Markov modeling of peptide folding in the presence of protein crowders

TL;DR

This study employs Markov state models to analyze peptide folding dynamics in the presence of protein crowders, revealing how crowders influence folding stability and relaxation times in Monte Carlo simulations.

Contribution

It introduces a method to accurately estimate peptide relaxation times using MSM eigenfunctions in crowded environments, highlighting crowders' stabilizing effects.

Findings

Crowders stabilize peptide folding, especially BPTI crowders.

MSM eigenfunctions enable stable relaxation-time estimates at small lag times.

Crowders reduce peptide unfolding rates without significantly affecting folding rates.

Abstract

We use Markov state models (MSMs) to analyze the dynamics of a $\beta$-hairpin-forming peptide in Monte Carlo (MC) simulations with interacting protein crowders, for two different types of crowder proteins [bovine pancreatic trypsin inhibitor (BPTI) and GB1]. In these systems, at the temperature used, the peptide can be folded or unfolded and bound or unbound to crowder molecules. Four or five major free-energy minima can be identified. To estimate the dominant MC relaxation times of the peptide, we build MSMs using a range of different time resolutions or lag times. We show that stable relaxation-time estimates can be obtained from the MSM eigenfunctions through fits to autocorrelation data. The eigenfunctions remain sufficiently accurate to permit stable relaxation-time estimation down to small lag times, at which point simple estimates based on the corresponding eigenvalues have large systematic uncertainties. The presence of the crowders have a stabilizing effect on the peptide, especially with BPTI crowders, which can be attributed to a reduced unfolding rate $k_\text{u}$, while the folding rate $k_\text{f}$ is left largely unchanged.