supplementary information generates more torque the … · 2016-02-02 · 1 supplementary...

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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: [email protected]

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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http://dx.doi.org/10.1038/nphys3528

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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).

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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



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





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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

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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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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

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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.





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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





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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

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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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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).

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