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.