iSSA: An incremental stochastic simulation algorithm for genetic circuits

Researchers are now developing synthetic genetic circuits to manipulate the biochemical processes within living cells. In order to model and predict the behavior of these circuits, the designer must account for numerous reactions among many chemical species and genetic components. The analysis of genetic circuits is complicated by the fact that small molecule counts and sporadic gene expression makes stochastic simulation necessary. However, the examination of statistics on ensembles of stochastic simulation runs can hide important behavior. To address this problem, this paper introduces a new method called the incremental stochastic simulation algorithm (iSSA) which determines statistics on typical behavior. This paper illustrates the utility of this algorithm on a circadian rhythm model and a model of a synthetic dual-feedback genetic oscillator.