Intrinsic Noise in Gene Expression and Its Impact on Cellular Function: Insights from Exact Solutions of the Chemical Master Equation

Intrinsic noise is not merely a byproduct of biological processes; rather, it is a fundamental aspect of cellular function that influences critical outcomes in development, differentiation, and disease. Despite its significance, the role of intrinsic noise has been relatively underexplored in cell trajectory inference using single-cell omics data. In this study, we conducted a comprehensive analysis of stochasticity across four gene expression models: the basic constitutive model, two distinct burst models, and the simplified Telegraph-Splicing Model (TSM). We utilized the finite-buffer Accurate Chemical Master Equation (ACME) algorithm to compute exact steady-state probability landscapes for these models. Additionally, we investigated the role of stochasticity in evolution and environmental adaptation. Our findings reveal substantial heterogeneity in transcriptional states among genetically identical cells, which we quantified through exact steady-state analysis. Moreover, we calculated the probability flux of the TSM model, revealing a continuous conversion between gene activation and repression states before reaching steady state. Overall, our research underscores the critical impact of intrinsic noise on gene transcription, offering a comprehensive characterization of its dynamics and implications for evolution and environmental adaptation.