Title: Markov modeling of peptide folding in the presence of protein crowders,
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.