Nonlinear oscillations of proteins

Abstract

Slow modes of proteins exhibit nonlinear characteristics. Large deformations in proteins correspond to collective deformations. These are at relatively low energy compared to kBTroom where Troom is approximately 3000K. Therefore the dynamics of slow modes can be understood through Classical Mechanical methods. In this work, we investigate the collective frequencies of proteins to see how big the effects of the nonlinearity on the collective modes of proteins. To do this, we take advantage of Canonical Perturbation Theory. We see that slow mode frequencies deviate from normal frequencies by (A/R0 ij)2 where A is a typical residue fluctuation from its equilibrium position and R0 ij is the distance between residue pairs at an equilibrium state.