Knotting and linking in macromolecules

Effect of Topology on the Statics and Dynamics of a Polymer Chain at the Fluid-Fluid Interface: A Molecular Dynamics Simulation Study

The effect of chain topology on the statics and dynamics of a chain at the interface of two immiscible fluids is studied by means of molecular dynamic simulations. For three topologically different chains, namely, linear, ring, and trefoil-knot, of the same molecular weight, the effect of varying both polymer-fluid and fluid-fluid interaction nature on the width of the fluid interface, chain conformation, shape, and chain dynamics is investigated. For a sharp-interface binary-fluid system, the interface width is insensitive to both topology and polymer-fluid interaction nature, while a weak nonmonotonic variation is seen for a broad-interface system. Chain extension normal to the interface plane is significantly affected by the topology with a trefoil-knot chain, due to the additional constraint, which has the largest value compared to both linear and ring polymers. Instantaneous shapes are also quantified through shape parameters. Furthermore, it is observed that the qualitative behavior of the center-of-mass mean-square displacement (MSD) is independent of topology, i.e., all the chain types show the same diffusion exponent α ( ∼ 1). However, the self-diffusion constant depends on the topology and it is the largest for the trefoil-knot chain. An interesting observation pertaining to the early time behavior of monomeric MSD is that, within the subdiffusive regime, the values of α for different parameters (independent of topology) are grouped into two distinct ranges (0.52 - 0.59 and 0.62 - 0.67), which are related to the different chain conformation for the polymer-fluid interaction range below and above a threshold value equal to that of the self-interaction of the pure fluid phase.

Topoly: Python package to analyze topology of polymers

The increasing role of topology in (bio)physical properties of matter creates a need for an efficient method of detecting the topology of a (bio)polymer. However, the existing tools allow one to classify only the simplest knots and cannot be used in automated sample analysis. To answer this need, we created the Topoly Python package. This package enables the distinguishing of knots, slipknots, links and spatial graphs through the calculation of different topological polynomial invariants. It also enables one to create the minimal spanning surface on a given loop, e.g. to detect a lasso motif or to generate random closed polymers. It is capable of reading various file formats, including PDB. The extensive documentation along with test cases and the simplicity of the Python programming language make it a very simple to use yet powerful tool, suitable even for inexperienced users. Topoly can be obtained from https://topoly.cent.uw.edu.pl.