On the sum of chemical reactions

Abstract

It is standard in chemistry to represent a sequence of reactions by a single overall reaction, often called a complex reaction in contrast to an elementary reaction. Photosynthesis $6{\text{CO}}_2+6{\text{H}}_2\text{O}\to {\text{C}}_6{\text{H}}_{12}{\text{O}}_6$ $+6{\text{O}}_2$ is an example of such complex reaction. We introduce a mathematical operation that corresponds to summing two chemical reactions. Specifically, we define an associative and non-communicative operation on the product space ${\mathbb{N}}_0^n\times {\mathbb{N}}_0^n$ (representing the reactant and the product of a chemical reaction, respectively). The operation models the overall effect of two reactions happening in succession, one after the other. We study the algebraic properties of the operation and apply the results to stochastic reaction networks, in particular to reachability of states, and to reduction of reaction networks.

References in corpus (6)

• Epidemic processes in complex networks
• Simplifying Biochemical Models With Intermediate Species
• Product-form Poisson-like distributions and complex balanced reaction systems
• Dynamical Properties of Discrete Reaction Networks
• Elimination of Intermediate Species in Multiscale Stochastic Reaction Networks
• Classification and threshold dynamics of stochastic reaction networks

Cited by in corpus (1)

• Fast reactions with non-interacting species in stochastic reaction networks