Topology-dependent mixing of knots in flexible polymer chains
Abstract
The organization of multiple knots along a polymer contour can depend sensitively on the topology of the constituent knots. Using coarse-grained Brownian-dynamics simulations, we investigate topology-dependent mixing of two knots in a flexible polymer at controlled normalized wall separation. We compare homogeneous (31⊗ 31) and heterogeneous (31⊗ 51) knot pairs using a contour-based coordinate that distinguishes mixed and demixed configurations. Starting from partially overlapping configurations, the 31⊗ 51 pair is observed in mixed configurations more frequently over the simulation time window than the 31⊗ 31 pair at intermediate wall separation. We further find that, over the intermediate range of normalized wall separation, mixing of the 31⊗51 pair produces a composite knotted region that occupies substantially less polymer contour than the two constituent knots collectively occupy in demixed configurations. The corresponding reduction in contour occupancy is much smaller for the 31⊗31 pair. This indicates that the heterogeneous constituent topologies can be accommodated within a smaller portion of the polymer contour in the composite configuration. These results establish that constituent topology can strongly influence multiple-knot organization in flexible polymers.
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BibTeX
@misc{sengupta2026topologydependent,
title = {{Topology-dependent mixing of knots in flexible polymer chains}},
author = {Souradeep Sengupta and Garima Mishra},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.10188},
eprint = {2609.10188},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.10188},
}
RIS
TY - UNPB
TI - Topology-dependent mixing of knots in flexible polymer chains
AU - Souradeep Sengupta
AU - Garima Mishra
PY - 2026
DA - 2026/09/09
PB - arXiv
DO - 10.48550/arxiv.2609.10188
UR - https://arxiv.org/abs/2609.10188
AB - The organization of multiple knots along a polymer contour can depend sensitively on the topology of the constituent knots. Using coarse-grained Brownian-dynamics simulations, we investigate topology-dependent mixing of two knots in a flexible polymer at controlled normalized wall separation. We compare homogeneous (3_1⊗ 3_1) and heterogeneous (3_1⊗ 5_1) knot pairs using a contour-based coordinate that distinguishes mixed and demixed configurations. Starting from partially overlapping configurations, the 3_1⊗ 5_1 pair is observed in mixed configurations more frequently over the simulation time window than the 3_1⊗ 3_1 pair at intermediate wall separation. We further find that, over the intermediate range of normalized wall separation, mixing of the 3_1⊗5_1 pair produces a composite knotted region that occupies substantially less polymer contour than the two constituent knots collectively occupy in demixed configurations. The corresponding reduction in contour occupancy is much smaller for the 3_1⊗3_1 pair. This indicates that the heterogeneous constituent topologies can be accommodated within a smaller portion of the polymer contour in the composite configuration. These results establish that constituent topology can strongly influence multiple-knot organization in flexible polymers.
ER -