A Langevin equation approach to bridge different timescales of relaxation in protein dynamics

While dynamics of synthetic macromolecular systems are well described by Langevin Equations (LE), the application of this approach to biological macromolecules presents additional challenges as short and long-range interactions, hydrogen bonding, secondary and tertiary structure, hydrophobic and other effects come into play. In the original LE approach presented here, all these effects are taken into account. In our approach, for the first time hydrophobic effects, through an internal friction coefficient, are included in the description of the protein local dynamics. The input to the theory is provided by atomistically detailed short time (ns) molecular dynamics simulations. The LE is then solved by matrix diagonalization and provides eigenvalues and eigenvectors in which all time correlation functions of interest are expressed. The test of the theory is performed on the signal transduction protein CheY. Without any adjustable parameters, good agreement between bond autocorrelation functions predicted from the theory and calculated directly from the simulation is found in the timescales of nanoseconds (ns). Theoretical predictions of NMR T1, T2, and NOE values are compared with experiments and found to be in close agreement also. In addition, the theory is in agreement with temperature factors as measured in X-ray experiments. A study of the Calcium-binding protein Calmodulin is also presented, in which the relative dynamics of this dumbbell-shaped molecule are discussed. The usefulness of this theory lies in its ability to provide a physical picture of the dynamics of protein in the complete range of timescales of interest. So that other proteins can be studied with this approach, the software package Bridget has been built, which calculates, among other dynamical properties, NMR relaxation parameters. This dissertation includes my co-authored material.