Chain stiffness bridges conventional polymer and bio-molecular phases

Abstract

Chain molecules play important roles in industry and in living cells. Our focus here is on distinct ways of modeling the stiffness inherent in a chain molecule. We consider three types of stiffnessesone yielding an energy penalty for local bends (energetic stiffness) and the other two forbidding certain classes of chain conformations (entropic stiffness). Using detailed Wang-Landau microcanonical Monte Carlo simulations, we study the interplay between the nature of the stiffness and the ground state conformation of a self-attracting chain. We find a wide range of ground state conformations including a coil, a globule, a toroid, rods, helices, zig-zag strands resembling β-sheets, as well as knotted conformations allowing us to bridge conventional polymer phases and biomolecular phases. An analytical mapping is derived between the persistence lengths stemming from energetic and entropic stiffness. Our study shows unambiguously that different stiffness play different physical roles and have very distinct effects on the nature of the ground state of the conformation of a chain, even if they lead to identical persistence lengths.

Monte–Carlo simulation of crystallization in single‐chain square‐well homopolymers

“…We retained all data for the low n SW states for the hottest chain and the high n SW states for the coldest chain. Figure 8 shows the results from all 16 tempering levels mapped from T * i to T * = 0:446 via Equation (14). This shows the strong internal consistency between mapped results, demonstrated by the high level of overlap between results from different tempering levels.…”

“…In computer simulations several classes of interactions are commonly used: lattice models 1–3 and off‐lattice interactions using the Lennard–Jones 4–9 or square well potential 10–14 . Bonded interactions can be chosen to give freely jointed 10–12 or semi flexible chains 4,6,8,13–15 . Long chains are of particular interest as they approach the chains lengths in realistic systems.…”

Transient helix formation in charged semiflexible polymers without confinement effects

“…The packing of tubular filaments in confined cylinders also lead to helix formation for particular ratios of pitch and radius [6]. Yet, another study shows that the ground state of a self-attracting chain shows a variety of o structural motifs including the helix, depending on the nature of the stiffness present in the chain (energetic or entropic) [11,33]. In our previous work we showed that a bead-spring model of a semiflexible polymer chain with monomers all having the same value and polarity of charges and long range Coulomb interaction between monomers attains a transient helical conformation, when repulsive interactions are switched on between the monomers [34].…”

“…This is because the tube can be considered as a compact object made up of discs which has very different symmetry properties in terms of interaction potentials compared to those acting between spherical beads, say, of a polymeric chain. Another study shows that the ground state of a self attracting chain shows a variety of structural motifs including the helix, depending on the nature of the stiffness present in the chain (energetic or entropic) [27]. Our study reports the self-emergence of free standing helical structures using the most generic of repulsive potentials such as Coulomb repulsion which could have in uence in understanding emergence of such structures at nm-µ length scales, in a variety of situations within the living cell or outside.…”

Spontaneous dimensional reduction and novel ground state degeneracy in a simple chain model

“…For fixed bond length, a chain conformation is specified by two angles θ and μ. θ is a measure of bond bending, a straight conformation has θ = π . Two distinct kinds of bending energy penalties have been commonly employed in the literature: an energy cost proportional to cos 2 ( θ /2); or zero cost when θ > θ 0 and infinite cost otherwise [13, 14]. Here we use a third approach and make the simplification of fixing θ = θ 0 resulting in θ no longer being a variable of the model but just a parameter.…”