Quantitative and qualitative nature of chemical noise propagation in a network of chemical reactions depend crucially on the topology of reaction networks. Multisite reversible phosphorylation-dephosphorylation of target proteins is one such recurrently found topology in various cellular networks regulating key functions in living cells. Here we analytically calculated the stochasticity in multistep reversible chemical reactions by determining variance of phosphorylated species at the steady state using linear noise approximation. We investigated the dependence of variance on the rate parameters in the reaction chain and the number of phosphorylation sites on the species. Assuming a quasi steady state approximation on the multistep reactions, originating from the disparity in time scales in the network, we propose a simulation scheme for coupled chemical reactions to improve the computational efficiency of stochastic simulation of the network. We performed case studies on signal transduction cascade and positive feedback loop with bistability to show the accuracy and efficiency of the method.
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