Complex Dynamics of Competitive First Order Chemical Self-Replication

Abstract

In most experimental conditions, the initial concentrations of a chemical system are at stoichiometric proportions, allowing us to eliminate at least one variable from the mathematical analysis. Under different initial conditions, we need to consider other manifolds defined by stoichiometry and the principle of conservation of mass. Therefore, a given set of initial conditions defines a dynamic manifold and the system, a tall times, has to satisfy a particular relation of its concentrations. To illustrate the relevance of the initial conditions in a dynamic analysis, we consider a chemical system consisting of two first-order self-replicating peptides competing for a common nucleophile in a semi-batch reactor. For the symmetric case, we find different complex oscillations for a given set of parameter values but different initial conditions.