Van_Kampen_System_Size_Expansion

This document demonstrates the proof of Van Kampen’s system size expansion: a useful tool in generating closed-form approximations for the moments of the copy number of chemical species in chemical reaction networks. We pay particular attention to when we have chemical equations of the form where , which induces combinatorial factors which many authors neglect to account for. We also emphasize that, in general, rate constants under a deterministic treatment of a chemical reaction network are not equivalent to rate constants under a stochastic treatment. This is the case even for unimolecular reactions, when the rate depends explicitly upon the state.