Emergence of glass-like behavior in Markov state models of protein folding dynamics

Abstract

The extent to which glass-like kinetics govern dynamics in protein folding has been heavily debated. Here, we address the subject with an application of space-time perturbation theory to the dynamics of protein folding Markov state models. Borrowing techniques from the s-ensemble method, we argue that distinct active and inactive phases exist for protein folding dynamics, and that kinetics for specific systems can fall into either dynamical regime. We do not, however, observe a true glass transition in any system studied. We go on to discuss how these inactive and active phases might relate to general protein folding properties.

Figure 1

Native state probabilities as a function of s for various values of t_obs in the WW domain MSM (τ_fold = 28 τ_lag). For finite trajectories, native probabilities are calculated at t = t_obs/2.

Figure 2

Mean activity per time step, K(s), versus s curves for protein folding MSMs of the Fip35 WW-domain (left, τ_fold = 28 τ_lag,), Protein G (middle, τ_fold = 1110 τ_lag), and NTL9 (right, τ_fold = 3332 τ_lag). Similar curves were computed for 13 additional systems; the results of this analysis are shown in Figure 3.

Figure 3

Plot of the s-ensemble parameter at coexistence, s*, as a function of folding time (in μs) and chain length (in number of residues) for 16 protein folding MSMs. Values of s* for Fs-peptide (1.20) and Chignolin (1.95) were omitted to preserve scale. The magnitude of an s-value suggests how far a model’s unbiased dynamics deviate from coexistence between active and glassy phases.