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Nonequivalence of Membrane Voltage and Ion-Gradient as Driving Forces for the Bacterial Flagellar Motor at Low Load

Clarendon Laboratory, Department of Physics, University of Oxford, Oxford, United Kingdom

Correspondence: Address reprint requests to Richard Berry, Clarendon Laboratory, Dept. of Physics, University of Oxford, Parks Rd., Oxford OX1 3PU, U.K. Tel.: 44-0-1865-282559; Fax: 44-0-1865-272400; E-mail: r.berry1{at}physics.ox.ac.uk.

Many bacterial species swim using flagella. The flagellar motor couples ion flow across the cytoplasmic membrane to rotation. Ion flow is driven by both a membrane potential (V_m) and a transmembrane concentration gradient. To investigate their relation to bacterial flagellar motor function we developed a fluorescence technique to measure V_m in single cells, using the dye tetramethyl rhodamine methyl ester. We used a convolution model to determine the relationship between fluorescence intensity in images of cells and intracellular dye concentration, and calculated V_m using the ratio of intracellular/extracellular dye concentration. We found V_m = –140 ± 14 mV in Escherichia coli at external pH 7.0 (pH_ex), decreasing to –85 ± 10 mV at pH_ex 5.0. We also estimated the sodium-motive force (SMF) by combining single-cell measurements of V_m and intracellular sodium concentration. We were able to vary the SMF between –187 ± 15 mV and –53 ± 15 mV by varying pH_ex in the range 7.0–5.0 and extracellular sodium concentration in the range 1–85 mM. Rotation rates for 0.35-µm- and 1-µm-diameter beads attached to Na⁺-driven chimeric flagellar motors varied linearly with V_m. For the larger beads, the two components of the SMF were equivalent, whereas for smaller beads at a given SMF, the speed increased with sodium gradient and external sodium concentration.