A generalized moment-based method for estimating parameters of stochastic gene transcription

Gene transcription is a stochastic process manifested by the mRNA distribution data at the single-cell level, which can be fitted using the mass function P_m that quantifies the probability of m mRNA molecules per cell for the gene of interest. Extensive studies have been conducted to infer gene parameter rates in mathematical models using maximum-likelihood method or moment-based method based on mRNA distribution data. However, current methods usually do not emphasize the exact fit to the data of single P₀, where P₀ plays a critical role in discriminating different distribution modalities. In this study, we highlighted the fit to the data of P₀, and developed a generalized moment-based protocol for more reliable parameter estimation in the classical two-state model. Our protocol is easy to follow and allows the estimation of parameters of E.coli and mammalian genes under varying conditions. We showed that our protocol performs much better than the traditional moment-based method, and more likely captures the bimodal mRNA distribution than that obtained using the maximum-likelihood method.