Modeling dynamics of chemical reaction networks using electrical analogs: Application to autocatalytic reactions

Abstract

Modeling complex chemical reaction networks has inspired a considerable body of research and a variety of approaches to modeling nonlinear pathways are being developed. Here, a general methodology is formulated to convert an arbitrary reaction network into its equivalent electrical analog. The topological equivalence of the electrical analog is mathematically established for unimolecular reactions using Kirchhoff's laws. The modular approach is generalized to bimolecular and nonlinear autocatalytic reactions. It is then applied to simulate the dynamics of nonlinear autocatalytic networks without making simplifying assumptions, such as use of the quasi-steady state/Bodenstein approximation or the absence of nonlinear steps in the intermediates. This is among the few papers that quantify the dynamics of a nonlinear chemical reaction network by generating and simulating an electrical network analog. As a realistic biological application, the early phase of the spread of COVID-19 is modeled as an autocatalytic process and the predicted dynamics are in good agreement with experimental data. The rate-limiting step of viral transmission is identified, leading to novel mechanistic insights.