The mean and noise of stochastic gene transcription

Gene transcription in single cells is inherently a probabilistic process. Even in a hypothetically homogeneous intracellular environment, the stochasticity of transcription would produce fluctuations in the number of transcripts, constituting the phenotypic heterogeneity in cell population. Noise, the variance normalized by the square of the mean, has typically been utilized to quantify the heterogeneity of transcript distribution. The noise has been thought to arise from random switching between gene on and gene off states, but what underlies the stochastic transition between the on state and the off state remains largely unknown. To examine how the environmental signals contribute to the gene transcription regulation, we employ a three states model to evaluate the dynamical and stationary mean transcript level, and the noise of transcript distribution. Our findings reinforce the assertion of Raser and O'Shea [2004. Control of stochasticity in eukaryotic gene expression. Science 304, 1811-1814] that two cells can produce the same mean mRNA population but display different noise characteristics. The theoretical analysis also brings new characteristics to the subtle correlations between the mean and the noise, which extends beyond the categorization of Raser and O'Shea.