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.

Various toxic compounds disrupt bacterial physiology. While bacteria harbor defense mechanisms to mitigate the toxicity, these mechanisms are often coupled to the physiological state of the cells and become ineffective when the physiology is severely disrupted.

for in vivo, single-cell imaging bacterial cells are commonly immobilised via physical confinement or surface attachment. Different surface attachment methods have been used both for atomic force and optical microscopy (including super resolution), and some have been reported to affect bacterial physiology. However, a systematic comparison of the effects these attachment methods have on the bacterial physiology is lacking. Here we present such a comparison for bacterium Escherichia coli, and assess the growth rate, size and intracellular pH of cells growing attached to different, commonly used, surfaces. We demonstrate that E. coli grow at the same rate, length and internal pH on all the tested surfaces when in the same growth medium. The result suggests that tested attachment methods can be used interchangeably when studying E. coli physiology. Microscopy has been a powerful tool for studying biological processes on the cellular level, ever since the first discovery of microorganisms by Antonie van Leeuwenhoek back in 17th century 1. Recently employed single-cell imaging allowed scientists to study population diversity 2 , physiology 3 , sub-cellular features 4 , and protein dynamics 5 in real-time. Single cell imaging of bacteria is particularly dependent on immobilisation, as majority of bacteria are small in size and capable of swimming. Immobilisation methods vary depending on the application, but typically fall into one of the two categories: use of physical confinement or attachment to the surface via specific molecules. The former group includes microfluidic platforms capable of mechanical trapping 6,7 , where some popular examples include the "mother machine" 8 , CellASIC 9 or MACS 10 devices, and porous membranes such as agarose gel pads 2,11-13. Physical confinement methods, while higher in throughput, can have drawbacks. For example, agarose gel pads do not allow fast medium exchange, and when mechanically confining bacteria the choice of enclosure dimensions should be done carefully in order to avoid influencing the growth and morphology with mechanical forces 14. Furthermore, mechanically confined bacteria cannot be used for studies of bacterial motility or energetics via detection of bacteria flagellar motor rotation 15-17. Chemical attachment methods rely on the interaction of various adhesive molecules, deposited on the cover glass surface, with the cell itself. Adhesion can be a result of electrostatic (polyethylenimine (PEI) 18,19 , poly-L-lysine (PLL) 15,17,19) or covalent interactions (3-aminopropyltriethoxysilane (APTES) 19), or a combination, such as with polyphenolic proteins (Cell-Tak) 19. Time scales on which researchers perform single-cell experiments vary. For example, scanning methods, like atomic force microscopy (AFM) or confocal laser scanning microscopy (CLSM) 19,20 , require enough time to probe each point of the sample, and stochastic approaches of super resolution microscopy (e.g. PALM and STORM) use low activation rate of fluorophores to achieve a single fluorophore localisati...

Bacterial Flagellar Motor is one of nature's rare rotary molecular machines. It enables bacterial swimming and it is the key part of the bacterial chemotactic network, one of the best studied chemical signalling networks in biology, which enables bacteria to direct its movement in accordance with the chemical environment. The network can sense down to nanomolar concentrations of specific chemicals on the time scale of seconds. Motor's rotational speed is linearly proportional to the electrochemical gradients of either proton or sodium driving ions, while its direction is regulated by the chemotactic network. Recently, it has been discovered that motor is also a mechanosensor. Given these properties, we discuss the motor's potential to serve as a multifunctional biosensor and a tool for characterising and studying the external environment, the bacterial physiology itself and single molecular motor biophysics.

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.