Abstract
Gene expression is a complex stochastic process composed of numerous enzymatic reactions with rates coupled to hidden cell-state variables. Despite advances in single-cell technologies, the lack of a theory accurately describing the gene expression process has restricted a robust, quantitative understanding of gene expression variability among cells. Here we present the Chemical Fluctuation Theorem (CFT), providing an accurate relationship between the environment-coupled chemical dynamics of gene expression and gene expression variability. Combined with a general, accurate model of environment-coupled transcription processes, the CFT provides a unified explanation of mRNA variability for various experimental systems. From this analysis, we construct a quantitative model of transcription dynamics enabling analytic predictions for the dependence of mRNA noise on the mRNA lifetime distribution, confirmed against stochastic simulation. This work suggests promising new directions for quantitative investigation into cellular control over biological functions by making complex dynamics of intracellular reactions accessible to rigorous mathematical deductions.
Highlights
Gene expression is a complex stochastic process composed of numerous enzymatic reactions with rates coupled to hidden cell-state variables
In the analysis of experimental data, we find that the mean messenger RNA (mRNA) level dependence of non-Poisson mRNA noise, or the difference between the relative variance and the inverse mean of the mRNA level, is far more sensitive to the transcription dynamics than the Fano factor or other previously used measures
Transcription consists of several major chemical processes, including the binding of RNA polymerase (RNAP) to the promoter, the activation of the RNAP–promoter complex, and transcriptional elongation during which mRNA is synthesized
Summary
Gene expression is a complex stochastic process composed of numerous enzymatic reactions with rates coupled to hidden cell-state variables. Accurate model of environment-coupled transcription processes, the CFT provides a unified explanation of mRNA variability for various experimental systems From this analysis, we construct a quantitative model of transcription dynamics enabling analytic predictions for the dependence of mRNA noise on the mRNA lifetime distribution, confirmed against stochastic simulation. Examples of the cell-state variables coupled to the gene expression rate include the populations of RNA polymerase (RNAP) and ribosomes[19]; the populations of transcription factors and micro-RNAs20; the interaction strength of genes with RNAP and transcription factors[21]; the gene copy number[22,23]; the phase of the cell cycle[24]; the density of nutrients[25]; and the conformation of chromosomes[26] All of these cellstate variables are stochastic variables that differ from cell to cell and fluctuate over time. Whether such a universal law exists or whether a unified, quantitative understanding of the above-mentioned experiments is even possible remains unknown
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