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

Abstract

Intrachain contact formation rates, fundamental to the dynamics of biopolymer self-organization such as protein folding, can be monitored in the laboratory through fluorescence quenching measurements. The common approximations for the intrachain 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 variational bounds: the SSS and WF approximations are lower and upper bounds, respectively, on the mean first contact times. As reported in the literature, the SSS approximation requires an effective diffusion coefficient 10 to 100 times smaller than expected to fit experimentally measured quenching rates. An all atom molecular dynamics simulation of an eleven residue peptide sequence in explicit water is analyzed to investigate the source of this surprising parameter value. In analytical work, the polymer is typically modeled by a Gaussian chain of effective monomers. Compared to Gaussian dynamics, the simulated end-to-end distance autocorrelation has a much slower relaxation. The long time behavior of the distance autocorrelation function can be approximated by a Gaussian model in which the monomer diffusion coefficient D_0 is reduced to D_0/6. This value of the diffusion coefficient brings the mean end-to-end contact time from analytical approximations and simulation into agreement in the sense that the SSS and WF approximations bracket the simulated mean first contact time.