Dynamics of large-scale fluctuations in native proteins. Analysis based on harmonic inter-residue potentials and random external noise

The fluctuations of residues of proteins about their equilibrium configurations are analyzed by the Langevin equation. Residue pairs that are covalently bonded and those that are within a given cutoff distance of each other are assumed to be connected by linear springs. The actions of the solvent and intramolecular interactions on each residue are treated as random noise. The correlations of fluctuations resulting from the solution of the Langevin equation are observed to be identical to those obtained by the Gaussian Network Model based on equilibrium statistical mechanics. The time-delayed correlations of fluctuations, and the response of the protein to a given frequency and to a window of frequencies are determined. The fluctuations of the residues resulting from a given fixed externally applied frequency are evaluated for different modes of the system. Synchronous and asynchronous components of correlations for different modes are formulated. The findings of the present paper are applied to the 241 residue protein S. marcescens endonuclease (1QL0).