Enhancement of the Coloring Invariant for Folded Molecular Chains

TL;DR

This paper improves the classification of folded molecular chains by enhancing quandle coloring invariants with Boltzmann weights, allowing better distinction of complex topologies in biomolecules.

Contribution

The authors introduce Boltzmann weights to quandle coloring invariants, significantly increasing their ability to differentiate molecular chain topologies.

Findings

Enhanced invariants distinguish more topologies

Improved resolution over traditional coloring methods

Applicable to complex biomolecular folds

Abstract

Folded linear molecular chains are ubiquitous in biology. Folding is mediated by intra-chain interactions that "glue" two or more regions of a chain. The resulting fold topology is widely believed to be a determinant of biomolecular properties and function. Recently, knot theory has been extended to describe the topology of folded linear chains such as proteins and nucleic acids. To classify and distinguish chain topologies, algebraic structure of quandles has been adapted and applied. However, the approach is limited as apparently distinct topologies may end up having the same number of colorings. Here, we enhance the resolving power of the quandle coloring approach by introducing Boltzmann weights. We demonstrate that the enhanced coloring invariants can distinguish fold topologies with an improved resolution.