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

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 the 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.

Limiting the valence: advancements and new perspectives on patchy colloids, soft functionalized nanoparticles and biomolecules

“…187 The results accumulated so far suggest that designability can be controlled by any strategy that reduces the configurational entropy per monomer, directionality being one example, another example being purely steric constraints. 188,189 It would thus be possible to define a general relationship between the configurational entropy per monomer and the alphabet size that controls the boundaries of the designability window, thus serving as a universal guideline to achieve designability. Novel experimentally realizable polymer systems could be conceived using such a guideline.…”

The elixir phase of chain molecules

“…Intriguingly, the geometries of the building block strands and helices in the elixir phase, as well as those in a larger surrounding region identified by dotted lines in Figure D, are statistically the same as those of strands and helices in protein native state structures. Each ground state in the phase diagram was assigned to a specific phase on the basis of suitable order parameters that includes the twist (for the helices) and the average triple scalar product of normal Frenet unit vectors (for the sheets). An additional fingerprint of the secondary structures stems from their characteristic representations in the contact maps.…”

“…Allowing adjoining spheres to overlap breaks the spherical symmetry of an individual main chain sphere. The overlap between adjoining main‐chain spheres results in an entropic stiffness because of the reduction in the ability to bend the chain . A hint that such symmetry breaking could be important is provided by the extreme case of a chain of coins, which, in the continuum limit, has a tube‐like geometry .…”

“…The overlap between adjoining mainchain spheres results in an entropic stiffness because of the reduction in the ability to bend the chain. 15 A hint that such symmetry breaking could be important is provided by the extreme case of a chain of coins, which, in the continuum limit, has a tube-like geometry. 16,17 And, as is well-known, a garden hose is often wound into a helical geometry in a hardware store.…”

Polymer models with optimal good-solvent behavior

“…The angle φ i defined in (1) is always smaller than φ 0 , with φ 0 → 180 • for b/d → ∞ (completely flexible chains), φ 0 = 120 • for b/d = 1 and φ 0 → 0 as b/d → 1/2 (rod limit). Because of this property, such a model has already been used to model semiflexible protein chains [81].…”