From polymers to proteins: effect of side chains and broken symmetry in the formation of secondary structures within a Wang-Landau approach

TL;DR

This study investigates how symmetry breaking and side chains influence secondary structure formation in polymers, using Wang-Landau and replica exchange simulations, revealing conditions for helix and globule states relevant to protein folding.

Contribution

It introduces a refined polymer model incorporating symmetry breaking and side chains, demonstrating their effects on secondary structure stability and formation, advancing understanding of protein-like conformations.

Findings

Symmetry breaking leads to helix formation depending on interaction range.

Side chains alone do not produce protein-like structures.

Combined effects enhance secondary structure stability.

Abstract

We study the equilibrium properties of a single flexible homopolymers where consecutive monomers are represented by impenetrable hard spherical beads tangential to each other, and non-consecutive monomers interact via a square-well potential. To this aim, we use both replica exchange canonical simulations and micro-canonical Wang-Landau techniques. We perform a close comparative analysis of the corresponding results, and find perfect agreement between the two methods as well as the past results. The model is then refined in two different directions. By allowing partial overlapping between consecutive beads, we break the spherical symmetry and thus provide a severe constraint on the possible conformations of the chain. This leads to a single helix or a double helix ground state, depending on the range of the interactions. Alternatively, we introduce additional spherical beads at specific positions to represent the steric hindrance of the side chains in real proteins. The ground state in this case is found to be again a globule, thus showing that contrary to some recent suggestions, side chains alone are not sufficient to insure a protein-like structure. Finally, we show that a combination of the above two effects increases the stability of the obtaining secondary structures, in agreement with previous results. The fundamental role played by the range of the square-well attraction is highlighted, and it is shown that they play a role similar to that found in simple liquids and polymers. Perspectives in terms of protein folding are finally discussed.