SIAM Conference on the Life Sciences (LS14)

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. For the sake of simplicity the intermediates are often ignored in the description of a reaction network, especially when they happen to be more unstable than the other species and they are degraded at a fast rate. It is not clear, however, whether this simplification can have consequences on the reliability of the model.

We focus on stochastically modelled reaction networks and provide a rigorous asymptotic result for the elimination of the eventual intermediate species from the model. In our setting, the intermediate species can only appear alone and with unitary stoichiometric coefficient in any reaction involving them. We define a suitable reduced system and we prove that the complete system tends to the reduced one in finite dimensional distribution when the rates of consumption of the intermediate species tend to zero. Further we show that our reduced system coincides with that obtained by C. Wiuf and E. Feliu, where the framework is different as the equilibrium points of the deterministic reaction network model are studied. Moreover, we extend our results to the situation when the non-intermediate species are described by a single scaled system. We only add the assumption that the rates of the intermediate consumption tend to infinity fast enough compared to the rates of their production.

Charlotte, NC, USA

Charlotte, NC, USA