Two-state protein-like folding of a homopolymer chain

Abstract

Many small proteins fold via a first-order "all-or-none" transition directly from an expanded coil to a compact native state. Here we study an analogous direct freezing transition from an expanded coil to a compact crystallite for a simple flexible homopolymer. Wang-Landau sampling is used to construct the 1D density of states for square-well chains of length 128. Analysis within both the micro-canonical and canonical ensembles shows that, for a chain with sufficiently short-range interactions, the usual polymer collapse transition is preempted by a direct freezing or "folding" transition. A 2D free-energy landscape, built via subsequent multi-canonical sampling, reveals a dominant folding pathway over a single free-energy barrier. This barrier separates a high entropy ensemble of unfolded states from a low entropy set of crystallite states and the transition proceeds via the formation of a transition-state folding nucleus. Despite the non-unique homopolymer ground state, the thermodynamics of this direct freezing transition are identical to the thermodynamics of two-state protein folding. The model chain satisfies the van't Hoff calorimetric criterion for two-state folding and an Arrhenius analysis of the folding/unfolding free energy barrier yields a Chevron plot characteristic of small proteins.

Folding mechanism of a polymer chain with short-range attractions

“…Our first result from analyzing the TSE is an observation made earlier by Taylor, Paul, and Binder 2 for the pure square-well chain: typical transition states consist of a crystalline nucleus with one or more chain fragments attached to it. The result of Taylor et al 7 was drawn from a visual inspection of states which are energetically in between the high-energy coil and the low-energy crystalline phase. Our committor analysis confirms this observation with a more rigorous approach.…”

“…This is indicative of the rough and diffusive nature of the freezing transition. From a two-dimensional free energy landscape as a function of the total energy U and the squared radius of gyration R 2 g , Taylor et al 7 identified the dominant folding pathway as the minimum free energy path. Our results strongly suggest that such a dominant folding pathway is only representative in an average sense, especially regarding the squared radius of gyration.…”

“…In the latter case, a free energy barrier separating the two phases imposes a pronounced two-state behavior on the system. 7 In this work, we focus on clarifying the mechanism of the coil-to-crystal transition of the polymer. In order to perform molecular dynamics simulations and hence obtain a realistic picture of the transition event, we have developed a continuous approximation to the pure square-well chain.…”

Collapse of a two-state sticky hard sphere chain

“…The present all-or-none model predicts a sharpening of the heat capacity spike in C v (T ) versus T as the number of F bonds increases 12 and it predicts that the transition temperature is independent of chain length for long chains, assuming that each added bead has the same number of F-bonds per bead as the previous bead. Simulations find evidence of a single spike in C v (T * ) versus T * as the interaction range /b decreases below 0.1, which is probably the upper bound for .…”

“…Our interest in the collapse problem originated from the works of Taylor et al [10][11][12] who investigated the all-or-none a) Electronic mail: glenn.evans@oregonstate.edu. transition from an expanded coil to a compact state for a freely jointed chain with SW nonbonded interactions.…”