Bacteria exploit a polymorphic instability of the flagellar filament to escape from traps

S. putrefaciens CN-32 is a bacterium with a primary single polar flagellum and additional lateral flagella that are implicated in realignment of the cells during swimming (30, 31). To concentrate on the role of the main polar flagellum, we used an S. putrefaciens CN-32 strain, which we genetically engineered to not produce the lateral flagellum by deleting the corresponding flagellin-encoding genes. To visualize flagellar filaments by fluorescence microscopy, we genetically introduced threonine-to-cysteine substitutions into the environment-exposed surface of the two flagellins, the building blocks of the filament, which were then used for the ligation of maleimide-ligated fluorescent dyes. Details of the strain constructions are given in SI Materials and Methods. To create a suitable structured environment that enables microscopic recordings of swimming cells, we used an agarose surface that was overlaid with a sample of medium containing an appropriate dilution of cells with fluorescently labeled flagella. A coverslip was added on top so that the liquid-covered uneven surface of the agarose provided a structured environment with varying distances between agarose and the glass surface (Fig. S1).

Fluorescence imaging revealed that the polar flagellum of S. putrefaciens CN-32 is on average ∼6.5 µm in length and exhibits a left-handed helical structure (diameter, 0.6 µm; pitch, 1.9 µm), which mediates forward and backward swimming upon CCW and CW rotation, respectively. Free-swimming cells displayed the expected “run–reverse–flick” motility patterns (30), whereas cells that got stuck between the glass coverslip and the agarose surface showed flagellar rotation without spatial propagation. In an effort to escape the trap, cells alternated between CCW and CW rotation of the motors. In cases where these changes in flagellar rotation did not suffice to free the cell, we frequently noticed that the flagellar filament eventually wrapped around the cell body, forming a spiral- or screw-like large helix (Fig. 1, Movie S1, and Dataset S1). This behavior was often accompanied by a backward translation of the cell body in a screw-like motion for up to several seconds. Notably, during this backward maneuver, the general orientation of the flagellar helix relative to the substratum did not change while the cell moved through the spiral formed by the flagellum (Fig. 2A and Movie S2). Once the cells had escaped the narrow passage, the motor reversed direction and the filament unwound the spiral to resume its normal helicity and position behind the cell, which then continued moving by normal forward swimming. Some cells could not escape by this mechanism and alternated between the two positions of the filament without moving the cell (Movie S3).

Because immobilizing the cell body increases the forces acting on the flagellar filament (32), we explored the possibility to trigger the transition also during free swimming by increasing the viscosity and hence the drag on the cell. To this end, we monitored cellular movement and position of the flagellar filament of free-swimming cells in media supplemented with increasing amounts of Ficoll to enhance the viscosity (33). In Ficoll-free media, we observed almost no cells with filaments wrapped around the cell body (Fig. 3). However, with increasing Ficoll concentrations, the number of cells displaying screw formation increased significantly to more than 74% of the population for Ficoll concentrations up to 25% (Fig. 3). The flagellum wrapped around the cell body rotated in CW direction. This suggests that the forces on the cell and the flagellar filament induce the formation of the spiral around the cell. At 10% Ficoll, the cells with the filament wrapped around the cell body moved slowly at about 5 µm/s, which is barely above the general background diffusion of immobile cells caused by Brownian motion and general drift (∼3 µm/s), but significantly slower than cells that were still pushed or pulled by the flagellar filament (both at ∼16 µm/s). Moreover, the flagellum moved around the cell body without efficient translation (Fig. 2B and Movie S4). In contrast, for cells near surfaces, the flagellar helix maintained a fixed location relative to the surroundings and the cell (Fig. 2A and Movie S2). We therefore propose that the propagation relies on an interaction between the flagellum and asperities on a surface, while continuous rotation of the flagellum around its molecular axis by the motor prevents strong binding. Thus, the screw-like state allows a backward movement of cells across surfaces or through appropriately structured environments but is not effective under free-swimming conditions with increased viscosity.

The effects of Ficoll are to slow down the motion of the flagellum and to increase the drag forces (32, 34). We therefore used Ficoll-supplemented medium on agarose surfaces to reduce the speed of the rotating flagellar filament, allowing us to obtain sufficient temporal resolution to monitor its motion and morphology during formation and release of the large helix around the cell body (Fig. 4, Fig. S2, Movie S5, and Dataset S2). Flagella of stuck cells rotating in CCW direction generally maintained the left-handed helical shape; however, diameter and pitch varied dynamically, indicative of flagellar filament polymorphism. When the rotational direction switched to CW, the flagellar helix quickly became unstable.

To gain more insight into the origin and the dynamics of the transition, we implemented an established model for the flagellum as an elastic rod coupled to the fluid through resistive force theory (35, 36). The elastic forces acting on the filament come from changes in the shape of the filament, from the interaction between segments of the filament and between filament and cell body. They are represented by free energies and local interaction potentials. Different polymorphisms of the flagellum can be implemented by switches in the equilibrium parameters and the requirement that the local minimum of the free energy is chosen, as shown for E. coli in refs. 37 and 38. The crystal structure of the S. putrefaciens CN-32 flagellar filament will be different from that of well-studied organisms like E. coli. However, we anticipate that its general mechanical properties and the different polymorphisms will not differ significantly, as the S. putrefaciens sequence and deduced structure is very similar to that of Salmonella in all five α-helices that constitute the polymorphic structural part of the filament (Fig. S3A). From our observations, we can deduce at least two equilibria, one for a stretched-helix flagellum typical during normal swimming, and one for the coiled state when the flagellum is wrapped around the cell body. For the frictional forces, we use resistive force theory, which characterizes the forces on the segments by three local friction coefficients, one each for motion perpendicular to the flagellums centerline, for motion along the centerline, and for rotations around the centerline. No measurements of the various parameters have been reported thus far, so we adopted values obtained for E. coli. Although some uncertainty about the precise values for the elastic constants and the presence of other morphologies during the transition remain, numerical simulations for several different parameter choices show that the qualitative features of the flagellar dynamics are insensitive to the details of the parameter choice. The full set of equations and the complete list of parameters values are given in SI Materials and Methods.

Close to the cell body we have to take the driving and the increased flexibility of the filament in the hook region into account. Because the hook region itself is not resolved in the numerical simulations, we model its properties by the boundary conditions. The flagellum’s rotation is driven by a constant motor torque. The angle under which the filament leaves the cell surface is not prescribed, accounting for the fact that the bacterial hook is much more flexible than the flagellum (24). The torque applied by the motor is split into a component parallel to the axis of the motor, and one parallel to the filament, with a parameter that controls the relative contributions. Formation of the screw was reliably observed when 10–50% of the torque acted along the centerline of the filament.

The motion of the flagellum with two different morphologies is shown in Movies S5 and S6, and the snapshots in Fig. 4. Both model and observations show that, when initiated with a left-handed spiral rotating CCW, the flagellum pushes the bacterium along. When increasing the torque on the cell, the flagellum begins to move sideways, as also observed in Movie S1 and in Fig. 1 (frames 2 and 3). Upon switching to CW rotation, the flagellum begins to pull on the bacterium. As the forces on the filament increase, the first loop of the helix above the motor is stretched and bends around toward a right-handed helix. In elastic filaments, such transitions in helicity under stress are known as “perversions” (39). Here, however, the formation of the perversion is not completed. Instead, the flagellum switches to another equilibrium shape reminiscent to the left-handed coiled forms observed for the E. coli flagellum (11, 13). The orientation of the filament, deduced from the direction of the tangent along filament, which initially points away from the cell, locally changes direction and points toward the cell. This induces a force on the upper part of the flagellum that pulls it toward the cell and the flagellum begins to wrap around the cell body. Because the formation of the perversion and the transition to a right-handed helix is not completed, the filament remains a left-handed helix.

The instability discovered and described here is different from the buckling instability described by Son et al. (24) and Xie et al. (25). They showed that the hook region buckles when the bacterium switches from a backward pull to a forward push: During the pull, the flagellum is stretched, but during the push, it experiences a strong compression, which, combined with the high flexibility of the hook region, triggers the buckling instability and the directional change. The instability described here occurs during the pulling phase, where the flagellum is stretched, and the motor forces push toward a right-handed helix. During normal swimming, when the cell body is free to rotate, the instability is avoided because the applied torque is reduced by the counterrotation of the cell body (32). When the bacterium is stuck, or the friction on the cell body is enlarged by an increase in viscosity, the full torque of the motor acts on the flagellum and triggers the transition to the screw-like state. The transition might also be assisted by an increase in torque due to the acquisition of additional motor proteins, which has been shown to occur under conditions of high load on the flagellum (40, 41).

All strains used in this study are listed in Table S1. Escherichia coli strains DH5α-λpir and WM3064 and Shewanella putrefaciens CN-32 were grown in LB medium at 37 and 30 °C, respectively. Cultures of the 2,6-diaminoheptanedioic acid (DAP)-auxotroph E. coli WM 3064 were supplemented with DAP at a final concentration of 300 µM. To solidify media, LB agar was prepared using 1.5% (wt/vol) agar. For soft-agar plates, 0.2–0.3% (wt/vol) agar was used. Whenever necessary, media were supplemented with 50 mg/mL kanamycin, 50 µM phenamil, and/or 10% (wt/vol) sucrose. Agarose pads for microscopy were prepared by solidifying LM100 medium [10 mM Hepes, pH 7.3; 100 mM NaCl; 100 mM KCl; 0.02% (wt/vol) yeast extract; 0.01% (wt/vol) peptone; 15 mM lactate] with 1% (wt/vol) agarose.

All genetic manipulations of S. putrefaciens CN-32 were introduced into the chromosome by sequential double homologous recombination using the suicide vector pNPTS138-R6K essentially as described previously (44). Plasmids and corresponding oligonucleotides are summarized in Tables S2 and S3, respectively. All kits for preparation and purification of nucleic acids (VWR International) and enzymes (Fermentas) were used according to the manufacturers’ protocols. Plasmids were constructed using standard Gibson assembly protocols (45) and introduced into Shewanella cells by conjugative mating with E. coli WM3064 as donor. In-frame deletions were generated by combining ∼500-bp fragments of the upstream and downstream regions of the gene to generate a deletion leaving only a few codons of the designated gene. Gene versions encoding flagellins bearing threonine-to-cysteine substitutions were reintegrated into those deletion strains in basically the same fashion. The design of these substitutions is described in detail below. As a background strain, we used S. putrefaciens CN-32 S2576 lacking the ability to produce lateral flagella due to deletion in the genes encoding the secondary flagellin subunits (31).

To visualize the flagellar filaments, maleimide-ligated dyes were coupled to surface-exposed cysteine residues, which were specifically introduced into the flagellins, FlaA and FlaB, of the S. putrefaciens CN-32 polar flagellum. However, the flagellins of the close relative S. oneidensis MR-1 were shown to be modified by O-linked glycosylation via threonine or serine residues. Single substitutions of the corresponding residues resulted in a clearly visible shift in the protein’s position when separated by polyacrylamide electrophoresis (PAGE) due to loss of the modification (49). We therefore performed a similar Western immunoblot analysis on the S. putrefaciens CN-32 flagellins bearing the serine- and threonine-to-cysteine substitutions to rule out that a functionally important modification was lost by the substitution. To determine potential differences in the molecular mass of flagellin protein, lysates from exponentially growing LB cultures were obtained for Western blot analyses by harvesting cells corresponding to an OD₆₀₀ of 10 by centrifugation, resuspending in sample buffer (50), and heating at 95 °C for 5 min. After separation by SDS/PAGE using 15% (wt/vol) polyacrylamide gels, the proteins were transferred to a nitrocellulose Roti-PVDF membrane (Roth) by semidry transfer. For detection of flagellins FlaA1 and FlaB1, polyclonal antibodies were used that were raised against the N-terminal conserved region of Shewanella oneidensis MR-1 FlaB (Eurogentec Deutschland) in the dilution of 1:500. Anti-rabbit IgG-horseradish peroxidase antibody (Thermo Fisher Scientific) was used as secondary antibody at a dilution of 1:20,000. For signal detection, the membranes were incubated with SuperSignalH West Pico Chemiluminescent Substrate (Thermo Scientific) and documented using the CCD System LAS 4000 (Fujifilm). The S. putrefaciens CN-32 flagellins were detected at a position corresponding to a molecular mass of ∼37 kDa (FlaA1) or ∼35 kDa (FlaB1) and thus significantly higher than the estimated molecular mass (∼28.5 kDa for both FlaA1 and FlaB1), strongly indicating that both FlaA1 and FlaB1 are decorated by modifications. No mass shifts were detected for the flagellins harboring the cysteine substitutions, demonstrating that no modified serine or threonine residues were lacking (Fig. S3).

Images of the flagellar helix, in regular or in screw mode, show a different pattern depending on the z position of the focal plane (51). An image taken of a left-handed helix appears to be left-handed when the focal plane is above the cell. However, when the focal plane is below the cell, the helix appears right-handed. This is due to the image of the cell body, which always seems to be below the focal plane, although it might be above the focal plane. To determine the handedness properly, the focal plane was slowly shifted through the cell body to reliably localize the cell body and to determine whether the flagellar helix continues upward or downward. In this study, this was done for 115 cells with normal flagellar filament and 108 cells with filaments in screwing mode using cell cultures with fluorescently labeled flagellar filaments (not or slowly rotating). The regular flagellar helix, aligned with the cell axis, was found to be left-handed. The flagellar helix wrapped around the cell body was also found to be left-handed. Because the appearance of the handedness of the flagellar helix depends on the z position of the focal plane and the image from the microscope is inverted technically, the microscopic images and movies were inverted appropriately, as stated in the legends, so that the visible handedness matches the true handedness of the flagellar helix.

Calculations were carried out in R, version 3.3.2, unless stated otherwise. Two-sided testing was used for all tests. The swimming behavior of the double flagellin-labeled strain (S4401) in medium with increased viscosity was investigated by supplementing LM medium with Ficoll 400 and recording multiple videos in bulk medium for each Ficoll 400 concentration from 0 to 25%, corresponding to 2, 5, 10, 18, and 33 cP (52). The experiment was repeated three times with always about 100 counted cells per concentration, resulting in a total of at least 300 counts. Only backward swimming was considered, and we determined whether it was regular backward swimming (flagellar filament behind the cell body aligned with the cell axis) or screw mode (flagellar filament wrapped around the cell body). Significance was tested pairwise using the Fisher’s exact test of independence (P < 0.05, Bonferroni corrected). The 95% confidence intervals were calculated with the exact binomial test.

These videos were also used to measure forward, backward, and screw swimming speed using the MTrackJ, version 1.5.1, plugin in the ImageJ distribution Fiji (48). For each swimming mode, 105 tracks were evaluated. Significance was tested using a two-sample t test (P < 0.01, Bonferroni corrected). Mean, SD, and 95% confidence intervals were calculated in Microsoft Excel 2013.

To determine swimming speeds and time between reversals, nine videos (three biological replicates with three technical replicates each) were recorded for each strain (S2576 and S4401) as described above. Cell tracks were obtained to measure the speed of individual cells as well as the total swim time. For calculating the mean of the swimming speeds, the track data were randomized and excess data were deleted to match the sample size of the comparative strain (598 for each strain). A two-sample t test was used to test significance (P < 0.05). Although both datasets were not perfectly normally distributed but slightly skewed to the left, the test should be reliable as both datasets show very similar distribution. Mean, SD, and 95% confidence intervals were calculated in Microsoft Excel 2013.

Cell tracks were examined manually to count reversals. The average time between reversals was calculated for each biological replicate using the total swim time. Therefore, the sample size is only three, and normal distribution could not be tested. Significance, mean, SD, and 95% confidence intervals were calculated similarly to swim speed calculations.

The numerical simulations are based on equations for an elastic rod and resistive force theory (35, 36), extended to allow for multiple polymorphic equilibrium states (38). The position along the rod is measured by the arclength s and the torsional state of the rod at position s is described by the rotational strain vector Ω(s). The flagellum is assumed to have a circular cross-section and a helical rest state, characterized by a vector ${\mathbf{\Omega }}_{\mathbf{0}}=\left(0,{\kappa }_0,{\tau }_0\right)$. The curvature κ₀ and torsion τ₀ are related to the helix radius R and pitch P by the following:Deviations from this rest state give quadratic contributions to the free energy:where A is the bending and C is the torsional rigidity.

The polymorphic states of the flagellum can be characterized by their equilibrium helical parameters ${\mathrm{\Omega }}_0=\left(0,{\kappa }_0,{\tau }_0\right)$. Transitions between the states are obtained by local minimization of the free energies for the different polymorphic states (38). From the observations, we can unambiguously deduce only two states, one corresponding to the initial helix during swimming, and the other to the state with the flagellum wrapped around the cell. Further states could be added as well, but without independent evidence for their existence and parameters, their addition has an element of arbitrariness. We label the two conformational states S for the stretched rest state and C for the coiled state around the cell. For each state, the curvature ${\kappa }_0^{S,C}$ and torsion ${\tau }_0^{S,C}$ are related to the helix radius $R_{S,C}$ and pitch $P_{S,C}$ by Eq. S1. For the quadratic deviations, we take the same elastic coefficients A and C, because we do not have independent numbers for the different equilibrium states. The flagellum is assumed to relax locally to the configuration with minimal free energy:with ${\delta }_C$ indicating the energy difference between coiled and stretched state.

To control the amount of stretching of the flagellum, a global harmonic spring potential is added:with an elastic constant that keeps the variations in length within 0.1%.

The elastic forces follow from variational derivative $\delta \mathrm{ℱ}/\delta r$ of the combined functional ${\mathrm{ℱ}}_K+{\mathrm{ℱ}}_S$. In the numerical representation, the flagellum is divided into N discrete segments that are characterized by a position ri and a local tripod of unit vectors [f⁽ⁱ⁾, v⁽ⁱ⁾, u⁽ⁱ⁾] to keep track of the torsional state of the flagellum. The points are distributed uniformly along the flagellum, so that each segment has a length h = L₀/N, where L₀ is the contour length of the flagellum. The unit vectors u are related to the positions by ${\mathbf{u}}_i=({\mathbf{r}}_{i+1}-{\mathbf{r}}_i)/|{\mathbf{r}}_{i+1}-{\mathbf{r}}_i|$. The vectors fi for the initial helix configuration are obtained from the relation ${\mathbf{f}}_{\mathbf{i}}=({\mathbf{u}}_{i-1}\times {\mathbf{u}}_i)/\text{sin}\left({\theta }_i\right)$, where θi is the angle between segment i − 1 and i. For each time step of the simulation, fi is adjusted following the procedure proposed by Chirico and Langowski (53). The tripod is completed with the vector ${\mathbf{v}}_i={\mathbf{u}}_i\times {\mathbf{f}}_i$.

The local strain Ω for each segment is calculated according to the following:where ${\varphi }_i$ is the local twist angle,The derivative of the free energy for the stretching force is obtained analytically, so that, for instance, the force acting on segment i is given by the following:whereas the derivatives of the free energy corresponding to bending and twisting forces are calculated by finite differences.

The flagellum’s rotation is driven by a constant motor torque M₀, applied to the first segment. To account for the effects of the bacterial hook, which is much more flexible than the flagellum (24), this segment is allowed to rotate freely and thereby transmit the torque to the following segments. The dynamics of the motor segment are described by the following:where the total torque is split between a component parallel the axis of the motor ${\mathbf{M}}_0^z=M_0(\sqrt{1-{\alpha }^2{\text{sin}}^2{\varphi }_m}-\alpha \text{cos}{\varphi }_m){\mathbf{e}}_z$, and one parallel to the first segment, ${\mathbf{M}}_0^u=\alpha M_0{\mathbf{u}}_1$, with the parameter α controlling the relative contributions. ${\varphi }_m$ is the angle between the tangential motor segment u₀ and the first filament segment u₁. Finally, µ₀ is the motor segment’s self-mobility, which depends of the rotational and the translational friction. The boundary conditions on the final segment are that no external torque is applied so that it is torque free.

In addition to the elastic forces, we have to model the interactions with the cell body, and also between segments of the flagellum, because the deformations become very large and parts of the flagellum come into mechanical contact. The cell body is modeled as a cylindrical object of radius R_cell = 0.45 µm that is sufficiently long that the flagellum does not pass underneath it. In the images, a length H_cell = 3 µm is shown. The flagellum is assumed to be 20 nm thick, and distances between approaching segments are computed following a procedure proposed by Adhyapak and Stark (54). In both cases, the repulsion between the segments of the flagellum and other segments or the cell body was modeled with a Lennard-Jones–type potential, truncated at its minimum, so that the forces vary continuously,where r_m is either the cell radius or the radius of the filament and is the strength of the potential.

For the frictional forces, we use resistive force theory (36). The local motion of the flagellum’s segments is characterized by three local friction coefficients (36) that depend on the geometry of the flagellum:is the friction coefficient for motion perpendicular to the flagellum’s centerline, where η is the viscosity, $r_f$ is the radius of the filament, and $l=\sqrt{4{\pi }^2{R}^2+P^2}$ is the contour length of one helical turn. The tangential friction coefficient is as follows:and the friction encountered by the filament during rotation is characterized by the following:The friction coefficients and the mobilities µ_t and µ_r that enter in the equations of motion are related by the following:and µ_r = 1/γr. The translational equation of motion for segment i is then obtained from the elastic forces Fel (2, 3) the stretching force Fs (8) and the repulsive forces Fc and Ffl, resulting from filament–cell and filament–filament interactions (10):The change in the torsion angle ${\varphi }_i$ of segment i depends on the elastic torque Mel only:To achieve high accuracy while keeping the computational costs down, the equations of motions were integrated using the Cash–Karp method (55), a high-order Runge–Kutta integrator with embedded error estimation and steps size control. During each partial integration step, the segment positions are updated according to $r_i(t+h_t)=r_i\left(t\right)+h_t{v}_i$, where and h_t is the partial step size. Using the new positions and velocities ${\mathbf{v}}_i=\partial {\mathbf{r}}_i/\partial t$, the attached tripods are aligned in a second step, following the procedure proposed by Chirico and Langowski (53).

As initial conditions for the simulations, we took a left-handed helix with P^S = 1.91 µm and R^S = 0.315 µm in accordance with observations, resulting in τ^S = 1.59/µm and κ^S = 1.64/µm. We adapted the helix parameters of the second state to the parameters of the screw, namely, R^C = 0.473 µm and P^C = 1.44 µm. The contour length of the flagellum was set to Lc = 6 µm, corresponding to two helical turns. The discretization length is h = 0.15 µm, comparable to the values taken by Vogel and Stark (35). For the elastic constants, no direct measurements of A and C have been reported so far. Although the flagellum’s crystal structure differs from that of well-studied organisms like E. coli, we anticipate that its mechanical properties will not differ significantly from that of E. coli, and hence choose the values A = C = 3.5 pN⋅µm² in accordance to values obtained by Darnton and Berg (16). We also explored values between A = C = 2.5 pN⋅µm² and A = C = 4 pN⋅µm² to study the influence of the rigidity on the screw formation, without noting significant differences. The various parameters in the model for the flagellum and their values are summarized in Table S4.

To probe the effects of the polymorphic transitions, we also did simulations with a single equilibrium configuration. They also show the formation of the screw, but require stronger torque and need more time to wrap the flagellum around the cell. We anticipate that further polymorphic states will similarly assist the formation of the screw but will not bring about qualitative changes.

Bacterial strains and plasmids are summarized in Tables S1 and S2. Construction of plasmids and genetically modified strains of S. putrefaciens CN-32 was essentially carried out as previously described (44, 45). Detailed information on strain construction, growth conditions, and media is provided in SI Materials and Methods.

To visualize the flagellar filaments, maleimide-ligated dyes were coupled to surface-exposed cysteine residues, which were specifically introduced into the flagellins, FlaA and FlaB, of the S. putrefaciens CN-32 polar flagellum as previously described (46, 47). A number of motility controls ensured that the modification did not negatively affect cell motility (SI Materials and Methods). Cells of an exponentially growing LB culture (OD₆₀₀, 0.6) were harvested by centrifugation (1,200 × g, 5 min, room temperature) and resuspended in 50 µL of PBS. For all cell-handling steps, the tip of the pipette tip was cut to prevent shearing off flagellar filaments. A volume of 0.5–1 µL of Alexa Fluor 488 C5 maleimide fluorescent dye (Thermo Fisher Scientific) was added, and the cell suspension was incubated in the dark for 15 min. Cells were sedimented again and carefully washed once with 1 mL of PBS to remove residual unbound dye. After final resuspension in LM100 medium in an appropriate volume (usually to reach a final OD₆₀₀ of 0.2), the cells were kept shaking in the dark until microscopy, but never longer than 1 h. If necessary, LM100 medium was supplemented with Ficoll 400 for final resuspension. Ficoll 400 was always diluted to the appropriate concentration from a 50% (wt/vol) stock solution in LM. After coupling of the maleimide fluorescent dye, the cells were carefully washed before microscopic analysis.

For microscopy in bulk medium (always about 100 µm away from the glass surface), a 250-µL aliquot was loaded on a swim slide [coverslip fixed on a microscope slide by four silicone droplets (Baysilone; VWR International) to generate a space of about 1 mm]. For microscopy in structured environments, a 1- to 3-µL aliquot was spotted on an agarose slide and topped with a coverslip before the liquid was taken up by the agarose surface. Agarose slides were made by pipetting hot LM100 medium with 1% (wt/vol) agarose between a microscope slide and a coverslip, both separated by two microscope slides as spacers. After solidification, the coverslip and both microscope slide spacers were removed, leaving an uneven surface on the microscopic scale (Fig. S1). Movies were taken at room temperature at a custom microscope setup (Visitron Systems) with a Leica DMI 6000 B inverse microscope (Leica) equipped with a pco.edge sCMOS camera (PCO), a SPECTRA light engine (lumencor), and an HCPL APO 63×/1.4–0.6 objective (Leica) using a custom filter set (T495lpxr, ET525/50m; Chroma Technology). Usually, 200–500 frames were taken with an exposure time of 5 ms as a compromise between temporal resolution and optical contrast. Image processing and analysis were carried out using the ImageJ distribution Fiji (48). Cells were counted using the cell counter plugin, and swimming-speed measurement was done using the TrackMate (semiautomatic) or MTrackJ (manual) plugin. Details on the statistical analysis can be found in SI Materials and Methods.

The equations, potentials, parameters, and method of integration for the numerical simulations are given in SI Materials and Methods.