The Chern-Simons Current in Time Series of Knots and Links in Proteins

TL;DR

This paper introduces a novel superspace model using Chern-Simons theory to analyze DNA knot and link structures, linking advanced mathematical physics to gene expression and protein interactions.

Contribution

It develops an $E_{8} imes E_{8}$ unified spin model with modified cohomologies to describe protein-DNA interactions and gene state transitions in a biological context.

Findings

Derives equations for gene expression transitions.

Models protein interactions using Chern-Simons current in higher dimensions.

Connects knot theory with genetic and protein data.

Abstract

A superspace model of knots and links for DNA time series data is proposed to take into account the feedback loop from docking to undocking state of protein-protein interactions. In particular, the direction of interactions between the 8 hidden states of DNA is considered. It is a $E_{8}\times E_{8}$ unified spin model where the genotype, from active and inactive side of DNA time data series, can be considered for any living organism. The mathematical model is borrowed from loop-quantum gravity and adapted to biology. It is used to derive equations for gene expression describing transitions from ground to excited states, and for the 8 coupling states between geneon and anti-geneon transposon and retrotransposon in trash DNA. Specifically, we adopt a modified Grothendieck cohomology and a modified Khovanov cohomology for biology. The result is a Chern-Simons current in $(8+3)$ extradimensions of a given unoriented super manifold with ghost fields of protein structures. The $8$ dimensions come from the 8 hidden states of spinor field of genetic code. The extradimensions come from the 3 types of principle fiber bundle in the secondary protein.