A Novel Approach for Calculating Exact Forms of mRNA Distribution in Single-Cell Measurements

Gene transcription is a stochastic process manifested by fluctuations in mRNA copy numbers in individual isogenic cells. Together with mathematical models of stochastic transcription, the massive mRNA distribution data that can be used to quantify fluctuations in mRNA levels can be fitted by P m ( t ) , which is the probability of producing m mRNA molecules at time t in a single cell. Tremendous efforts have been made to derive analytical forms of P m ( t ) , which rely on solving infinite arrays of the master equations of models. However, current approaches focus on the steady-state ( t → ∞ ) or require several parameters to be zero or infinity. Here, we present an approach for calculating P m ( t ) with time, where all parameters are positive and finite. Our approach was successfully implemented for the classical two-state model and the widely used three-state model and may be further developed for different models with constant kinetic rates of transcription. Furthermore, the direct computations of P m ( t ) for the two-state model and three-state model showed that the different regulations of gene activation can generate discriminated dynamical bimodal features of mRNA distribution under the same kinetic rates and similar steady-state mRNA distribution.