A Dynamic Study of Biochemical Self-Replication

Desire T Gijima,Enrique Peacock-López

doi:10.3390/math8061042

Abstract

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.

Highlights

During the early 1900s, Bray [1] reported periodic changes, which we refer as damped oscillations, in the catalytic decomposition of hydrogen peroxide
During the 1960s the interest on chemical oscillations grew considerably [5,6,7,8,9,10], and we find that periodic changes are found in many physical, biological, chemical, physiological and ecological systems, and the study of nonlinear dynamics has developed into a major field of research
We introduce an extension of a minimal model, the so-called Templator model [46,47,48,49,50,51], as a means by which we can study the behavior of biochemical self-replication

Summary

Introduction

During the early 1900s, Bray [1] reported periodic changes, which we refer as damped oscillations, in the catalytic decomposition of hydrogen peroxide. Interesting enough, Lotka’s 1910 paper [2] reported such damped oscillations, but Lotka’s or Bray’s work did not motivate the study of chemical oscillations. It took until the 1950s, when Belousov [3] first, and Zhabotinskii [4]. Later, reported a chemical system that showed periodic changes over a period of an hour, the so-called BZ reaction. Both Belousov and Zhabotinsky considered a simple solution of an organic acids and bromate in the presence of an inorganic catalyst. The systems considered were closed, periodic color changes were observed, yellow *

Objectives

Discussion

Conclusion