(1) Chemical Physics Department, Weizmann Institute of Science, Rehovot, 76100, Israel
(2) Department of Chemistry, University of Bath, Bath, UK
(3) Center for Advanced Research in Biotechnology,
MBI, University of Maryland, Rockville, MD, USA
Conformational flexibility is essential to many biological events. As yet, no experimental technique is capable of providing detailed information about protein motion at the atomic level. Computational methods offer a means of exploring the details of the possible motions. The two main approaches to investigating molecular motion are normal mode dynamics and molecular dynamics simulations.
Normal mode dynamics (NM) has long been used as a tool in interpreting vibrational spectra of small molecules and homobiopolymers. In recent years it has been extended to the study of proteins. In this method, the motion is modeled as a superposition of a set of independent harmonic oscillations about the equilibrium atomic positions. Of particular interest is the ability to study slow collective motions of large biological molecules.
Molecular dynamics (MD) involves solving Newton's equations of motion to yield a trajectory of atomic positions. Although the laws of motion are very simple, the resultant trajectories are very complicated and interpreting the complex motion is not trivial. In particular, it is difficult to investigate long range collective motions. This problem has been addressed recently in a few studies using different approaches.
We have used digital signal processing techniques to characterize the motion in MD simulations. Fourier transforming all the atomic trajectories yields the overall frequency distribution. We then choose the frequency ranges corresponding to motions of interest and eliminate the rest. In this way, it is possible to remove high frequency bond stretches and valence angle bending and focus on the low frequency conformational motion. Moreover, we are able to use this approach to extract the vectors defining the characteristic motion for each frequency of interest in a MD simulation. These vectors are analogous to those obtained from NM and provide a pictorial description of the motion as well as a means for comparing the results of the two methods.
We have applied this method to a comparison of the motion of the protein molecule Streptomyces Griseus Protease A (SGPA) obtained with NM and MD. We compare the amplitudes of motion about the mean positions for the two methods with each other and with X-ray data and examine the correlation of the directions of atomic fluctuations from the two simulations. We address the issues of how well the three descriptions of motion agree and what the implications of the results are for the nature of the factors controlling motion in protein molecules. For the two types of simulation, the motions have been characterized in additional detail. This includes examining the nature of the motion as a function of the frequency, revealing the dependence of overall correlated motion on structural properties of the protein, and comparing specific modes of motion obtained by NM and MD.