Integrated Calendar

Mammalian brains store and update quantitative internal variables. Primates and rodents, for example, have an internal sense of whether they are 1 or 10 meters away from a landmark and whether a ripe fruit is twice or four times as appetizing as a less ripe counterpart. Such quantitative internal signals are the basis of cognitive function, however, our understanding of how the brain stores and updates these variables remains fragmentary. In this talk, I will discuss imaging and perturbation experiments in tethered, walking Drosophila. The goal of these experiments is to determine how internal variables are calculated by the tiny Drosophila brain and how these variables influence behavior. Specifically, in the Drosophila central complex a set of heading neurons have been described, whose activity tracks the fly’s orientation, similar to head direction cells in rodents. However, the circuit architecture that gives rise to these orientation tracking properties remains largely unknown in any species. I will describe a set of clockwise- and counterclockwise-shifting neurons whose wiring and calcium dynamics provide a means to rotate the heading system’s angular estimate over time. Shifting neurons are required for the heading system to properly track the fly's movements in the dark, and, their stimulation induces a rotation of the heading signal in the expected direction and by the expected amount. The central features of this circuit are analogous to models proposed for head-direction cells in rodents and may thus inform how neural systems, in general, perform addition.

E. coli is well equipped for living in rapidly changing conditions of its natural ecosystem. For example, it is able to navigate by modulating the rotation of the bidirectional flagellar motor, and it has the ability of switching to anaerobic respiration that involves fumarate reduction, when oxygen is limited. A decade ago it was discovered that there is a crosstalk between the fumarate reduction system and the flagellar motor: fumarate reductase (FRD) was found to be required for flagellar clockwise (CW) rotation, which is essential for the navigation process. Here, by combining biochemical techniques with super resolution microscopy, we found that FRD affects the motor via its cytosolic subunit FrdA, and that this subunit preferentially binds to the CW state of the flagellar rotary unit FliG. This suggests that FrdA stabilizes the CW state of individual FliG subunits, thus increasing the probability of CW-conformational spread over the entire rotor. We further found that a natural increase in FrdA expression levels during microaerophilic growth conditions increases the probability of CW rotation to a level shown earlier to be more efficient for navigation. Thus, FrdA-motor interaction may be a mean of adjusting the navigation efficiency to the microaerophilic conditions found in the mammalian gut.

We derive a spectral sum rule in the shear channel for conformal field theories in general d> 2 dimensions held at finite temperature. The sum rule result from the OPE of the stress tensor at high frequency as well as the hydrodynamic behaviour of the theory at low frequencies. The sum rule states that a weighted integral of the spectral density over frequencies is proportional to the energy density of the theory. We show that the proportionality constant can be written in terms the Maldacena-Hofman variables t_2, t_4 which rely on data which determines the three point function of the stress tensor of the CFT. For theories which admit a two derivative gravity dual this proportionality constant is given by d/2(d+1) . We then use causality constraints and obtain bounds on the sum rule which are valid for any conformal field theory. We illustrate the sum rule by applying it to well studied conformal field theories in d=3, 4, 6. dimensions