9th European Conference on Mathematical and Theoretical Biology (ECMTB 2014)

Algebraic methods for biochemical reaction networks

Elimination of Intermediate Species in Reaction Networks

Biochemical reactions often proceed through the formation of intermediate species. These species are transient species, such as the substrate-enzyme complex appearing in Michaelis-Menten kinetics. Suitable reduced systems with no intermediate have been defined in the deterministic setting, and the relation between the number of non-degenerate positive steady states of the full and the reduced networks have already been studied by C. Wiuf and E. Feliu. We focus on stochastically modelled reaction networks and provide a rigorous asymptotic result for the elimination of the intermediate species from the model. Our key assumption is that the rates of the intermediate consumption tend to infinity fast enough compared to the rates of their production. Linear algebra techniques allow us to have a parallel result on the convergence of solutions of reaction network in the deterministic case. It is also worth noting that the rates of the reduced model we obtain for the stochastic reduced system are the same obtained in the studies of C. Wiuf and E. Feliu.