Knots are Generic Stable Phases in Semiflexible Polymers

Abstract

Semiflexible polymer models are widely used as a paradigm to understand structural phases in biomolecules including folding of proteins. Since stable knots are not so common in real proteins, the existence of stable knots in semiflexible polymers has not been explored much. Here, via extensive replica exchange Monte Carlo simulation we investigate the same for a bead-stick and a bead-spring homopolymer model that covers the whole range from flexible to stiff. We establish the fact that the presence of stable knotted phases in the phase diagram is dependent on the ratio $r_b/r_{\min }$ where $r_b$ is the equilibrium bond length and $r_{\min }$ is the distance for the strongest nonbonded contacts. Our results provide evidence for both models that if the ratio $r_b/r_{\min }$ is outside a small window around unity then depending on the bending stiffness one always encounters stable knotted phases along with the usual frozen and bent-like structures at low temperatures. These findings prompt us to conclude that knots are generic stable phases in semiflexible polymers.

References in corpus (14)

• Exchange Monte Carlo Method and Application to Spin Glass Simulations
• Phase Transitions of Single Semi-stiff Polymer Chains
• Freezing and Collapse of Flexible Polymers on Regular Lattices in Three Dimensions
• Scaling Properties of a Parallel Implementation of the Multicanonical Algorithm
• Elastic Lennard-Jones Polymers Meet Clusters -- Differences and Similarities
• Surface effects in the crystallization process of elastic flexible polymers
• Sequence determines degree of knottedness in a coarse-grained protein model
• Knots as Topological Order Parameter For Semi-Flexible Polymers
• From amorphous aggregates to polymer bundles: The role of stiffness on structural phases in polymer aggregation
• Phase behavior of flexible and semiflexible polymers in solvents of varying quality
• Linear Dimensions of Adsorbed Semiflexible Polymers: What can be learned about their persistence length?
• Adsorption and Pattern Recognition of Polymers at Complex Surfaces with Attractive Stripe-like Motifs
• Aggregation of theta-polymers in spherical confinement
• Intricate Knots in Proteins: Function and Evolution

Cited by in corpus (8)

• Impact of bending stiffness on ground-state conformations for semiflexible polymers
• Stable intermediate phase of secondary structures for semiflexible polymers
• How cooperatively folding are homopolymer molecular knots?
• Phase behaviour and self-assembly of semiflexible polymers in poor-solvent solutions
• Secondary-Structure Phase Formation for Semifelxible Polymers by Bifurcation in Hyperphase Space
• Monte Carlo Simulation of Long Hard-Sphere Polymer Chains in Two to Five Dimensions
• Scale-free cluster-cluster aggregation during polymer collapse
• Collapse of a single polymer chain: Effects of chain stiffness and attraction range