Nonequivalence of membrane voltage and ion-gradient as driving forces for the bacterial flagellar motor at low load

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.