Fig. S4.

Torque versus speed curves. (A and B) Measurements derived from various studies, which measured the speed of a rotating bead stuck to the filament or hook of an immobilized cell. (A) WT E. coli BFMs and (B) E. coli BFMs with chimeric Na⁺ stator units (at 85 mM [Na⁺], pH 7.0). B is an enlarged copy of the region demarcated by the gray box in B, Inset. For consistency, we recalculated torque from previously published speeds using a single model for the viscous drag coefficient of beads of different sizes attached to hooks (26) or filament stubs (9, 11, 12, 19, 25, 48). Marker color denotes the data source, and the number within each marker shows the number of units previously assigned, some of which are incorrect in retrospect. Data from motors presumed to have a full complement of stator units are labeled F and likely represent variable numbers of units given the load dependence of stator units (15, 16). Where measurements were made over more than two viscous loads, a line connects data points from the same study. Details regarding the calculation of torque are given in SI Materials and Methods. (C) Normalized torque–speed curves for Na⁺ (black squares and gray line; average of the 75 curves from Fig. 3B; mean $\pm$ SD) and Na⁺ (black circles and black lines) motors. For normalization of the Na⁺ motor, we have used a PMF of –125 mV and an empirical normalization function $f$([Na⁺]) = 1. For pH 7.0, this value of $f$([Na⁺]) corresponds to the saturation value of $f$([Na⁺]) (Fig. 3B).