Effective stiffness and formation of secondary structures in a protein-like model

TL;DR

This study investigates how increasing stiffness influences secondary structure formation in protein-like polymers using computational techniques, revealing different structural phases and a geometrical mapping between models.

Contribution

It introduces two models of polymer stiffness, compares their effects on secondary structures, and establishes a geometrical mapping explaining their similar persistence length behavior.

Findings

Transition from beta-like to helical structures with increased interpenetration.

Similar persistence length dependence in both models at intermediate temperatures.

Mapping between models remains valid even with zero-sized side chains.

Abstract

We use Wang-Landau and replica exchange techniques to study the effect of an increasing stiffness on the formation of secondary structures in protein-like systems. Two possible models are considered. In both models, a polymer chain is formed by tethered beads where non-consecutive backbone beads attract each other via a square-well potential representing the tendency of the chain to fold. In addition, smaller hard spheres are attached to each non-terminal backbone bead along the direction normal to the chain to mimic the steric hindrance of side chains in real proteins. The two models, however, differ in the way bending rigidity is enforced. In the first model, partial overlap between consecutive beads is allowed. This reduces the possible bending angle between consecutive bonds thus producing an effective entropic stiffness that competes with a short-range attraction, and leads to a formation of secondary structures characteristic of proteins. We discuss the low-temperature phase diagram as a function of increasing interpenetration, and find a transition from a planar, beta-like structure, to helical shape. In the second model, an energetic stiffness is explicitly introduced by imposing an infinitely large energy penalty for bending above a critical angle between consecutive bonds, and no penalty below it. The low-temperature phase of this model does not show any sign of protein-like secondary structures. At intermediate temperatures, however, where the chain is still in the coil conformation but stiffness is significant, we find the two models to predict a quite similar dependence of the persistence length as a function of the stiffness. This behaviour is rationalized in terms of a simple geometrical mapping between the two models. Finally, we discuss the effect of shrinking side chains to zero, and find the above mapping to still hold true.