Cellular Chemical Dynamics Governing Signal Transduction and Adaptive Gene Expression: Beyond Classical Kinetics

Cellular adaptation is inherently nonstationary processes with complex stochastic dynamics1-5. Despite remarkable progress in quantitative biology6-11, a quantitative understanding of the cell adaptation dynamics in terms of the underlying cellular network remains elusive. Here, we present the next-generation chemical dynamics model and theory for cellular networks, providing an effective, quantitative description of the adaptive gene expression dynamics in living cells responding to external stimuli. Unlike conventional kinetics, chemical dynamics of cellular network modules are characterized by their reaction-time distributions, rather than by rate coefficients12. For a general model of cell signal transduction and adaptive gene expression, we derive exact analytical expressions for the time-dependent mean and variance of protein numbers produced in response to external stimuli, validated by accurate stochastic simulations. These results provide a unified, quantitative explanation of the stochastic responses of diverse E. coli genes to antibiotic stress and transcriptional induction. Our analysis reveals existence of a general quadratic relationship between the mean and variance of activation times across diverse genes. The gene activation process influences transient dynamics of downstream protein levels, but not their steady-state levels. In contrast, post-translational maturation process affects both transient dynamics and steady-state variability of mature protein levels. This finding indicates that the gene expression variability measured by fluorescent reporter proteins depends on the maturation time of the reporters. This work suggests a new direction for the development of digital twins of living cells.