Electrochemical gradient of protons, or proton motive force (PMF), is at the basis of bacterial energetics. It powers vital cellular processes and defines the physiological state of the cell. Here we use an electric circuit analogy of an Escherichia coli cell to mathematically describe the relationship between bacterial PMF, electric properties of the cell membrane and catabolism. We combine the analogy with the use of bacterial flagellar motor as a single-cell "voltmeter" to measure cellular PMF in varied and dynamic external environments, for example, under different stresses. We find that butanol acts as an ionophore, and functionally characterise membrane damage caused by the light of shorter wavelengths. Our approach coalesces non-invasive and fast single-cell voltmeter with a well-defined mathematical framework to enable quantitative bacterial electrophysiology.Keywords: bacterial energetics, proton motive force, bacterial membrane damage, single-cell measurements, bacterial physiology, indole, butanol, photodamage arXiv:1809.05306v1 [physics.bio-ph] 14 Sep 2018 cytoplasm, and for Escherichia coli the latter is known (Slonczewski et al., 1981;Zilberstein et al., 1984;Wilks and Slonczewski, 2007), V m in the circuit equals the PMF.The circuit analogy in Fig. 1A gives a mathematical framework that helps us understand cellular free energy maintenance in a range of different conditions. For example, we can predict changes in V m when circuit parameters change: a battery depends on the available carbon source and internal resistance R i increases in presence of electron transport chain inhibitors (such as sodium azide (Noumi et al., 1987)). Furthermore, if we could measure V m with an equivalent of a "voltmeter" we could predict the mechanism and dynamics of the damage as the cells are exposed to various external stresses, as well as obtain functional dependence between affected circuit parameters and the amplitude of the stress.Here we report the use of bacterial flagellar motor as such a "voltmeter" and reveal the mechanisms of damage caused by chosen stresses. We confirm the behaviour of a known ionophore (indole) (Chimerel et al., 2012), discover that butanol is an ionophore, and quantitatively describe the nature of damage caused by the light of shorter wavelengths. Our approach of combining high-precision PMF (V m ) measurements and the "electrical circuit interpretation" of the cell serves as a powerful tool needed for quantitative bacterial electrophysiology.

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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.