The speed of the flagellar rotary motor of Escherichia coli varies linearly with protonmotive force - PubMed (original) (raw)
The speed of the flagellar rotary motor of Escherichia coli varies linearly with protonmotive force
Christopher V Gabel et al. Proc Natl Acad Sci U S A. 2003.
Abstract
A protonmotive force (pmf) across the cell's inner membrane powers the flagellar rotary motor of Escherichia coli. Speed is known to be proportional to pmf when viscous loads are heavy. Here we show that speed also is proportional to pmf when viscous loads are light. Two motors on the same bacterium were monitored as the cell was slowly deenergized. The first motor rotated the entire cell body (a heavy load), while the second motor rotated a small latex bead (a light load). The first motor rotated slowly and provided a measure of the cell's pmf. The second motor rotated rapidly and was compared with the first, to give the speed-pmf relation for light loads. Experiments were done at 24.0 degrees C and 16.2 degrees C, with initial speeds indicating operation well into the high-speed, low-torque regime. Speed was found to be proportional to pmf over the entire (accessible) dynamic range (0-270 Hz). If the passage of a fixed number of protons carries the motor through each revolution, i.e., if the motor is tightly coupled, a linear speed-pmf relation is expected close to stall, where the work done against the viscous load matches the energy dissipated in proton flow. A linear relation is expected at high speeds if proton translocation is rate-limiting and involves multiple steps, a model that also applies to simple proton channels. The present work shows that a linear relation is true more generally, providing an additional constraint on possible motor mechanisms.
Figures
Fig. 1.
(a) Flagella of a single bacterium were tethered to a glass coverslip and to a small, 0.4-μm-diameter latex bead, respectively. One flagellum rotated slowly because of the large viscous load of the entire bacterium. The other rotated rapidly because of the small viscous load of the latex bead. (b) The rotation speeds of both flagella were monitored simultaneously by aligning the image with a pinhole in front of a photomultiplier tube. As the bead and cell rotated past the pinhole, they generated a signal that contained both the low- and high-frequency components of the compound movement. (c) The power spectrum of this signal taken from a 5-s window revealed the two rotation rates (≈5 and ≈75 Hz, respectively). The rotation axis of the tether for the body of this cell was off center, so that whereas the long end of the cell spanned the full width of the pinhole, the short end did not. This asymmetry generated a low-amplitude peak at twice the rotation frequency (at ≈10 Hz), which was ignored. The power at ≈5 Hz is off scale on the plot shown here.
Fig. 2.
(a) Data for two motors on the same bacterium at 24.0°C are shown. The fully energized bacterium was monitored for ≈40 s, and then sodium azide (187 μM) was added (arrow). The cell gradually deenergized. Black points represent the speed of the latex bead (scale on the left), and gray points represent the speed of the cell body (scale on the right). (b) The data from a are plotted with fast motor speed vs. slow motor speed. Because the slow motor speed (lower x axis) is proportional to pmf, it can be rescaled to give the pmf of the cell (upper_x_ axis). The regression line was constrained to pass through the origin.
Fig. 3.
(a) Data from five bacteria at 24.0°C were plotted on the same graph and marked with different symbols (with the data for the cell of Fig. 2 shown as filled circles). The regression lines were not constrained. The initial speeds of the cell bodies were 2.7, 4.7, 1.8, 3.1, and 2.8 Hz, and the initial speeds of the beads were 80, 175, 201, 233, and 271 Hz, respectively. (b) Data from the bacteria in a were plotted cumulatively by scaling the slow-speed axis to match slopes; see the text. The regression line was constrained to pass through the origin. (c) Data from six bacteria at 16.2°C were plotted on the same graph and marked with different symbols. The regression lines were not constrained. The initial speeds of the cell bodies were 5.0, 4.6, 2.6, 1.5, 2.8, and 3.2 Hz, and the initial speeds of the beads were 83, 110, 121, 130, 136, and 151 Hz, respectively. (d) Data from the bacteria in c were plotted cumulatively by scaling the slow-speed axis to match slopes. The regression line was constrained to pass through the origin.
Fig. 4.
(a) Speeds observed for objects with different frictional drag coefficients, _f_1 < _f_2 <_f_3, shown as a function of relative pmf._f_1 and _f_2 span the range of frictional drag coefficients observed at 24°C with different beads, and_f_3 approximates the frictional drag coefficient observed with different cells. (b) Idealized torque–speed curves of a flagellar motor at four different relative pmfs, Δ_p_1–Δ_p_4 = 25%, 50%, 75%, and 100%, respectively. Load lines are shown for the same three frictional drag coefficients represented in a. Because the motor runs at the speed at which the torque generated matches the viscous drag on the object spun, i.e., at the speed corresponding to the intersection of the torque–speed curve and the specified load line, the linearity of the speed curves plotted in a demands that the torque–speed curves scale linearly with pmf, as shown in b.
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