A recursive method to calculate the expected molecule numbers for a polymerization network with a small number of subunits

We compare the deterministic method and the stochastic method for a polymerization network when the number of available subunits is small. For the stochastic method, we prove there is a recursive method to compute the expected molecule numbers of various components in the reaction network, using the stationary probability distribution of molecule numbers which we illustrate to have a multivariate Poisson form. For the deterministic method, ordinary differential equations for the component concentrations are built following the mass action law. The steady state of the system is extracted to estimate the corresponding molecule numbers. Identities involving the propensity function parameters for the stochastic method and the reaction rate constants in the deterministic method are used to connect the two methods. Computations are conducted for a group of combinations of total number of subunits and reaction rate constant ratios, and the results are compared.