Volume dependence in stochastic models of gene expression.

Living systems violate detailed balance, thus maintaining the non-equilibrium states necessary for biological function. A key cellular function is regulating the internal chemical environment. To investigate the emergence of this macroscopic function despite local fluctuations in particle number within the cellular volume, we investigate whether dynamical parameters in a minimal, stochastic model of gene expression are volume dependent. From this model, we derive the time evolution of the cell’s chemical state. On the mean-level, we compare the analytically derived and simulated protein number. To correlate this to the underlying microscopic dynamics, we analyze single-cell data of E. coli growth and division within a mother machine¹, and use maximum likelihood estimation (MLE) to recover these dynamical parameters. In doing so, we hope to relate the microscopic mechanisms of protein production to the macroscopic emergence of concentration regulation.

¹ Tanouchi, Y et al., Sci Data 4, 170036 (2017).