Growth impacts a range of phenotypic responses. Identifying the sources of growth variation and their propagation across the cellular machinery can thus unravel mechanisms that underpin cell decisions. We present a stochastic cell model linking gene expression, metabolism and replication to predict growth dynamics in single bacterial cells. Alongside we provide a theory to analyse stochastic chemical reactions coupled with cell divisions, enabling efficient parameter estimation, sensitivity analysis and hypothesis testing. The cell model recovers population-averaged data on growth-dependence of bacterial physiology and how growth variations in single cells change across conditions. We identify processes responsible for this variation and reconstruct the propagation of initial fluctuations to growth and other processes. Finally, we study drug-nutrient interactions and find that antibiotics can both enhance and suppress growth heterogeneity. Our results provide a predictive framework to integrate heterogeneous data and draw testable predictions with implications for antibiotic tolerance, evolutionary and synthetic biology.

The electrical membrane potential (V m) is one of the components of the electrochemical potential of protons across the biological membrane (proton motive force), which powers many vital cellular processes. Because V m also plays a role in signal transduction, measuring it is of great interest. Over the years, a variety of techniques have been developed for the purpose. In bacteria, given their small size, Nernstian membrane voltage probes are arguably the favorite strategy, and their cytoplasmic accumulation depends on V m according to the Nernst equation. However, a careful calibration of Nernstian probes that takes into account the tradeoffs between the ease with which the signal from the dye is observed and the dyes' interactions with cellular physiology is rarely performed. Here, we use a mathematical model to understand such tradeoffs and apply the results to assess the applicability of the Thioflavin T dye as a V m sensor in Escherichia coli. We identify the conditions in which the dye turns from a V m probe into an actuator and, based on the model and experimental results, propose a general workflow for the characterization of Nernstian dye candidates.

Cellular growth impacts a range of phenotypic responses. Identifying the sources of fluctuations in growth and how they propagate across the cellular machinery can unravel mechanisms that underpin cell decisions. We present a stochastic cell model linking gene expression, metabolism and replication to predict growth dynamics in single bacterial cells. In addition to several population-averaged data, the model quantitatively recovers how growth fluctuations in single cells change across nutrient conditions. We develop a framework to analyse stochastic chemical reactions coupled with cell divisions and use it to identify sources of growth heterogeneity. By visualising cross-correlations we then determine how such initial fluctuations propagate to growth rate and affect other cell processes. We further study antibiotic responses and find that complex drugnutrient interactions can both enhance and suppress heterogeneity. Our results provide a predictive framework to integrate single-cell and bulk data and draw testable predictions with implications for antibiotic tolerance, evolutionary biology and synthetic biology.

Maintaining intracellular homeostases is a hallmark of life, and key physiological variables, such as cytoplasmic pH, osmotic pressure, and proton motive force (PMF), are typically interdependent. Developing a mathematical model focused on these links, we predict that Escherichia coli uses proton-ion antiporters to generate an out-of-equilibrium plasma membrane potential and so maintain the PMF at the constant levels observed. The strength of the PMF consequently determines the range of extracellular pH over which the cell is able to preserve its near neutral cytoplasmic pH. In support, we concurrently measure the PMF and cytoplasmic pH in single cells and demonstrate both that decreasing the PMF’s strength impairs E. coli’s ability to maintain its pH and that artificially collapsing the PMF destroys the out-of-equilibrium plasma membrane potential. We further predict the observed ranges of extracellular pH for which three of E. coli’s antiporters are expressed, through defining their cost by the rate at which they divert imported protons from generating ATP. Taken together, our results suggest a new perspective on bacterial electrophysiology, where cells regulate the plasma membrane potential by changing the activities of antiporters to maintain both the PMF and cytoplasmic pH.

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