Stochastic simulation algorithm for isotope labeling metabolic networks

Carbon isotope labeling method is a standard metabolic engineering tool for flux quantification in living cells. To cope with the high dimensionality of isotope labeling systems, diverse algorithms have been developed to reduce the number of variables or operations in metabolic flux analysis (13C-MFA), but lacks generalizability to dynamic metabolic responses (13C-DMFA). In this study, we present a stochastic simulation algorithm (SSA) derived from the chemical master equation of the isotope labeling system. This algorithm allows to compute the time evolution of isotopomer and metabolite concentrations in non-steady conditions where the computational time only scales with the number of reactions of the metabolic system, not the number of isotopomers. The computational efficiency of the algorithm is benchmarked with two metabolic networks of different sizes and topologies. SSA method for the forward simulation of the isotope labeling system can be easily combined with Monte Carlo Markov Chain method for the inverse problem of dynamic flux estimation.