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A Dynamic Study of Biochemical Self-Replication

Department of Chemistry, Williams College, Williamstown, MA 01267, USA
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Author to whom correspondence should be addressed.
The authors contributed equally to this work.
Mathematics 2020, 8(6), 1042; https://doi.org/10.3390/math8061042
Received: 3 May 2020 / Revised: 20 June 2020 / Accepted: 24 June 2020 / Published: 26 June 2020
(This article belongs to the Special Issue Advanced Mathematics for Physical Chemistry and Chemical Physics)
As it is well understood, in biological systems, small regulatory motifs are present at all scales, thus looking at simple negative feedback loops give us some information of how autocatalytic systems may be affected by regulation. For a single template self-replication, we consider a plausible mechanism, which we reduce to a 2-variable dimensionless set of ordinary differential equations, (ODE). The stability analysis of the steady states allows us to obtain exact relations to describe two-parameter bifurcation diagrams. We include a negative feedback to the reactants input to study the effect of regulation in biochemical self-replication. Surprisingly, the simpler regulation has the largest impact on the parameter space. View Full-Text
Keywords: chemical self-replication; chemical oscillations; negative feedback; Poincare sections chemical self-replication; chemical oscillations; negative feedback; Poincare sections
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Gijima, D.T.; Peacock-López, E. A Dynamic Study of Biochemical Self-Replication. Mathematics 2020, 8, 1042.

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