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.

For quantitative understanding of probabilistic behaviors of living cells, it is essential to construct a correct mathematical description of intracellular networks interacting with complex cell environments, which has been a formidable task. Here, we present a novel model and stochastic kinetics for an intracellular network interacting with hidden cell environments, employing a complete description of cell state dynamics and its coupling to the system network. Our analysis reveals that various environmental effects on the product number fluctuation of intracellular reaction networks can be collectively characterized by Laplace transform of the time-correlation function of the product creation rate fluctuation with the Laplace variable being the product decay rate. On the basis of the latter result, we propose an efficient method for quantitative analysis of the chemical fluctuation produced by intracellular networks coupled to hidden cell environments. By applying the present approach to the gene expression network, we obtain simple analytic results for the gene expression variability and the environment-induced correlations between the expression levels of mutually noninteracting genes. The theoretical results compose a unified framework for quantitative understanding of various gene expression statistics observed across a number of different systems with a small number of adjustable parameters with clear physical meanings.

Even in the steady-state, the number of biomolecules in living cells fluctuates dynamically, and the frequency spectrum of this chemical fluctuation carries valuable information about the dynamics of the reactions creating these biomolecules. Recent advances in single-cell techniques enable direct monitoring of the time-traces of the protein number in each cell; however, it is not yet clear how the stochastic dynamics of these time-traces is related to the reaction mechanism and dynamics. Here, we derive a rigorous relation between the frequency-spectrum of the product number fluctuation and the reaction mechanism and dynamics, starting from a generalized master equation. This relation enables us to analyze the time-traces of the protein number and extract information about dynamics of mRNA number and transcriptional regulation, which cannot be directly observed by current experimental techniques. We demonstrate our frequency spectrum analysis of protein number fluctuation, using the gene network model of luciferase expression under the control of the Bmal 1a promoter in mouse fibroblast cells. We also discuss how the dynamic heterogeneity of transcription and translation rates affects the frequency-spectra of the mRNA and protein number.

Sequence-dependent pausing by RNA polymerase (RNAP) is critical in regulating transcription.At the single molecule level, the analysis of optical trapping assays reveals interrupted transcription of RNAP with pauses.

Living cells exhibit multi-mode transport that switches between an active, self-propelled motion and a seemingly passive, random motion. Cellular decision-making over transport mode switching is a stochastic process that depends on the dynamics of the intracellular chemical network regulating the cell migration process. Here, we propose a theory and an exactly solvable model of multi-mode active matter. Our exact model study shows that the reversible transition between a passive mode and an active mode is the origin of the anomalous, super-Gaussian transport dynamics, which has been observed in various experiments for multimode active matter. We also present the generalization of our model to encompass complex multi-mode matter with arbitrary internal state chemical dynamics and internal state dependent transport dynamics.