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We use a micro-canonical Wang-Landau technique to study the equilibrium properties of a single flexible homopolymer 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 mimic the characteristics of a protein-like system, the model is then refined in two different directions. Firstly, by allowing partial overlap between consecutive beads, we break the spherical symmetry and thus provide a severe constraint on the possible conformations of the chain. Alternatively, we introduce additional spherical beads at specific positions in the direction normal to the backbone, to represent the steric hindrance of the side chains in real proteins. Finally, we consider also a combination of these two ingredients. In all three systems, we obtain the full phase diagram in the temperature-interaction range plane and find the presence of helicoidal structures at low temperatures in the intermediate range of interactions. The effect of the range of the square-well attraction is highlighted, and shown to play a role similar to that found in simple liquids and polymers. Perspectives in terms of protein folding are finally discussed.

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