Mathematics of the Genome
Indika Rajapakse, Steve Smale
TL;DR
This paper develops a mathematical framework to analyze bifurcations in genomic dynamics, providing foundational insights into gene circuit behaviors like the Repressilator and Toggle switch.
Contribution
It introduces a novel mathematical foundation for bifurcation analysis in genomic systems and models key gene circuits within this framework.
Findings
Bifurcation analysis of stable genomic equilibria
Mathematical modeling of Repressilator and Toggle circuits
Framework applicable to gene regulatory network dynamics
Abstract
This work gives a mathematical foundation for bifurcation from a stable equilibrium in the genome. We construct idealized dynamics associated with the genome. For this dynamics we investigate the two main bifurcations from a stable equilibrium. Finally, we give a mathematical framework for the Repressilator and the Toggle gene circuits.
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