Effects of chain stiffness on the dynamics of loop formation in polypeptides. Appendix: Testing a 1-dimensional diffusion model for peptide dynamics

Quenching of the triplet state of tryptophan by cysteine provides an important new tool for measuring the rate at which a specific intramolecular contact is formed in disordered polypeptides. By measuring the viscosity dependence of the quenching rate, both the reaction-limited and the diffusion-limited quenching rates can be determined. The diffusion-limited rate corresponds to the rate of forming a short-range contact. The reaction-limited rate, which depends solely on the equilibrium end-to-end distribution, becomes essentially length-independent for short chains, providing clear-cut evidence that the chain is stiff. The length dependence of the reaction-limited rate can be accurately calculated using the distance dependence of the quenching rate determined at room temperature in a rigid glass, together with the end-to-end distance distribution for a wormlike chain having a persistence length of 0.6-0.7 nm. In addition, the length dependence of the diffusion-limited rate can also be reproduced by treating the dynamics as diffusion on the 1D potential of mean force obtained from this distribution. The diffusion coefficient for the chain ends required to fit the diffusion-influenced rates is about 1.7 x 10(-6) cm(2) s(-1) at a viscosity of 1 cp and 293 K, almost 10 times smaller than the value expected for free diffusion of the contacting residues. Molecular dynamics simulations performed using a Ramachandran-like potential provide justification for this analysis. Diffusion-limited rates calculated from-the trajectories are in excellent agreement with those calculated with the ID diffusion model using the simulated end-to-end distance distributions.