  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.
