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SUPPLEMENTARY INFORMATION
The flagellar motor of Caulobacter crescentus generates more torque
when a cell swims backward
Pushkar P. Lele‡a1
, Thibault Rolanda
, Abhishek Shrivastavaa
, Yihao Chen and Howard C.
Berga
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
The flagellar motor of Caulobacter crescentus generates more torque when a cell swims backwards
SUPPLEMENTARY INFORMATIONDOI: 10.1038/NPHYS3528
NATURE PHYSICS | www.nature.com/naturephysics 1
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2
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).
3
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 sub-
pixel 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
2 NATURE PHYSICS | www.nature.com/naturephysics
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPHYS3528
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2
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).
3
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 sub-
pixel 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
SUPPLEMENTARY INFORMATIONDOI: 10.1038/NPHYS3528
© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved
4
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
5
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.
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SUPPLEMENTARY INFORMATION DOI: 10.1038/NPHYS3528
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4
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
5
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
SUPPLEMENTARY INFORMATIONDOI: 10.1038/NPHYS3528
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6
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
7
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 brightness-
weighted 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 ΩCW/ΩCCW ~ 1.56 +/- 0.41) consistent with our
hypothesis that motors rotate faster in the CCW direction. Since the mechanism of cell-
rotation 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.
6 NATURE PHYSICS | www.nature.com/naturephysics
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPHYS3528
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6
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
7
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 brightness-
weighted 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 ΩCW/ΩCCW ~ 1.56 +/- 0.41) consistent with our
hypothesis that motors rotate faster in the CCW direction. Since the mechanism of cell-
rotation 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
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8
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 cell-
body 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 CWbias
9
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 CWbias 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
8 NATURE PHYSICS | www.nature.com/naturephysics
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPHYS3528
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8
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 cell-
body 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 CWbias
9
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 CWbias 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
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10
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 nc). 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
11
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.
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10
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 nc). 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
11
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.
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12
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).
13
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 right-
handed 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).
12 NATURE PHYSICS | www.nature.com/naturephysics
SUPPLEMENTARY INFORMATION DOI: 10.1038/NPHYS3528
© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved© 2015 Macmillan Publishers Limited. All rights reserved
12
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).
13
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 right-
handed 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
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