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Biological systems often involve chemical reactions occurring in lowmolecule-number regimes, where fluctuations are not negligible and thus stochastic models are required to capture the system behaviour. The resulting models are generally quite large and complex, involving many reactions and species. For clarity and computational tractability, it is important to be able to simplify these systems to equivalent ones involving fewer elements. While many model simplification approaches have been developed for deterministic systems, there has been limited work on applying these approaches to stochastic modelling. Here, we describe a method that reduces the complexity of stochastic biochemical network models, and apply this method to the reduction of a mammalian signalling cascade and a detailed model of the process of bacterial gene expression. Our results indicate that the simplified model gives an accurate representation for not only the average numbers of all species, but also for the associated fluctuations and statistical parameters.

Abstract. Biochemical systems involve chemical reactions occurring in low-number regimes, wherein fluctuations are not negligible and thus stochastic models are required to capture the system behaviour. The resulting models are often quite large and complex, involving many reactions and species. For clarity and computational tractability, it is important to be able to simplify these systems to equivalent ones involving fewer elements. While many model simplification approaches have been developed for deterministic systems, there has been limited work on applying these approaches to stochastic modelling. Here, we propose a method that reduces the complexity of stochastic biochemical network models, and apply this method to the reduction of a mammalian signalling cascade. Our results indicate that the simplified model gives an accurate representation for not only the average number of all species, but also for the associated fluctuations and statistical parameters.Key words: stochastic biochemical modelling (modeling), model reduction, signalling (signaling, signal) cascadeThe goal of achieving a quantitative, systematic understanding of biological phenomena has driven a recent surge of interest in the formulation of mathematical models in biology [1,2]. The resulting models tend to be complex, exhibiting both nonlinear and stochastic behaviours; further, detailed models quickly grow to include large numbers of interacting species and their associated chemical reactions. Signalling cascades are a classic example of this complexity, involving many participating species interacting in highly branched networks [3]. Models of such systems are computationally expensive and difficult to understand and analyze, and thus any reduction in their complexity is welcome, provided it can be achieved without substantially altering the system's behaviour. Here, we propose a systematic method for reducing the complexity of stochastic biochemical models while keeping their statistical properties unchanged. We apply the method to a mammalian receptor tyrosine kinase signalling cascade, reducing it to substantially fewer reactions and species while maintaining the same overall behaviour.