Efficient sampling of knotting-unknotting pathways for semiflexible Gaussian chains

Cristian Micheletti (1) , Henri Orland (2, 3)

1 SISSA / ISAS - Scuola Internazionale Superiore di Studi Avanzati / International School for Advanced Studies
2 IPHT - Institut de Physique Théorique - UMR CNRS 3681
3 CSRC - Beijing Computational Science Research Center [Beijing]

We propose a stochastic method to generate exactly the overdamped Langevin dynamics of semi-flexible Gaussian chains, conditioned to evolve between given initial and final conformations in a preassigned time. The initial and final conformations have no restrictions, and hence can be in any knotted state. Our method allows the generation of statistically independent paths in a computationally efficient manner. We show that these conditioned paths can be exactly generated by a set of local stochastic differential equations. The method is used to analyze the transition routes between various knots in crossable filamentous structures, thus mimicking topological reconnections occurring in soft matter systems or those introduced in DNA by topoisomerase enzymes. We find that the average number of crossings, writhe and unknotting number are not necessarily monotonic in time and that more complex topologies than the initial and final ones can be visited along the route.

Keywords: knots; Langevin bridges; reconnection paths

Domains: Physics [physics]

Cristian Micheletti, Henri Orland. Efficient sampling of knotting-unknotting pathways for semiflexible Gaussian chains. Polymers, 2017, 9, pp.196. ⟨10.3390/polym9060196⟩. ⟨cea-01708269⟩