A computational package for measuring Topological Entanglement in Polymers, Proteins and Periodic systems (TEPPP)

Abstract

Many materials, like polymer melts, solutions, biopolymers and textiles, are composed of entangled filaments. The entanglement in these systems significantly affects their mechanical properties and their function. We introduce the Topological Entanglement in Polymers, Proteins and Periodic systems (TEPPP) software, that enables to measure the topological and geometrical complexity in such systems. In particular, this software enables the computation of the Writhe, the Gauss linking integral and the Jones polynomial of each filament or pair of filaments in the system, whether they are open or closed. In particular, for systems employing Periodic Boundary Conditions (PBC), the software also allows to compute the total pairwise entanglement in PBC, using the Periodic linking number and the Periodic Writhe. For linear (open) chains, TEPPP can calculate all these topological parameters (including the Jones polynomial) without any closure scheme. In addition, TEPPP also enables measuring self and pairwise entanglement at different length-scales along a chain or a pair of chains. With appropriate preprocessing of input files, the code can also be used for star or branched architectures. We provide examples of how the code is used and we present results on the entanglement effect in polymers obtained using this package. We show how TEPPP can be used to measure the topological entanglement of linear polymer chains in a melt, revealing subtle entanglement transitions never seen before. We also used TEPPP to analyze the effect of knotting and its location in diblock copolymer melts, which reveals that knotting localization transition coincides with lamellar-disorder transition in these systems. Finally, we use TEPPP to reveal some of the topological structure of the SARS-CoV-2 Spike protein, which points to interesting structure in a region that contains the S1/S2 cleavage site. Program summaryProgram Title: Topological Entanglement in Polymers, Proteins and Periodic systems (TEPPP) softwareCPC Library link to program files:https://doi.org/10.17632/ygdbpnhpzw.1Developer's repository link:https://github.com/TEPPP-softwareLicensing provisions: BSD 3-clauseProgramming language: C++Supplementary material:Nature of problem: Measuring single and pairwise entanglement and knotting in systems of linear or ring filaments (open or closed curves) in 3-space or in systems employing Periodic Boundary Conditions (PBC) at different length scales.Solution method: TEPPP can be used to measure topological entanglement complexity in single or multi-chain filament systems in 3-space or in systems employing PBC. Given as input the coordinates of the curves, TEPPP can compute the Gauss linking integral, the Writhe, the Jones polynomial, the Periodic Linking Number and the Periodic Writhe. Also, TEPPP can measure effects of local linking and knotting using scanning methods along the chains.