Mathematical Model for Temperature Regulation of Self-Sustained Glycolytic Oscillations in a Closed Reactor

Abstract

We base on the Selkov system [1] to construct the model for temperaturecontrol of glycolytic reaction in a closed spatial reactor. To establish acorrespondence with the experiment [2] we add the slow catalytic term xwhich describes the small value of additional substrate influx and productoutflow and introduce a temperature-dependent coefficient satisfying theArrhenius law... The considered model explains the key experimentally observed phenomena[2]: 1) decaying of the average concentrations of reagents duringthe reaction, 2) Arrhenius-type temperature dependence for frequency of oscillations,3) change of the form of oscillations with the temperature growth,4) modulations of oscillations induced by a periodic temperature variation.The addition of the diffusion terms to the system (1) allows to reproducethe emerging of glycolytic travelling waves observed in a closed reactor inthe presence of a temperature gradient [2]. Comparison of the dynamics of travelling waves in the numerical solution with the experimental data [2]permits to propose a new method to estimate the diffusion coefficients of reagents in the case of a chemical reaction occurring in a dense media