Non-Gaussian dynamics from a simulation of a short peptide: Loop closure rates and effective diffusion coefficients

摘要

Intrachain contact formation rates, fundamental to the dynamics of biopolymerself-organization such as protein folding, can be monitored in the laboratorythrough fluorescence quenching measurements. The common approximations for theintrachain contact rate given by the theory of Szabo, Schulten, and Schulten(SSS) [J. Chem. Phys. {\bf 72}, 4350 (1980)] and Wilemski--Fixman (WF) [J.\Chem. Phys. {\bf 60},878 (1973)] are shown to be complementary variationalbounds: the SSS and WF approximations are lower and upper bounds, respectively,on the mean first contact times. As reported in the literature, the SSSapproximation requires an effective diffusion coefficient 10 to 100 timessmaller than expected to fit experimentally measured quenching rates. An allatom molecular dynamics simulation of an eleven residue peptide sequence inexplicit water is analyzed to investigate the source of this surprisingparameter value. In analytical work, the polymer is typically modeled by aGaussian chain of effective monomers. Compared to Gaussian dynamics, thesimulated end-to-end distance autocorrelation has a much slower relaxation. Thelong time behavior of the distance autocorrelation function can be approximatedby a Gaussian model in which the monomer diffusion coefficient D_0 is reducedto D_0/6. This value of the diffusion coefficient brings the mean end-to-endcontact time from analytical approximations and simulation into agreement inthe sense that the SSS and WF approximations bracket the simulated mean firstcontact time.