Tracking Polypeptide Folds on the Free Energy Surface: Effects of the Chain Length and Sequence

Characterization of the folding transition in polypeptides
and
assessing the thermodynamic stability of their structured folds are
of primary importance for approaching the problem of protein folding.
We use molecular dynamics simulations for a coarse grained polypeptide
model in order to (1) obtain the equilibrium conformation diagram
of homopolypeptides in a broad range of the chain lengths, N = 10, ..., 100, and temperatures, T (in
a multicanonical ensemble), and (2) determine free energy profiles
(FEPs) projected onto an optimal, so-called “natural”,
reaction coordinate that preserves the height of barriers and the
diffusion coefficients on the underlying free energy hyper-surface.
We then address the following fundamental questions. (i) How well
does a kinetically determined free energy landscape of a single chain
represent the polypeptide equilibrium (ensemble) behavior? In particular,
under which conditions might the correspondence be lost, and what
are the possible implications for the folding processes? (ii) How
does the free energy landscape depend on the chain length (homopolypeptides)
and the monomer interaction sequence (heteropolypeptides)? Our data
reveal that at low T values equilibrium structures
adopted by relatively short homopolypeptides (N <
60) are dominated by α-helical folds which correspond to the
primary and secondary minima of the FEP. In contrast, longer homopolypeptides
(N > 70), upon quasi-equilibrium cooling, fold
preferentially
in β-bundles with small helical portions, while the FEPs exhibit
no distinct global minima. Moreover, subject to the choice of the
initial configuration, at sufficiently low T, essentially
metastable structures can be found and prevail far from the true thermodynamic
equilibrium. We also show that, by sequence-enabling the polypeptide
model, it is possible to restrict the chain to a very specific part
of the configuration space, which results in substantial simplification
and smoothing of the free energy landscape as compared to the case
of the corresponding homopolypeptide.