The flagellar motor of Caulobacter crescentus generates more torque when a cell swims backwards Pushkar P. Lele a1, Thibault Roland a, Abhishek Shrivastava a, Yihao Chen and Howard C. Berg a Affiliations: Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station TX 77843-3122 a Department of Molecular and Cellular Biology, Harvard University, Cambridge MA 02138. 1 Corresponding Author. Pushkar P. Lele, Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station TX 77843-3122. Tel: 979 845 3363, Fax: 979 845 6446, email: plele@tamu.edu NATURE PHYSICS www.nature.com/naturephysics 1
Fluid joint The fluid joint is likely made up of the polysaccharide that covers the entire cell in Caulobacter crescentus. Consistent with this, cells were observed to tether near the poles as well as near the center of the body. In the data we selected and analyzed, the tether point was predominantly observed near the flagellar pole (the pole at which the flagellum is located). In ~ 10% of the cells, the point of tether was near the center of the body. The speeds of cell-rotation in the two directions were dissimilar irrespective of the type of tether-geometry. Variations in hydrodynamic drag due to changes in tether location The hydrodynamic drag on the cell body could vary with direction of rotation if the location of the tether changed with direction. To determine if the center of rotation shifted substantially during CW and CCW rotation of the same cell, we analyzed single cell traces (Fig. S1a). For each cell, we separated the frames corresponding to the two intervals (CW and CCW). Each batch contained a single interval and we ensured that the intervals in either direction had a minimum of 5 full turns of the cell body. A single, averaged image of the rotating cell body was generated from each batch. The bright spot (with a 2D Gaussian profile) in the averaged image indicated the center of rotation for the corresponding interval (Fig. S1b, top). The corresponding 1D profiles for the respective centers of rotation for the two directions appear to superimpose (Fig. S1b, bottom). 2 NATURE PHYSICS www.nature.com/naturephysics
Supplementary Figure S1. Tether position on the cell body a) Separation of frames in single intervals in which the cell rotates CW and CCW. b) Calculated average images from the two batches of frames (top). Corresponding 1D intensity profiles (bottom). c) Relative speeds versus calculated deviation of the center of rotation in the two directions. To accurately determine the centers of rotation in the two images, we used standard particle tracking algorithm based on centroid-detection that is capable of subpixel accuracy 1. The accuracy was ~ 15 nm on our setup. The absolute deviation in the tether location in the two directions for each cell, and the corresponding ratio of CW to CCW rotation speeds is shown in Fig. S1c. There is no significant correlation (Pearson s ρ = 0.27, p-value = 0.22 for the hypothesis of no correlation). The deviations in centers NATURE PHYSICS www.nature.com/naturephysics 3
of rotation in the two directions were on an average 60 nm (n = 17 cells). Since the cell body is ~ 2 µm in length, such minor deviations in the center of rotation do not contribute to more than 10% variation in the hydrodynamic drag in the two directions. Properties of fluid joint A) Elastic response To determine if the fluid joint contributed to any kind of unwinding/winding that progressively made it difficult for the cell to rotate in any particular direction, we analyzed the long time traces of cell-rotation. A representative trace is shown in Fig. S2a and b. Trends that could indicate a winding effect (which would progressively slow down or speed up cell-rotation in a given direction) are absent over long times (~100 s) and short times (~ 1 s). At shorter time-scales (a few ms), it is not possible to differentiate between the internal switch dynamics (the molecular switch that switches rotor conformation between the clockwise and counterclockwise conformations) and tether dynamics. However, the two effects can be discriminated against by analyzing the behavior of a tethered cell in which the motor stops rotating* after a short while. In such cases, if the tether was winding up during cell-rotation, the stored potential energy would be released once the driving force disappeared, causing the cell to rotate in the opposite direction (that is a switch from one direction to the other) with decreasing speeds over a short time. The higher the potential energy stored due to winding, the higher the magnitude of unwinding speeds. We conducted experiments to determine if the fluid 4 NATURE PHYSICS www.nature.com/naturephysics
joint exhibited such elastic responses. One such cell can be seen in movie 3. No significant unwinding was observed when rotation stopped. Instead, the cell appeared to undergo Brownian rotation, as expected. We analyzed this and other cells for any signs of unwinding. The average trend in rotational speed (when CCW cells stopped rotating) is shown in Fig. S2c. The arrow points to the time-instants when different cells all stopped rotation (green curves are for 5 such instances from 3 cells, black curve is averaged data). There was no measurable, reproducible evidence that showed a jump from positive speeds to negative speeds, followed by a gradual decay to zero speeds. Note that two time-points on this plot are separated by 15 ms. Clearly, unwinding if any, is negligible. The same was observed for the other direction, that is, for CW cells that stop rotation (not shown). *It is possible to tell when a motor stops by observing the filament, which appears as a bright rod of light during rotation (due to the limited acquisition rates) but appears as a helix when rotation stops. NATURE PHYSICS www.nature.com/naturephysics 5
Figure S2 Elastic response of the tether a) Single-cell raw data. There is no long-time trend in the data such as a gradual reduction or increase in speed. b) First 14 s of the same data. No apparent change occurred over short times either. c) Behavior of cells that stopped rotating at the time indicated by the blue arrow. Raw data (green, n = 5) and average (black curve). As is evident, there is no unwinding effect (see movie 3 also). B) Viscous resistance to rotation Some cells were observed to tether via the fluid joint in a manner that enabled them to remain approximately perpendicular to the surface, irrespective of the direction of rotation (see movie 4, slowed by a factor of 7x). Such occurrences were rare (~1% of total data) since most cells exhibited the kinds of trajectories shown in Fig. 1a and b (main text). In these perpendicularly-oriented cells, the filaments pointed away from the surface (Fig. S3a). We selected a small dataset in which the deviation in the apparent radius of rotation in the focal plane (Fig. S3a) was < 100 nm between the two 6 NATURE PHYSICS www.nature.com/naturephysics
rotational directions. For such small deviations, the hydrodynamic drag is not expected to vary by more than 5%. Because these cells rotated at faster speeds (20-60 Hz), the images were recorded at 300-350 Hz and the rotation frequencies were calculated as before. Upright cells have a Gaussian intensity profile in the focal plane similar to polystyrene beads, and hence we applied algorithms that calculate the brightnessweighted centroid to determine the center of the particle image in each frame. The speeds of rotation were calculated from particle positions. The frequency of rotation of one such cell is shown in Fig S3b. The cell rotated about 1.64 times faster in the CW direction. Here, the body counter-rotated due to motor-rotation. Filament interactions with the surface were not relevant, since the filament was not close to the surface. The inversion in body rotation was preserved CW rotation of the cell was caused by CCW rotation of the motor. A similar anisotropy was observed in five other cells (average Ω CW /Ω CCW ~ 1.56 +/- 0.41) consistent with our hypothesis that motors rotate faster in the CCW direction. Since the mechanism of cellrotation reported here is different from that seen in Fig. 2 (main-text), these results represent an independent test of the speed anisotropy. Also, the absolute speeds observed here are similar in magnitude to the counter-rotation speeds of swimming cells observed by Liu and co-workers (~160-320 rad/s). This suggests that the resistance offered by the fluid joint to cell-rotation is negligible. NATURE PHYSICS www.nature.com/naturephysics 7
Figure S3. Independent test of torque-anisotropy a) A cell that is approximately perpendicular to the surface when rotating in either direction. The apparent radius of rotation in the focal plane is indicated by the colored line (see movie 4). The cell appeared as a bright, circular spot in the imaging plane. b) Representative data for counter-rotation frequency of a cell with geometry indicated in a). Cell-rotation speeds were similar to the counter-rotation speeds observed for freely swimming cells. Measurements at high viscous loads We irreversibly tethered the cysteine-mutant filaments to maleimide-coated glass surfaces. Due to such tethering, the cell body oriented perpendicular to the glass surface, irrespective of the direction of rotation. In such geometry (also seen in the schematic in Fig. 1a, gray cell), there is no inversion between cell and filament rotational directions, and the true direction of motor rotation is the same as the direction of cellbody rotation. Since the flagellum is tethered to the surface, the motor is under a high viscous load due to the size of the object it rotates (the cell-body). The average CW bias 8 NATURE PHYSICS www.nature.com/naturephysics
at such high loads was ~ 0.85 (Fig S4a), similar to that measured under medium viscous loads (Fig. 3d, main text). On the other hand, the ratio of the absolute speeds of motor rotation in either direction was found to be ~ 1 (Fig S4a). This is similar to the motors in E. coli which spin at similar speeds regardless of the direction of rotation at very high loads 2 (Fig S4b). Figure S4. Anisotropy in speed as a function of viscous load a) The CW bias and the ratios of cell-rotation speeds (n = 5 motors), when the flagellar filament is irreversibly tethered to the surface (high viscous loads). b) Ratio of CCW to CW motor speeds vs. viscous loads in E. coli 2. Alternate cell rotation mechanisms A) Differences in filament shapes Differences in cell-rotation speeds, such as those observed in Fig. 2c (main text), could potentially arise due to polymorphic transformations of the kind observed in NATURE PHYSICS www.nature.com/naturephysics 9
filaments in E. coli when motors switch between CW and CCW 3,4. To determine if such changes in filament shape are indeed present in C. crescentus, we imaged fluorescently labeled filaments in swimming cells. The filaments rotate several times faster than our camera capture rate and thus, every filament appears as 2D projection of a cylinder of light (a bar with a finite thickness). The amplitude or the radius of the helical waveform (R) is approximately half of the thickness of this bar, whereas the length of the bar is a good measure of the pitch times the number of helical turns (~ λ x n c ). An example of one such swimming cell with a visible filament is shown in movie 5 (slowed 3X). Although the cell body is not visible, the direction of motion of the cell can be discerned from the motion of the filament. As seen in the movie, the cell swims along one direction and then reverses its direction. We compared the length of the visible filament before and after the cell reversed its direction of swimming. The change was minimal. Similarly, there was a negligible change in the width before and after the cell reversed its direction of swimming. The average ratio of the lengths of flagellum in the two directions, measured in such cells that switched the direction of swimming in our field of view, was 0.99 ± 0.02 (11 cells). The average ratio of the widths (amplitudes) obtained from such measurements was 0.97 ± 0.05 (Fig. S5a, 11 cells). This indicated that R and λ were unlikely to change significantly in the two modes. However, this approach suffers from a limitation that the angle of orientation of the swimmer with the focal plane may change between the two modes. Thus, minor changes in filament form (R and λ) may not be readily detectable with such an approach. However, as seen in Fig. 4b (main text), a 0-20% change in filament form does not affect the thrust generated 10 NATURE PHYSICS www.nature.com/naturephysics
significantly. In motors that were stalled, the filament form could be easily visualized using epi-fluorescence. We confirmed the accuracy of our setup by calculating the ratio of R to λ in filaments attached to such stalled motors (Fig. S5b). Our measured values (0.11± 0.01, n = 8 filaments) are consistent with previous measurements via SEM imaging 5,6. Thus, within the limits of the accuracy of our imaging setup, it appears that C. crescentus filaments are probably similar to those found in monoflagellated Vibrio alginolyticus 7,8, in the sense that filaments do not undergo a polymorphic transformation when motors change the direction of rotation. Figure S5. Filament shape versus swimming direction a) Ratios of flagellar lengths and diameters measured in cells that switch directions when swimming (n = 11 cells). b) Flagellar filaments on stalled motors visualized by fluorescence. White scale bar ~ 1 µm. NATURE PHYSICS www.nature.com/naturephysics 11
B) Differences in interactions between the filament and surface Other possible reasons for the anisotropy in tethered-cell speeds observed in Fig. 2c could involve changes in the way the filament interacts with the surface in the two modes. It is possible that certain amino acid residues on the filament surface, which lie buried in one mode, are exposed in the other mode. Then, even though the motor might spin at identical speeds in either direction, the efficiency of rotation will be different. However, we repeated our experiments by replacing the cell environment with a motility buffer containing ~ 0.067 M NaCl. The presence of salt screens out electrostatic interactions by reducing the double layer thickness to ~ 1 nm. The separation between the filament and the surface however, is likely to be several times this distance. The presence or absence of salt had little effect on the type of anisotropy in rotation speeds. Therefore, this type of mechanism is unlikely to explain our observations. Other mechanisms could involve anisotropic, direction-dependent deformations of the hook that connects the motor drive shaft to the filament, thus altering the amount of thrust developed in each mode. However, as discussed in Fig. 3c, since the sign of the torque on the cell body would depend on the relative point of tether, anisotropy in hook deformations are unlikely to explain the data in Fig. 2c (main text). 12 NATURE PHYSICS www.nature.com/naturephysics
References 1 Crocker, J. C. & Grier, D. G. Methods of digital video microscopy for colloidal studies. J. Colloid Interf. Sci. 179, 298-310, (1996). 2 Yuan, J., Fahrner, K. A., Turner, L. & Berg, H. C. Asymmetry in the clockwise and counterclockwise rotation of the bacterial flagellar motor. Proc. Natl Acad. Sci. USA 107, 12846-12849, (2010). 3 Hotani, H. Micro-video study of moving bacterial flagellar filaments.3. cyclic transformation induced by mechanical force. J Mol Biol 156, 791-806, (1982). 4 Darnton, N. C. & Berg, H. C. Force-extension measurements on bacterial flagella: Triggering polymorphic transformations. Biophys J 92, 2230-2236, (2007). 5 Li, G. & Tang, J. X. Low flagellar motor torque and high swimming efficiency of Caulobacter crescentus swarmer cells. Biophys J 91, 2726-2734, (2006). 6 Koyasu, S. & Shirakihara, Y. Caulobacter-crescentus flagellar filament has a righthanded helical form. J Mol Biol 173, 125-130, (1984). 7 Goto, T., Nakata, K., Baba, K., Nishimura, M. & Magariyama, Y. A fluid-dynamic interpretation of the asymmetric motion of singly flagellated bacteria swimming close to a boundary. Biophys J 89, 3771-3779, (2005). 8 Ping, L. Y. Cell orientation of swimming bacteria: From theoretical simulation to experimental evaluation. Sci China Life Sci 55, 202-209, (2012). NATURE PHYSICS www.nature.com/naturephysics 13