorously classroom-tested, this edition includes new chapters on exciting advances made in the last decade. Features: Includes seven new chapters The new edition has 189 exercises, the previous edition had 66 Offers new examples relevant to human physiology and disease

Can knowledge accumulated in systems biology on mechanisms governing cell behavior help us to elucidate cognitive processes, such as human creative search? To address this, we focus on the property of scale invariance, which allows sensory systems to adapt to environmental signals spanning orders of magnitude. For example, bacteria search for nutrients, by responding to relative changes in nutrient concentration rather than absolute levels, via a sensory mechanism termed fold-change detection (FCD). Scale invariance is prevalent in cognition, yet the specific mechanisms are mostly unknown. Here, we screen many possible dynamic equation topologies, to find that an FCD model best describes creative search dynamics. The model further predicts robustness to variations in meaning perception, in agreement with behavioral data. We thus suggest FCD as a specific mechanism for scale invariant search, connecting sensory processes of cells and cognitive processes in human.

Mentoring has been an efficient tool to help young PIs to deal with the challenges that come with establishing a research groups. Peer Mentoring is an alternative to "classical" mentoring that could benefit female scientists in particular.

Plants experience light intensity over several orders of magnitude. High light is stressful, and plants have several protective feedback mechanisms against this stress. Here we asked how plants respond to sudden rises at low ambient light, far below stressful levels. For this, we studied the fluorescence of excited chlorophyll a of photosystem II in Arabidopsis thaliana plants in response to step increases in light level at different background illuminations. We found a response at low-medium light with characteristics of a sensory system: fold-change detection (FCD), Weber law, and exact adaptation, in which the response depends only on relative, and not absolute, light changes. We tested various FCD circuits and provide evidence for an incoherent feedforward mechanism upstream of known stress response feedback loops. These findings suggest that plant photosynthesis may have a sensory modality for low light background that responds early to small light increases, to prepare for damaging high light levels.

New toolkits of biological parts allow powerful cell programming by synthetic biologists

Bacterial growth follows simple laws in constant conditions. However, bacteria in nature often face fluctuating environments. We therefore ask whether there are growth laws that apply to changing environments. We derive a law for upshifts using an optimal resource-allocation model: the post-shift growth rate equals the geometrical mean of the pre-shift growth rate and the growth rate on saturating carbon. We test this using chemostat and batch culture experiments, as well as previous data from several species. The increase in growth rate after an upshift indicates that ribosomes have spare capacity (SC). We demonstrate theoretically that SC has the cost of slow steady-state growth but is beneficial after an upshift because it prevents large overshoots in intracellular metabolites and allows rapid response to change. We also provide predictions for downshifts. The present study quantifies the optimal degree of SC, which rises the slower the growth rate, and suggests that SC can be precisely regulated. Bacterial growth depends on numerous reactions and yet in constant conditions follows surprisingly simple laws. Korem Kohanim et al. combine theory and experiment to find patterns in bacterial growth also for changing environments. These emerging patterns imply that bacteria save unused ribosomal capacity to better respond to change.

Populations of organisms show genetic differences called polymorphisms. Understanding the effects of polymorphisms is important for biology and medicine. Here, we ask which polymorphisms occur at high frequency when organisms evolve under trade-offs between multiple tasks. Multiple tasks present a problem, because it is not possible to be optimal at all tasks simultaneously and hence compromises are necessary. Recent work indicates that trade-offs lead to a simple geometry of phenotypes in the space of traits: phenotypes fall on the Pareto front, which is shaped as a polytope: a line, triangle, tetrahedron etc. The vertices of these polytopes are the optimal phenotypes for a single task. Up to now, work on this Pareto approach has not considered its genetic underpinnings. Here, we address this by asking how the polymorphism structure of a population is affected by evolution under trade-offs. We simulate a multi-task selection scenario, in which the population evolves to the Pareto front: the line segment between two archetypes or the triangle between three archetypes. We find that polymorphisms that become prevalent in the population have pleiotropic phenotypic effects that align with the Pareto front. Similarly, epistatic effects between prevalent polymorphisms are parallel to the front. Alignment with the front occurs also for asexual mating. Alignment is reduced when drift or linkage is strong, and is replaced by a more complex structure in which many perpendicular allele effects cancel out. Aligned polymorphism structure allows mating to produce offspring that stand a good chance of being optimal multi-taskers in at least one of the locales available to the species.

Existing approaches to describe social interactions consider emotional states or use ad-hoc descriptors for microanalysis of interactions. Such descriptors are different in each context thereby limiting comparisons, and can also mix facets of meaning such as emotional states, short term tactics and long-term goals. To develop a systematic set of concepts for second-by-second social interactions, we suggest a complementary approach based on practices employed in theater. Theater uses the concept of dramatic action, the effort that one makes to change the psychological state of another. Unlike states (e.g. emotions), dramatic actions aim to change states; unlike long-term goals or motivations, dramatic actions can last seconds. We defined a set of 22 basic dramatic action verbs using a lexical approach, such as 'to threaten'-the effort to incite fear, and 'to encourage'-the effort to inspire hope or confidence. We developed a set of visual cartoon stimuli for these basic dramatic actions, and find that people can reliably and reproducibly assign dramatic action verbs to these stimuli. We show that each dramatic action can be carried out with different emotions, indicating that the two constructs are distinct. We characterized a principal valence axis of dramatic actions. Finally, we re-analyzed three widely-used interaction coding systems in terms of dramatic actions, to suggest that dramatic actions might serve as a common vocabulary across research contexts. This study thus operationalizes and tests dramatic action as a potentially useful concept for research on social interaction, and in particular on influence tactics.

Cell communication within tissues is mediated by multiple paracrine signals including growth factors, which control cell survival and proliferation. Cells and the growth factors they produce and receive constitute a circuit with specific properties that ensure homeostasis. Here, we used computational and experimental approaches to characterize the features of cell circuits based on growth factor exchange between macrophages and fibroblasts, two cell types found in most mammalian tissues. We found that the macrophage-fibroblast cell circuit is stable and robust to perturbations. Analytical screening of all possible two-cell circuit topologies revealed the circuit features sufficient for stability, including environmental constraint and negative-feedback regulation. Moreover, we found that cell-cell contact is essential for the stability of the macrophage-fibroblast circuit. These findings illustrate principles of cell circuit design and provide a quantitative perspective on cell interactions. How is the cellular composition of a tissue stably maintained?

Cells in tissues communicate by secreted growth factors (GF) and other signals. An important function of cell circuits is tissue homeostasis: maintaining proper balance between the amounts of different cell types. Homeostasis requires negative feedback on the GFs, to avoid a runaway situation in which cells stimulate each other and grow without control. Feedback can be obtained in at least two ways: endocytosis in which a cell removes its cognate GF by internalization and cross-inhibition in which a GF down-regulates the production of another GF. Here we ask whether there are design principles for cell circuits to achieve tissue homeostasis. We develop an analytically solvable framework for circuits with multiple cell types and find that feedback by endocytosis is far more robust to parameter variation and has faster responses than cross-inhibition. Endocytosis, which is found ubiquitously across tissues, can even provide homeostasis to three and four communicating cell types. These design principles form a conceptual basis for how tissues maintain a healthy balance of cell types and how balance may be disrupted in diseases such as degeneration and fibrosis.

Embryonic stem cells (ESCs), with their dual capacity to self-renew and differentiate, are commonly used to study differentiation, epigenetic regulation, lineage choices, and more. Using non-directed retroviral integration of a YFP/Cherry exon into mouse ESCs, we generated a library of over 200 endogenously tagged fluorescent fusion proteins and present several proof-of-concept applications of this library. We show the utility of this library to track proteins in living cells; screen for pluripotency-related factors; identify heterogeneously expressing proteins; measure the dynamics of endogenously labeled proteins; track proteins recruited to sites of DNA damage; pull down tagged fluorescent fusion proteins using anti-Cherry antibodies; and test for interaction partners. Thus, this library can be used in a variety of different directions, either exploiting the fluorescent tag for imaging-based techniques or utilizing the fluorescent fusion protein for biochemical pull-down assays, including immunoprecipitation, co-immunoprecipitation, chromatin immunoprecipitation, and more.

Cocktails of drugs can be more effective than single drugs, because they can potentially work at lower doses and avoid resistance. However, it is impossible to test all drug cocktails drawn from a large set of drugs because of the huge number of combinations. To overcome this combinatorial explosion problem, one can sample a relatively small number of combinations and use a model to predict the rest. Recently, Zimmer and Katzir et al. presented a model that accurately predicted the effects of cocktails at all doses based on measuring pairs of drugs. This model requires measuring each pair at several different doses and uses interpolation to reduce experimental noise. However, often, it is not possible to measure each pair at multiple doses (for example, in scarce patient-derived tumor material or in large screens). Here, we ask whether measurements at only a single dose can also predict high-order drug cocktails. To address this, we present a fully factorial experimental dataset on all drug cocktails built of 6 chemotherapy drugs on 2 cancer cell lines. We develop a formula that uses only pair measurements at a single dose to predict much of the variation up to 6-drug cocktails in the present data, outperforming commonly used Bliss independence and regression approaches. This model, called the pairs model, is an extension of the Bliss independence model to pairs: For M drugs, it equals the product of all pair effects to the power 1/(M-1). The pairs model also shows good agreement with previously published data on antibiotic triplets and quadruplets. The present model can only predict combinations at the same doses in which the pairs were measured and is not able to predict effects at other doses. This study indicates that pair-based approaches might be able to usefully predict and prioritize high-order combinations, even in large screens or when material for testing is limited.

Background: The placebo effect is usually studied in clinical settings for decreasing negative symptoms such as pain, depression and anxiety. There is interest in exploring the placebo effect also outside the clinic, for enhancing positive aspects of performance or cognition. Several studies indicate that placebo can enhance cognitive abilities including memory, implicit learning and general knowledge. Here, we ask whether placebo can enhance creativity, an important aspect of human cognition. Methods: Subjects were randomly assigned to a control group who smelled and rated an odorant (n = 45), and a placebo group who were treated identically but were also told that the odorant increases creativity and reduces inhibitions (n = 45). Subjects completed a recently developed automated test for creativity, the creative foraging game (CFG), and a randomly chosen subset (n = 57) also completed two manual standardized creativity tests, the alternate uses test (AUT) and the Torrance test (TTCT). In all three tests, participants were asked to create as many original solutions and were scored for originality, flexibility and fluency. Results: The placebo group showed higher originality than the control group both in the CFG (p

Creative exploration is central to science, art and cognitive development. However, research on creative exploration is limited by a lack of high-resolution automated paradigms. To address this, we present such an automated paradigm, the creative foraging game, in which people search for novel and valuable solutions in a large and well-defined space made of all possible shapes made of ten connected squares. Players discovered shape categories such as digits, letters, and airplanes as well as more abstract categories. They exploited each category, then dropped it to explore once again, and so on. Aligned with a prediction of optimal foraging theory (OFT), during exploration phases, people moved along meandering paths that are about three times longer than the shortest paths between shapes; when exploiting a category of related shapes, they moved along the shortest paths. The moment of discovery of a new category was usually done at a non-prototypical and ambiguous shape, which can serve as an experimental proxy for creative leaps. People showed individual differences in their search patterns, along a continuum between two strategies: a mercurial quick-to-discover/quick-to-drop strategy and a thorough slow-to-discover/slow-to-drop strategy. Contrary to optimal foraging theory, players leave exploitation to explore again far before categories are depleted. This paradigm opens the way for automated high-resolution study of creative exploration.

Tissues use feedback circuits in which cells send signals to each other to control their growth and survival. We show that such feedback circuits are inherently unstable to mutants that misread the signal level: Mutants have a growth advantage to take over the tissue, and cannot be eliminated by known cell-intrinsic mechanisms. To resolve this, we propose that tissues have biphasic responses in and the signal is toxic at both high and low levels, such as glucotoxicity of beta cells, excitotoxicity in neurons, and toxicity of growth factors to T cells. This gives most of these mutants a frequency-dependent selective disadvantage, which leads to their elimination. However, the biphasic mechanisms create a new unstable fixed point in the feedback circuit beyond which runaway processes can occur, leading to risk of diseases such as diabetes and neurodegenerative disease. Hence, glucotoxicity, which is a dangerous cause of diabetes, may have a protective anti-mutant effect. Biphasic responses in tissues may provide an evolutionary stable strategy that avoids invasion by commonly occurring mutants, but at the same time cause vulnerability to disease.

Background: Drugs often kill some cancer cells while others survive. This stochastic outcome is seen even in clonal cells grown under the same conditions. Understanding the molecular reasons for this stochastic outcome is a current challenge, which requires studying the proteome at the single cell level over time. In a previous study we used dynamic proteomics to study the response of cancer cells to a DNA damaging drug, camptothecin. Several proteins showed bimodal dynamics: they rose in some cells and decreased in others, in a way that correlated with eventual cell fate: death or survival. Here we ask whether bimodality is a special case for camptothecin, or whether it occurs for other drugs as well. To address this, we tested a second drug with a different mechanism of action, an HSP90 inhibitor. We used dynamic proteomics to follow 100 proteins in space and time, endogenously tagged in their native chromosomal location in individual living human lung-cancer cells, following drug administration. Results: We find bimodal dynamics for a quarter of the proteins. In some cells these proteins strongly rise in level about 12 h after treatment, but in other cells their level drops or remains constant. The proteins which rise in surviving cells included anti-apoptotic factors such as DDX5, and cell cycle regulators such as RFC1. The proteins that rise in cells that eventually die include pro-apoptotic factors such as APAF1. The two drugs shared some aspects in their single-cell response, including 7 of the bimodal proteins and translocation of oxidative response proteins to the nucleus, but differed in other aspects, with HSP90i showing more bimodal proteins. Moreover, the cell cycle phase at drug administration impacted the probability to die from HSP90i but not camptothecin. Conclusions: Single-cell dynamic proteomics reveals sub-populations of cells within a clonal cell line with different protein dynamics in response to a drug. These different dynamics correlate with cell survival or death. Bimodal proteins which correlate with cell fate may be potential drug targets to enhance the effects of therapy.

Evolution repeatedly converges on only a few regulatory circuit designs that achieve a given function. This simplicity helps us understand biological networks. However, why so few circuits are rediscovered by evolution is unclear. We address this question for the case of fold-change detection (FCD): a response to relative changes of input rather than absolute changes. Two types of FCD circuits recur in biological systems-the incoherent feed-forward and non-linear integral-feedback loops. We performed an analytical screen of all three-node circuits in a class comprising similar to 500,000 topologies. We find that FCD is rare, but still there are hundreds of FCD topologies. The two experimentally observed circuits are among the very few minimal circuits that optimally trade off speed, noise resistance, and response amplitude. This suggests a way to understand why evolution converges on only few topologies for a given function and provides FCD designs for synthetic construction and future discovery.

Face-to-face conversations are central to human communication and a fascinating example of joint action. Beyond verbal content, one of the primary ways in which information is conveyed in conversations is body language. Body motion in natural conversations has been difficult to study precisely due to the large number of coordinates at play. There is need for fresh approaches to analyze and understand the data, in order to ask whether dyads show basic building blocks of coupled motion. Here we present a method for analyzing body motion during joint action using depth-sensing cameras, and use it to analyze a sample of scientific conversations. Our method consists of three steps: defining modes of body motion of individual participants, defining dyadic modes made of combinations of these individual modes, and lastly defining motion motifs as dyadic modes that occur significantly more often than expected given the single-person motion statistics. As a proof-of-concept, we analyze the motion of 12 dyads of scientists measured using two Microsoft Kinect cameras. In our sample, we find that out of many possible modes, only two were motion motifs: synchronized parallel torso motion in which the participants swayed from side to side in sync, and still segments where neither person moved. We find evidence of dyad individuality in the use of motion modes. For a randomly selected subset of 5 dyads, this individuality was maintained for at least 6 months. The present approach to simplify complex motion data and to define motion motifs may be used to understand other joint tasks and interactions. The analysis tools developed here and the motion dataset are publicly available.

Organisms adjust their gene expression to improve fitness in diverse environments. But finding the optimal expression in each environment presents a challenge. We ask how good cells are at finding such optima by studying the control of carbon catabolism genes in Escherichia coli. Bacteria show a growth law: growth rate on different carbon sources declines linearly with the steady-state expression of carbon catabolic genes. We experimentally modulate gene expression to ask if this growth law always maximizes growth rate, as has been suggested by theory. We find that the growth law is optimal in many conditions, including a range of perturbations to lactose uptake, but provides sub-optimal growth on several other carbon sources. Combining theory and experiment, we genetically re-engineer E. coli to make sub-optimal conditions into optimal ones and vice versa. We conclude that the carbon growth law is not always optimal, but represents a practical heuristic that often works but sometimes fails.

The cellular response to viral infection is usually studied at the level of cell populations. Currently, it remains an open question whether and to what extent cell-to-cell variability impacts the course of infection. Here we address this by dynamic proteomics-imaging and tracking 400 yellow fluorescent protein (YFP)-tagged host proteins in individual cells infected by herpes simplex virus 1. By quantifying time-lapse fluorescence imaging, we analyze how cell-to-cell variability impacts gene expression from the viral genome. We identify two proteins, RFX7 and geminin, whose levels at the time of infection correlate with successful initiation of gene expression. These proteins are cell cycle markers, and we find that the position in the cell cycle at the time of infection (along with the cell motility and local cell density) can reasonably predict in which individual cells gene expression from the viral genome will commence. We find that the onset of cell division dramatically impacts the progress of infection, with 70% of dividing cells showing no additional gene expression after mitosis. Last, we identify four host proteins that are specifically modulated in infected cells, of which only one has been previously recognized. SUMO2 and RPAP3 levels are rapidly reduced, while SLTM and YTHDC1 are redistributed to form nuclear foci. These modulations are dependent on the expression of ICP0, as shown by infection with two mutant viruses that lack ICP0. Taken together, our results provide experimental validation for the long-held notion that the success of infection is dependent on the state of the host cell at the time of infection.IMPORTANCE High-throughput assays have revolutionized many fields in biology, both by allowing a more global understanding of biological processes and by deciphering rare events in subpopulations. Here we use such an assay, dynamic proteomics, to study viral infection at the single-cell level. We follow tens of thousands of individual cells infected by herpes simplex virus using fluorescence live imaging. Our results link the state of a cell at the time of virus infection with its probability to successfully initiate gene expression from the viral genome. Further, we identified three cellular proteins that were previously unknown to respond to viral infection. We conclude that dynamic proteomics provides a powerful tool to study single-cell differences during viral infection.

Biological systems can maintain constant steady-state output despite variation in biochemical parameters, a property known as exact adaptation. Exact adaptation is achieved using integral feedback, an engineering strategy that ensures that the output of a system robustly tracks its desired value. However, it is unclear how physiological circuits also keep their output dynamics precise-including the amplitude and response time to a changing input. Such robustness is crucial for endocrine and neuronal homeostatic circuits because they need to provide a precise dynamic response in the face of wide variation in the physiological parameters of their target tissues; how such circuits compensate their dynamics for unavoidable natural fluctuations in parameters is unknown. Here, we present a design principle that provides the desired robustness, which we call dynamical compensation (DC). We present a class of circuits that show DC by means of a nonlinear feedback loop in which the regulated variable controls the functional mass of the controlling endocrine or neuronal tissue. This mechanism applies to the control of blood glucose by insulin and explains several experimental observations on insulin resistance. We provide evidence that this mechanism may also explain compensation and organ size control in other physiological circuits.

Motion synchrony correlates with effective and well-rated human interaction. However, people do not remain locked in synchrony; Instead, they repeatedly enter and exit synchrony. In many important interactions, such as therapy, marriage and parent-infant communication, it is the ability to exit and then re-enter synchrony that is thought to build strong relationship. The phenomenon of entry into zero-phase synchrony is well-studied experimentally and in terms of mathematical modeling. In contrast, exit-from-synchrony is understudied. Here, we focus on human motion coordination, and examine the exit-from-synchrony phenomenon using experimental data from the mirror game paradigm, in which people perform joint improvised motion, and from human tracking of computer-generated stimuli. We present a mathematical mechanism that captures aspects of exit-from-synchrony in human motion. The mechanism adds a random motion component when the accumulated velocity error between the players is small. We introduce this mechanism to several models for human coordinated motion, including the widely studied HKB model, and the predictor-corrector model of Noy, Dekel and Alon. In all models, the new mechanism produces realistic simulated behavior when compared to experimental data from the mirror game and from tracking of computer generated stimuli, including repeated entry and exit from zero-phase synchrony that generates a complexity of motion similar to that of human players. We hope that these results can inform future research on exit-from-synchrony, to better understand the dynamics of coordinated action of people and to enhance human-computer and human-robot interaction.

Finding potent multidrug combinations against cancer and infections is a pressing therapeutic challenge; however, screening all combinations is difficult because the number of experiments grows exponentially with the number of drugs and doses. To address this, we present a mathematical model that predicts the effects of three or more antibiotics or anticancer drugs at all doses based only on measurements of drug pairs at a few doses, without need for mechanistic information. The model provides accurate predictions on available data for antibiotic combinations, and on experiments presented here on the response matrix of three cancer drugs at eight doses per drug. This approach offers a way to search for effective multidrug combinations using a small number of experiments.

Data of gene expression levels across individuals, cell types, and disease states is expanding, yet our understanding of how expression levels impact phenotype is limited. Here, we present a massively parallel system for assaying the effect of gene expression levels on fitness in Saccharomyces cerevisiae by systematically altering the expression level of 100 genes at 100 distinct levels spanning a 500-fold range at high resolution. We show that the relationship between expression levels and growth is gene and environment specific and provides information on the function, stoichiometry, and interactions of genes. Wild-type expression levels in some conditions are not optimal for growth, and genes whose fitness is greatly affected by small changes in expression level tend to exhibit lower cell-to-cell variability in expression. Our study addresses a fundamental gap in understanding the functional significance of gene expression regulation and offers a framework for evaluating the phenotypic effects of expression variation.

Non-verbal communication plays a significant role in establishing good rapport between physicians and patients and may influence aspects of patient health outcomes. It is therefore important to analyze non-verbal communication in medical settings. Current approaches to measure non-verbal interactions in medicine employ coding by human raters. Such tools are labor intensive and hence limit the scale of possible studies. Here, we present an automated video analysis tool for non-verbal interactions in a medical setting. We test the tool using videos of subjects that interact with an actor portraying a doctor. The actor interviews the subjects performing one of two scripted scenarios of interviewing the subjects: in one scenario the actor showed minimal engagement with the subject. The second scenario included active listening by the doctor and attentiveness to the subject. We analyze the cross correlation in total kinetic energy of the two people in the dyad, and also characterize the frequency spectrum of their motion. We find large differences in interpersonal motion synchrony and entrainment between the two performance scenarios. The active listening scenario shows more synchrony and more symmetric followership than the other scenario. Moreover, the active listening scenario shows more high-frequency motion termed jitter that has been recently suggested to be a marker of followership. The present approach may be useful for analyzing physician-patient interactions in terms of synchrony and dominance in a range of medical settings.

Background: Performance is paramount in traditional healing rituals. From a Western perspective, such performative behavior can be understood principally as inducing patients' faith in the performer's supernatural healing powers and effecting positive changes through the same mechanisms attributed to the placebo response, which is defined as improvement of clinical outcome in individuals receiving inactive treatment. Here we examined the possibility of using theatrical performance tools, including stage directions and scripting, to reproducibly manipulate the style and content of a simulated doctor-patient encounter and influence the placebo response in experimental pain. Methods: A total of 122 healthy volunteers (18-45 years, 76 men) exposed to experimental pain (the cold pressor test) were assessed for pain threshold and tolerance before and after receiving a placebo cream from a "doctor" impersonated by a trained actor. The actor alternated between two distinct scripts and stage directions, i.e., performance styles created by a theater director/playwright, one emulating a standard doctor-patient encounter (scenario A) and the other emphasizing attentiveness and strong suggestion, elements also present in ritual healing (scenario B). The placebo response size was calculated as the %difference in pain threshold and tolerance after exposure relative to baseline. In addition, subjects demonstrating a ≥30% increase in pain threshold or tolerance relative to baseline were defined as responders. Each encounter was videotaped in its entirety. Results: Inspection of the videotapes confirmed the reproducibility and consistency of the distinct scenarios enacted by the "doctor"-performer. Furthermore, scenario B resulted in a significant increase in pain threshold relative to scenario A. Interestingly, this increase derived from the placebo responder subgroup; as shown by two-way analysis of variance (performance style, F = 4.30; p = 0.040; η² = 0.035; style × responder status interaction term, F = 5.21; p = 0.024) followed by post hoc analysis showing a ~60% increase in pain threshold in responders exposed to scenario B (p = 0.020). Conclusion: These results support the hypothesis that structured manipulation of physician's verbal and non-verbal performance, designed to build rapport and increase faith in treatment, is feasible and may have a significant beneficial effect on the size of the response to placebo analgesia. They also demonstrate that subjects, who are not susceptible to placebo, are also not susceptible to performance style.

In most conditions, glucose is the best carbon source for E. coli: it provides faster growth than other sugars, and is consumed first in sugar mixtures. Here we identify conditions in which E. coli strains grow slower on glucose than on other sugars, namely when a single amino acid (arginine, glutamate, or proline) is the sole nitrogen source. In sugar mixtures with these nitrogen sources, E. coli still consumes glucose first, but grows faster rather than slower after exhausting glucose, generating a reversed diauxic shift. We trace this counterintuitive behavior to a metabolic imbalance: levels of TCA-cycle metabolites including α-ketoglutarate are high, and levels of the key regulatory molecule cAMP are low. Growth rates were increased by experimentally increasing cAMP levels, either by adding external cAMP, by genetically perturbing the cAMP circuit or by inhibition of glucose uptake. Thus, the cAMP control circuitry seems to have a 'bug' that leads to slow growth under what may be an environmentally rare condition.

In C. elegans, small RNAs enable transmission of epigenetic responses across multiple generations. While RNAi inheritance mechanisms that enable "memorization'' of ancestral responses are being elucidated, the mechanisms that determine the duration of inherited silencing and the ability to forget the inherited epigenetic effects are not known. We now show that exposure to dsRNA activates a feedback loop whereby gene-specific RNAi responses dictate the transgenerational duration of RNAi responses mounted against unrelated genes, elicited separately in previous generations. RNA-sequencing analysis reveals that, aside from silencing of genes with complementary sequences, dsRNA-induced RNAi affects the production of heritable endogenous small RNAs, which regulate the expression of RNAi factors. Manipulating genes in this feedback pathway changes the duration of heritable silencing. Such active control of transgenerational effects could be adaptive, since ancestral responses would be detrimental if the environments of the progeny and the ancestors were different.

Why is it easy for some people to play together and difficult for others? In this interdisciplinary pilot study, we looked at dyadic interaction in motion as a paradigm to explore the expression of attachment in adulthood. We used a device that gives simple, quantitative and automated indicators for the quality of interaction while playing the mirror game. Forty-seven participants played the mirror game with the same gender-matched expert players. In addition, participants were interviewed on the Adult Attachment Interview to assess their quality of attachment. Using high resolution kinematic measures, we found that secure attachment was correlated with high complexity of the game and low synchrony compared to insecure attachment. The findings suggest that security of attachment is related to a more exploratory and less rigid game than insecure-dismissing attachment. These preliminary findings imply that high resolution analysis of simple movement interaction could carry information about attachment behavior.

Nervous system maps are of critical importance for understanding how nervous systems develop and function. We systematically map here all cholinergic neuron types in the male and hermaphrodite C. elegans nervous system. We find that acetylcholine (ACh) is the most broadly used neurotransmitter and we analyze its usage relative to other neurotransmitters within the context of the entire connectome and within specific network motifs embedded in the connectome. We reveal several dynamic aspects of cholinergic neurotransmitter identity, including a sexually dimorphic glutamatergic to cholinergic neurotransmitter switch in a sex-shared interneuron. An expression pattern analysis of ACh-gated anion channels furthermore suggests that ACh may also operate very broadly as an inhibitory neurotransmitter. As a first application of this comprehensive neurotransmitter map, we identify transcriptional regulatory mechanisms that control cholinergic neurotransmitter identity and cholinergic circuit assembly.

We present a novel framework for high-throughput cell lineage analysis in time-lapse microscopy images. Our algorithm ties together two fundamental aspects of cell lineage construction, namely cell segmentation and tracking, via a Bayesian inference of dynamic models. The proposed contribution exploits the Kalman inference problem by estimating the time-wise cell shape uncertainty in addition to cell trajectory. These inferred cell properties are combined with the observed image measurements within a fast marching (FM) algorithm, to achieve posterior probabilities for cell segmentation and association. Highly accurate results on two different cell-tracking datasets are presented.

There is a revolution in the ability to analyze gene expression of single cells in a tissue. To understand this data we must comprehend how cells are distributed in a high-dimensional gene expression space. One open question is whether cell types form discrete clusters or whether gene expression forms a continuum of states. If such a continuum exists, what is its geometry? Recent theory on evolutionary trade-offs suggests that cells that need to perform multiple tasks are arranged in a polygon or polyhedron (line, triangle, tetrahedron and so on, generally called polytopes) in gene expression space, whose vertices are the expression profiles optimal for each task. Here, we analyze single-cell data from human and mouse tissues profiled using a variety of single-cell technologies. We fit the data to shapes with different numbers of vertices, compute their statistical significance, and infer their tasks. We find cases in which single cells fill out a continuum of expression states within a polyhedron. This occurs in intestinal progenitor cells, which fill out a tetrahedron in gene expression space. The four vertices of this tetrahedron are each enriched with genes for a specific task related to stemness and early differentiation. A polyhedral continuum of states is also found in spleen dendritic cells, known to perform multiple immune tasks: cells fill out a tetrahedron whose vertices correspond to key tasks related to maturation, pathogen sensing and communication with lymphocytes. A mixture of continuum-like distributions and discrete clusters is found in other cell types, including bone marrow and differentiated intestinal crypt cells. This approach can be used to understand the geometry and biological tasks of a wide range of single-cell datasets. The present results suggest that the concept of cell type may be expanded. In addition to discreet clusters in gene-expression space, we suggest a new possibility: a continuum of states within a polyhedron, in which the vertices represent specialists at key tasks.

Background: Organisms that need to perform multiple tasks face a fundamental tradeoff: no design can be optimal at all tasks at once. Recent theory based on Pareto optimality showed that such tradeoffs lead to a highly defined range of phenotypes, which lie in low-dimensional polyhedra in the space of traits. The vertices of these polyhedra are called archetypes- the phenotypes that are optimal at a single task. To rigorously test this theory requires measurements of thousands of species over hundreds of millions of years of evolution. Ammonoid fossil shells provide an excellent model system for this purpose. Ammonoids have a well-defined geometry that can be parameterized using three dimensionless features of their logarithmic-spiral-shaped shells. Their evolutionary history includes repeated mass extinctions.Results: We find that ammonoids fill out a pyramid in morphospace, suggesting five specific tasks - one for each vertex of the pyramid. After mass extinctions, surviving species evolve to refill essentially the same pyramid, suggesting that the tasks are unchanging. We infer putative tasks for each archetype, related to economy of shell material, rapid shell growth, hydrodynamics and compactness.Conclusions: These results support Pareto optimality theory as an approach to study evolutionary tradeoffs, and demonstrate how this approach can be used to infer the putative tasks that may shape the natural selection of phenotypes.

Bow-tie or hourglass structure is a common architectural feature found in many biological systems. A bow-tie in a multi-layered structure occurs when intermediate layers have much fewer components than the input and output layers. Examples include metabolism where a handful of building blocks mediate between multiple input nutrients and multiple output biomass components, and signaling networks where information from numerous receptor types passes through a small set of signaling pathways to regulate multiple output genes. Little is known, however, about how bow-tie architectures evolve. Here, we address the evolution of bow-tie architectures using simulations of multi-layered systems evolving to fulfill a given input-output goal. We find that bow-ties spontaneously evolve when the information in the evolutionary goal can be compressed. Mathematically speaking, bow-ties evolve when the rank of the input-output matrix describing the evolutionary goal is deficient. The maximal compression possible (the rank of the goal) determines the size of the narrowest part of the networkthat is the bow-tie. A further requirement is that a process is active to reduce the number of links in the network, such as product-rule mutations, otherwise a non-bow-tie solution is found in the evolutionary simulations. This offers a mechanism to understand a common architectural principle of biological systems, and a way to quantitate the effective rank of the goals under which they evolved.

A characteristic of visuomotor tracking of non-regular oscillating stimuli are high-frequency jittery corrective motions, oscillating around the tracked stimuli. However, the properties of these corrective jitter responses are not well understood. For example, does the jitter response show an idiosyncratic signature? What is the relationship between stimuli properties and jitter properties? Is the jitter response similar across effectors with different inertial properties? To answer these questions, we measured participants jitter frequencies in two tracking tasks in the arm and the finger. Thirty participants tracked the same set of eleven non-regular oscillating stimuli, vertically moving on a screen, once with forwardbackward arm movements (holding a tablet stylus) and once with upwarddownward index finger movements (with a motion tracker attached). Participants jitter frequencies and tracking errors varied systematically as a function of stimuli frequency and amplitude. Additionally, there were clear individual differences in average jitter frequencies between participants, ranging from 0.7 to 1.15 Hz, similar to values reported previously. A comparison of individual jitter frequencies in the two tasks showed a strong correlation between participants jitter frequencies in the finger and the arm, despite the very different inertial properties of the two effectors. This result suggests that the corrective jitter response stems from common neural processes.

We present the Pareto task inference method (ParTI; http://www.weizmann.ac.il/mcb/UriAlon/download/ParTI) for inferring biological tasks from high-dimensional biological data. Data are described as a polytope, and features maximally enriched closest to the vertices (or archetypes) allow identification of the tasks the vertices represent. We demonstrate that human breast tumors and mouse tissues are well described by tetrahedrons in gene expression space, with specific tumor types and biological functions enriched at each of the vertices, suggesting four key tasks.

When organisms need to perform multiple tasks they face a fundamental tradeoff: no phenotype can be optimal at all tasks. This situation was recently analyzed using Pareto optimality, showing that tradeoffs between tasks lead to phenotypes distributed on low dimensional polygons in trait space. The vertices of these polygons are archetypesphenotypes optimal at a single task. This theory was applied to examples from animal morphology and gene expression. Here we ask whether Pareto optimality theory can apply to life history traits, which include longevity, fecundity and mass. To comprehensively explore the geometry of life history trait space, we analyze a dataset of life history traits of 2105 endothermic species. We find that, to a first approximation, life history traits fall on a triangle in log-mass log-longevity space. The vertices of the triangle suggest three archetypal strategies, exemplified by bats, shrews and whales, with specialists near the vertices and generalists in the middle of the triangle. To a second approximation, the data lies in a tetrahedron, whose extra vertex above the mass-longevity triangle suggests a fourth strategy related to carnivory. Each animal species can thus be placed in a coordinate system according to its distance from the archetypes, which may be useful for genome-scale comparative studies of mammalian aging and other biological aspects. We further demonstrate that Pareto optimality can explain a range of previous studies which found animal and plant phenotypes which lie in triangles in trait space. This study demonstrates the applicability of multi-objective optimization principles to understand life history traits and to infer archetypal strategies that suggest why some mammalian species live much longer than others of similar mass.

Background: Understanding how cells make decisions, and why they make the decisions they make, is of fundamental interest in systems biology. To address this, we study the decisions made by E. coli on which genes to express when presented with two different sugars. It is well-known that glucose, E. coli's preferred carbon source, represses the uptake of other sugars by means of global and gene-specific mechanisms. However, less is known about the utilization of glucose-free sugar mixtures which are found in the natural environment of E. coli and in biotechnology. Results: Here, we combine experiment and theory to map the choices of E. coli among 6 different non-glucose carbon sources. We used robotic assays and fluorescence reporter strains to make precise measurements of promoter activity and growth rate in all pairs of these sugars. We find that the sugars can be ranked in a hierarchy: In a mixture of a higher and a lower sugar, the lower sugar system shows reduced promoter activity. The hierarchy corresponds to the growth rate supported by each sugar- the faster the growth rate, the higher the sugar on the hierarchy. The hierarchy is 'soft' in the sense that the lower sugar promoters are not completely repressed. Measurement of the activity of the master regulator CRP-cAMP shows that the hierarchy can be quantitatively explained based on differential activation of the promoters by CRP-cAMP. Comparing sugar system activation as a function of time in sugar pair mixtures at sub-saturating concentrations, we find cases of sequential activation, and also cases of simultaneous expression of both systems. Such simultaneous expression is not predicted by simple models of growth rate optimization, which predict only sequential activation. We extend these models by suggesting multi-objective optimization for both growing rapidly now and preparing the cell for future growth on the poorer sugar. Conclusion: We find a defined hierarchy of sugar utilization, which can be quantitatively explained by differential activation by the master regulator cAMP-CRP. The present approach can be used to understand cell decisions when presented with mixtures of conditions.

A widespread feature of extracellular signaling in cell circuits is paradoxical pleiotropy: the same secreted signaling molecule can induce opposite effects in the responding cells. For example, the cytokine IL-2 can promote proliferation and death of T cells. The role of such paradoxical signaling remains unclear. To address this, we studied CD4⁺ T cell expansion in culture. We found that cells with a 30-fold difference in initial concentrations reached a homeostatic concentration nearly independent of initial cell levels. Below an initial threshold, cell density decayed to extinction (OFF-state). We show that these dynamics relate to the paradoxical effect of IL-2, which increases the proliferation rate cooperatively and the death rate linearly. Mathematical modeling explained the observed cell and cytokine dynamics and predicted conditions that shifted cell fate from homeostasis to the OFF-state. We suggest that paradoxical signaling provides cell circuits with specific dynamical features that are robust to environmental perturbations.

Two central biophysical laws describe sensory responses to input signals. One is a logarithmic relationship between input and output, and the other is a power law relationship. These laws are sometimes called the Weber-Fechner law and the Stevens power law, respectively. The two laws are found in a wide variety of human sensory systems including hearing, vision, taste, and weight perception; they also occur in the responses of cells to stimuli. However the mechanistic origin of these laws is not fully understood. To address this, we consider a class of biological circuits exhibiting a property called fold-change detection (FCD). In these circuits the response dynamics depend only on the relative change in input signal and not its absolute level, a property which applies to many physiological and cellular sensory systems. We show analytically that by changing a single parameter in the FCD circuits, both logarithmic and power-law relationships emerge; these laws are modified versions of the Weber-Fechner and Stevens laws. The parameter that determines which law is found is the steepness (effective Hill coefficient) of the effect of the internal variable on the output. This finding applies to major circuit architectures found in biological systems, including the incoherent feed-forward loop and nonlinear integral feedback loops. Therefore, if one measures the response to different fold changes in input signal and observes a logarithmic or power law, the present theory can be used to rule out certain FCD mechanisms, and to predict their cooperativity parameter. We demonstrate this approach using data from eukaryotic chemotaxis signaling.

Bacteria often face complex environments. We asked how gene expression in complex conditions relates to expression in simpler conditions. To address this, we obtained accurate promoter activity dynamical measurements on 94 genes in E. coli in environments made up of all possible combinations of four nutrients and stresses. We find that the dynamics across conditions is well described by two principal component curves specific to each promoter. As a result, the promoter activity dynamics in a combination of conditions is a weighted average of the dynamics in each condition alone. The weights tend to sum up to approximately one. This weighted-average property, called linear superposition, allows predicting the promoter activity dynamics in a combination of conditions based on measurements of pairs of conditions. If these findings apply more generally, they can vastly reduce the number of experiments needed to understand how E. coli responds to the combinatorially huge space of possible environments.

To understand gene function, genetic analysis uses large perturbations such as gene deletion, knockdown or over-expression. Large perturbations have drawbacks: they move the cell far from its normal working point, and can thus be masked by off-target effects or compensation by other genes. Here, we offer a complementary approach, called noise genetics. We use natural cell-cell variations in protein level and localization, and correlate them to the natural variations of the phenotype of the same cells. Observing these variations is made possible by recent advances in dynamic proteomics that allow measuring proteins over time in individual living cells. Using motility of human cancer cells as a model system, and time-lapse microscopy on 566 fluorescently tagged proteins, we found 74 candidate motility genes whose level or localization strongly correlate with motility in individual cells. We recovered 30 known motility genes, and validated several novel ones by mild knockdown experiments. Noise genetics can complement standard genetics for a variety of phenotypes.

Actors, dancers and musicians that improvise together report special moments of togetherness: high performance and synchrony, seemingly without a leader and a follower. Togetherness seems to conflict with individuality- the idiosyncratic character of each person's performance. To understand the relation of individuality and togetherness, we employed the mirror game paradigm in which two players are asked to mirror each other and create interesting synchronized motion, with and without a designated leader. The mirror game enables quantitative characterization of moments of togetherness in which complex motion is generated with high synchrony. We find that each person as a leader does basic strokes of motion with a characteristic signature, in terms of the shape of their velocity profile between two stopping events. In moments of togetherness both players change their signature to a universal stroke shape. This universal velocity profile resembles a half-period of a sine wave, and is therefore symmetric and maximally smooth. Thus, instead of converging to an intermediate motion signature, or having one player dominate, players seem to shift their basic motion signatures to a shape that is altogether different from their individually preferred shapes; the resulting motion may be easier to predict and to agree on. The players then build complex motion by using such smooth elementary strokes.

Covalent modification provides a mechanism for modulating molecular state and regulating physiology. A cycle of competing enzymes that add and remove a single modification can act as a molecular switch between "on" and "off" and has been widely studied as a core motif in systems biology. Here, we exploit the recently developed "linear framework" for time scale separation to determine the general principles of such switches. These methods are not limited to Michaelis-Menten assumptions, and our conclusions hold for enzymes whose mechanisms may be arbitrarily complicated. We show that switching efficiency improves with increasing irreversibility of the enzymes and that the on/off transition occurs when the ratio of enzyme levels reaches a value that depends only on the rate constants. Fluctuations in enzyme levels, which habitually occur due to cellular heterogeneity, can cause flipping back and forth between on and off, leading to incoherent mosaic behavior in tissues, that worsens as switching becomes sharper. This trade-off can be circumvented if enzyme levels are correlated. In particular, if the competing catalytic domains are on the same protein but do not influence each other, the resulting bifunctional enzyme can switch sharply while remaining coherent. In the mammalian liver, the switch between glycolysis and gluconeogenesis is regulated by the bifunctional 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase (PFK-2/FBPase-2). We suggest that bifunctionality of PFK-2/FBPase-2 complements the metabolic zonation of the liver by ensuring coherent switching in response to insulin and glucagon.

Background: Lag phase is a period of time with no growth that occurs when stationary phase bacteria are transferred to a fresh medium. Bacteria in lag phase seem inert: their biomass does not increase. The low number of cells and low metabolic activity make it difficult to study this phase. As a consequence, it has not been studied as thoroughly as other bacterial growth phases. However, lag phase has important implications for bacterial infections and food safety. We asked which, if any, genes are expressed in the lag phase of Escherichia coli, and what is their dynamic expression pattern. Results: We developed an assay based on imaging flow cytometry of fluorescent reporter cells that overcomes the challenges inherent in studying lag phase. We distinguish between lag1 phase- in which there is no biomass growth, and lag2 phase- in which there is biomass growth but no cell division. We find that in lag1 phase, most promoters are not active, except for the enzymes that utilize the specific carbon source in the medium. These genes show promoter activities that increase exponentially with time, despite the fact that the cells do not measurably increase in size. An oxidative stress promoter, katG, is also active. When cells enter lag2 and begin to grow in size, they switch to a full growth program of promoter activity including ribosomal and metabolic genes. Conclusions: The observed exponential increase in enzymes for the specific carbon source followed by an abrupt switch to production of general growth genes is a solution of an optimal control model, known as bang-bang control. The present approach contributes to the understanding of lag phase, the least studied of bacterial growth phases.

Evolutionary theory has long argued that the entrenched rules of development constrain the range of variations in a given form, but few empirical examples are known. Here we provide evidence for a very deeply conserved skeletal module constraining the morphology of the phalanges within a digit. We measured the sizes of phalanges within populations of two bird species and found that successive phalanges within a digit exhibit predictable relative proportions, whether those phalanges are nearly equal in size or exhibit a more striking gradient in size from large to small. Experimental perturbations during early stages of digit formation demonstrate that the sizes of the phalanges within a digit are regulated as a system rather than individually. However, the sizes of the phalanges are independent of the metatarsals. Temporal studies indicate that the relative sizes of the phalanges are established at the time of initial cell condensation. Measurements of phalanges across species from six major taxonomic lineages showed that the same predictable range of variants is conserved across vast taxonomic diversity and evolutionary time, starting with the very origins of tetrapods. Although in general phalangeal variations fall within a range of nearly equal-sized phalanges to those following a steep large-to-small gradient, a novel derived condition of excessive elongation of the distal-most phalanges has evolved convergently in multiple lineages, for example under selection for grasping rather than walking or swimming. Even in the context of this exception, phalangeal variations observed in nature are a small subset of potential morphospace.

Most genes change expression levels across conditions, but it is unclear which of these changes represents specific regulation and what determines their quantitative degree. Here, we accurately measured activities of ∼900 S. cerevisiae and ∼1800 E. coli promoters using fluorescent reporters. We show that in both organisms 60-90% of promoters change their expression between conditions by a constant global scaling factor that depends only on the conditions and not on the promoter's identity. Quantifying such global effects allows precise characterization of specific regulation - promoters deviating from the global scale line. These are organized into few functionally related groups that also adhere to scale lines and preserve their relative activities across conditions. Thus, only several scaling factors suffice to accurately describe genome-wide expression profiles across conditions. We present a parameter-free passive resource allocation model that quantitatively accounts for the global scaling factors. It suggests that many changes in expression across conditions result from global effects and not specific regulation, and provides means for quantitative interpretation of expression profiles.

Biological systems exhibit two structural features on many levels of organization: sparseness, in which only a small fraction of possible interactions between components actually occur; and modularity - the near decomposability of the system into modules with distinct functionality. Recent work suggests that modularity can evolve in a variety of circumstances, including goals that vary in time such that they share the same subgoals (modularly varying goals), or when connections are costly. Here, we studied the origin of modularity and sparseness focusing on the nature of the mutation process, rather than on connection cost or variations in the goal. We use simulations of evolution with different mutation rules. We found that commonly used sum-rule mutations, in which interactions are mutated by adding random numbers, do not lead to modularity or sparseness except for in special situations. In contrast, product-rule mutations in which interactions are mutated by multiplying by random numbers - a better model for the effects of biological mutations - led to sparseness naturally. When the goals of evolution are modular, in the sense that specific groups of inputs affect specific groups of outputs, product-rule mutations also lead to modular structure; sum-rule mutations do not. Product-rule mutations generate sparseness and modularity because they tend to reduce interactions, and to keep small interaction terms small.

Biological regulatory systems face a fundamental tradeoff: they must be effective but at the same time also economical. For example, regulatory systems that are designed to repair damage must be effective in reducing damage, but economical in not making too many repair proteins because making excessive proteins carries a fitness cost to the cell, called protein burden. In order to see how biological systems compromise between the two tasks of effectiveness and economy, we applied an approach from economics and engineering called Pareto optimality. This approach allows calculating the best-compromise systems that optimally combine the two tasks. We used a simple and general model for regulation, known as integral feedback, and showed that best-compromise systems have particular combinations of biochemical parameters that control the response rate and basal level. We find that the optimal systems fall on a curve in parameter space. Due to this feature, even if one is able to measure only a small fraction of the system's parameters, one can infer the rest. We applied this approach to estimate parameters in three biological systems: response to heat shock and response to DNA damage in bacteria, and calcium homeostasis in mammals.

When organisms perform a single task, selection leads to phenotypes that maximize performance at that task. When organisms need to perform multiple tasks, a trade-off arises because no phenotype can optimize all tasks. Recent work addressed this question, and assumed that the performance at each task decays with distance in trait space from the best phenotype at that task. Under this assumption, the best-fitness solutions (termed the Pareto front) lie on simple low-dimensional shapes in trait space: line segments, triangles and other polygons. The vertices of these polygons are specialists at a single task. Here, we generalize this finding, by considering performance functions of general form, not necessarily functions that decay monotonically with distance from their peak. We find that, except for performance functions with highly eccentric contours, simple shapes in phenotype space are still found, but with mildly curving edges instead of straight ones. In a wide range of systems, complex data on multiple quantitative traits, which might be expected to fill a high-dimensional phenotype space, is predicted instead to collapse onto low-dimensional shapes; phenotypes near the vertices of these shapes are predicted to be specialists, and can thus suggest which tasks may be at play. We studied the effect of trade-offs between tasks on the suite of variation of phenotypes. We find that, for a wide range of performance function shapes, Pareto optimal phenotypes lie in morphospace on low-dimensional polygons with mildly curved edges, whose vertices are phenotypes specialized for a single task, known as archetypes. We also present bounds on the Pareto front for general, non-monotonic performance functions, showing that the suite of variation is restricted to a region spanning the archetypes.

Theoretical models that describe oscillations in biological systems are often either a limit cycle oscillator, where the deterministic nonlinear dynamics gives sustained periodic oscillations, or a noise-induced oscillator, where a fixed point is linearly stable with complex eigenvalues, and addition of noise gives oscillations around the fixed point with fluctuating amplitude. We investigate how each class of models behaves under the external periodic forcing, taking the well-studied van der Pol equation as an example. We find that when the forcing is additive, the noise-induced oscillator can show only one-to-one entrainment to the external frequency, in contrast to the limit cycle oscillator which is known to entrain to any ratio. When the external forcing is multiplicative, on the other hand, the noise-induced oscillator can show entrainment to a few ratios other than one-to-one, while the limit cycle oscillator shows entrain to any ratio. The noise blurs the entrainment in general, but clear entrainment regions for limit cycles can be identified as long as the noise is not too strong.

Sensory systems often detect multiple types of inputs. For example, a receptor in a cell-signaling system often binds multiple kinds of ligands, and sensory neurons can respond to different types of stimuli. How do sensory systems compare these different kinds of signals? Here, we consider this question in a class of sensory systems - including bacterial chemotaxis- which have a property known as fold-change detection: their output dynamics, including amplitude and response time, depends only on the relative changes in signal, rather than absolute changes, over a range of several decades of signal. We analyze how fold-change detection systems respond to multiple signals, using mathematical models. Suppose that a step of fold F₁ is made in input 1, together with a step of F₂ in input 2. What total response does the system provide? We show that when both input signals impact the same receptor with equal number of binding sites, the integrated response is multiplicative: the response dynamics depend only on the product of the two fold changes, F₁F₂. When the inputs bind the same receptor with different number of sites n₁ and n₂, the dynamics depend on a product of power laws, F₁ⁿ¹F₂ⁿ². Thus, two input signals which vary over time in an inverse way can lead to no response. When the two inputs affect two different receptors, other types of integration may be found and generally the system is not constrained to respond according to the product of the fold-change of each signal. These predictions can be readily tested experimentally, by providing cells with two simultaneously varying input signals. The present study suggests how cells can compare apples and oranges, namely by comparing each to its own background level, and then multiplying these two fold-changes.

Background: Bacterial growth as a function of nutrients has been studied for decades, but is still not fully understood. In particular, the growth laws under dynamically changing environments have been difficult to explore, because of the rapidly changing conditions. Here, we address this challenge by means of a robotic assay and measure bacterial growth rate, promoter activity and substrate level at high temporal resolution across the entire growth curve in batch culture. As a model system, we study E. coli growing under nitrogen or carbon limitation, and explore the dynamics in the last generation of growth where nutrient levels can drop rapidly.Results: We find that growth stops abruptly under limiting nitrogen or carbon, but slows gradually when nutrients are not limiting. By measuring growth rate at a 3 min time resolution, and inferring the instantaneous substrate level, s, we find that the reduction in growth rate μ under nutrient limitation follows Monod's law, μ = μ₀ s/k_s+s. By following promoter activity of different genes we found that the abrupt stop of growth under nitrogen or carbon limitation is accompanied by a pulse-like up-regulation of the expression of genes in the relevant nutrient assimilation pathways. We further find that sharp stop of growth is conditional on the presence of regulatory proteins in the assimilation pathway.Conclusions: The observed sharp stop of growth accompanied by a pulsed expression of assimilation genes allows bacteria to compensate for the drop in nutrients, suggesting a strategy used by the cells to prolong exponential growth under limiting substrate.

Edelaar raises concerns about the way we tested our theory. Our mathematical theorem predicts that despite the high dimensionality of trait space, trade-offs between tasks lead to phenotypes in low-dimensional regions in trait space, such as lines and triangles. We address Edelaar's questions with statistical tests that eliminate pseudoreplication concerns, finding that our predictions remain convincingly supported.

A recurring theme in biological circuits is the existence of components that are antagonistically bifunctional, in the sense that they simultaneously have two opposing effects on the same target or biological process. Examples include bifunctional enzymes that carry out two opposing reactions such as phosphorylating and dephosphorylating the same target, regulators that activate and also repress a gene in circuits called incoherent feedforward loops, and cytokines that signal immune cells to both proliferate and die. Such components are termed "paradoxical", and in this review we discuss how they can provide useful features to cell circuits that are otherwise difficult to achieve. In particular, we summarize how paradoxical components can provide robustness, generate temporal pulses, and provide fold-change detection, in which circuits respond to relative rather than absolute changes in signals.

The growth behavior in well-mixed bacterial cultures is relatively well understood. However, bacteria often grow in heterogeneous conditions on surfaces where their growth is dependent on spatial position, especially in the case of motile populations. For such populations, the relation between growth, motility and spatial position is unclear. We developed a microscope-based assay for quantifying in situ growth and gene expression in space and time, and we observe these parameters in populations of Escherichia coli swimming in galactose soft agar plates. We find that the bacterial density and the shape of the motile population, after an initial transient, are constant in time. By considering not only the advancing population but also the fraction that lags behind, we propose a growth model that relates spatial distribution, motility and growth rate. This model, that is similar to bacterial growth in a chemostat predicts that the fraction of the population lagging behind is inversely proportional to the velocity of the motile population. We test this prediction by modulating motility using inducible expression of the flagellar sigma factor FliA. Finally, we observe that bacteria in the chemotactic ring express higher relative levels of the chemotaxis and galactose metabolism genes fliC, fliL and galE than those that stay behind in the center of the plate.

Regulation of proteins across the cell cycle is a basic process in cell biology. It has been difficult to study this globally in human cells due to lack of methods to accurately follow protein levels and localizations over time. Estimates based on global mRNA measurements suggest that only a few percent of human genes have cell-cycle dependent mRNA levels. Here, we used dynamic proteomics to study the cell-cycle dependence of proteins. We used 495 clones of a human cell line, each with a different protein tagged fluorescently at its endogenous locus. Protein level and localization was quantified in individual cells over 24h of growth using time-lapse microscopy. Instead of standard chemical or mechanical methods for cell synchronization, we employed in-silico synchronization to place protein levels and localization on a time axis between two cell divisions. This non-perturbative synchronization approach, together with the high accuracy of the measurements, allowed a sensitive assay of cell-cycle dependence. We further developed a computational approach that uses texture features to evaluate changes in protein localizations. We find that 40% of the proteins showed cell cycle dependence, of which 11% showed changes in protein level and 35% in localization. This suggests that a broader range of cell-cycle dependent proteins exists in human cells than was previously appreciated. Most of the cell-cycle dependent proteins exhibit changes in cellular localization. Such changes can be a useful tool in the regulation of the cell-cycle being fast and efficient.

Biological systems that perform multiple tasks face a fundamental trade-off: A given phenotype cannot be optimal at all tasks. Here we ask how trade-offs affect the range of phenotypes found in nature. Using the Pareto front concept from economics and engineering, we find that best-trade-off phenotypes are weighted averages of archetypes - phenotypes specialized for single tasks. For two tasks, phenotypes fall on the line connecting the two archetypes, which could explain linear trait correlations, allometric relationships, as well as bacterial gene-expression patterns. For three tasks, phenotypes fall within a triangle in phenotype space, whose vertices are the archetypes, as evident in morphological studies, including on Darwin's finches. Tasks can be inferred from measured phenotypes based on the behavior of organisms nearest the archetypes.

A gene can be said to be insulated from environmental variations if its expression level depends only on its cognate inducers, and not on variations in conditions. We tested the insulation of the lac promoter of E. coli and of synthetic constructs in which the transcription factor CRP acts as either an activator or a repressor, by measuring their input function-their expression as a function of inducers-in different growth conditions. We find that the promoter activities show sizable variation across conditions of 10%-100% (SD/mean). When the promoter is bound to its cognate regulator(s), variation across conditions is smaller than when it is unbound. Thus, mode of regulation affects insulation: activators seem to show better insulation at high expression levels, and repressors at low expression levels. This may explain the Savageau demand rule, in which E. coli genes needed often in the natural environment tend to be regulated by activators, and rarely needed genes by repressors. The present approach can be used to study insulation in other genes and organisms.

Biological systems display complex networks of interactions both at the level of molecules inside the cell and at the level of interactions between cells. Networks of interacting molecules, such as transcription networks, have been shown to be composed of recurring circuits called network motifs, each with specific dynamical functions. Much less is known about the possibility of such circuit analysis in networks made of communicating cells. Here, we study models of circuits in which a few cell types interact by means of signaling molecules. We consider circuits of cells with architectures that seem to recur in immunology. An intriguing feature of these circuits is their use of signaling molecules with a pleiotropic or paradoxical role, such as cytokines that increase both cell growth and cell death. We find that pleiotropic signaling molecules can provide cell circuits with systems-level functions. These functions include for different circuits maintenance of homeostatic cell concentrations, robust regulation of differentiation processes, and robust pulses of cells or cytokines.

Protein removal has a central role in numerous cellular processes. Obtaining systematic measurements of multiple protein removal rates is necessary to understand the principles that govern these processes, but it is currently a major technical challenge. To address this, we developed 'bleach-chase', a noninvasive method for measuring the half-lives of multiple proteins at high temporal resolution in living cells. The method uses a library of annotated human reporter cell clones, each with a unique fluorescently tagged protein expressed from its native chromosomal location. In this protocol, we detail a simple procedure that bleaches the cells and uses time-lapse fluorescence microscopy and automated image analysis to systematically measure the half-life dynamics of multiple proteins. The duration of the protocol is 4-5 d. The method may be applicable to a wide range of fluorescently tagged proteins and cell lines.

Gene expression is subject to random perturbations that lead to fluctuations in the rate of protein production. As a consequence, for any given protein, genetically identical organisms living in a constant environment will contain different amounts of that particular protein, resulting in different phenotypes. This phenomenon is known as "phenotypic noise." In bacterial systems, previous studies have shown that, for specific genes, both transcriptional and translational processes affect phenotypic noise. Here, we focus on how the promoter regions of genes affect noise and ask whether levels of promoter-mediated noise are correlated with genes' functional attributes, using data for over 60% of all promoters in Escherichia coli. We find that essential genes and genes with a high degree of evolutionary conservation have promoters that confer low levels of noise. We also find that the level of noise cannot be attributed to the evolutionary time that different genes have spent in the genome of E. coli. In contrast to previous results in eukaryotes, we find no association between promoter-mediated noise and gene expression plasticity. These results are consistent with the hypothesis that, in bacteria, natural selection can act to reduce gene expression noise and that some of this noise is controlled through the sequence of the promoter region alone.

Joint improvisation is the creative action of two or more people without a script or designated leader. Examples include improvisational theater and music, and day-to-day activities such as conversations. In joint improvisation, novel action is created, emerging from the interaction between people. Although central to creative processes and social interaction, joint improvisation remains largely unexplored due to the lack of experimental paradigms. Here we introduce a paradigm based on a theater practice called the mirror game. We measured the hand motions of two people mirroring each other at high temporal and spatial resolution. We focused on expert actors and musicians skilled in joint improvisation. We found that players can jointly create novel complex motion without a designated leader, synchronized to less than 40 ms. In contrast, we found that designating one player as leader deteriorated performance: The follower showed 2-3 Hz oscillation around the leader's smooth trajectory, decreasing synchrony and reducing the range of velocities reached. A mathematical model suggests a mechanism for these observations based on mutual agreement on future motion in mirrored reactive-predictive controllers. This is a step toward understanding the human ability to create novelty by improvising together.

Playback theatre is a community-building improvisational theatre in which a personal story told by a group member is transformed into a theatre piece on the spot by other group members. Playback theatre combines artistic expression and social connection based on story-telling and empathic listening, thus bringing together modes thought to promote healing. Here, we explore the potential of playback theatre to promote recovery in the field of mental health. We conducted two playback courses for a total of 19 adults in a university-based program for recovery, and collected qualitative reports pre-post self-report measures for self-esteem, personal growth and recovery. We also developed a self-report measure named the playback impact scale that includes items related to creativity, confidence in performing, social connectedness and seeing one's life as full of stories. We find significant enhancement in the playback impact scale following a 10 week playback course. The qualitative reports indicate recurring themes of enhanced self-esteem, self-knowledge, as well as fun and relaxation, and enhanced sense of connection and empathy for others. These preliminary results suggest that playback theatre can serve as an effective practice for enhancing recovery processes from serious mental illness.

Background: C ₄ plants such as corn and sugarcane assimilate atmospheric CO ₂ into biomass by means of the C ₄ carbon fixation pathway. We asked how PEP formation rate, a key step in the carbon fixation pathway, might work at a precise rate, regulated by light, despite fluctuations in substrate and enzyme levels constituting and regulating this process.Results: We present a putative mechanism for robustness in C ₄ carbon fixation, involving a key enzyme in the pathway, pyruvate orthophosphate dikinase (PPDK), which is regulated by a bifunctional enzyme, Regulatory Protein (RP). The robust mechanism is based on avidity of the bifunctional enzyme RP to its multimeric substrate PPDK, and on a product-inhibition feedback loop that couples the system output to the activity of the bifunctional regulator. The model provides an explanation for several unusual biochemical characteristics of the system and predicts that the system's output, phosphoenolpyruvate (PEP) formation rate, is insensitive to fluctuations in enzyme levels (PPDK and RP), substrate levels (ATP and pyruvate) and the catalytic rate of PPDK, while remaining sensitive to the system's input (light levels).Conclusions: The presented PPDK mechanism is a new way to achieve robustness using product inhibition as a feedback loop on a bifunctional regulatory enzyme. This mechanism exhibits robustness to protein and metabolite levels as well as to catalytic rate changes. At the same time, the output of the system remains tuned to input levels.

Background: Gene regulation networks are made of recurring regulatory patterns, called network motifs. One of the most common network motifs is negative auto-regulation, in which a transcription factor represses its own production. Negative auto-regulation has several potential functions: it can shorten the response time (time to reach halfway to steady-state), stabilize expression against noise, and linearize the gene's input-output response curve. This latter function of negative auto-regulation, which increases the range of input signals over which downstream genes respond, has been studied by theory and synthetic gene circuits. Here we ask whether negative auto-regulation preserves this function also in the context of a natural system, where it is embedded within many additional interactions. To address this, we studied the negative auto-regulation motif in the arabinose utilization system of Escherichia coli, in which negative auto-regulation is part of a complex regulatory network. Results: We find that when negative auto-regulation is disrupted by placing the regulator araC under constitutive expression, the input dynamic range of the arabinose system is reduced by 10-fold. The apparent Hill coefficient of the induction curve changes from about n = 1 with negative auto-regulation, to about n = 2 when it is disrupted. We present a mathematical model that describes how negative auto-regulation can increase input dynamic-range, by coupling the transcription factor protein level to the input signal. Conclusions: Here we demonstrate that the negative auto-regulation motif in the native arabinose system of Escherichia coli increases the range of arabinose signals over which the system can respond. In this way, negative auto-regulation may help to increase the input dynamic-range while maintaining the specificity of cooperative regulatory systems. This function may contribute to explaining the common occurrence of negative autoregulation in biological systems.

Cells remove proteins by two processes: degradation and dilution due to cell growth. The balance between these basic processes is poorly understood. We addressed this by developing an accurate and noninvasive method for measuring protein half-lives, called "bleach-chase," that is applicable to fluorescently tagged proteins. Assaying 100 proteins in living human cancer cells showed half-lives that ranged between 45 minutes and 22.5 hours. A variety of stresses that stop cell division showed the same general effect: Long-lived proteins became longer-lived, whereas short-lived proteins remained largely unaffected. This effect is due to the relative strengths of degradation and dilution and suggests a mechanism for differential killing of rapidly growing cells by growth-arresting drugs. This approach opens a way to understand proteome half-life dynamics in living cells.

Bacteria regulate the assimilation of multiple nutrients to enable growth. How is balanced utilization achieved, despite fluctuations in the concentrations of the enzymes that make up the regulatory circuitry? Here we address this question by studying the nitrogen system of E. coli. A mechanism based on the avidity of a bifunctional enzyme, adenylyltransferase (AT/AR), to its multimeric substrate, glutamine synthetase, is proposed to maintain a robust ratio between two key metabolites, glutamine and α-ketoglutarate. This ratio is predicted to be insensitive to variations in protein levels of the core circuit and to the rate of nitrogen utilization. We find using mass spectrometry that the metabolite ratio is robust to variations in protein levels and that this robustness depends on the bifunctional enzyme. Moreover, robustness carries through to the bacteria growth rate. Interrupting avidity by adding a monofunctional AT/AR mutant to the native system abolishes robustness, as predicted by the proposed mechanism.

The study of transcription regulation was initiated more than half a century ago, and has since then yielded a wealth of information on the regulation of gene expression. As transcriptional response was found to arise from a complicated set of interactions, system-level approaches became essential to their studies. Such approaches led to the presentation of transcription interactions in a network structure with consequence studies on the network topology. In particular, system-level studies led to the identification of a set of a recurring regulation patterns, called network motifs, that appear to serve as basic building blocks of transcription networks. In this chapter we will uncover the progress of the last few years in our understanding of the architecture of bacterial transcriptional networks, as well as functions provided by the network structure, focusing mainly on network motifs and their distinct dynamical properties. Because the transcriptional network of Escherichia coli, is the best studied network, most of the findings presented are from this bacterium. In many cases, however, they are applicable to other species as well.

This paper studies invariance with respect to symmetries in sensory fields, a particular case of which, scale-invariance, has recently been found in certain eukaryotic as well as bacterial cell signaling systems. We describe a necessary and sufficient characterization of symmetry invariance in terms of equivariant transformations, show how this characterization helps find all possible symmetries in standard models of biological adaptation, and discuss symmetry-invariant searches.

For a general class of dynamical systems, this paper presents a necessary and sufficient characterization of invariance of transient responses to symmetries in inputs. A particular example of this property, scale-invariance or "fold-change detection" (FCD), has been shown to be exhibited in biological sensory systems ranging from bacterial chemotaxis pathways to signal transduction mechanisms in eukaryotes. The characterization is in terms of a notion of equivariance and amounts to the solvability of an associated partial differential equation. For several simple system motifs that are recurrent in biology, the solvability criterion may be checked explicitly.

Recent studies suggest that certain cellular sensory systems display fold-change detection (FCD): a response whose entire shape, including amplitude and duration, depends only on fold changes in input and not on absolute levels. Thus, a step change in input from, for example, level 1 to 2 gives precisely the same dynamical output as a step from level 2 to 4, because the steps have the same fold change. We ask what the benefit of FCD is and show that FCD is necessary and sufficient for sensory search to be independent of multiplying the input field by a scalar. Thus, the FCD search pattern depends only on the spatial profile of the input and not on its amplitude. Such scalar symmetry occurs in a wide range of sensory inputs, such as source strength multiplying diffusing/convecting chemical fields sensed in chemotaxis, ambient light multiplying the contrast field in vision, and protein concentrations multiplying the output in cellular signaling systems. Furthermore,weshowthatFCD entailstwofeatures found across sensory systems, exact adaptation and Weber's law, but that these two features are not sufficient for FCD. Finally, we present a wide class of mechanisms that have FCD, including certain nonlinear feedback and feed-forward loops. We find that bacterial chemotaxis displays feedback within the present class and hence, is expected to show FCD. This can explain experiments in which chemotaxis searches are insensitive to attractant source levels. This study, thus, suggests a connection between properties of biological sensory systems and scalar symmetry stemming from physical properties of their input fields.

Central carbon metabolism uses a complex series of enzymatic steps to convert sugars into metabolic precursors. These precursors are then used to generate the entire biomass of the cell. Are there simplifying principles that can explain the structure of such metabolic networks? Here we address this question by studying central carbon metabolism in E. coli. We use all known classes of enzymes that work on carbohydrates to generate rules for converting compounds and for generating possible paths between compounds. We find that central carbon metabolism is built as a minimal walk between the 12 precursor metabolites that form the basis for biomass and one precursor essential for the positive net ATP balance in glycolysis: every pair of consecutive precursors in the network is connected by the minimal number of enzymatic steps. Similarly, input sugars are converted into precursors by the shortest possible enzymatic paths. This suggests an optimality principle for the structure of central carbon metabolism. The present approach may be used to study other metabolic networks and to design new minimal pathways.

A key circuit in the response of cells to damage is the p53-mdm2 feedback loop. This circuit shows sustained, noisy oscillations in individual human cells following DNA breaks. Here, we apply an engineering approach known as systems identification to quantify the in vivo interactions in the circuit on the basis of accurate measurements of its power spectrum. We obtained oscillation time courses of p53 and Mdm2 protein levels from several hundred cells and analyzed their Fourier spectra. We find characteristic spectra with distinct low-frequency components that are well-described by a third-order linear model with white noise. The model identifies the sign and strength of the known interactions, including a negative feedback loop between p53 and its upstream regulator. It also implies that noise can trigger and maintain the oscillations. The model also captures the power spectra of p53 dynamics without DNA damage. Parameters such as noise amplitudes and protein lifetimes are estimated. This approach employs natural biological noise as a diagnostic that stimulates the system at many frequencies at once. It seems to be a useful way to find the in vivo design of circuits and may be applied to other systems by monitoring their power spectrum in individual cells.

When E. coli cells express unneeded protein, they grow more slowly. Such penalty to fitness associated with making proteins is called protein cost. Protein cost is an important component in the cost-benefit tradeoffs that underlie the evolution of protein circuits, but its origins are still poorly understood. Here, we ask how the protein cost varies during the exponential growth phase of E. coli. We find that cells growing exponentially following an upshift from overnight culture show a large cost when producing unneeded proteins. However, after several generations, while still in exponential growth, the cells enter a phase where cost is much reduced despite vigorous unneeded protein production. We find that this reduced-cost phase depends on the ppGpp system, which adjusts the amount of ribosomes in the cell and does not occur after a downshift from rich to poor medium. These findings suggest that protein cost is a transient phenomenon that happens upon an upshift in conditions and that cost is reduced when ribosomes and other cellular systems have increased to their appropriate steady-state level in the new condition.

Debates concerning the roles of different factors that may limit an organism's reproductive success pervade evolutionary ecology. We suggest that a broad class of limiting-factors problems involving essential resources or essential components of reproductive effort can be analyzed with an evolutionary application of Liebig's law of the minimum. We explore life-history evolution using the metaphor of an organism that must harvest two essential resources (resources 1 and 2) from a stochastically varying environment. Our models make three predictions. First, organisms should overinvest, relative to the deterministic case, in harvesting the resource whose per-offspring harvest cost is smaller. Second, at the optimum, organisms balance multiple fitness-limiting factors rather than being consistently limited by one factor. Third, the optimal investment in harvesting a resource is directly linked to the probability that the organism's fitness will be limited by that resource. Under temporal variation, the optimal proportional investment in harvesting resource 1 is equal to the probability that resource 1 will limit fitness. Our results help to explain why the responses of populations to environmental perturbations are hard to predict: as an organism transitions between different limiting factors, its responses to perturbations of those factors will likewise change.

Drugs and drug combinations have complex biological effects on cells and organisms. Little is known about how drugs affect protein dynamics that determine these effects. Here, we use a dynamic proteomics approach to accurately follow 15 protein levels in human cells in response to 13 different drugs. We find that protein dynamics in response to combinations of drugs are described accurately by a linear superposition (weighted sum) of their response to individual drugs. The weights in this superposition describe the relative impact of each drug on each protein. Using these weights, we show that one can predict the dynamics in a three-drug or four-drug combination on the basis of the dynamics in drug pairs. Our approach might eliminate the need to increase the number of experiments exponentially with the number of drugs and suggests that it might be possible to rationally control protein dynamics with specific drug combinations. PaperClip: {An electronic component is presented}.

Motivated group members experience a full sense of choice: of doing what one wants. Such behavior shows high performance, is enjoyable, and enhances innovation. This essay describes principles of building a motivated research group.

Understanding the dynamic relationship between components of a system or pathway at the individual cell level is a current challenge. To address this, we developed an approach that allows simultaneous tracking of several endogenous proteins of choice within individual living human cells. The approach is based on fluorescent tagging of proteins at their native locus by directed gene targeting. A fluorescent tag-encoding DNA is introduced as a new exon into the intronic region of the gene of interest, resulting in expression of a full-length fluorescently tagged protein. We used this approach to establish human cell lines simultaneously expressing two components of a major antioxidant defense system, thioredoxin 1 (Trx) and thioredoxin reductase 1 (TrxR1), labeled with CFP and YFP, respectively. We find that the distributions of both proteins between nuclear and cytoplasmic compartments were highly variable between cells. However, the two proteins did not vary independently of each other: protein levels of Trx and TrxR1 in both the whole cell and the nucleus were substantially correlated. We further find that in response to a stress-inducing drug (CPT), both Trx and TrxR1 accumulated in the nuclei in a manner that was highly temporally correlated. This accumulation considerably reduced cell-to-cell variability in nuclear content of both proteins, suggesting a uniform response of the thioredoxin system to stress. These results indicate that Trx and TrxR1 act in concert in response to stress in regard to both time course and variability. Thus, our approach provides an efficient tool for studying dynamic relationship between components of systems of interest at a single-cell level.

Signal-transduction cascades are usually studied on cell averages, masking variability between individual cells. To address this, we studied in individual cells the dynamic response of ERK2, a well-characterized MAPK signaling protein, which enters the nucleus upon stimulation. Using fluorescent tagging at the endogenous chromosomal locus, we found that cells show wide basal variation in ERK2 nuclear levels. Upon EGF stimulation, cells show (1) a fold-change response, where peak nuclear accumulation of ERK2 is proportional to basal level in each cell; and (2) exact adaptation in nuclear levels of ERK2, returning to original basal level of each cell. The timing of ERK2 dynamics is more precise between cells than its amplitude. We further found that in some cells ERK2 exhibits a second pulse of nuclear entry, smaller than the first. The present study suggests that this signaling system compensates for natural biological noise: despite large variation in nuclear basal levels, ERK2's fold dynamics is similar between cells.

Many sensory systems (e.g., vision and hearing) show a response that is proportional to the fold-change in the stimulus relative to the background, a feature related to Weber's Law. Recent experiments suggest such a fold-change detection feature in signaling systems in cells: a response that depends on the fold-change in the input signal, and not on its absolute level. It is therefore of interest to find molecular mechanisms of gene regulation that can provide such fold-change detection. Here, we demonstrate theoretically that fold-change detection can be generated by one of the most common network motifs in transcription networks, the incoherent feedforward loop (I1-FFL), in which an activator regulates both a gene and a repressor of the gene. The fold-change detection feature of the I1-FFL applies to the entire shape of the response, including its amplitude and duration, and is valid for a wide range of biochemical parameters.

Summary: Protein structures can be viewed as networks of contacts (edges) between amino-acid residues (nodes). Here we dissect proteins into sub-graphs consisting of six nodes and their corresponding edges, with an edge being either a backbone hydrogen bond (H-bond) or a covalent interaction. Six thousand three hundred and twenty-two such sub-graphs were found in a large non-redundant dataset of high-resolution structures, from which 35 occur much more frequently than in a random model. Many of these significant sub-graphs (also called network motifs) correspond to sub-structures of α helices and β-sheets, as expected. However, others correspond to more exotic sub-structures such as 3₁₀ helix, Schellman motif and motifs that were not defined previously. This topological characterization of patterns is very useful for producing a detailed differences map to compare protein structures. Here we analyzed in details the differences between NMR, molecular dynamics (MD) simulations and X-ray structures for Lysozyme, SH3 and the lambda repressor. In these cases, the same structures solved by NMR and simulated by MD showed small but consistent differences in their motif composition from the crystal structures, despite a very small root mean square deviation (RMSD) between them. This may be due to differences in the pair-wise energy functions used and the dynamic nature of these proteins.

Recent advances allow tracking the levels and locations of a thousand proteins in individual living human cells over time using a library of annotated reporter cell clones (LARC). This library was created by Cohen et al. to study the proteome dynamics of a human lung carcinoma cell-line treated with an anti-cancer drug. Here, we report the Dynamic Proteomics database for the proteins studied by Cohen et al. Each cell-line clone in LARC has a protein tagged with yellow fluorescent protein, expressed from its endogenous chromosomal location, under its natural regulation. The Dynamic Proteomics interface facilitates searches for genes of interest, downloads of protein fluorescent movies and alignments of dynamics following drug addition. Each protein in the database is displayed with its annotation, cDNA sequence, fluorescent images and movies obtained by the time-lapse microscopy. The protein dynamics in the database represents a quantitative trace of the protein fluorescence levels in nucleus and cytoplasm produced by image analysis of movies over time. Furthermore, a sequence analysis provides a search and comparison of up to 50 input DNA sequences with all cDNAs in the library. The raw movies may be useful as a benchmark for developing image analysis tools for individual-cell dynamic-proteomics. The database is available at http://www.dynamicproteomics.net/.

We depend on talks to communicate our work, and we spend much of our time as audience members in talks. However, few scientists are taught the well-established principles of giving good talks. Here, I describe how to prepare, present, and answer questions in a scientific talk. We will see how a talk prepared with a single premise and delivered with good eye contact is clear and enjoyable.

Cells need to allocate their limited resources to express a wide range of genes. To understand how Escherichia coli partitions its transcriptional resources between its different promoters, we employ a robotic assay using a comprehensive reporter strain library for E. coli to measure promoter activity on a genomic scale at high-temporal resolution and accuracy. This allows continuous tracking of promoter activity as cells change their growth rate from exponential to stationary phase in different media. We find a heavy-tailed distribution of promoter activities, with promoter activities spanning several orders of magnitude. While the shape of the distribution is almost completely independent of the growth conditions, the identity of the promoters expressed at different levels does depend on them. Translation machinery genes, however, keep the same relative expression levels in the distribution across conditions, and their fractional promoter activity tracks growth rate tightly. We present a simple optimization model for resource allocation which suggests that the observed invariant distributions might maximize growth rate. These invariant features of the distribution of promoter activities may suggest design constraints that shape the allocation of transcriptional resources.

Choosing good problems is essential for being a good scientist. But what is a good problem, and how do you choose one? The subject is not usually discussed explicitly within our profession. Scientists are expected to be smart enough to figure it out on their own and through the observation of their teachers. This lack of explicit discussion leaves a vacuum that can lead to approaches such as choosing problems that can give results that merit publication in valued journals, resulting in a job and tenure.

Extinctions of local subpopulations are common events in nature. Here, we ask whether such extinctions can affect the design of biological networks within organisms over evolutionary timescales. We study the impact of extinction events on modularity of biological systems, a common architectural principle found on multiple scales in biology. As a model system, we use networks that evolve toward goals specified as desired input-output relationships. We use an extinction-recolonization model, in which metapopulations occupy and migrate between different localities. Each locality displays a different environmental condition (goal), but shares the same set of subgoals with other localities. We find that in the absence of extinction events, the evolved computational networks are typically highly optimal for their localities with a nonmodular structure. In contrast, when local populations go extinct from time to time, we find that the evolved networks are modular in structure. Modular circuitry is selected because of its ability to adapt rapidly to the conditions of the free niche following an extinction event. This rapid adaptation is mainly achieved through genetic recombination of modules between immigrants from neighboring local populations. This study suggests, therefore, that extinctions in heterogeneous environments promote the evolution of modular biological network structure, allowing local populations to effectively recombine their modules to recolonize niches.

A current challenge in biology is to understand the dynamics of protein circuits in living human cells. Can one define and test equations for the dynamics and variability of a protein over time? Here, we address this experimentally and theoretically, by means of accurate time-resolved measurements of endogenously tagged proteins in individual human cells. As a model system, we choose three stable proteins displaying cell-cycle-dependant dynamics. We find that protein accumulation with time per cell is quadratic for proteins with long mRNA life times and approximately linear for a protein with short mRNA lifetime. Both behaviors correspond to a classical model of transcription and translation. A stochastic model, in which genes slowly switch between ON and OFF states, captures measured cell-cell variability. The data suggests, in accordance with the model, that switching to the gene ON state is exponentially distributed and that the cell-cell distribution of protein levels can be approximated by a Gamma distribution throughout the cell cycle. These results suggest that relatively simple models may describe protein dynamics in individual human cells.

Biological systems often display modularity, in the sense that they can be decomposed into nearly independent subsystems. Recent studies have suggested that modular structure can spontaneously emerge if goals (environments) change over time, such that each new goal shares the same set of sub-problems with previous goals. Such modularly varying goals can also dramatically speed up evolution, relative to evolution under a constant goal. These studies were based on simulations of model systems, such as logic circuits and RNA structure, which are generally not easy to treat analytically. We present, here, a simple model for evolution under modularly varying goals that can be solved analytically. This model helps to understand some of the fundamental mechanisms that lead to rapid emergence of modular structure under modularly varying goals. In particular, the model suggests a mechanism for the dramatic speedup in evolution observed under such temporally varying goals.

The glyoxylate bypass allows Escherichia coli to grow on carbon sources with only two carbons by bypassing the loss of carbons as CO(2) in the tricarboxylic acid cycle. The flux toward this bypass is regulated by the phosphorylation of the enzyme isocitrate dehydrogenase (IDH) by a bifunctional kinase-phosphatase called IDHKP. In this system, IDH activity has been found to be remarkably robust with respect to wide variations in the total IDH protein concentration. Here, we examine possible mechanisms to explain this robustness. Explanations in which IDHKP works simultaneously as a first-order kinase and as a zero-order phosphatase with a single IDH binding site are found to be inconsistent with robustness. Instead, we suggest a robust mechanism where both substrates bind the bifunctional enzyme to form a ternary complex.

Heterogeneous cell populations form an interconnected network that determine their collective output. One example of such a heterogeneous immune population is tumor-infiltrating lymphocytes (TILs), whose output can be measured in terms of its reactivity against tumors. While the degree of reactivity varies considerably between different TILs, ranging from null to a potent response, the underlying network that governs the reactivity is poorly understood. Here, we asked whether one can predict and even control this reactivity. To address this we measured the subpopulation compositions of 91 TILs surgically removed from 27 metastatic melanoma patients. Despite the large number of subpopulations compositions, we were able to computationally extract a simple set of subpopulation-based rules that accurately predict the degree of reactivity. This raised the conjecture of whether one could control reactivity of TILs by manipulating their subpopulation composition. Remarkably, by rationally enriching and depleting selected subsets of subpopulations, we were able to restore anti-tumor reactivity to nonreactive TILs. Altogether, this work describes a general framework for predicting and controlling the output of a cell mixture.

For a wide class of chemical reaction networks, including all those governed by detailed balanced mass-action kinetics, we examine the robustness of equilibrium species concentrations against fluctuations in the overall reactant supply. In particular, we present lower bounds on the individual species-concentration sensitivities that derive from reaction network structure alone, independent of kinetic parameters or even of the particular equilibrium state at which sensitivities are calculated. These bounds suggest that, in the class of reaction networks considered here, very high robustness (i.e., very low sensitivities) should be expected only when the various molecules are constructed from a large number of distinct elemental building blocks that appear in high multiplicity or that combine gregariously. This situation is often encountered in biology.

Why do seemingly identical cells respond differently to a drug? To address this, we studied the dynamics and variability of the protein response of human cancer cells to a chemotherapy drug, camptothecin. We present a dynamic-proteomics approach that measures the levels and locations of nearly 1000 different endogenously tagged proteins in individual living cells at high temporal resolution. All cells show rapid translocation of proteins specific to the drug mechanism, including the drug target (topoisomerase-1), and slower, wide-ranging temporal waves of protein degradation and accumulation. However, the cells differ in the behavior of a subset of proteins. We identify proteins whose dynamics differ widely between cells, in a way that corresponds to the outcomes - cell death or survival. This opens the way to understanding molecular responses to drugs in individual cells.

One of the striking features of evolution is the appearance of novel structures in organisms. Recently, Kirschner and Gerhart have integrated discoveries in evolution, genetics, and developmental biology to form a theory of facilitated variation (FV). The key observation is that organisms are designed such that random genetic changes are channeled in phenotypic directions that are potentially useful. An open question is how FV spontaneously emerges during evolution. Here, we address this by means of computer simulations of two well-studied model systems, logic circuits and RNA secondary structure. We find that evolution of FV is enhanced in environments that change from time to time in a systematic way: the varying environments are made of the same set of subgoals but in different combinations. We find that organisms that evolve under such varying goals not only remember their history but also generalize to future environments, exhibiting high adaptability to novel goals. Rapid adaptation is seen to goals composed of the same subgoals in novel combinations, and to goals where one of the subgoals was never seen in the history of the organism. The mechanisms for such enhanced generation of novelty (generalization) are analyzed, as is the way that organisms store information in their genomes about their past environments. Elements of facilitated variation theory, such as weak regulatory linkage, modularity, and reduced pleiotropy of mutations, evolve spontaneously under these conditions. Thus, environments that change in a systematic, modular fashion seem to promote facilitated variation and allow evolution to generalize to novel conditions.

Organisms often adapt to new conditions by means of beneficial mutations that become fixed in the population. Often, full adaptation requires several different mutations in the same cell, each of which may affect a different aspect of the behavior. Can one predict order in which these mutations become fixed? To address this, we experimentally studied evolution of Escherichia coli in a growth medium in which the effects of different adaptations can be easily classified as affecting growth rate or the lag-phase duration. We find that adaptations are fixed in a defined and reproducible order: first reduction of lag phase, and then an increase of the exponential growth rate. A population genetics theory explains this order, and suggests growth conditions in which the order of adaptations is reversed. We experimentally find this order reversal under the predicted conditions. This study supports a view in which the evolutionary path to adaptation in a new environment can be captured by theory and experiment.

Cells respond to signals by regulating gene expression. The relation between the level of input signals and the transcription rate of the gene is called the gene's input function. Because most genes are regulated by more than one signal, the input functions are usually multidimensional. To understand cellular responses, it is essential to know the shapes of these functions. Here, we map the two-dimensional input functions of 19 sugar-utilization genes at high resolution in living E. coli cells. We find diverse, intricately shaped input functions, despite the similarity in the regulatory circuitry of these genes. Surprisingly, some of the input functions are nonmonotonic, peaking at intermediate signal levels. Furthermore, most of the input functions show separation of variables, in the sense that they can be described as the product of simple functions that depend on a single input. This first broad survey of two-dimensional input functions can be extended to map the logic of gene regulation in other systems.

Gene regulation networks contain recurring circuit patterns called network motifs. One of the most common network motif is the incoherent type 1 feed-forward loop (I1-FFL), in which an activator controls both gene and repressor of that gene. This motif was shown to act as a pulse generator and response accelerator of gene expression. Here we consider an additional function of this motif: the I1-FFL can generate a non-monotonic dependence of gene expression on the input signal. Here, we study this experimentally in the galactose system of Escherichia coli, which is regulated by an I1-FFL. The promoter activity of two of the gal operons, galETK and galP, peaks at intermediate levels of the signal cAMP. We find that mutants in which the I1-FFL is disrupted lose this non-monotonic behavior, and instead display monotonic input functions. Theoretical analysis suggests that non-monotonic input functions can be achieved for a wide range of parameters by the I1-FFL. The models also suggest regimes where a monotonic input-function can occur, as observed in the mglBAC operon regulated by the same I1-FFL. The present study thus experimentally demonstrates how upstream circuitry can affect gene input functions and how an I1-FFL functions within its natural context in the cell.

Biological signaling systems produce an output, such as the level of a phosphorylated protein, in response to defined input signals. The output level as a function of the input level is called the system's input-output relation. One may ask whether this input-output relation is sensitive to changes in the concentrations of the system's components, such as proteins and ATP. Because component concentrations often vary from cell to cell, it might be expected that the input-output relation will likewise vary. If this is the case, different cells exposed to the same input signal will display different outputs. Such variability can be deleterious in systems where survival depends on accurate match of output to input. Here we suggest a mechanism that can provide input-output robustness, that is, an input-output relation that does not depend on variations in the concentrations of any of the system's components. The mechanism is based on certain bacterial signaling systems. It explains how specific molecular details can work together to provide robustness. Moreover, it suggests an approach that can help identify a wide family of nonequilibrium mechanisms that potentially have robust input-output relations.

A basic assumption underlying synthetic biology is that analysis of genetic circuit elements, such as regulatory proteins and promoters, can be used to understand and predict the behavior of circuits containing those elements. To test this assumption, we used time-lapse fluorescence microscopy to quantitatively analyze two autoregulatory negative feedback circuits. By measuring the gene regulation functions of the corresponding repressor-promoter interactions, we accurately predicted the expression level of the autoregulatory feedback loops, in molecular units. This demonstration that quantitative characterization of regulatory elements can predict the behavior of genetic circuits supports a fundamental requirement of synthetic biology.

Simulations of biological evolution, in which computers are used to evolve systems toward a goal, often require many generations to achieve even simple goals. It is therefore of interest to look for generic ways, compatible with natural conditions, in which evolution in simulations can be speeded. Here, we study the impact of temporally varying goals on the speed of evolution, defined as the number of generations needed for an initially random population to achieve a given goal. Using computer simulations, we find that evolution toward goals that change over time can, in certain cases, dramatically speed up evolution compared with evolution toward a fixed goal. The highest speedup is found under modularly varying goals, in which goals change over time such that each new goal shares some of the subproblems with the previous goal. The speedup increases with the complexity of the goal: the harder the problem, the larger the speedup. Modularly varying goals seem to push populations away from local fitness maxima, and guide them toward evolvable and modular solutions. This study suggests that varying environments might significantly contribute to the speed of natural evolution. In addition, it suggests a way to accelerate optimization algorithms and improve evolutionary approaches in engineering.

Transcription regulation networks control the expression of genes. The transcription networks of well-studied microorganisms appear to be made up of a small set of recurring regulation patterns, called network motifs. The same network motifs have recently been found in diverse organisms from bacteria to humans, suggesting that they serve as basic building blocks of transcription networks. Here I review network motifs and their functions, with an emphasis on experimental studies. Network motifs in other biological networks are also mentioned, including signalling and neuronal networks.

We present a protocol to tag proteins expressed from their endogenous chromosomal locations in individual mammalian cells using central dogma tagging. The protocol can be used to build libraries of cell clones, each expressing one endogenous protein tagged with a fluorophore such as the yellow fluorescent protein. Each round of library generation produces 100-200 cell clones and takes about 1 month. The protocol integrates procedures for high-throughput single-cell cloning using flow cytometry, high-throughput cDNA generation and 3 rapid amplification of cDNA ends, semi-automatic protein localization screening using fluorescent microscopy and freezing cells in 96-well format.

DNA sequences that code for proteins need to convey, in addition to the protein-coding information, several different signals at the same time. These "parallel codes" include binding sequences for regulatory and structural proteins, signals for splicing, and RNA secondary structure. Here, we show that the universal genetic code can efficiently carry arbitrary parallel codes much better than the vast majority of other possible genetic codes. This property is related to the identity of the stop codons. We find that the ability to support parallel codes is strongly tied to another useful property of the genetic code - minimization of the effects of frame-shift translation errors. Whereas many of the known regulatory codes reside in nontranslated regions of the genome, the present findings suggest that protein-coding regions can readily carry abundant additional information.

Signaling pathways invoke interplays between forward signaling and feedback to drive robust cellular response. In this study, we address the dynamics of growth factor signaling through profiling of protein phosphorylation and gene expression, demonstrating the presence of a kinetically defined cluster of delayed early genes that function to attenuate the early events of growth factor signaling. Using epidermal growth factor receptor signaling as the major model system and concentrating on regulation of transcription and mRNA stability, we demonstrate that a number of genes within the delayed early gene cluster function as feedback regulators of immediate early genes. Consistent with their role in negative regulation of cell signaling, genes within this cluster are downregulated in diverse tumor types, in correlation with clinical outcome. More generally, our study proposes a mechanistic description of the cellular response to growth factors by defining architectural motifs that underlie the function of signaling networks.

Background. Biological systems are often modular: they can be decomposed into nearly-independent structural units that perform specific functions. The evolutionary origin of modularity is a subject of much current interest. Recent theory suggests that modularity can be enhanced when the environment changes over time. However, this theory has not yet been tested using biological data. Results. To address this, we studied the relation between environmental variability and modularity in a natural and well-studied system, the metabolic networks of bacteria. We classified 117 bacterial species according to the degree of variability in their natural habitat. We find that metabolic networks of organisms in variable environments are significantly more modular than networks of organisms that evolved under more constant conditions. Conclusion. This study supports the view that variability in the natural habitat of an organism promotes modularity in its metabolic network and perhaps in other biological systems.

Cells respond to the environment by regulating the expression of genes according to environmental signals. The relation between the input signal level and the expression of the gene is called the gene regulation function. It is of interest to understand the shape of a gene regulation function in terms of the environment in which it has evolved and the basic constraints of biological systems. Here we address this by presenting a cost-benefit theory for gene regulation functions that takes into account temporally varying inputs in the environment and stochastic noise in the biological components. We apply this theory to the well-studied lac operon of E. coli. The present theory explains the shape of this regulation function in terms of temporal variation of the input signals, and of minimizing the deleterious effect of cell-cell variability in regulatory protein levels. We also apply the theory to understand the evolutionary tradeoffs in setting the number of regulatory proteins and for selection of feed-forward loops in genetic circuits. The present cost-benefit theory can be used to understand the shape of other gene regulatory functions in terms of environment and noise constraints.

Background: Three networks of intercellular communication can be associated with cytokine secretion; one limited to cells of the immune system (immune cells), one limited to parenchymal cells of organs and tissues (body cells), and one involving interactions between immune and body cells (immune-body interface). These cytokine connections determine the inflammatory response to injury and subsequent healing as well as the biologic consequences of the adaptive immune response to antigens. We informatically probed the cytokine database to uncover the underlying network architecture of the three networks. Results: We now report that the three cytokine networks are among the densest of complex networks yet studied, and each features a characteristic profile of specific three-cell motifs. Some legitimate cytokine connections are shunned (anti-motifs). Certain immune cells can be paired by their input-output positions in a cytokine architecture tree of five tiers: macrophages (MΦ) and B cells (BC) comprise the first tier; the second tier is formed by T helper 1 (Th1) and T helper 2 (Th2) cells; the third tier includes dendritic cells (DC), mast cells (MAST), Natural Killer T cells (NK-T) and others; the fourth tier is formed by neutrophils (NEUT) and Natural Killer cells (NK); and the Cytotoxic T cell (CTL) stand alone as a fifth tier. The three-cell cytokine motif architecture of immune system cells places the immune system in a super-family that includes social networks and the World Wide Web. Body cells are less clearly stratified, although cells involved in wound healing and angiogenesis are most highly interconnected with immune cells. Conclusion: Cytokine network architecture creates an innate cell-communication platform that organizes the biologic outcome of antigen recognition and inflammation. Informatics sheds new light on immune-body systems organization.

Background: Transcription factor proteins bind specific DNA sequences to control the expression of genes. They contain DNA binding domains which belong to several super-families, each with a specific mechanism of DNA binding. The total number of transcription factors encoded in a genome increases with the number of genes in the genome. Here, we examined the number of transcription factors from each super-family in diverse organisms. Results: We find that the number of transcription factors from most super-families appears to be bounded. For example, the number of winged helix factors does not generally exceed 300, even in very large genomes. The magnitude of the maximal number of transcription factors from each super-family seems to correlate with the number of DNA bases effectively recognized by the binding mechanism of that super-family. Coding theory predicts that such upper bounds on the number of transcription factors should exist, in order to minimize cross-binding errors between transcription factors. This theory further predicts that factors with similar binding sequences should tend to have similar biological effect, so that errors based on mis-recognition are minimal. We present evidence that transcription factors with similar binding sequences tend to regulate genes with similar biological functions, supporting this prediction. Conclusion: The present study suggests limits on the transcription factor repertoire of cells, and suggests coding constraints that might apply more generally to the mapping between binding sites and biological function.

Gene arrangement into operons varies between bacterial species. Genes in a given system can be on one operon in some organisms and on several operons in other organisms. Existing theories explain why genes that work together should be on the same operon, since this allows for advantageous lateral gene transfer and accurate stoichiometry. But what causes the frequent separation into multiple operons of co-regulated genes that act together in a pathway? Here we suggest that separation is due to benefits made possible by differential regulation of each operon. We present a simple mathematical model for the optimal distribution of genes into operons based on a balance of the cost of operons and the benefit of regulation that provides 'just-when-needed' temporal order. The analysis predicts that genes are arranged such that genes on the same operon do not skip functional steps in the pathway. This prediction is supported by genomic data from 137 bacterial genomes. Our work suggests that gene arrangement is not only the result of random historical drift, genome re-arrangement and gene transfer, but has elements that are solutions of an evolutionary optimization problem. Thus gene functional order may be inferred by analyzing the operon structure across different genomes.

E. coli is widely used for systems biology research; there exists a need, however, for tools that can be used to accurately and comprehensively measure expression dynamics in individual living cells. To address this we present a library of transcriptional fusions of gfp to each of about 2,000 different promoters in E. coli K12, covering the great majority of the promoters in the organism. Each promoter fusion is expressed from a low-copy plasmid. We demonstrate that this library can be used to obtain highly accurate dynamic measurements of promoter activity on a genomic scale, in a glucose-lactose diauxic shift experiment. The library allowed detection of about 80 previously uncharacterized transcription units in E. coli, including putative internal promoters within previously known operons, such as the lac operon. This library can serve as a tool for accurate, high-resolution analysis of transcription networks in living E. coli cells.

Quantitative in vivo measurements are essential for developing a predictive understanding of cellular behavior. Here we present a technique that converts observed fluorescence intensities into numbers of molecules. By transiently expressing a fluorescently tagged protein and then following its dilution during growth and division, we observe asymmetric partitioning of fluorescence between daughter cells at each division. Such partition asymmetries are set by the actual numbers of proteins present, and thus provide a means to quantify fluorescence levels. We present a Bayesian algorithm that infers from such data both the fluorescence conversion factor and an estimate of the measurement error. Our algorithm works for arbitrarily sized data sets and handles consistently any missing measurements. We verify the algorithm with extensive simulation and demonstrate its application to experimental data from Escherichia coli. Our technique should provide a quantitative internal calibration to systems biology studies of both synthetic and endogenous cellular networks.

We examined cell cycle-dependent changes in the proteome of human cells by systematically measuring protein dynamics in individual living cells. We used time-lapse microscopy to measure the dynamics of a random subset of 20 nuclear proteins, each tagged with yellow fluorescent protein (YFP) at its endogenous chromosomal location. We synchronized the cells in silico by aligning protein dynamics in each cell between consecutive divisions. We observed widespread (40%) cell-cycle dependence of nuclear protein levels and detected previously unknown cell cycle-dependent localization changes. This approach to dynamic proteomics can aid in discovery and accurate quantification of the extensive regulation of protein concentration and localization in individual living cells.

Understanding the dynamics and variability of protein circuitry requires accurate measurements in living cells as well as theoretical models. To address this, we employed one of the best-studied protein circuits in human cells, the negative feedback loop between the tumor suppressor p53 and Mdm2. We measured the dynamics of fluorescently tagged p53 and Mdm2 over several days in individual living cells. We found that isogenic cells in the same environment behaved in highly variable ways following DNA-damaging gamma irradiation: some cells showed undamped oscillations for at least 3 days (more than 10 peaks). The amplitude of the oscillations was much more variable than the period. Sister cells continued to oscillate in a correlated way after cell division, but lost correlation after about 11 h on average. Other cells showed low-frequency fluctuations that did not resemble oscillations. We analyzed different families of mathematical models of the system, including a novel checkpoint mechanism. The models point to the possible source of the variability in the oscillations: low-frequency noise in protein production rates, rather than noise in other parameters such as degradation rates. This study provides a view of the extensive variability of the behavior of a protein circuit in living human cells, both from cell to cell and in the same cell over time.

The transcription rate of a gene is often controlled by several regulators that bind specific sites in the gene's cis-regulatory region. The combined effect of these regulators is described by a cis-regulatory input function. What determines the form of an input function, and how variable is it with respect to mutations? To address this, we employ the well-characterized lac operon of Escherichia coli, which has an elaborate input function, intermediate between Boolean AND-gate and OR-gate logic. We mapped in detail the input function of 12 variants of the lac promoter, each with different point mutations in the regulator binding sites, by means of accurate expression measurements from living cells. We find that even a few mutations can significantly change the input function, resulting in functions that resemble Pure AND gates, OR gates, or single-input switches. Other types of gates were not found. The variant input functions can be described in a unified manner by a mathematical model. The model also lets us predict which functions cannot be reached by point mutations. The input function that we studied thus appears to be plastic, in the sense that many of the mutations do not ruin the regulation completely but rather result in new ways to integrate the inputs.

The control of gene expression involves complex mechanisms that show large variation in design. For example, genes can be turned on either by the binding of an activator (positive control) or the unbinding of a repressor (negative control). What determines the choice of mode of control for each gene? This study proposes rules for gene regulation based on the assumption that free regulatory sites are exposed to nonspecific binding errors, whereas sites bound to their cognate regulators are protected from errors. Hence, the selected mechanisms keep the sites bound to their designated regulators for most of the time, thus minimizing fitness-reducing errors. This offers an explanation of the empirically demonstrated Savageau demand rule: Genes that are needed often in the natural environment tend to be regulated by activators, and rarely needed genes tend to be regulated by repressors; in both cases, sites are bound for most of the time, and errors are minimized. The fitness advantage of error minimization appears to be readily selectable. The present approach can also generate rules for multi-regulator systems. The error-minimization framework raises several experimentally testable hypotheses. It may also apply to other biological regulation systems, such as those involving protein-protein interactions.

Complex gene regulation networks are made of simple recurring gene circuits called network motifs. One of the most common network motifs is the incoherent type-1 feed-forward loop (I1-FFL), in which a transcription activator activates a gene directly, and also activates a repressor of the gene. Mathematical modeling suggested that the I1-FFL can show two dynamical features: a transient pulse of gene expression, and acceleration of the dynamics of the target gene. It is important to experimentally study the dynamics of this motif in living cells, to test whether it carries out these functions even when embedded within additional interactions in the cell. Here, we address this using a system with incoherent feed-forward loop connectivity, the galactose (gal) system of Escherichia coli. We measured the dynamics of this system in response to inducing signals at high temporal resolution and accuracy by means of green fluorescent protein reporters. We show that the galactose system displays accelerated turn-on dynamics. The acceleration is abolished in strains and conditions that disrupt the I1-FFL. The I1-FFL motif in the gal system works as theoretically predicted despite being embedded in several additional feedback loops. Response acceleration may be performed by the incoherent feed-forward loop modules that are found in diverse systems from bacteria to humans.

Western harmony is comprised of sequences of chords, which obey grammatical rules. It is of interest to develop a compact representation of the harmonic movement of chord sequences. Here, we apply an approach from analysis of complex networks, known as "network motifs" to define repeating dynamical patterns in musical harmony. We describe each piece as a graph, where the nodes are chords and the directed edges connect chords which occur consecutively in the piece. We detect several patterns, each of which is a walk on this graph, which recur in diverse musical pieces from the Baroque to modern-day popular music. These patterns include cycles of three or four nodes, with up to two mutual edges (edges that point in both directions). Cliques and patterns with more than two mutual edges are rare. Some of these universal patterns of harmony are well known and correspond to basic principles of music theory such as hierarchy and directionality. This approach can be extended to search for recurring patterns in other musical components and to study other dynamical systems that can be represented as walks on graphs.

Protein expression is a stochastic process that leads to phenotypic variation among cells. The cell-cell distribution of protein levels in microorganisms has been well characterized but little is known about such variability in human cells. Here, we studied the variability of protein levels in human cells, as well as the temporal dynamics of this variability, and addressed whether cells with higher than average protein levels eventually have lower than average levels, and if so, over what timescale does this mixing occur. We measured fluctuations over time in the levels of 20 endogenous proteins in living human cells, tagged by the gene for yellow fluorescent protein at their chromosomal loci. We found variability with a standard deviation that ranged, for different proteins, from about 15% to 30% of the mean. Mixing between high and low levels occurred for all proteins, but the mixing time was longer than two cell generations (more than 40 h) for many proteins. We also tagged pairs of proteins with two colours, and found that the levels of proteins in the same biological pathway were far more correlated than those of proteins in different pathways. The persistent memory for protein levels that we found might underlie individuality in cell behaviour and could set a timescale needed for signals to affect fully every member of a cell population.

Biological networks have an inherent simplicity: they are modular with a design that can be separated into units that perform almost independently. Furthermore, they show reuse of recurring patterns termed network motifs. Little is known about the evolutionary origin of these properties. Current models of biological evolution typically produce networks that are highly nonmodular and lack understandable motifs. Here, we suggest a possible explanation for the origin of modularity and network motifs in biology. We use standard evolutionary algorithms to evolve networks. A key feature in this study is evolution under an environment (evolutionary goal) that changes in a modular fashion. That is, we repeatedly switch between several goals, each made of a different combination of subgoals. We find that such "modularly varying goals" lead to the spontaneous evolution of modular network structure and network motifs. The resulting networks rapidly evolve to satisfy each of the different goals. Such switching between related goals may represent biological evolution in a changing environment that requires different combinations of a set of basic biological functions. The present study may shed light on the evolutionary forces that promote structural simplicity in biological networks and offers ways to improve the evolutionary design of engineered systems.

Different proteins have different expression levels. It is unclear to what extent these expression levels are optimized to their environment. Evolutionary theories suggest that protein expression levels maximize fitness, but the fitness as a function of protein level has seldom been directly measured. To address this, we studied the lac system of Escherichia coli, which allows the cell to use the sugar lactose for growth. We experimentally measured the growth burden due to production and maintenance of the Lac proteins (cost), as well as the growth advantage (benefit) conferred by the Lac proteins when lactose is present. The fitness function, given by the difference between the benefit and the cost, predicts that for each lactose environment there exists an optimal Lac expression level that maximizes growth rate. We then performed serial dilution evolution experiments at different lactose concentrations. In a few hundred generations, cells evolved to reach the predicted optimal expression levels. Thus, protein expression from the lac operon seems to be a solution of a cost-benefit optimization problem, and can be rapidly tuned by evolution to function optimally in new environments.

The SOS genetic network is responsible for the repair/bypass of DNA damage in bacterial cells. While the initial stages of the response have been well characterized, less is known about the dynamics of the response after induction and its shutoff. To address this, we followed the response of the SOS network in living individual Escherichia coli cells. The promoter activity (PA) of SOS genes was monitored using fluorescent protein-promoter fusions, with high temporal resolution, after ultraviolet irradiation activation. We find a temporal pattern of discrete activity peaks masked in studies of cell populations. The number of peaks increases, while their amplitude reaches saturation, as the damage level is increased. Peak timing is highly precise from cell to cell and is independent of the stage in the cell cycle at the time of damage. Evidence is presented for the involvement of the umuDC operon in maintaining the pattern of PA and its temporal precision, providing further evidence for the role UmuD cleavage plays in effecting a timed pause during the SOS response, as previously proposed. The modulations in PA we observe share many features in common with the oscillatory behavior recently observed in a mammalian DNA damage response. Our results, which reveal a hitherto unknown modulation of the SOS response, underscore the importance of carrying out dynamic measurements at the level of individual living cells in order to unravel how a natural genetic network operates at the systems level.

Gene-regulation networks contain recurring elementary circuits termed network motifs. It is of interest to understand under which environmental conditions each motif might be selected. To address this, we study one of the most significant network motifs, a three-gene circuit called the coherent feed-forward loop (FFL). The FFL has been demonstrated theoretically and experimentally to perform a basic information-processing function: it shows a delay following ON steps of an input inducer, but not after OFF steps. Here, we ask under what environmental conditions might the FFL be selected over simpler gene circuits, based on this function. We employ a theoretical cost-benefit analysis for the selection of gene circuits in a given environment. We find conditions that the environment must satisfy in order for the FFL to be selected over simpler circuits: the FFL is selected in environments where the distribution of the input pulse duration is sufficiently broad and contains both long and short pulses. Optimal values of the biochemical parameters of the FFL circuit are determined as a function of the environment such that the delay in the FFL blocks deleterious short pulses of induction. This approach can be generally used to study the evolutionary selection of other network motifs.

The quantitative relation between transcription factor concentrations and the rate of protein production from downstream genes is central to the function of genetic networks. Here we show that this relation, which we call the gene regulation function (GRF), fluctuates dynamically in individual living cells, thereby limiting the accuracy with which transcriptional genetic circuits can transfer signals. Using fluorescent reporter genes and fusion proteins, we characterized the bacteriophage lambda promoter P_R in Escherichia coli. A novel technique based on binomial errors in protein partitioning enabled calibration of in vivo biochemical parameters in molecular units. We found that protein production rates fluctuate over a time scale of about one cell cycle, while intrinsic noise decays rapidly. Thus, biochemical parameters, noise, and slowly varying cellular states together determine the effective single-cell GRF. These results can form a basis for quantitative modeling of natural gene circuits and for design of synthetic ones.

Many real-world networks describe systems in which interactions decay with the distance between nodes. Examples include systems constrained in real space such as transportation and communication networks, as well as systems constrained in abstract spaces such as multivariate biological or economic data sets and models of social networks. These networks often display network motifs: subgraphs that recur in the network much more often than in randomized networks. To understand the origin of the network motifs in these networks, it is important to study the subgraphs and network motifs that arise solely from geometric constraints. To address this, we analyze geometric network models, in which nodes are arranged on a lattice and edges are formed with a probability that decays with the distance between nodes. We present analytical solutions for the numbers of all three- and four-node subgraphs, in both directed and nondirected geometric networks. We also analyze geometric networks with arbitrary degree sequences and models with a bias for directed edges in one direction. Scaling rules for scaling of subgraph numbers with system size, lattice dimension, and interaction range are given. Several invariant measures are found, such as the ratio of feedback and feed-forward loops, which do not depend on system size, dimension, or connectivity function. We find that network motifs in many real-world networks, including social networks and neuronal networks, are not captured solely by these geometric models. This is in line with recent evidence that biological network motifs were selected as basic circuit elements with defined information-processing functions.

Can complex engineered and biological networks be coarse-grained into smaller and more understandable versions in which each node represents an entire pattern in the original network? To address this, we define coarse-graining units as connectivity patterns which can serve as the nodes of a coarse-grained network and present algorithms to detect them. We use this approach to systematically reverse-engineer electronic circuits, forming understandable high-level maps from incomprehensible transistor wiring: first, a coarse-grained version in which each node is a gate made of several transistors is established. Then the coarse-grained network is itself coarse-grained, resulting in a high-level blueprint in which each node is a circuit module made of many gates. We apply our approach also to a mammalian protein signal-transduction network, to find a simplified coarse-grained network with three main signaling channels that resemble multi-layered perceptrons made of cross-interacting MAP-kinase cascades. We find that both biological and electronic networks are "self-dissimilar," with different network motifs at each level. The present approach may be used to simplify a variety of directed and nondirected, natural and designed networks.

Complex gene-regulation networks are made of simple recurring gene circuits called network motifs. The functions of several network motifs have recently been studied experimentally, including the coherent feed-forward loop (FFL) with an AND input function that acts as a sign-sensitive delay element. Here, we study the function of the coherent FFL with a sum input function (SUM-FFL). We analyze the dynamics of this motif by means of high-resolution expression measurements in the flagella gene-regulation network, the system that allows Escherichia coli to swim. In this system, the master regulator FlhDC activates a second regulator, FliA, and both activate in an additive fashion the operons that produce the flagella motor. We find that this motif prolongs flagella expression following deactivation of the master regulator, protecting flagella production from transient loss of input signal. Thus, in contrast to the AND-FFL that shows a delay following signal activation, the SUM-FFL shows delays after signal deactivation. The SUM-FFL in this system works as theoretically predicted despite being embedded in at least two additional feedback loops. The present function might be carried out by the SUM-FFL in systems found across organisms.

Background: Does the C. elegans nervous system contain multi-neuron computational modules that perform stereotypical functions? We attempt to answer this question by searching for recurring multi-neuron inter-connectivity patterns in the C. elegans nervous system's wiring diagram. Results: Our statistical analysis reveals that some inter-connectivity patterns containing two, three and four (but not five) neurons are significantly over-represented relative to the expectations based on the statistics of smaller inter-connectivity patterns. Conclusions: Over-represented patterns (or motifs) are candidates for computational modules that may perform stereotypical functions in the C. elegans nervous system. These modules may appear in other species and need to be investigated further.

King [preceding Comment, Phys. Rev. E 70, 058101 (2004)) points out biases in one of the two common algorithms for generating simple random graphs-the matching. or stub-pairing.. algorithm. We clarify that in our simulations of simple graphs we used a different algorithm, the Markov-chain Monte Carlo switching algorithm, which is more uniform. As for multigraphs, the stub-pairing algorithm indeed samples uniformly configurations rather than multigraphs, as King points out, and thus is relevant for our model, which perians to configurations. Finally, we demonstrate that the algorithm we used to generate families of random networks with scale-free out-degree and compact in-degree does not result in noticeable biases.

Summary: Biological and engineered networks have recently been shown to display network motifs: a small set of characteristic patterns that occur much more frequently than in randomized networks with the same degree sequence. Network motifs were demonstrated to play key information processing roles in biological regulation networks. Existing algorithms for detecting network motifs act by exhaustively enumerating all subgraphs with a given number of nodes in the network. The runtime of such algorithms increases strongly with network size. Here, we present a novel algorithm that allows estimation of subgraph concentrations and detection of network motifs at a runtime that is asymptotically independent of the network size. This algorithm is based on random sampling of subgraphs. Network motifs are detected with a surprisingly small number of samples in a wide variety of networks. Our method can be applied to estimate the concentrations of larger subgraphs in larger networks than was previously possible with exhaustive enumeration algorithms. We present results for high-order motifs in several biological networks.

Detailed understanding and control of biological networks will require a level of description similar to that of electronic engineering blueprints. Currently, however, even the best-studied systems are usually described using qualitative arrow diagrams. A quantitative blueprint requires in vivo measurements of (1) the relative strength of the interactions (numbers on the arrows) and (2) the functions that integrate multiple inputs. Here, we address this using a well-studied system, the flagella biosynthesis transcription network in Escherichia coli. We use theory and high-resolution experiments to obtain a quantitative blueprint with (1) numbers on the arrows, finding different hierarchies of activation coefficients for the two regulators, FlhDC and FliA; and (2) cis-regulatory input functions, which summate the input from the two regulators (SUM gates). We then demonstrate experimentally how this blueprint can be used to reprogram temporal expression patterns in this system, using controlled expression of the regulators or point mutations in their binding sites. The present approach can be used to define blueprints of other gene networks and to quantitatively reprogram their dynamics.

A primary goal of systems biology is to understand the design principles of the transcription networks that govern the timing of gene expression. Here we measured promoter activity for ∼100 genes in parallel from living cells at a resolution of minutes and accuracy of 10%, based on GFP and Lux reporter libraries. Focusing on the amino-acid biosynthesis systems of Escherichia coli, we identified a previously unknown temporal expression program and expression hierarchy that matches the enzyme order in unbranched pathways. We identified two design principles: the closer the enzyme is to the beginning of the pathway, the shorter the response time of the activation of its promoter and the higher its maximal promoter activity. Mathematical analysis suggests that this 'just-in-time' (ref. 5) transcription program is optimal under constraints of rapidly reaching a production goal with minimal total enzyme production. Our findings suggest that metabolic regulation networks are designed to generate precision promoter timing and activity programs that can be understood using the engineering principles of production pipelines.

Genes and proteins generate molecular circuitry that enables the cell to process information and respond to stimuli. A major challenge is to identify characteristic patterns in this network of interactions that may shed light on basic cellular mechanisms. Previous studies have analyzed aspects of this network, concentrating on either transcription-regulation or protein-protein interactions. Here we search for composite network motifs: characteristic network patterns consisting of both transcription-regulation and protein-protein interactions that recur significantly more often than in random networks. To this end we developed algorithms for detecting motifs in networks with two or more types of interactions and applied them to an integrated data set of protein-protein interactions and transcription regulation in Saccharomyces cerevisiae. We found a two-protein mixed-feedback loop motif, five types of three-protein motifs exhibiting coregulation and complex formation, and many motifs involving four proteins. Virtually all four-protein motifs consisted of combinations of smaller motifs. This study presents a basic framework for detecting the building blocks of networks with multiple types of interactions.

Complex biological, technological, and sociological networks can be of very different sizes and connectivities, making it difficult to compare their structures. Here we present an approach to systematically study similarity in the local structure of networks, based on the significance profile (SP) of small subgraphs in the network compared to randomized networks. We find several superfamilies of previously unrelated networks with very similar SPs. One superfamily, including transcription networks of microorganisms, represents "rate-limited" information-processing networks strongly constrained by the response time of their components. A distinct superfamily includes protein signaling, developmental genetic networks, and neuronal wiring. Additional superfamilies include power grids, protein-structure networks and geometric networks, World Wide Web links and social networks, and word-adjacency networks from different languages.

The tumor suppressor p53, one of the most intensely investigated proteins, is usually studied by experiments that are averaged over cell populations, potentially masking the dynamic behavior in individual cells. We present a system for following, in individual living cells, the dynamics of p53 and its negative regulator Mdm2 (refs. 1, 4-7): this system uses functional p53-CFP and Mdm2-YFP fusion proteins and time-lapse fluorescence microscopy. We found that p53 was expressed in a series of discrete pulses after DNA damage. Genetically identical cells had different numbers of pulses: zero, one, two or more. The mean height and duration of each pulse were fixed and did not depend on the amount of DNA damage. The mean number of pulses, however, increased with DNA damage. This approach can be used to study other signaling systems and suggests that the p53-Mdm2 feedback loop generates a 'digital' clock that releases well-timed quanta of p53 until damage is repaired or the cell dies.

Biological and technological networks contain patterns, termed network motifs, which occur far more often than in randomized networks. Network motifs were suggested to be elementary building blocks that carry out key functions in the network. It is of interest to understand how network motifs combine to form larger structures. To address this, we present a systematic approach to define \u201cmotif generalizations\u201d: families of motifs of different sizes that share a common architectural theme. To define motif generalizations, we first define \u201croles\u201d in a subgraph according to structural equivalence. For example, the feedforward loop triada motif in transcription, neuronal, and some electronic networkshas three roles: an input node, an output node, and an internal node. The roles are used to define possible generalizations of the motif. The feedforward loop can have three simple generalizations, based on replicating each of the three roles and their connections. We present algorithms for efficiently detecting motif generalizations. We find that the transcription networks of bacteria and yeast display only one of the three generalizations, the multi-output feedforward generalization. In contrast, the neuronal network of C. elegans mainly displays the multi-input generalization. Forward-logic electronic circuits display a multi-input, multi-output hybrid. Thus, networks which share a common motif can have very different generalizations of that motif. Using mathematical modeling, we describe the information processing functions of the different motif generalizations in transcription, neuronal, and electronic networks.

The nonlinear growth, of the multimode incompressible Kelvin-Helmholtz shear flow instability at all density ratios is treated by a large-scale statistical-mechanics eddy-pairing model that is based on the behavior of a single eddy and on the two eddy pairing process. From the model, a linear time growth of the mixing zone is obtained and the linear growth coefficient is derived for several density ratios. Furthermore, the asymptotic eddy size distribution and the average eddy life time probability are calculated. Very good agreement with experimental results and full numerical simulations is achieved.

Recent analysis of the structure of transcription regulation networks revealed several "network motifs": regulatory circuit patterns that occur much more frequently than in randomized networks. It is important to understand whether these network motifs have specific functions. One of the most significant network motifs is the coherent feedforward loop, in which transcription factor X regulates transcription factor Y, and both jointly regulate gene Z. On the basis of mathematical modeling and simulations, it was suggested that the coherent feedforward loop could serve as a sign-sensitive delay element: a circuit that responds rapidly to step-like stimuli in one direction (e.g. ON to OFF), and at a delay to steps in the opposite direction (OFF to ON). Is this function actually carried out by feedforward loops in living cells? Here, we address this experimentally, using a system with feedforward loop connectivity, the L-arabinose utilization system of Escherichiacoli. We measured responses to step-like cAMP stimuli at high temporal resolution and accuracy by means of green fluorescent protein reporters. We show that the arabinose system displays sign-sensitive delay kinetics. This type of kinetics is important for making decisions based on noisy inputs by filtering out fluctuations in input stimuli, yet allowing rapid response. This information-processing function may be performed by the feedforward loop regulation modules that are found in diverse systems from bacteria to humans.

Engineered systems are often built of recurring circuit modules that carry out key functions. Transcription networks that regulate the responses of living cells were recently found to obey similar principles: they contain several biochemical wiring patterns, termed network motifs, which recur throughout the network. One of these motifs is the feed-forward loop (FFL). The FFL, a three-gene pattern, is composed of two input transcription factors, one of which regulates the other, both jointly regulating a target gene. The FFL has eight possible structural types, because each of the three interactions in the FFL can be activating or repressing. Here, we theoretically analyze the functions of these eight structural types. We find that four of the FFL types, termed incoherent FFLs, act as sign-sensitive accelerators: they speed up the response time of the target gene expression following stimulus steps in one direction (e.g., off to on) but not in the other direction (on to off). The other four types, coherent FFLs, act as sign-sensitive delays. We find that some FFL types appear in transcription network databases much more frequently than others. In some cases, the rare FFL types have reduced functionality (responding to only one of their two input stimuli), which may partially explain why they are selected against. Additional features, such as pulse generation and cooperativity, are discussed. This study defines the function of one of the most significant recurring circuit elements in transcription networks.

This viewpoint comments on recent advances in understanding the design principles of biological networks. It highlights the surprising discovery of "good-engineering" principles in biochemical circuitry that evolved by random tinkering.

An approximate solution for the average number of directed connected subgraphs in an ensemble of random networks with arbitrary degree sequence is presented. Scaling formulas for the number of subgraphs in scale-free random networks are given. It is shown that the subgraph numbers can be very different from those in Erdos random networks. The scaling exponent α exhibits three different scaling laws in three regimes, depending on the control parameter γ.

Most genes are regulated by multiple transcription factors that bind specific sites in DNA regulatory regions. These cis-regulatory regions perform a computation; the rate of transcription is a function of the active concentrations of each of the input transcription factors. Here, we used accurate gene expression measurements from living cell cultures, bearing GFP reporters, to map in detail the input function of the classic lacZYA operon of Escherichia coli, as a function of about a hundred combinations of its two inducers, cAMP and isopropyl β-D-thiogalactoside (IPTG). We found an unexpectedly intricate function with four plateau levels and four thresholds. This result compares well with a mathematical model of the binding of the regulatory proteins cAMP receptor protein (CRP) and LacI to the lac regulatory region. The model is also used to demonstrate that with few mutations, the same region could encode much purer AND-like or even OR-like functions. This possibility means that the wild-type region is selected to perform an elaborate computation in setting the transcription rate. The present approach can be generally used to map the input functions of other genes.

Sensory transcription networks generally control rapid and reversible gene expression responses to external stimuli. Developmental transcription networks carry out slow and irreversible temporal programs of gene expression during development. It is important to understand the design principles that underlie the structure of sensory and developmental transcription networks. Cascades, which are chains of regulatory reactions, are a basic structural element of transcription networks. When comparing databases of sensory and developmental transcription networks, a striking difference is found in the distribution of cascade lengths. Here, we suggest that delay times in the responses of the network present a design constraint that influences the network architecture. We experimentally studied the response times in simple cascades constructed of well-characterized repressors in Escherichia coli. Accurate kinetics at high temporal resolution was measured using green fluorescent protein (GFP) reporters. We find that transcription cascades can show long delays of about one cell-cycle time per cascade step. Mathematical analysis suggests that such a delay is characteristic of cascades that are designed to minimize the response times for both turning-on and turning-off gene expression. The need to achieve rapid reversible responses in sensory transcription networks may help explain the finding that long cascades are very rare in databases of E.coli and Saccharomyces cerevisiae sensory transcription networks. In contrast, long cascades are common in developmental transcription networks from sea urchin and from Drosophila melanogaster. Response delay constraints are likely to be less important for developmental networks, since they control irreversible processes on the timescale of cell-cycles. This study highlights a fundamental difference between the architecture of sensory and developmental transcription networks.

Cells regulate gene expression using networks of transcription interactions; it is of interest to discover the principles that govern the dynamical behavior of such networks. An important characteristic of these systems is the rise-time: the delay from the initiation of production until half maximal product concentration is reached. Here we employ synthetic gene circuits in Escherichia coli to measure the rise-times of non-self-regulated and of negatively autoregulated transcription units. Non-self-regulated units have a rise-time of one cell-cycle. We demonstrate experimentally that negative autoregulation feedback (also termed autogenous control) reduces the rise-time to about one fifth of a cell-cycle. This agrees with an analytical solution of a mathematical model for negative autoregulation. This may help in understanding the function of negative autoregulation, which appears in over 40% of known transcription factors in E. coli.

Complex networks are studied across many fields of science. To uncover their structural design principles, we defined "network motifs," patterns of interconnections occurring in complex networks at numbers that are significantly higher than those in randomized networks. We found such motifs in networks from biochemistry, neurobiology, ecology, and engineering. The motifs shared by ecological food webs were distinct from the motifs shared by the genetic networks of Escherichia coli and Saccharomyces cerevisiae or from those found in the World Wide Web. Similar motifs were found in networks that perform information processing, even though they describe elements as different as biomolecules within a cell and synaptic connections between neurons in Caenorhabditis elegans. Motifs may thus define universal classes of networks. This approach may uncover the basic building blocks of most networks.

A basic challenge in systems biology is to understand the dynamical behavior of gene regulation networks. Current approaches aim at determining the network structure based on genomic-scale data. However, the network connectivity alone is not sufficient to define its dynamics; one needs to also specify the kinetic parameters for the regulation reactions. Here, we ask whether effective kinetic parameters can be assigned to a transcriptional network based on expression data. We present a combined experimental and theoretical approach based on accurate high temporal-resolution measurement of promoter activities from living cells by using green fluorescent protein (GFP) reporter plasmids. We present algorithms that use these data to assign effective kinetic parameters within a mathematical model of the network. To demonstrate this, we employ a well defined network, the SOS DNA repair system of Escherichia coli. We find a strikingly detailed temporal program of expression that correlates with the functional role of the SOS genes and is driven by a hierarchy of effective kinetic parameter strengths for the various promoters. The calculated parameters can be used to determine the kinetics of all SOS genes given the expression profile of just one representative, allowing a significant reduction in complexity. The concentration profile of the master SOS transcriptional repressor can be calculated, demonstrating that relative protein levels may be determined from purely transcriptional data. This finding opens the possibility of assigning kinetic parameters to transcriptional networks on a genomic scale.

Little is known about the design principles of transcriptional regulation networks that control gene expression in cells. Recent advances in data collection and analysis, however, are generating unprecedented amounts of information about gene regulation networks. To understand these complex wiring diagrams, we sought to break down such networks into basic building blocks. We generalize the notion of motifs, widely used for sequence analysis, to the level of networks. We define 'network motifs' as patterns of interconnections that recur in many different parts of a network at frequencies much higher than those found in randomized networks. We applied new algorithms for systematically detecting network motifs to one of the best-characterized regulation networks, that of direct transcriptional interactions in Escherichia coli. We find that much of the network is composed of repeated appearances of three highly significant motifs. Each network motif has a specific function in determining gene expression, such as generating temporal expression programs and governing the responses to fluctuating external signals. The motif structure also allows an easily interpretable view of the entire known transcriptional network of the organism. This approach may help define the basic computational elements of other biological networks.

The late-time nonlinear evolution of the three-dimensional (3D) Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) instabilities for random initial perturbations is investigated. Using full 3D numerical simulations, a statistical mechanics bubble-competition model, and a Layzer-type drag-buoyancy model, it is shown that the RT scaling parameters, α_B and α_S, are similar in two and three dimensions, but the RM exponents, θ_B and θ_S are lower by a factor of 2 in three dimensions. The similarity parameter h_B/〈λ〉 is higher by a factor of 3 in the 3D case compared to the 2D case, in very good agreement with recent Linear Electric Motor (LEM) experiments. A simple drag-buoyancy model, similar to that proposed by Youngs [see J. C. V. Hanson et al., Laser Part. Beams 8, 51 (1990)], but using the coefficients from the A = 1 Layzer model, rather than phenomenological ones, is introduced.

The recent advances in large-scale monitoring of gene expression raise the challenge of mapping systems on the basis of kinetic expression data in living cells. To address this, we measured promoter activity in the flagellar system of Escherichia coli at high accuracy and temporal resolution by means of reporter plasmids. The genes in the pathway were ordered by analysis algorithms without dependence on mutant strains. The observed temporal program of transcription was much more detailed than was previously thought and was associated with multiple steps of flagella assembly.

Using a statistical mechanics bubble competition model, Alon et al. (1994,1995) have shown that the two-dimensional Rayleigh-Taylor (RT) mixing zone bubble and spike fronts evolves as h=α_B/S·A·g·t² with α_B∼0.05 and α_S∼α_S· (1+A). The Richtmyer-Meshkov (RM) mixing zone fronts have been found to evolve as h=a₀·t^θ with different θ's for bubble and spikes. The model predictions were θ_B∼0.4 and θ_S∼θ_B at low A's and rises to 1.0 for A close to 1. Full 2D numerical simulations confirmed these scaling laws. Recent experimental results (Dimonte, 1999,2000) have indicated similar scaling laws of the mixing zone evolution, but there were some discrepancies in the values of the scaling parameters, mainly in the value of θ_B and the similarity parameter, h/〈λ〉. It will be shown, based on full 3D numerical simulations, a Layzer type model and a 3D statistical-mechanics model that these discrepancies are mainly the effect of dimensionality. Accounting for the 3D nature of the problem results in scaling parameters that are very similar to the experimental values. The 3D single mode evolution, used in this model, was confirmed by shock tube experiments.

The intracellular activity of the p53 tumor suppressor protein is regulated through a feedback loop involving its transcriptional target, mdm2. We present a simple mathematical model suggesting that, under certain circumstances, oscillations in p53 and Mdm2 protein levels can emerge in response to a stress signal. A delay in p53-dependent induction of Mdm2 is predicted to be required, albeit not sufficient, for this oscillatory behavior. In line with the predictions of the model, oscillations of both p53 and Mdm2 indeed occur on exposure of various cell types to ionizing radiation. Such oscillations may allow cells to repair their DNA without risking the irreversible consequences of continuous excessive p53 activation.

A statistical model predicting the evolution of turbulent mixing zone fronts was developed recently by Alon et al. It suggests that the three physical elements that govern the Rayleigh-Taylor and Richtmyer-Meshkov mixing zone evolution are the single-bubble evolution, the single-spike evolution, and the interaction between neighboring bubbles. In this paper we present an experimental investigation of these three elements in the Richtmyer-Meshkov case. The experiments were performed in a double-diaphragm shock tube. The interface evolution was studied both before and after the arrival of a secondary reflected shock. Experimental results for the single-bubble and two-bubble cases show distinct bubble and spike evolution. The results of the bubble competition, which determines the front evolution, were found to be in good agreement with both full numerical simulations and a simple potential flow model. These results strengthen the assumptions on which the statistical model is based.

The nonlinear growth of the multimode Rayleigh-Taylor (RT), Richtmyer-Meshkov (RM), and Kelvin-Helmholtz (KH) instabilities is treated by a similar statistical mechanics merger model, using bubbles as the elementary particle in the RM and RT instabilities and eddies in the KH instability. Two particle interaction is demonstrated and merger rates are calculated. Using a statistical merger model, the mixing front evolution scaling law is derived. For the RT bubble front height a scaling law of αAgt2, with α ≅ 0.05, is derived. For the RM bubble front, a power law of t0.4 is obtained for all Atwood numbers. For the KH case the mixing zone grows linearly with time through a mechanism of eddy merger. Good agreement with simulations and experiments is achieved.

Chemotactic behavior as a function of growth stage in an Escherichia coli strain commonly used for chemotaxis studies was characterized using computerized image analysis. The response and adaptation to saturating, step- like additions of the attractant L-aspartate were measured. Steady-state average tumbling frequency and adaptation time increased nearly twofold during logarithmic phase. In contrast, precision of adaptation, P, defined as the ratio between steady-state tumbling frequencies in the presence and absence of attractant, appeared to be constant throughout growth (P = 1.0 ± 0.2). The variation of tumble duration over growth was consistent with a hydrodynamic mechanism for tumble termination.

Hydrodynamic instabilities, such as the RayleighTaylor and RichtmyerMeshkov instabilities, play a central role when trying to achieve net thermonuclear fusion energy via the method of inertial confinement fusion (ICF). The development of hydrodynamic instabilities on both sides of the compressed shell may cause shell breakup and ignition failure. A newly developed statistical mechanics model describing the evolution of the turbulent mixing zone from an initial random perturbation is presented. The model will be shown to compare very well both with full numerical simulations and with experiments, performed using high power laser systems, and using shock tubes. Applying the model to typical ICF implosion conditions, an estimation of the maximum allowed target, in-flight aspect ratio as a function of equivalent surface roughness, will be derived.

Networks of interacting proteins orchestrate the responses of living cells to a variety of external stimuli, but how sensitive is the functioning of these protein networks to variations in their biochemical parameters? One possibility is that to achieve appropriate function, the reaction rate constants and enzyme concentrations need to be adjusted in a precise manner, and any deviation from these 'fine-tuned' values ruins the network's performance. An alternative possibility is that key properties of biochemical networks are robust; that is, they are insensitive to the precise values of the biochemical parameters. Here we address this issue in experiments using chemotaxis of Escherichia coli, one of the best-characterized sensory systems. We focus on how response and adaptation to attractant signals vary with systematic changes in the intracellular concentration of the components of the chemotaxis network. We find that some properties, such as steady- state behaviour and adaptation time, show strong variations in response to varying protein concentrations. In contrast, the precision of adaptation is robust and does not vary with the protein concentrations. This is consistent with a recently proposed molecular mechanism for exact adaptation, where robustness is a direct consequence of the network's architecture.

A theoretical model for the ablatively driven RayleighTaylor (RT) instability single-mode and multimode mixing fronts is presented. The effect of ablation is approximately included in a Layzer-type potential flow model, yielding the description of both the single-mode evolution and the two-bubble nonlinear competition. The reduction factor of the linear growth rate due to ablative stabilization obtained by the model is similar to the Takabe formula. The single-bubble terminal velocity is found to be similarly reduced by ablation, in good agreement with numerical simulations. Two-bubble competition is calculated, and a statistical mechanics model for multimode fronts is presented. The asymptotic ablation correction to the classical RT [formula omitted] mixing zone growth law is derived. The effect of ablative stabilization on the allowed in-flight aspect ratio of inertial confinement fusion pellets is estimated using the results of the statistical mechanics model.

Shock-tube experiments were performed in order to verify recently developed theoretical models for the evolution of the shock-wave induced Richtmyer-Meshkov instability [Phys. Rev. Lett. 74, 534 (1995)]. Single-mode bubble and spike evolution and two-bubble interaction in both early and late nonlinear stages were investigated in a M≈1.3 Air−to−SF6 shock-tube experiment. Experimental results for the single-mode and two-bubble cases, showing distinct bubble and spike evolution, were found to be in very good agreement with the theoretical model prediction as well as numerical simulations, verifying the key elements of the bubble-merger model used for the prediction of the multimode bubble and spike front evolution.

A class of solid-on-solid growth models with short-range interactions and sequential updates is studied. The models exhibit both smooth and rough phases in dimension [Formula Presented]. Some of the features of the roughening transition which takes place in these models are related to contact processes or directed percolation type problems. The models are analyzed using a mean field approximation, scaling arguments, and numerical simulations. In the smooth phase the symmetry of the underlying dynamics is spontaneously broken. A family of order parameters which are not conserved by the dynamics is defined, as well as conjugate fields which couple to these order parameters. The corresponding critical behavior is studied, and novel exponents identified and measured. We also show how continuous symmetries can be broken in one dimension. A field theory appropriate for studying the roughening transition is introduced and discussed.

A model for the motion of ring-shaped DNA in a gel is introduced and studied by numerical simulations and a mean-field approximation. The ring motion is mediated by finger-shaped loops that move in an amoebalike fashion around the gel obstructions. This constitutes an extension of previous reptation tube treatments. It is shown that tension is essential for describing the dynamics in the presence of loops. It is included in the model as long-range interactions over stretched DNA regions. The mobility of ring-shaped DNA is found to saturate much as in the well-studied case of linear DNA. Experiments in agarose gels, however, show that the mobility drops exponentially with the DNA ring size. This is commonly attributed to dangling ends in the gel that can impale the ring. The predictions of the present model are expected to apply to artificial two-dimensional obstacle arrays [W. D. Volkmuth and R. H. Austin, Nature 358, 600 (1992)] which have no dangling ends. In the zero-field case an exact solution of the model steady state is obtained, and quantities such as the average ring size are calculated. An approximate treatment of the ring dynamics is given, and the diffusion coefficient is derived. The model is also discussed in the context of spontaneous symmetry breaking in one dimension.

A class of nonequilibrium models with short-range interactions and sequential updates is presented.The models describe one-dimensional growth processes which display a roughening transition between a smooth and a rough phase.This transition is accompanied by spontaneous symmetry breaking, which is described by an order parameter whose dynamics is nonconserving.Some aspects of models in this class are related to directed percolation in 1+1 dimensions, although unlike directed percolation the models have no absorbing states.Scaling relations are derived and compared with Monte Carlo simulations.

A modal model for the Rayleigh-Taylor (RT) instability, applicable at all stages of the flow, is introduced. The model includes a description of nonlinear low-order mode coupling, mode growth saturation, and post-saturation mode coupling. It is shown to significantly extend the range of applicability of a previous model proposed by Haan, to cases where nonlinear mode generation is important. Using the new modal model, we study the relative importance of mode coupling at late nonlinear stages and resolve the difference between cases in which mode generation assumes a dominant role, leading to the late time inverse cascade of modes and loss of memory of initial conditions, and cases where mode generation is not important and memory of initial conditions is retained. Effects of finite density ratios (Atwood number A

The nonlinear evolution of the Rayleigh-Taylor instability from multimode initial perturbations is studied by two complementary approaches. First, a statistical-mechanics bubble-merger model is presented, that enables determination of the late-time scaling properties based on single-mode and two-bubble interaction physics. The results for Rayleigh-Taylor (RT) and Richtmyer-Meshkov (RM) bubble and spike front penetrations are given, as well as scaling laws for mixing under a time-dependent driving acceleration. The second approach is a modal model, in which nonlinear mode coupling and saturation are included in an equation for effective modes that describe the mixed region. The importance of mode coupling in the generation of large structure that dominates the late stage evolution, and the relative importance of long-wavelength components in the initial perturbation spectra on the late-stage evolution are studied. Finally, multimode RT instability in three dimensions is studied by both full-scale simulations and the modal model. The effect and late-stage memory loss of different aspect ratios in the initial perturbation are demonstrated.

A potential flow model of RayleighTaylor and RichtmyerMeshkov bubbles on an interface between an incompressible fluid and a constant supporting pressure (Atwood number A=1) is presented. In the model, which extends the work of Layzer [Astrophys. J. 122, 1 (1955)], ordinary differential equations for the bubble heights and curvatures are obtained by considering the potential flow equations near the bubble tips. The model is applied to twodimensional singlemode evolution as well as twobubble competition, for both the RayleighTaylor (RT) and the RichtmyerMeshkov (RM) instabilities, the latter treated in an impulse approximation. The model predicts that the asymptotic velocity of a singlemode RM bubble of wavelength λ decays as λt −1, in contrast with the constant asymptotic velocity attained in the RT case. Bubble competition, which is believed to determine the multimode front evolution, is demonstrated for both the RT and RM instabilities. The capability of the model to predict bubble growth in a finitethickness fluid layer is shown. Finally, the model is applied to the evolution of threedimensional modes with an initial rectangular geometry. The model yields the aspect ratio dependence of the early nonlinear stages, in agreement with thirdorder perturbation theory. However, in the late nonlinear stage, the model predicts that the bubbles forget the initial geometry and attain the fastest growing shape, with a circular tip. The model results are in good agreement with full hydrodynamic simulations and analytic solutions, where available.

The late time evolution and structure of 2D Rayleigh-Taylor and Richtmyer-Meshkov bubble fronts is calculated, using a new statistical merger model based on the potential flow equations. The merger model dynamics are shown to reach a scale invariant reigme. It is found that the Rayleigh-Taylor front reaches a constant acceleration, growing as 0.05gt2, while the Richtmyer-Meshkov front grows as at0.4 where a depends on the initial perturbation. The model results are in good agreement with experiments and simulations.

A statistical model of Rayleigh-Taylor bubble fronts in two dimensions is introduced. Float and merger of bubbles lead to a scale-invariant regime, with a stable distribution of scaled bubble radii and a constant front acceleration. The model is solved for a simple merger law, showing that a family of such stable distributions exists. The basins of attraction of each of these are mapped. The properties of the scale-invariant distributions for various merger laws, including a merger law derived from the Sharp-Wheeler model, are analyzed. The results are in good agreement with computer simulations. Finally, it is shown that for some merger laws, a runaway bubble regime develops. A criterion for the appearance of runaway growth is presented.

We present a systematic derivation of the percolation thresholds in anisotropic systems composed of permeable elongated boxes. The analytic calculation is based on an order-by-order diagrammatic expansion of the pair-connectedness function. A comparison of the results with those of Monte Carlo simulations shows excellent quantitative agreement. We conclude that, of the analytic methods suggested thus far, the present approach is the most suitable one for quantitative derivation of system properties in continuum percolation.