Solving the problem of negative populations in approximate accelerated stochastic simulations using the representative reaction approach.

Methods based on the stochastic formulation of chemical kinetics have the potential to accurately reproduce the dynamical behavior of various biochemical systems of interest. However, the computational expense makes them impractical for the study of real systems. Attempts to render these methods practical have led to the development of accelerated methods, where the reaction numbers are modeled by Poisson random numbers. However, for certain systems, such methods give rise to physically unrealistic negative numbers for species populations. The methods which make use of binomial variables, in place of Poisson random numbers, have since become popular, and have been partially successful in addressing this problem. In this manuscript, the development of two new computational methods, based on the representative reaction approach (RRA), has been discussed. The new methods endeavor to solve the problem of negative numbers, by making use of tools like the stochastic simulation algorithm and the binomial method, in conjunction with the RRA. It is found that these newly developed methods perform better than other binomial methods used for stochastic simulations, in resolving the problem of negative populations.