Cell-body curvature reduces stall frequency to enhance Vibrio cholerae swimming and chemotaxis through hydrogels

Abstract

The swimming motility of the bacterial pathogen Vibrio cholerae is a virulence factor that aids in breaching the mucus layer. V. cholerae has a curved cell shape, and previous work demonstrated that loss of curvature decreases infectivity. Here, we investigate the mechanism by which curvature affects single-cell motility. We compared the chemotactic performance of wild-type curved cells and straight mutants. The two exhibit similar swimming properties in liquid and viscous solutions but differ significantly in mucus-mimicking hydrogels, where curved cells demonstrate an 86% increase in chemotactic drift. Trajectory analysis indicates comparable swimming speeds, but straight mutants experience more frequent stalls, reducing total swimming time. Stalls further reduce chemotactic performance by imposing an average reorientation down the chemical gradient, regardless of cell shape. Coarse-grained molecular dynamics simulations corroborate these results across intestinal mucus hydrogel stiffnesses and identify an optimal curvature for movement through hydrogel-like meshes, close to the pathogen’s median curvature. These findings highlight cell shape’s role in pathogenicity and the need to study bacterial behaviors under conditions more closely mimicking the host environment.

Introduction

Vibrio cholerae, the causative agent of cholera, remains a global human health concern. This bacterium has a characteristic curved (“comma-shaped”) morphology and can swim by rotating a single polar flagellum. Its swimming motility has been recognized as a virulence factor^1,2, likely for allowing V. cholerae to swim through the mucus protecting the small intestine³ during the early steps of infection. This active crossing of the intestinal mucus barrier is thought to be enhanced by the ability of V. cholerae to bias its motility to climb or descend chemical gradients⁴, in a process called chemotaxis.

Two genes (crvA and crvB) have been shown to directly determine V. cholerae’s body curvature⁵. Their deletion brings its cell-body shape to a straight rod. A straight-shaped crvA mutant displayed an infectivity defect in two animal models of infection⁶. Why does the ability of V. cholerae to increase its cell-body curvature improve its infectivity? Cell shape and size are known in various other pathogens to contribute to host colonization and infection, mostly through enhanced mucus penetration, surface colonization, adhesion and immune evasion⁷. The helical shape of H. pylori, for example, has been shown to enhance penetration of viscous purified mucin solutions by improving its swimming speed⁸.

For Vibrio cholerae, given the importance of swimming motility and chemotaxis during host colonization, we aimed to test if cell-body curvature could enhance these processes. In simple liquid medium, one study demonstrated a marginal (approx. 5%) increase in swimming speed due to cell-body curvature⁹. However, the effect of V. cholerae cell shape on single-cell swimming behaviors has not been studied previously in viscous or hydrogel environments, more closely mimicking the host environment. This gap is likely due to the difficulty of collecting the large number of long single-cell trajectories necessary to resolve navigation performances, especially in complex media. Navigation performances are understood here as encompassing both swimming motility (random movement) and chemotaxis (biased movement in chemical gradients).

To meet this challenge, we made use of a recent multiscale chemotaxis assay^10,11. In this assay, single-cell behaviors are 3D tracked under a well-defined linear chemical gradient in liquid solutions, viscous media, or agar hydrogels. As no 3D tracking method currently allows tracking in real mucus, a dilute agar hydrogel was used as the main (simple) mucus-mimicking environment, owing to its hydrogel structure with pores of similar size to pores in intestinal mucus hydrogels (see SI Discussion). The assay simultaneously resolves population-scale performances (e.g., chemotactic drift speed) and how individual cells swim in order to achieve such performances. By comparing the curved phenotype (wt strain) against the straight-shaped phenotype (ΔcrvAB deletion mutant strain), we aimed to directly resolve the potential boost offered by the curved shape compared to the straight rod shape, and pinpoint which navigation properties (speed, turning rate, turning angle, stop duration, etc.) are leveraged to do so. We also developed an in-silico coarse-grained molecular dynamics model of curved or straight cells moving and rotating through a hydrogel-like mesh. By varying cell curvature and properties of the mesh, we were able to dissect the biophysical parameters that govern how effectively cells traverse crowded or obstructive surroundings, thereby complementing and extending insights gained from our experimental observations.

Results

Chemotactic performances in buffer are independent of cell-body curvature

Wild-type (wt, O1 El Tor C6706) and straight ΔcrvAB strains were grown to late exponential phase to maximize curvature of wt⁵ (Fig. 1a). High bacterial densities (yielding high curvature) correlated with a high motile fraction and fast swimming speed (SI Fig. 1a). Overall, in buffer environments, wt and ΔcrvAB strains exhibited remarkably similar swimming properties with indistinguishable chemotactic performances in a 200 µM/mm L-serine gradient.

Fig. 1. In buffer, V. cholerae C6706 str2 wild-type (wt) and its non-curved mutant ΔcrvAB show run-reverse-flick motility with similar properties.

a Phase-contrast images from 3D-tracking acquisitions (see Methods) of the two phenotypes, and the associated symbols subsequently used. Scale bars represent 8 µm. b Example 6.66-s trajectory of wt strain from 3D tracking in motility medium (M9TB), with color reflecting instantaneous speed. Turning events identified as reverses (above 150°) or flicks (under 140°) are indicated by closed circles and dotted circles, respectively, while a deceleration event during a run is indicated by a black arrow. The start of the trajectory is indicated by a grey arrow and a forward-swimming bacterium. c Example bivariate histogram of consecutive turning angles observed after versus before the same run, for the wt strain. The distribution confirms run-reverse-flick motility, where reversals can be preceded and followed by reversals or flicks, but two flicks never occur in a row. d Average swimming speed distributions of motile wt (black, 6897 trajectories) and ΔcrvAB (red, 5305 trajectories) with averages and standard deviations over three biological replicates. In trajectories where at least one run was detected, turning frequencies (e) and turning angle distributions (with error bar representing the standard deviation across n = 3 independent experiments) (f) of wt (black, 3554 trajectories) and ΔcrvAB (red, 2796 trajectories) are indistinguishable. The full characteristics of the above-analyzed biological triplicates are available in SI Table 1.

We first analyzed random single-cell motility by high-throughput 3D tracking in homogeneous liquid motility medium lacking a chemotactic gradient (M9 salts with 0,01% TB, M9TB) over three biological replicates (detailed datasets available in SI Table 1). These experimental conditions were chosen to ensure stable motility properties over at least 130 minutes (SI Fig. 1), within which all later acquisitions were made. Wt and ΔcrvAB displayed similar average swimming speed within a few micrometers per second (Fig. 1d). We applied an automated turn event detection to trajectories of at least 0.8 s and with speed over 15 µm/s (see Methods) to further analyse the random swimming properties. Both strains displayed a run-reverse-flick motility, where turning angles are characterized by a succession of reversal and flick or reversal and reversal but never two flicks in a row (Fig. 1b, c). Decelerations were occasionally visible in trajectories during runs (Fig. 1b, arrow) as previously described for V. cholerae strain O395¹². Turning frequencies and turning angle distributions were indistinguishable between the curved and the straight cell-body phenotypes (Fig. 1e, f).

Chemotaxis to L-serine was captured by a multiscale chemotaxis assay: bacteria were 3D tracked in the middle of a 200 µM/mm linear serine gradient established by pure diffusion between two reservoirs containing dilute bacteria with or without 200 µM serine in M9TB medium (Fig. 2a). From the thousands of trajectories, we found that the average swimming speed of wt is 4.2(0.6 95% CI)% higher than that of ΔcrvAB (SI Fig. 2a, b), similar to previous observations by Fernandez et al.⁹. However, this small difference did not result in any significant chemotactic advantage for the curved-cell shape over its straight-cell counterpart (Fig. 2b, c). Specifically, the populations’ chemotactic performances, defined here as their chemotactic drift velocity (average population’s displacement up the gradient due to active biasing of its motility), showed no significant difference between wt and ΔcrvAB (Fig. 2b, c). On average, the chemotactic drift of the straight-shaped population was 103(±7 95%C.I.)% that of the curved one over ten replicates.

Fig. 2. Population-scale chemotactic performances in buffer and mucus-mimicking media.

a Schematic of the multiscale chemotaxis assay (see also Grognot et al.^10,11). Bacteria are 3D tracked in the middle of a microfluidic channel (blue box) where a linear serine gradient is established by diffusion between two reservoirs with equal bacterial concentrations, but with or without 200 µM L-serine. The chemotactic drift of the population is its net speed up the 200 µM/mm serine gradient, computed as the average of all signed instantaneous velocity components along the gradient direction. b Comparison of chemotactic drift velocity of curved wt against non-curved ΔcrvAB mutant in buffer (black, n = 10), viscous polymer PVP K90 (purple, approx. 38 centipoises, n = 5), or soft agar hydrogels (green, n = 7, 0.19–0.21% (w/v)). Each point is an independent biological replicate, representing a pair of drift measurements for both phenotypes, acquired on the same day in the same media. One independent biological replicate (one point) gathers per phenotype at least 2000 bacterial trajectories in buffer (typically 3000–6000), 900 in agar (typically 2000–4000), 500 in PVP (typ. 800–1200). Error bars reflect 95% confidence intervals estimated by a jackknife resampling procedure consisting of dividing the data into subsets of 200 trajectories and computing the SEM drift obtained for different subsets. The dotted red reference line marks identical performance of both phenotypes. c Normalized chemotactic drift velocity of ΔcrvAB relative to wt from the same biological replicate, in buffer (grey, n = 10), PVP K90 (purple, n = 5), or agar hydrogels (green, n = 7). Indicated p-values are from a two-sided paired t-test with unknown variance (p = 0.70, 0.0079, and 0.29 in buffer, hydrogels, and PVP, respectively). Error bars reflect 95% confidence intervals across ratios computed within each independent experiment. Datasets used in panels b and c are detailed in Table 1.

Cell curvature enhances chemotactic performances in soft hydrogels

In contrast to liquid environments, experiments conducted under the same 200 µM/mm L-serine gradient but within the structured environments of agar hydrogels (0.19–0.21% w/v) revealed notable differences between the chemotactic performances of the wt and ΔcrvAB strains. The curved phenotype outcompeted its straight-shaped counterpart: out of seven experimental replicates, only one instance showed no significant difference in chemotactic drift within 95% confidence intervals (Fig. 2b). On average, the chemotactic drift of the straight-shaped population was only 60(±7 95% CI)% that of the curved one (Fig. 2c).

We also compared chemotactic performances in highly viscous polymer solutions of PVP K90, a simple linear polymer with non-Newtonian behavior at the bacterial scale¹³, at a bulk viscosity of approximately 38 cP (5% w/v, see Methods). No significant difference in chemotactic drift was observed between the two phenotypes over 5 experimental replicates, with, on average, a chemotactic drift of the straight-shaped population of 106 (±14 95% CI)% that of the curved one. Trajectory inspection revealed a slow run-reverse-flick motility, as reported previously in other strains¹². The average swimming speeds were also similar, at 11.9 µm/s and 12.0 µm/s for the wt and ΔcrvAB strains, respectively. When further comparing average speeds or chemotactic performances for subpopulations of similar speeds, no significant differences were found (SI Fig. 2c, d). We conclude that the presence of uncrosslinked polymers per se does not lead to a chemotactic advantage for curved cells. Because the mesh structure of hydrogel seems to be important for curved cells to outperform their straight counterparts, we focused the rest of our work on the analysis of navigation in hydrogels to investigate the mechanism(s) behind the clear outperformance by the curved cell body.

Cell curvature improves performance in soft hydrogels by increasing swimming extents

Analysis of single-cell trajectories in agar hydrogels revealed a distinct swim-stall motility pattern (Fig. 3a), similar to another polar flagellated Vibrio, Vibrio alginolyticus¹¹. To distinguish swimming phases from stalling (i.e., trapping) phases we ran an automated trajectory analysis (see Methods) on each of the many trajectories yielded per experimental replicate (see detailed datasets SI Table 2). Phases were defined as periods of 0.2 s or more at instantaneous speed over (swimming) or under (stalling) 1 µm/ s (Fig. 3b). Notably, swimming speeds and root-mean-squared swimming speeds were not significantly different between wt and ΔcrvAB strains (Fig. 3c). In contrast, there was a marked increase in stall frequency for straight bacteria (Fig. 3d). This result indicates that cell-body curvature enables V. cholerae to swim significantly further before encountering a stalling event (Fig. 3e), a motility characteristic maintained even if the gradient is washed away (SI Fig. 7). Additionally, despite similar instantaneous swimming speed, the chemotactic speed during swimming phases was significantly lower for the straight mutant (Fig. 3f). The overall decrease in chemotactic performance in the absence of curvature can be understood as a result of two factors: an increase by ~10% of time not moving, and a decrease by ~35% of chemotactic efficiency during swimming. In other words, decreasing swimming extents not only increases the time spent stuck in a stall, but also leads to worse performance between stalls.

Fig. 3. Swim-stall motility in soft agar.

a A 1-min long example trajectory for the curved phenotype (wt) with an average speed of 19.5 µm/s. Inset shows a segment of trajectory with run-reverse-flick appearance. b Time trace of instantaneous speed for the same trajectory. Swim (black) and stall phases (blue) begin when the bacterium’s instantaneous speed is above, respectively below, 1 µm/s for at least 0.2 seconds. The swim-stall analysis was applied to a total of 28,984 and 20,937 trajectories of wt and ΔcrvAB, respectively. Swim-stall motility parameters averaged over each 7 independent replicates and each phenotype: rms swim speeds (c), stall frequency over swim phases (d), and swim extent computed either as cumulative distance traveled during a swim phase (e, black) or as the physical distance between the beginning and end of a swim phase (e, pink). f Average chemotactic drifts computed over the swimming phases only. Indicated p-values are from two-sided paired t-tests with unknown variance. The dotted red reference lines mark identical performance of both phenotypes. g Angle between the entrance direction and the exit direction of stall phases, computed respectively on two instantaneous speed vectors before and two after the stall. The median angle was 122° and 126° for wt and ΔcrvAB, respectively. h Chemotactic drift velocities just before or just after a stall, respectively, from two instantaneous speed vectors before and two after the stall, for wt (black) or ΔcrvAB (red) strains, averaged over all replicates in agar hydrogels. Error bars indicate the standard error of the mean across all analyzed stalls. Analysis included all fully defined (i.e., with a start and an end) stalls detected over the n = 7 replicates, totaling 103,677 and 95,151 stalls for wt and ΔcrvAB, respectively. Indicated p-values are from a two-sided paired t-test with unknown variance. A summary of the swim-stall analysis (and exact p-values) can also be found in SI Table 2.

Cell curvature helps avoid stalls, but turning rates determine escape from stalls

In our analysis, no significant effect of cell-body curvature was observed on stall durations, with an average of 1.28 (±0.16 SD) and 1.27 (±0.16 SD) seconds for curved and straight shapes, respectively. These observations prompted us to interrogate further the mechanisms of stall escape. We hypothesized that once bacteria enter a stall state, turning (i.e., reversing or flicking) dominates the chance of successful escape. Turning rates were similar for curved and straight bacteria in buffer, which would explain their similar stall escape rates in hydrogel. Consistent with this hypothesis, the escape rate of stalls (approx. 0.8 s⁻¹) is close but lower than the turning rate observed in buffer (approx. 1.3 s⁻¹). Similarly, the distribution of angles at which a bacterium escapes a stall (relative to its direction upon entering it) is reminiscent of the typical distribution of reverses and flicks in buffer (Fig. 3g) as also qualitatively observed in Fig. 3a (inset).

To further test our hypothesis, we induced a reduction in turning frequency by imposing a serine shock treatment (50 mM) to wt bacteria in an agar hydrogel. In buffer, the sudden presence of 50 mM serine in motility medium sharply decreased turning frequency, especially during the first 5–10 minutes, and for at least 30 minutes (SI Fig. 4a). Similar imperfect adaptation to high concentrations of serine was previously observed in Escherichia coli¹⁴. In agar hydrogel, the sudden presence of 50 mM serine in both reservoirs led to a 1.5-fold increase in average stall durations (SI Fig. 4b) relative to before the shock. These findings suggest that in hydrogels, cell-body curvature facilitates avoidance of stalls, while cell curvature-independent turning is the main mechanism for escaping stalls.

Stalls decrease chemotactic performance during swimming by reorienting bacteria down the chemical gradient

We next sought to understand our observation that stalls not only reduce time spent moving but also decrease chemotactic efficiency during swimming phases (Fig. 3f). We hypothesized that the effect of stalling on chemotaxis could be related to the turning-based mechanism of stall escape. The average chemotactic drift of bacteria just before entering a stall is positive, while it is negative (and similar between curved and straight strains) at the exit of a stall (Fig. 3h). As such, a stall is not a simple reset of chemotactic sensing randomly reorienting the bacterium, but an adverse event that on average tends to orient bacteria away from the chemotactic gradient. This can be understood because bacteria are typically oriented towards the gradient when they stall, but to escape the stall they require a turn that typically changes their angle more than 90° away from their initial trajectory (Fig. 3g). In other words, a bacterium is more likely to be swimming up the gradient before a stall, which means that bacteria initially escaping a stall are more likely to be moving in the “wrong” direction (down the gradient). Consequently, the ability of cell curvature to reduce the rate of stalling increases chemotactic performance by both increasing the time spent swimming and decreasing the encounter of events negatively affecting the performance of the following swimming phase.

An in-silico model reveals a biophysical mechanism for curvature-enhanced motility in hydrogels and highlights a curvature optimum

To further interrogate the biophysical mechanism(s) underpinning our findings, we developed an in silico coarse-grained molecular dynamics model of curved or straight cells moving and rotating through a hydrogel-like mesh (see Methods). To simplify the model and focus on the key parameter of stall onset frequency, reversals and flicks were not included: once the forward-swimming model “bacterium” enters a stall, it never escapes. The in silico hydrogel was characterized by an average pore size of 3.49 μm (±1.79 μm SD, SI Fig. 6a), within the estimated range of mean pore size for soft (0.25%) agarose hydrogels¹⁵ and close to recent estimates of median pore sizes of canine intestinal mucus using Cryo-SEM¹⁶. We kept these pore sizes constant but modified the elasticity of the links between mesh elements to screen a larger range of model hydrogel stiffnesses, covering the expected range of soft agar hydrogels (hundreds of Pa) but also the expected typical 1–100 Pa stiffness range of human intestinal mucus.

When comparing a thousand trajectories from straight or curved (0.71 µm⁻¹) “bacteria”, the model replicated the experimentally observed boost in travel distance before stall conferred by curvature. Upon estimation of exponential decay lengths of these travel-distance distributions (dashed lines in Fig. 4a, summary in SI Table 3), the model returns an exponential decay length ratio of 1.25, which, despite the model’s simplicity, is in good quantitative agreement with experimental values of 1.26 (±0.10 SD, n = 7). This curved-cell advantage is robust over a wide range of mesh stiffnesses (Fig. 4b). As stiffness decreases, the model even predicts a higher advantage for the curved shape, with a ratio increasing up to almost 1.5 for shear modulus close to human small-intestine mucus (under 10 Pa).

Fig. 4. Curved shape advantage in in-silico model.

a Survival distributions of travel extents in experimental data (left) or in a coarse-grained molecular dynamics model (right, n = 1000 simulations for each cell shape). Dashed lines represent the slopes from the estimates of exponential decay lengths λ. In the in-silico model, curvatures are 0.71 and 0 µm⁻¹ for curved and straight cells, respectively, and the network’s shear modulus is 95.2 Pa. b Ratio of decay lengths λ for curved (0.71 µm⁻¹) relative to straight in silico bacteria in networks of different shear moduli obtained by modification of the properties of the mesh (the higher the deformability, the lower the shear modulus). Error bars represent the extrema of combined 95% confidence intervals determined for each λ estimate (each computed across n = 1000 in silico trajectories) used in the ratio. The orange dotted line denotes the shear modulus of agarose 0.20% reported by Shahab et al.²⁶. c Representative example trajectory from one simulation with curved shape, including a slower phase that does not result in a stall. c inset Detail of the trajectory segment with strongly decreased speed, where the in-silico bacterium (dark blue) can be seen rotating (light blue segment for each bead) and avoiding a complete stall within the network (yellow). The corresponding movie is provided to clarify further the observed effect; see SI Movie 1. d Ratio of decay lengths λ for in silico bacteria with different curvatures, relative to λ_straight. A ratio significantly over 1 signifies that the straight shape is outperformed. The black dotted line denotes the experimental median curvature reported for wt in late exponential phase by Martin et al.⁵. Error bars represent the extrema of combined 95% confidence intervals determined for each λ estimate (each computed across n = 1000 in-silico trajectories) used in the ratio.

Importantly, the model allowed us to precisely visualize cell-body movement in the mesh, as opposed to our experimental techniques. We observed multiple events of curved cells decelerating, sometimes to an almost complete stop, followed by a screw-like process that leads to a direction change and a return to previous speed without stalling (see example in Fig. 4c and SI Movie 1). While both straight and curved cells can slide along a single obstacle, straight cells may get stuck in pocket-like traps formed by multiple obstacles, whereas curved cells can often adjust their attack angle to avoid a stall. We conclude that the advantage of model curved cells lies in their ability to avoid true stalls by deflecting their trajectory away from the trap, preventing themselves from stalling.

Interestingly, upon variation of cell curvature, the model also highlighted an optimum in cell curvature to avoid stalling (Fig. 4d). This optimum is close to realistic 3D curvature values for the wt strain in late exponential phase published by Martin et al.⁵ with a median of 0.75 µm⁻¹. At higher curvature, the advantage decreases, which suggests that cells with more U-shaped geometries do not efficiently reorient themselves to escape traps.

Discussion

Our work highlights the significant role of cell-body curvature in enhancing the chemotactic performance of V. cholerae within hydrogels, as well as the underlying mechanisms at play. Its curved cell body allows V. cholerae to extend swimming phases between stalls when navigating hydrogel meshes under a chemical gradient, thereby improving its ability to cross the hydrogel. Altogether, our work extends the understanding of how curvature improves motility and chemotaxis by addressing these behaviors in more complex and realistic environments. While our work does not directly prove it, we provide here quantitative arguments to explain the previously demonstrated defect in infectivity when curvature is lost by a resulting defect in mucus barrier crossing during host colonization. Interestingly, another recent study highlighted that a filamentous shape of the curved phenotype of V. cholerae could further enhance the pathogen’s penetration at a liquid-mucin interface¹⁷. We suggest that our findings are not only relevant to understanding how V. cholerae crosses the mucus hydrogel protecting the human small intestine but also for the pathogen’s escape from biofilms, as biofilms also represent hydrogels whose pore sizes can be in the range of those hindering bacterial movements¹⁸.

Our computational model allows us to extend the role of curvature in boosting navigation over a wider range of hydrogels, beyond experimental reach. It also provides some mechanistic insight into how curved cells avoid traps. Notably, the naïve intuition that a curved cell acts as a “screw” boring through the simulated hydrogel is only partially borne out. Unlike the motion of a screw, the rotating curved cell can change its angle of attack to avoid being trapped. This is evident in the example in Fig. 4c (see also Movie S1). The model also reveals an optimal cell curvature close to that observed in real V. cholerae cells. Within the model, increasing curvature beyond the optimum has two drawbacks: First, increasing curvature slows the average speed of cells through the hydrogel (SI Fig. 5a), which is expected from the extra collisions of the rotating cell with the hydrogel. However, this is only a small effect (~10%) over the range of curvatures considered. Instead, the more highly curved cells fail to find alternative paths through the simulated hydrogel. This suggests a strong adaptive value for the fine control Vibrio cholerae has of its curvature⁶. Since the model is only a rough simulacrum of a real hydrogel, how high curvature affects escape from traps in real systems, including mucus or V. cholerae biofilms, remains a topic for further exploration.

Our findings draw an intriguing parallel with Vibrio alginolyticus, which employs a different strategy to achieve similar enhancements in swim extents despite lacking cell-body curvature. Instead, V. alginolyticus features a dual flagellar system that includes both polar and lateral flagella. The presence of lateral flagella has been shown to increase swimming distances in soft agar hydrogels (0.15-0.25%), resulting in better chemotactic performance compared to a population expressing only a polar flagellum¹¹. Interestingly, while both body-curvature and lateral flagella improve swim extents in hydrogels, lateral flagella also improve swimming and chemotaxis of V. alginolyticus in high-viscosity PVP K90, while cell-body curvature of V. cholerae does not. Another notable difference is that V. cholerae’s curvature does not hinder navigation in buffer (compared to a straight shape), while V. alginolyticus’s lateral flagella significantly decrease swimming speed and chemotactic performance (compared to the polar-flagellum-only phenotype). Expression of lateral flagella also entails significantly reduced growth rates, due to the metabolic load of producing many long proteinaceous helical filaments, while expression of the CrvA/B complex (which generates curvature) does not. In the Vibrio family, cell-body curvature and dual flagellation appear to be mutually exclusive: the three known Vibrio species lacking CrvA/CrvB homologs^5,6 have dual flagellar architectures^19–21, while none of the species containing CrvA/B homologs are known to have lateral flagella. Might body curvature and lateral flagella, while both efficient ways to improve hydrogel penetration, be incompatible, or are they two independent strategies to improve navigation properties under different selection criteria? For example, curvature could represent a way to specifically improve infectivity without significantly reducing growth or becoming more immunogenic by increasing flagellin presentation, while lateral flagella could promote motility in more diverse environments at a higher adaptive cost. Altogether, these observations suggest a fascinating and complex landscape of bacterial adaptation where cell-body curvature and lateral flagella are two distinct exemplary strategies for improving bacterial navigation. Our work ultimately highlights the importance of interrogating navigational properties in host-relevant environments, here by combining a high-throughput experimental method with parallel mechanistic simulations.

Materials and Methods

Bacterial strains and growth conditions

V. cholerae C6706str2 wild-type (wt) and its non-curved mutant obtained by deletion of curvature-inducing proteins CrvA and CrvB (ΔcrvAB) originated from Martin et al.⁵. Overnight cultures were inoculated in 2 ml LB (1% Bacto Tryptone, 0.5% Bacto Yeast extract, 0.5% NaCl, pH 7) from individual colonies grown on 2% agar LB plates streaked from frozen glycerol stocks less than 1 week earlier, and grown to saturation at 30 °C, 250 rpm. Day cultures were inoculated with the overnight cultures at 1:200 dilution in 10 ml TB (1% Bacto Tryptone, 0.5% NaCl, pH 7) in and grown in parallel at 30 °C, 250 rpm in 100-ml glass culture flasks with ventilated caps (DWK Life Sciences), until they reached an optical density (OD) at 600 nm between 2.2 and 2.4 and within 0.01 of each other (to ensure comparability, see SI Fig. 3). Volumes of 0.5 ml of bacterial culture mixed with 0.5 ml of M9TB were washed once by centrifugation in 1.5 ml microcentrifuge tubes (7 min at 2500 rcf), followed by gentle resuspension in 1 ml of M9TB. M9TB consisted of M9 salts (M6030 Sigma-Aldrich) sterile filtered and 0.01% (v/v) TB (autoclaved) added to it. Bacterial suspensions were diluted to a target OD of approximately 0.005 for chemotaxis experiments in buffer, 0.003 for polymer solutions, or 0.002 for chemotaxis experiments in agar, either in M9TB (chemotaxis experiment in buffer or agar) or in M9TB with PVP K90 (chemotaxis experiment in viscous media), with or without chemoattractant, for injection into the chemotaxis device. For bulk viscosity estimates of 5% PVP K90 solutions, a previously established relationship was used¹².

Chemotaxis assay preparation in buffer or polymer solution

The chemotaxis assays were performed using a high-throughput chemotaxis assay¹⁰ where bacteria are tracked in 3D in a controlled chemical gradient established in a commercially available microfluidic device (µ-slide Chemotaxis, IBIDI), consisting of two reservoirs of different chemical concentrations connected by a small channel in which a linear gradient is formed. The device’s reservoirs were respectively filled with bacterial solutions with or without 200 µM L-serine (84959, Sigma-Aldrich), as previously described¹¹, so as to obtain a 200 µM/mm stable and repeatable linear gradient within approximately 40 minutes after closing the device¹⁰. The full characterization of gradient establishment and stability, carried out with fluorescein (approx. 332 Da) can be found in Reference 11 (Supplementary Materials). As gradient establishment is governed here by diffusion, the gradients of L-serine (approx. 105 Da) are expected to establish in a similar fashion. Each independent biological replicate reported is a set of acquisitions made in a pair of microfluidic devices, one for each phenotype, on the same day and with parallel preparation steps.

Chemotaxis assay preparation in agar

For chemotaxis assays performed in agar, the central channel of the microfluidic device was filled in advance with molten agar (0.19–0.21% w/v Bacto agar in M9TB). For filling the device, each reservoir is successively emptied, filled with bacterial solution with or without chemoattractant, and then closed. Biological replicates comparing phenotypes at a given agar concentration were prepared in parallel to limit the influence of technical variability in agar gel properties. Chemotaxis experiments in buffer and polymer solutions were concluded typically within 60 min after closing the chamber for experiments. Experiments in agar concluded typically within 1.5 hours, maximally 2 hours.

Motility experiments

After washing and resuspension in M9TB as described above, cells were diluted to a target OD of approximately 0.005 in M9TB, incubated at room temperature for at least 15 minutes, to allow adaptation to the medium. Preliminary experiments followed a similar protocol but with different resuspension media or preincubation time, as indicated in Supplementary Fig. 1. Sample chambers with a height of approximately 300 µm were created as described previously²², by using three layers of parafilm as spacers between a slide and a cover glass, filled, sealed with Valap, and immediately brought to the microscope for data acquisition.

Data acquisition

Phase contrast microscopy recordings were obtained at room temperature (∼21 °C) on a Nikon Ti2-E inverted microscope using an sCMOS camera (PCO Edge 5.5) and a 40x objective lens (Nikon CFI S Plan Fluor ELWD 40x ADM Ph2, correction collar set to 1.2 mm to induce spherical aberrations²²) focused at the center of the channel in all three dimensions. The integration time was 3 ms. The frame rate was 30 fps for recordings in buffer, 15 fps in agar, and 5% PVP K90 solutions. Typical cumulative acquisition time for one condition in one chemotaxis experiment (one point in Fig. 2b,c) ranged from 4 to 10 minutes in buffer, 6 to 12 minutes in viscous medium, and 15 to 20 minutes in agar. All acquisitions were made within 150 minutes of resuspension in motility medium after washing.

Data processing and 3D tracking

Video recordings were binned by a factor of 2 × 2 pixels by averaging pixel counts and then subjected to a background correction procedure based on dividing the image by a pixel-wise median computed across a sliding time window of 101 frames, except for data acquired for agar experiments, where a sliding window of 2001 frames was used to ensure that stalled bacteria were not erased. 3D trajectories were extracted from phase-contrast recordings using a high-throughput 3D tracking method based on image similarity between diffraction rings of bacteria and those in a reference library with known vertical positions²² improved in previous works by correcting images for the diffraction rings of already tracked bacteria¹¹.

Positions were smoothed using 2nd-order ADMM-based trend filtering²³ with regularization parameter λ = 0.1 in agar and λ = 0.3 otherwise. Three-dimensional velocities were computed as forward differences in positions divided by the time interval between frames. In chemotaxis experiments, the vertical position of the top and bottom of the chamber was identified by visual inspection of trajectory data. All trajectory segments within at least 12 µm of the top or bottom of the central channel were removed to avoid surface interaction effects¹⁰, except in the soft agar experiments. The number of motile bacteria tracked for one condition in one chemotaxis experiment was at least 2000 bacterial trajectories in buffer (typically 3000–6000), 900 in agar (typ. 2000–4000), 500 in PVP (typ. 800–1200). A dataset summary is provided in Table 1, and the main bacterial trajectory datasets can be found in ref. 24.

Table 1.

Detailed chemotaxis of the main datasets of wt and ΔcrvAB strains in 200 µM/mm serine gradients

Conditions	Strain	Number of independent replicates	Motility threshold (µm/s)	Chemotactic drift vd (µm/s)	Number (duration) of motile trajectories
Buffer	wt	n = 10	15	17.8 ± .9SE	48,894 (51,710 s)
	ΔcrvAB			18.1 ± .7SE	48,062 (53,822 s)
Agar 0.19–0.21%	wt	n = 7	0	0.45 ± .08SE	32,577 (290,991 s)
	ΔcrvAB			0.26 ± .05SE	23,113 (239,891 s)
PVP K90 5% (w/v) ~38 cP	wt	n = 5	4	1.70 ± .11SE	5101 (31,754 s)
	ΔcrvAB			1.81 ± .17SE	4108 (25,589 s)

These datasets are at the source of the data and analysis displayed in Fig. 2 and SI Fig. 2ab (buffer), Figs. 2 and 3 (agar), Fig. 2 and SI Fig. 2c, d (PVP). For all chemotaxis acquisitions, the number of independent biological replicates n reflects the number of pairs of microfluidic devices (one per phenotype), prepared the same day, following the same steps. More details can be found in Methods. In Fig. 2c and in the text, the v_d ratios are first made pairwise (within one experiment), then averaged; the v_d ratios from the averaged drifts here yield ΔcrvAB 58% of wt (instead of 60%) and wt 173% of ΔcrvAB (instead of 186%).

Run-reverse-flick analysis in buffer

The turning event detection that we previously applied to another V. cholerae strain (including sharing of the code)¹², is based on the local rate of angular change, computed from the dot product between the sums of the three consecutive velocity vectors preceding and subsequent to a time point. The threshold for a turn to begin is a 7-fold rate relative to the median rate of angular change of the run segments, as determined in three iterations of the procedure. A new run begins with at least one time point (at least 0.033 s) under this threshold. The 3D turning angle for a turn beginning at frame i and ending at frame j is computed as the angle between the sum of the instantaneous velocity vectors at frames i-2 and i-1 and the sum of those at frames j and j + 1. Backward (CCW rotation) and forward (CW rotation) runs were identified as runs with a turn under 140°, respectively at the end or at the beginning of the run, and a turn above 150° at the other end of the run. All trajectories with a minimum speed of 15 µm/s and with a minimum duration of 0.8 s were analyzed.

Stall-swim analysis in soft agar hydrogels

The stall event detection is based on the instantaneous velocity: If the speed is under 1 µm/s for 0.2 s or more, a stall starts. During a stalling event, if the instantaneous speed exceeds 1 µm/s for 0.2 s or more, the stall ends, and a new swimming phase starts. All trajectories with a minimum duration of 1 s entered stall-swim analysis. For each phenotype, in each of the 7 replicates, this resulted in analysis of more than 80% of all trajectories (totaling 28,984 and 20,937 analyzed trajectories for wt and ΔcrvAB, respectively), of which at least 90% had at least one stall event detected. Swim-stall analysis results are detailed in SI Table 2.

Simulation model

Coarse-grained molecular dynamics simulations are conducted using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS²⁵). In the simulations, the gel matrix is represented as a crosslinked network of chains of spherical beads of 1 µm diameter and 9.42478 pg mass. The beads within a polymer chain are interconnected by stretchable bonds, defined by energy:

$$E=K{\left(r-r_0\right)}^2,$$ 1

where K is 2.2 nN/µm and $r_0$ is 1.25 µm. The swimming cell is modeled as a rigid body consisting of 13 spherical beads, each of 1 µm diameter and 1 pg mass. For the straight cell, all beads are aligned linearly, whereas for the curved cell, the beads form an arc. Interactions between gel-cell beads and gel-gel beads are modeled by a purely repulsive Lennard-Jones potential defined as:

$$E_{LJ}=\left\{\begin{array}{cc}4ϵ\left[{\left(\sigma /r\right)}^{12}-{\left(\sigma /r\right)}^6+1/4\right]\hfill & r<2^{\frac{1}{6}}\sigma \hfill \\ 0\hfill & r\ge 2^{\frac{1}{6}}\sigma \hfill \end{array},\right)$$ 2

where ϵ is 0.0001fJ, σ is 1 µm. The equations of motion are integrated in the microcanonical ensemble (NVE), ensuring conservation of energy through direct integration of Newton’s equations. Simultaneously, a Langevin thermostat is applied to maintain the system at each desired temperature (see below).

Gel initialization

First, a gel matrix formation process is simulated. 125 chains, each consisting of 150 beads, are introduced into a simulation box of dimension 100 µm × 100 µm × 100 µm with periodic boundary conditions. To better replicate the compactness and pore size distribution typical of a hydrogel, the system is geometrically transformed: all bead coordinates (x, y, z) and the simulation box are scaled by a factor of 0.5 to uniformly shrink the system, generating a compact initial configuration. The system is then fully relaxed for 3 × 10⁵ time steps (the timestep is 1 µs) at 300 K. Following this, crosslinking between gel beads is allowed during 3 × 10⁵ time steps, while the system is cooled down from 300 to 100 K. During the crosslinking phase of the simulation, bond formation is implemented by the fix bond/create command in LAMMPS. A check for possible new bonds is performed every 100 time steps. If two beads i and j are within a distance of 1.125 µm of each other, and if a bond does not already exist between i and j, and if both i and j are below their respective maximum bond limit (no more than 4 bonds), then i and j are labeled as a “possible” bond pair. If several beads are close to a bead, it may have multiple possible bond partners. Every bead checks its list of possible bond partners and labels the closest such partner as its “sole” possible bond partner. After this is done, if bead i has bead j as its sole possible partner and bead j has bead i as its sole possible partner, then the i,j bond is formed with a probability of 0.5. Note that these rules mean that a bead will only be part of at most one newly created bond at a given time step. It also means that if i chooses j as its sole possible partner, but j chooses k as its sole possible partner (because distance_jk < distance_ji), then i will not form a bond in this time step, even if it has other possible bond partners. This crosslinking phase is then followed by a final cool-down, from 100 K to 0 K during another 3 × 10⁵ timesteps, with no new crosslinking. To mimic the tensioned structure of hydrated gels, the simulated polymer network is again geometrically transformed (in the manner described above) prior to introducing swimming cells: to impose mechanical tension, the coordinates are uniformly expanded by a factor of 1.2. This procedure yields a starting conformation that is both dense and under tension, reflecting the structural characteristics of real hydrogels, which swell under hydration. Subsequently, the system is allowed to mechanically equilibrate for an additional 3 × 10⁵ time steps at 0 K.

Simulation procedure

Within the constructed gel matrix, a swimming cell is introduced at a random location, ensuring no overlap with the gel matrix by briefly relaxing any intersecting gel beads. To mimic bacterial swimming, including both rotational and translational motion, a torque of 500 pN.nm about its axis and an external force of 0.1 pN along its axis are applied, corresponding to approximately one full rotation per cell-length of forward displacement during free swimming. For the simulation of varied curvatures, a smaller torque (100 pN.nm) is applied. The motion of the swimming cell in the gel is then simulated at 0 K, and the positions and velocities of all cell beads are recorded every 500 timesteps (each timestep is 0.5 µs) for subsequent analysis. Each simulation is ran for 2 × 10⁷ timesteps. To determine when a swimming cell stopped moving, displacements are calculated over a time interval of 10⁴ timesteps. At each frame, the Euclidean distance between the current position and the position 10⁴ timesteps later is computed. If this displacement is less than 2 µm for 4 × 10⁴ consecutive timesteps, the cell is considered to have stopped. The first frame meeting this condition is recorded as the stopping point. If no such event occurs, the cell is classified as motile throughout the trajectory. A total of 1000 simulations per condition (e.g., per curvature) are performed.

Gel shear modulus measurement

Following an initial equilibration phase and a relaxation phase of the gel as described above, shear deformation is introduced by applying an affine box deformation in the xy plane at a constant strain rate of 0.001 ms⁻¹. During the subsequent simulation, which lasts 5 × time steps at 0 K, the shear stress σ_xy of the gel matrix, box tilt L_xy, and box length L_y (see SI Fig. 6c) are recorded every 500 time steps. The shear strain is calculated as $\gamma =L_{XY}/L_Y$, and the shear modulus is determined from $G=\mathrm{\Delta }{\sigma }_{xy}/\mathrm{\Delta }{\gamma }_{xy}$.

Cell curvature measurement

To estimate cell curvature, we fit a circle that passes through two central body atoms and is tangent to the directions of the two arms (see SI Fig. 6b). Specifically, we first extract two short segments representing the left and right arms of the cell, each comprising 3–4 beads. Linear regression is used to fit a line to each arm segment, yielding estimates of their orientations. Two beads located near the midpoint of the body — one at the junction with each arm — are used to define the arc of the cell body. We then compute the position and radius of the circle that passes through these two central atoms and is tangent to the previously fitted arm directions. The circle is determined by minimizing a cost function that penalizes deviation from both distance constraints (points lying on the circle) and angular constraints (tangency with arm directions), using nonlinear optimization. The fitted radius is used to quantify cell curvature.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

M.G., Z.G. and N.S.W. designed the research. M.M. performed experimental research. Z.C. and A.G.T.P. performed in silico research. M.G. and M.M. analyzed experimental data. Z.C. and N.S.W. analyzed in silico data. M.G. wrote the manuscript with support from Z.G. and N.S.W. All authors commented on the manuscript.

Peer review

Peer review information

Communications Biology thanks Dr. Kyamazak and the other anonymous reviewer(s) for their contribution to the peer review of this work. Primary Handling Editors: Dr Ophelia Bu, Dr Tobias Goris and Professor Haichun Gao.

Funding

This research project was funded by the START-Program of the Faculty of Medicine of the RWTH Aachen University and by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – Project 570781731. This research was also supported by the National Institute of General Medical Sciences (NIGMS) of the National Institutes of Health (NIH) under Award Number R01 GM082938 (NSW). The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. This work was supported in part by the National Science Foundation, through the Center for the Physics of Biological Function (PHY-1734030). A.G.T.P. is a Stanford Science Fellow. Open Access funding enabled and organized by Projekt DEAL.

Data availability

All the bacterial trajectories analyzed in the main text (including core datasets as detailed in Table 1), as well as swim extent data (both experimental and in silico) and supplementary movies, are publicly available on the repository RWTHPublications at https://doi.org/10.18154/RWTH-2025-05690. Numerical source data under graphs can be obtained in Supplementary Data. Any other data (e.g. experiments displayed only in SI) can be obtained from the corresponding author upon reasonable request.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s42003-026-10883-9.