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-microm- and 1-microm-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.