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The Chern-Simons current in time series of knots and links in proteins. (English) Zbl 1390.92095

Summary: 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 supermanifold 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.

MSC:

92D20 Protein sequences, DNA sequences
81T99 Quantum field theory; related classical field theories
58Z05 Applications of global analysis to the sciences
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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