1. Physics of Living Systems
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Asymmetric random walks reveal that the chemotaxis network modulates flagellar rotational bias in Helicobacter pylori

  1. Jyot D Antani
  2. Anita X Sumali
  3. Tanmay P Lele
  4. Pushkar P Lele  Is a corresponding author
  1. Artie McFerrin Department of Chemical Engineering, Texas A&M University, United States
  2. Department of Biomedical Engineering, Texas A&M University, College Station, TX 77840, United States
  3. Department of Translational Medical Sciences, Texas A&M University, United States
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Cite this article as: eLife 2021;10:e63936 doi: 10.7554/eLife.63936

Abstract

The canonical chemotaxis network modulates the bias for a particular direction of rotation in the bacterial flagellar motor to help the cell migrate toward favorable chemical environments. How the chemotaxis network in Helicobacter pylori modulates flagellar functions is unknown, which limits our understanding of chemotaxis in this species. Here, we determined that H. pylori swim faster (slower) whenever their flagella rotate counterclockwise (clockwise) by analyzing their hydrodynamic interactions with bounding surfaces. This asymmetry in swimming helped quantify the rotational bias. Upon exposure to a chemo-attractant, the bias decreased and the cells tended to swim exclusively in the faster mode. In the absence of a key chemotaxis protein, CheY, the bias was zero. The relationship between the reversal frequency and the rotational bias was unimodal. Thus, H. pylori’s chemotaxis network appears to modulate the probability of clockwise rotation in otherwise counterclockwise-rotating flagella, similar to the canonical network.

Introduction

Over half of the human population is colonized by the motile gram-negative bacteria, Helicobacter pylori. H. pylori infections have been implicated in peptic ulcers as well as non-cardia gastric cancer (Peek and Blaser, 2002). Infections are promoted by the ability of the bacterium to swim with the aid of helical appendages called flagella (Aihara et al., 2014; Ottemann and Lowenthal, 2002). The flagellar filaments are rotated by transmembrane flagellar motors that repeatedly switch their direction of rotation. Owing to the unipolar location of the left-handed flagellar filaments (Constantino et al., 2016), counterclockwise (CCW) rotation of the motors causes the cell to run with the flagella lagging behind the body – a mode of motility termed as the pusher mode. The cell reverses with the body lagging the flagella when the motors switch the direction of rotation to clockwise (CW). This mode of motility is termed as the puller mode (Lauga and Powers, 2009). Modulation of the reversals between the two modes enables the cell to undergo chemotaxis — migration toward favorable chemical habitats (Lertsethtakarn et al., 2011; Howitt et al., 2011; Johnson and Ottemann, 2018). The core chemotaxis network is similar to that in E. coli (Lertsethtakarn et al., 2011; Abedrabbo et al., 2017; Lertsethtakarn et al., 2015; Lowenthal et al., 2009b; Pittman et al., 2001). Several components that form the flagellar motor are also similar to those in E. coli (Lertsethtakarn et al., 2011). How the chemotaxis network modulates flagellar functions in H. pylori remains unknown (Lertsethtakarn et al., 2011; Lertsethtakarn et al., 2015; Jiménez-Pearson et al., 2005).

Switching in the direction of flagellar rotation is promoted by the binding of a phosphorylated response regulator, CheY-P, to the flagellar switch. In the canonical chemotaxis network, chemoreceptors sense extracellular ligands and modulate the activity of the chemotaxis kinase, which in turn modulates CheY-P levels. Increased CheY-P binding to the motor promotes CW rotation in an otherwise CCW rotating motor (Sourjik and Wingreen, 2012). The output of the flagellar switch is quantified by the fraction of the time that the motor rotates CW, termed CWbias (Block et al., 1983; Yuan et al., 2012; Yang et al., 2020). A decrease (increase) in CheY-P levels causes corresponding decrease (increase) in CWbias (Cluzel et al., 2000; Scharf et al., 1998). Thus, dynamic variations in the CWbias sensitively report changes in the kinase activity due to external stimuli as well as due to the internal noise in the network (Cluzel et al., 2000; Korobkova et al., 2004). In contrast, the frequency at which motors switch their direction does not accurately represent changes in the chemotaxis output as the frequency decreases when CheY-P levels increase as well as when CheY-P levels decrease (Cluzel et al., 2000). Prior work has focused on the effects of extracellular ligands on the frequency of cell reversals (Collins et al., 2016; Machuca et al., 2017; Goers Sweeney et al., 2012; Rader et al., 2011; Sanders et al., 2013; Schweinitzer et al., 2008) rather than the motor bias. It is unknown whether the chemotaxis network in H. pylori modulates the rotational bias.

In run-reversing bacteria, reversal frequencies can be readily quantified based on the number of reversals made by the swimming cell per unit time. To quantify the CWbias, the duration for which the cell swims in each mode needs to be determined by distinguishing between the two modes. However, discriminating between the swimming modes of single H. pylori cells is difficult owing to the technical challenges in visualizing flagellar filaments in swimmers (Constantino et al., 2016; Lowenthal et al., 2009a). A popular method to quantify the CWbias is by monitoring the rotation of tethered cells, where a single flagellar filament is attached to a glass surface while the cell freely rotates (Block et al., 1983). Alternatively, the bias is determined by sticking the cell to the surface and monitoring the rotation of a probe bead attached to a single flagellar filament (Ford et al., 2017; Yuan et al., 2010). Such single motor assays have been employed successfully in E. coli because the filaments are spaced apart on the cell body. In H. pylori, however, the flagella are distributed in close proximity to one another at a single pole (Qin et al., 2017), increasing the likelihood of tethering more than one filament. Tethering of multiple flagella on the same cell eliminates rotational degrees of freedom, inhibiting motor function. Because of the limited measurements of the CWbias, crucial features of the signaling network, such as the dynamic range of signal detection, adaptation mechanisms, and the roles of key chemotaxis-related proteins, remain unknown in H. pylori.

Here, we report a novel approach to measure the CWbias based on differences in the swimming speeds in the pusher and puller modes of H. pylori. We successfully employed this method to determine the effect of a known chemoattractant and varying temperatures on the CWbias. Our observations suggest that the CWbias decreases upon stimulation with an attractant, similar to the canonical model. The default direction of flagellar rotation is CCW and the presence of CheY increases the CWbias. The relationship between reversal frequencies and rotational bias is unimodal. These results are consistent with the notion that the chemotaxis network modulates the flagellar rotational bias (as well as the reversal frequencies) under environmental stimulus. Our quantitative model and simulations suggest that the basal chemotaxis output is likely tuned in H. pylori and other run-reversing bacteria to enhance diffuse spread. The approach discussed in this work provides a solid framework to study chemotaxis signaling and the behavior of the flagellar switch in H. pylori.

Results

Swimming speeds are asymmetric

To determine the behavior of flagellar motors in H. pylori, we tracked cell motility in the bulk fluid with a phase contrast microscope. The positions of single cells were quantitatively determined from digital videos with the aid of particle tracking (see Materials and methods). Owing to the use of low magnification microscopy, we were able to observe several cells exhibiting reversals in the field of view. A representative cell trajectory at 37°C is shown in Figure 1A (see another example in Video 1). With each reversal, the cell appeared to change from one mode of swimming to the other, although the modes could not be identified (as puller or pusher) because the flagella were not visible. Changes in the swimming modes were distinguished from rotational turns of the cell body – where the swimming mode remains unchanged – by visually inspecting each reversal for each cell. The turn angle between the original direction just before and the new direction just after a reversal () followed an exponential distribution with a peak ~180° (Figure 1B), indicating that cells simply retraced their paths for brief durations following each reversal. The flick of the flagellum that causes turn angles to be distributed ~90° in another run-reversing species Vibrio alginolyticus (Stocker, 2011), is unlikely to occur in H. pylori. The distance traveled between any two reversals was identified as a segment and numbered (Figure 1A). The swimming speeds over six consecutive segments are indicated in Figure 1C. The speeds were binned as per the segments, yielding n+1 bins for n reversals. The mean speed from each bin was plotted for all the n+1 bins (Figure 1D). Mean speeds in alternate bins were anti-correlated: each reversal either decreased or increased the speed. This suggested that the speeds in the two modes were unequal. Such anti-correlation was consistently observed in a large population of cells (n = 250). The distribution of the ratio of their mean speeds in the fast and slow modes is shown in Figure 1E. The speed in the fast mode was ~1.5 times the speed in the slow mode.

H. pylori swim forward and backward at different speeds.

(A) Representative swimming trace of a single bacterium. Each reversal is represented by a filled circle. The beginning of the trajectory is denoted by an open circle. Uninterrupted swimming between two reversals was labeled as a segment and the segments were numbered chronologically. (B) The turn angles were exponentially distributed (n = 1653 samples); reversals mostly caused the cells to retrace their movements. (C) The swimming speed for a single cell over 1.5 s is indicated. The speeds alternated between high and low values with each reversal. Raw data is indicated in gray; filtered data is indicated in black. (D) The mean speed for each segment is indicated chronologically. Standard deviations are indicated. (E) The mean speed for the high (low) mode for each cell was calculated by averaging over all its high- (low-) speed segments. The distribution of the ratios of the high and low mean speeds for each cell is indicated. The mean ratio was 1.5 ± 0.4 (n = 250 cells).

Video 1
A representative cell exhibits reversals within the field of view (movie has been slowed 3X).

Cell swims faster in the pusher mode

A recent study attempted to visualize the flagella in H. pylori with high-magnification microscopy, and suggested that the cells swim faster in the pusher mode. However, the sample sizes were severely limited by the difficulties in visualizing flagella on the swimmers (Constantino et al., 2016). To conclusively determine the faster mode in H. pylori, we exploited the hydrodynamic coupling between swimmers and glass boundaries. Cells that swim very close to an underlying solid boundary exhibit circular trajectories owing to the increased viscous drag on the bottom of the cell and the flagellar filaments. CCW rotation of the left-handed helical filament causes the pusher to experience a lateral force that promotes CW circular tracks (Figure 2A, DiLuzio et al., 2005; Lauga et al., 2006). The situation is reversed when the filaments rotate CW. Thus, it is possible to discriminate between the two modes when a bacterium swims near a surface. We analyzed each cell that swam in circular trajectories near the surface and determined the mean speeds for the two directions. The cells were viewed from the bulk fluid, as indicated in Figure 2A (right panel). Four sample trajectories are shown in Figure 2B. For each cell, the CW trajectories were always faster relative to the CCW trajectories, indicating that the pusher mode was the faster mode (Figure 2C). This was confirmed over n = 116 cells; the mean ratio of the speeds of the CW trajectories to that of the respective CCW trajectories was ~1.6 ± 0.5 (Figure 2D).

Cells swim faster in the pusher mode.

(A) The viscous drag on the bottom of the cell body and the flagellar filament is higher near an underlying surface (indicated by the blue line in the left panel). The drag is lower on the top half of the body and filament. This difference in drag causes a lateral thrust on the cell, giving rise to circular trajectories: CW trajectory in the pusher mode and CCW trajectory in the puller mode (right panel). (B) Top row: Blue segments indicate CW trajectories; red segments indicate CCW trajectories. Filled circles indicate reversals; open circle indicates the beginning of the trajectory. Bottom row: The corresponding mean speeds and standard deviations are indicated for the two trajectories: CW tracks were always faster than CCW tracks. (C) The distribution of the ratio of the speeds along the pusher and puller modes is indicated (n = 116 cells). The mean ratio = 1.6 ± 0.5.

Partitioning of swimming speeds enables estimation of chemotaxis response to attractants

As H. pylori rotate their flagella CW in the puller mode, the CWbias could be calculated from the fraction of the time that the cells swam slower (see Materials and methods). This method worked for all the cells that reversed at least once in the field of view: the faster and slower modes could be discriminated from each other based on comparisons between the mean speeds before and after a reversal (as shown in Figure 1D). These cells consisted ~81% of the total data. The remaining cells did not reverse under observation; they persisted in a particular direction before exiting the field of view. Hence, these cells were termed as single-mode swimmers. As the mode of swimming could not be readily determined for these cells, those data were grouped into cells that swam near the surface for at least some time and those that did not. In the former group of cells, the majority was identified as pushers based on the direction of their circular trajectories near surfaces, as discussed in Figure 2. About 8% of the cells could not be identified and were excluded from the analysis. The distribution of the bias is shown in Figure 3A. The bias was similar to that observed in E. coli (Block et al., 1983; Segall et al., 1986; Ford et al., 2018; Sagawa et al., 2014; Block et al., 1982; Stock et al., 1985), suggesting that the basal chemotactic output in the two species is similar. As evident, most cells tended to rotate their motors CCW for a higher fraction of time.

Asymmetric swimming speeds enable quantification of chemotaxis output.

(A) CWbias was determined at 37°C in the absence of chemical stimulants. Cell trajectories with durations of 1 s or more were considered for calculation. The distribution was obtained from n = 240 cells. A Gaussian fit to the switching population (n = 212 cells) yielded CWbias = 0.35 ± 0.23 (mean ± standard deviation). (B) Single-cell trajectories of a ΔcheY mutant are indicated. Cells swam in CW-only trajectories, which indicate CCW flagellar rotation. Open green circles denote the start of a trajectory; filled red circles denote the end. The trajectories were spatially displaced to group them for the purpose of illustration and truncated to show the direction of rotation. Full trajectories and additional cells are included in Appendix 1—figure 1. (C) The post-stimulus CWbias was monitored for ~30–60 s immediately following exposure to 20 mM urea (n = 20 cells); 14 cells swam exclusively in the pusher mode during the period of observation and displayed CW-only trajectories near surfaces. In the control case, cells were exposed to the buffer-only. The average post-stimulus CWbias was 0.31 ± 0.04 (mean ± standard error, n = 20 cells). The difference in the mean bias for the attractant and the control cases was significant (p-value<0.001). (D) The post-stimulus reversal frequency for cells treated with urea was 0.23 ± 0.09; those treated with the buffer had an average reversal frequency of 1.4 ± 0.04. The difference in the mean frequency for the attractant and the control cases was significant (p-value<0.001).

Next, we imaged swimmers belonging to a cheY-deleted strain and observed that the trajectories of cells near a surface were exclusively CW circles. More than 150 cells were observed near surfaces and they exhibited CW trajectories. A fraction of the data is shown in Figure 3B and in Appendix 1—figure 1. This suggested that the default direction of flagellar rotation is CCW, similar to E. coli (Ford et al., 2018; Liu et al., 2020). Considering that the bias is zero in the absence and ~0.35 in the presence of CheY, CheY-P binding likely promotes CW rotation in an otherwise CCW rotating motor in H. pylori.

To test the idea that the chemotaxis network modulates the rotational bias, we employed our technique to quantify changes in the CWbias in swimmers when stimulated by a chemical attractant. We stimulated cells by adding them to a bath of urea (20 mM in motility buffer-MB, see Materials and methods), which is a potent chemoattractant for H. pylori (Huang et al., 2015). Following exposure to the attractant, the majority of the cells swam exclusively in the pusher mode – their post-stimulus CWbias was ~0 (Figure 3C). The reversal frequency also decreased in response to the chemo-attractant (Figure 3D), which is in agreement with previous reports (Machuca et al., 2017; Perkins et al., 2019). In comparison, the post-stimulus CWbias in swimmers exposed to MB-only (control case) did not change significantly and continued to exhibit both modes of motility (Figure 3C,D). These observations are consistent with the notion that a reduction in the kinase activity upon the sensing of chemo-attractants inhibits the rotational bias of flagellar motors, similar to how the chemotaxis network modulates the response of E. coli to attractants (Block et al., 1983).

Effect of thermal stimuli on chemotactic output

Several studies have characterized motility and chemotaxis in H. pylori at room temperatures (Constantino et al., 2016; Howitt et al., 2011; Martínez et al., 2016). Here, we explored how changes in the surrounding temperatures modulated the flagellar output in H. pylori. We recorded cell motility at different temperatures. The recording began ~5–10 min after each temperature change to provide adequate time for transient processes to stabilize (see Materials and methods for additional information). The mean pusher and puller speeds trended upwards with the temperature (Figure 4A, left panel), presumably through modulation of proton translocation kinetics that power the motor (Yuan and Berg, 2010). The ratio of the speeds in the two modes appeared to be independent of the temperature (Figure 4A, right panel). These responses are consistent with experiments in E. coli that show a strong influence of temperatures on the rotational speeds of the flagellar motor (Yuan and Berg, 2010; Turner et al., 1996; Turner et al., 1999).

Steady-state chemotactic output is independent of temperature.

(A) Left: Swimming speeds for each mode are plotted (mean ± standard deviation) for different temperatures. The speeds increased with temperature till 37°C, after which they plateaued. The shaded regions indicate standard deviation. Right: The ratios of the pusher and puller speeds are independent of the temperatures, as indicated. A red horizontal line indicates the median ratio at each temperature, and the bottom and top borders of the encompassing box indicate the 25th and 75th percentiles. The extended lines span 99.3% of the data and the dots indicate outliers. (B) Mean CWbias (open squares) and mean reversal frequencies (filled circles) are plotted over a range of temperatures. The switching frequency was at a maximum at the physiological temperature (37°C) and decreased at higher and lower temperatures. The CWbias increased with the temperature and plateaued above 30°C. The mean values are indicated with standard error. Each data-point was averaged over n ≥ 80 cells. (C) The relationship between reversal frequency and CWbias is indicated. The values were obtained from the combined datasets over the entire range of temperatures that we studied (n = 972 cells). The CWbias was binned (bin size = 0.05), and the mean reversal frequency for each bin was estimated. The mean and standard errors are indicated in grey. The black curve is a guide to the eye. (D) The estimated ratio of the CheY-P dissociation constant (K) and the intracellular CheY-P concentrations (C) is indicated as a function of the temperature. The ratios were calculated from the data in (B) following a previous approach (Turner et al., 1999). The number of binding sites for CheY-P in H. pylori ~ 43 was estimated from the relative sizes of the flagellar C-ring (see Appendix 2 and Qin et al., 2017). The ratio of the dissociation constants for the CCW and the CW motor conformations was assumed to be similar to that in E. coli (~ 4.7 from Fukuoka et al., 2014).

The frequency of reversals increased steadily with temperature up to 37°C, whereas the steady-state CWbias varied weakly with temperature (Figure 4B). At room temperatures, the CWbias was the lowest, indicating that the cells mostly prefer to swim in the pusher mode. Next, we combined our data over the entire range of temperatures (25–43°C) and for each cell, plotted the reversal frequency against its CWbias. The reversal frequency was maximum at ~0.4 CWbias and decreased on either side (Figure 4C); also see Appendix 3—figure 1. As our results suggest that CheY-P binding increases the CWbias (Figure 3B,C), this also means that the reversal frequency has a similar unimodal dependence on CheY-P levels. Hence, we propose that changes in the reversal frequency in H. pylori cannot provide accurate information about the effect of stimulants on the kinase activity (i.e. whether a stimulant increases or decreases the activity). On the other hand, the rotational bias is likely a better measure of the kinase activity, similar to that in E. coli.

In E. coli, flagellar switching has been well described by a two-state model, where the binding of phosphorylated CheY (CheY-P) to the flagellar switch stabilizes the CW conformation (Turner et al., 1999). In the absence of CheY-P, the probability of observing CW rotation in an otherwise CCW-rotating motor decreases with increasing temperatures (Turner et al., 1996). The chemotaxis network itself adapts such that the steady-state levels of CheY-P are independent of the temperatures (Paulick et al., 2017). Assuming that CheY-P levels are also independent of the temperature in H. pylori, the relative insensitivity of the rotational bias in Figure 4B suggested that the dissociation constant for CheY-P/switch interactions likely decreased with rising temperatures. Following the thermodynamic analysis of Turner and co-workers for a two-state flagellar switch (Turner et al., 1999), we calculated the dissociation constant normalized by CheY-P levels, as shown in Figure 4D (see Appendix 2 for details). Assuming that the CheY-P levels are ~3 μM (Cluzel et al., 2000), we estimate the dissociation constant to be ~9 μM at 37°C.

Speed asymmetry promotes diffusion

Even without chemotaxis, motility enhances the spread of bacteria, lending a significant advantage over immotile bacteria in exploring three-dimensional spaces (Josenhans and Suerbaum, 2002). Bacterial motion becomes uncorrelated over long times and large length-scales in the absence of a signal. Several previous works have modeled the diffusion of motile bacteria by assuming that the reversal wait-times are exponentially distributed (Berg, 1993; Lovely and Dahlquist, 1975; Lauga, 2016; Theves et al., 2013). The wait-time refers to the time between two consecutive reversals. In some bacterial species that exhibit runs and reversals, the wait-time is Gamma distributed (Theves et al., 2013; Morse et al., 2016; Xie et al., 2011). The assumption of exponentially distributed wait-times leads to inaccurate predictions in such species (Theves et al., 2013).

Our cell-tracking analysis revealed that the reversal wait-times were Gamma distributed in H. pylori (Figure 5A, also see separate distributions for the two swimming modes in Appendix 3—figure 2). When calculating the wait-times, we excluded the beginning of each cell-trajectory just before the first reversal and the end of each cell-trajectory just after the final reversal. To derive an explicit expression for the diffusivity of asymmetric run-reversers that exhibit Gamma distributed reversal intervals, we preferred to modify a previous approach developed for symmetric run-reversers (Großmann et al., 2016) rather than a more general model (Detcheverry, 2017) – see Appendix 4 for details. Briefly, the velocities of a bacterium that swims at v0 μm/s in its slower mode was expressed as: vt=v0 ht 1+aHhet. The direction of swimming was described by the function h(t), which alternated between +1 and −1 with each reversal (Figure 5B). A Heaviside function, H(h) and the asymmetry parameter, a, characterized the magnitudes of the speeds in the two directions: v0 and a. The CWbias was assumed to be constant (= 0.5) for simplicity.

Asymmetric random walks in a run-reversing bacterium.

(A) Experimentally observed wait-time intervals for runs and reversals obey a Gamma distribution (n = 515 samples): the shape and scale parameters were k = 2.92 ± 0.06 and θ = 0.11 ± 0.00, respectively. (B) Cell swims at v0 μm/s in the puller (slower) mode, and at v0(1+a) μm/s in the pusher (faster) mode. The symmetric case is described by a = 0, where the run and reverse speeds are equal. Cell alignment is described by the unit vector e. (C) The diffusion coefficients predicted from equation 1 are indicated as a function of the asymmetry in speeds (blue curve). An alternate model that assumes exponentially distributed wait-time intervals in asymmetric swimmers under predicted the diffusivity, as shown by the dotted curve (Theves et al., 2013). Symbols indicate coefficients calculated from simulation runs (see Appendix 5). The parameters were based on experimental measurements: mean wait-time = 0.3 s, α = 0.86, and v0= 25 μm/s. Dθ = 0.02 s−1 from (Großmann et al., 2016). Diffusion coefficients have been non-dimensionalized with D0=v02/3ωpLovely and Dahlquist, 1975), where ωp is the mean reversal frequency at the physiological temperature (Figure 4B). (D) Diffusion coefficients were calculated from simulations of cell motility in the absence of a stimulus over a range of a and CWbias values (see Appendix 5 for details). The diffusion coefficients were normalized with D0. The sum of the mean wait-times (CW and CCW) was fixed at 0.35 s. (E) Predicted diffusivity is indicated over a range of typical reversal frequencies. Here, α = 0.86 and Dθ = 0.02 s−1.

The deviation of the cell from a straight line during a run (or reversal) occurred due to rotational diffusion, described by dθdt=2Dθξ(t). White noise characteristics were ξ(t)=0, and ξ(t)ξ(t+τ)=δ(τ), where Dθ is the rotational diffusion coefficient. Another randomizer of the bacterial walk is the turn angle, , which is the angle between the original direction just before and the new direction just after a reversal. The turn angle is likely influenced by kinematic properties: cell shape, filament bundling dynamics, and the flexibility of the flagellar hook. After taking into account the specific form of the reversal wait-time distribution for H. pylori (Figure 5A), we obtained the following expression for the asymptotic diffusion coefficient from the velocity correlation over long-times:

(1) D=v022Dθ[(1+a)2+12 {1ωDθ(1(3ω)3(3ω+Dθ)3)+|cos|2ωDθ(3ω)3(3ω+Dθ)3((3ω+Dθ)3(3ω)3)2(3ω+Dθ)6|cos|2(3ω)6}(1+a){|cos|ωDθ((3ω+Dθ)3(3ω)3)2(3ω+Dθ)6|cos|2(3ω)6}]

The reversal frequency is indicated by ω. The expression correctly reduces to that for the symmetric swimmer (Großmann et al., 2016), for α (=|cos|) = 1, and a = 0.

As shown in Figure 5C, the diffusion coefficients increased with the asymmetry-parameter, a. As per the predictions, asymmetric run-reversers (a ≠ 0) spread faster than symmetric run-reversers (a = 0). Next, we carried out stochastic simulations of 1000 cells that underwent asymmetric run-reversals with Gamma distributed intervals (see Appendix 5). The diffusion coefficients from the simulations matched predictions from our model that incorporated Gamma distributed wait-times. Having validated our simulations, we estimated the diffusion coefficients for arbitrary CWbias values over varying a. As shown in Figure 5D, the simulated diffuse spread was low when cells covered similar distances in the forward and backward directions, thereby minimizing net displacement. This tended to occur for swimmers with low a values that swam for equal durations in the two directions (CWbias ~ 0.5). For any given a, the diffuse spread increased with the net displacement during a run-reversal, for example, when the swimmer preferred the slower mode much more than the faster mode. The net displacement, and hence, the spread tended to be the highest when the cells spent a greater fraction of the time swimming in the faster mode compared to the slower mode. Thus, in H. pylori, the tendency to spend more time in the faster pusher mode (basal CWbias ~ 0.35, Figure 3A) is advantageous (Figure 5D). This advantage is amplified by increasing pusher speeds relative to the puller speeds. However, a very low basal value of the CWbias is disadvantageous from a chemotaxis perspective. H. pylori appear to respond to attractants by reducing their CWbias (Figure 3C). They would lose their ability to respond to attractants if the pre-stimulus (basal) bias was close to its minimum value (=0). It is possible, therefore, that the basal activity of the chemotaxis network is optimized in asymmetrically run-reversing bacteria to promote higher diffusive spread while retaining the ability to respond to chemical stimuli.

Finally, longer durations of runs and reversals helped cells cover larger distances. Thus, the diffusion coefficient was inversely dependent on the run-reversal frequency (Figure 5E). As the reversal frequencies reach a maximum at 37°C (Figure 4B), it is possible that cells at physiological temperatures spread slower in a niche over long times, providing more time for cells to adhere to surfaces.

Discussion

H. pylori experience physiological temperatures (~37°C) in their human hosts. Here, we characterized flagellar functions at physiologically relevant temperatures. Our experiments with a mutant lacking cheY showed that the flagellar motors in H. pylori rotate CCW by default (Figure 3B). At native CheY-P levels, motors in wild-type cells spent about 35% of the time rotating CW (Figure 3A) – thus, the probability of CW rotation increases with CheY. Our experiments further showed that treatment of wild-type cells with a potent attractant (urea) decreased the rotational bias (CWbias). These results are consistent with a model in which the chemotaxis network controls the levels of CheY-P to modulate the probability of CW rotation in an otherwise CCW rotating flagellar motor. If so, then the chemotaxis networks in the two species, E. coli and H. pylori, modulate flagellar functions in a similar manner.

Earlier works focused exclusively on the effect of chemoeffectors on steady-state reversal frequencies in H. pylori to characterize chemotaxis responses (Collins et al., 2016; Machuca et al., 2017; Goers Sweeney et al., 2012; Rader et al., 2011; Sanders et al., 2013; Schweinitzer et al., 2008). Because diffusion scales inversely with the reversal frequency (Figure 5E), increases in frequency might help a cell linger in a niche. However, mere variations of the steady-state reversal frequencies with the local stimulant concentrations (or temperatures) does not enable chemotaxis (Berg, 1993). By combining data collected over a range of temperatures, we showed that the dependence of the reversal frequency on the rotational bias is unimodal (Figure 4C). This means that the reversal frequency does not have a unique value with respect to the rotational bias (other than at maximal frequency), similar to that in E. coli (Figure 6A). Hence, the reversal frequency value is also unlikely to be unique with respect to the kinase activity (the corresponding relationship in E. coli is depicted in Figure 6B). Therefore, changes in the reversal frequencies by themselves are unlikely to accurately report changes in the chemotaxis output in H. pylori. Our results suggest that the rotational bias must be quantified to accurately determine the chemotaxis output in H. pylori.

Motor reversal (switching) frequencies versus CWbias and CheY-P.

(A) The dependence of motor reversal frequencies in E. coli on the CWbias is unimodal (Montrone et al., 1998), similar to H. pylori (Figure 4B). The symbols indicate experimental data from Montrone et al., 1998. The black curve is a guide to eye. The blue and red arrows indicate the effect of attractants and repellents on the CWbias, respectively. The corresponding changes in the reversal frequency are similar (Δωatt ~ Δωrep). (B) The dependence of switching frequency on CheY-P levels is also unimodal in E. coli (Cluzel et al., 2000). Thus, an attractant as well as a repellent can induce a drop in the frequency.

Our model for diffusive spread of motile bacteria indicated that run-reversing bacteria that undergo asymmetric random walks diffuse faster than symmetric run-reversers (Figure 5C). This is expected, as symmetric run-reversals tend to minimize net displacements. Simulations of bacterial diffusion in the absence of stimulants indicated that the diffusive spread is higher in asymmetric run-reversers when the cells spend a greater fraction of the time swimming in the faster mode compared to the slower mode. Thus, the preference for the faster pusher mode (lower CWbias) in H. pylori is advantageous as it helps them spread faster (Figure 5D). However, H. pylori appear to respond to attractants by reducing their CWbias (Figure 3C). A very low value of the basal bias would inhibit the ability to respond to attractants entirely. Hence, we propose that the basal activity of the chemotaxis network is probably tuned to promote higher diffusive spread while optimizing chemotaxis performance. In general, asymmetry in swimming – differences in swimming speeds or differences in the amount of time spent in any one mode or both – may provide evolutionary benefits to run-reversing bacteria by enhancing their spread.

The response of the chemotaxis network to external stimuli is conventionally measured by determining the rotational bias (Block et al., 1983; Yang et al., 2020; Lele et al., 2015; Jasuja et al., 1999). Tethering cells to glass surfaces is the preferred method of determining the rotational bias. This approach is only useful when one can ascertain that the filament has adhered to the surface, for example with the use of antiflagellin antibodies that irreversibly link the filament to the surface. However, some studies may forego the use of antibodies when determining the bias. This is problematic as the cell can appear to be tethered but instead it pivots about its non-flagellated pole on a surface while the free rotation of the invisible filament causes the cell to rotate. This can lead to the mischaracterization of the direction of flagellar rotation, and therefore the rotational bias (Dominick and Wu, 2018; Lele et al., 2016; Chawla et al., 2020). Alternately, the signaling output has been determined via Förster resonance energy transfer-based measurements of in vivo enzymatic reactions (Sourjik et al., 2007). But, neither of these approaches has been realized in H. pylori. Here, we characterized the rotational bias based on the asymmetry in the swimming speeds. Our use of low-magnification microscopy allowed us to collect large sample sizes to characterize flagellar functions, considerably improving on earlier efforts (Constantino et al., 2016).

To prevent the cell from tumbling during a reversal, all the flagellar motors in a single cell of H. pylori must switch synchronously from one direction to the other. Indeed, tumbles were rarely observed. The most frequent turn angles were ~180°, which confirmed that the cells retraced their paths following a reversal – this would not have been the case if only a fraction of the motors switched to the opposite direction. This makes our approach feasible for determining the CWbias for an individual cell from its swimming speeds – which reflects the collective action of all the motors – rather than sampling individual motors. How are such multiple stochastic switchers coupled in H. pylori? One possibility is that the flagellar switch in H. pylori is ultrasensitive to small fluctuations in CheY-P levels, similar to the switch in E. coli (Cluzel et al., 2000). The close proximity of the multiple motors at a single pole in H. pylori also means that the local concentration of CheY-P in the vicinity of each flagellar switch is similar. This increases the probability of concerted switching in all the motors.

In V. alginolyticus, asymmetry in swimming speeds has been observed only near bounding surfaces but not in the bulk fluid (Magariyama et al., 2005). A limitation of our method is that it is unsuitable for tracking chemotaxis response dynamics in such species, as the asymmetry is lost whenever the cells migrate away from surfaces. In H. pylori, although, we observed asymmetric speeds in some cells even at a separation of ~200 μm from any bounding surfaces (see Appendix 6), similar to Pseudomonas putida (Theves et al., 2013). Therefore, the asymmetry is unlikely to be a surface-effect in H. pylori. The effect could be due to differences in the flagellar shape and forms (Kinosita et al., 2018) or the swimming gait in the pusher and puller modes (Lele et al., 2016; Liu et al., 2014). It is more likely that the asymmetry in speeds arises due to the differences in the CW and CCW flagellar rotational speeds, as is the case with E. coli – which run and tumble – and Caulobacter cresecentus (Yuan et al., 2010; Lele et al., 2016) – which exhibit symmetric swimming speeds in the pusher and puller modes (Table 1). Such differences in the speeds at which motors rotate CW and CCW depend on the external viscous loads (Yuan et al., 2010; Lele et al., 2016). It is possible therefore, that the asymmetry in H. pylori is also load-dependent; vanishing for longer filament lengths in highly viscous microenvironments or for very short filaments. The asymmetry is further expected to depend sensitively on the expression of the flagellar genes, which is modulated by environmental conditions (Spohn and Scarlato, 1999). The asymmetry was prominently observable in our work with a careful control of experimental conditions (Materials and methods).

Table 1
Speed asymmetry across different bacterial species.
SpeciesSwimming Speed RatioMotor Speed RatioReference
H. pylori1.5-This work
P. putida2-Theves et al., 2013
V. alginolyticus1.5-Magariyama et al., 2005
Burkholderia spp.3.9-Kinosita et al., 2018
Vibrio fischeri3.4-Kinosita et al., 2018
C. crescentus1~2Lele et al., 2016; Liu et al., 2014
E. coli~1.31.3Yuan et al., 2010; Lele and Berg, 2015

The flagellar motors in H. pylori and E. coli share structural similarities and have several orthologous components. The core chemotaxis network in the two species is also similar with the exception of a few enzymes (Lertsethtakarn et al., 2011; Howitt et al., 2011; Lertsethtakarn et al., 2015; Jiménez-Pearson et al., 2005). CheY, in its phosphorylated form, modulates flagellar functions in both species by interacting with components of the flagellar switch (Lertsethtakarn et al., 2011; Lowenthal et al., 2009a; Qin et al., 2017; Lam et al., 2010). Our results suggest that the regulatory function of CheY-P is also similar in the two species, that is, CheY-P binding to the motor increases the probability of CW rotation. If so, then the implications of this finding are significant. Because H. pylori can retrace their paths upon a reversal unlike E. coli, modulation of the rotational bias is bound to undermine chemotaxis when the cell enters the puller mode. Then, the cell would likely need a mechanism to rectify its movements with respect to the source or some type of feedback between the motors and the receptors to successfully migrate in response to chemical gradients. We anticipate that the approaches described in this work will help uncover these mechanisms and identify unknown protein functions. Our approach is extensible to any run-reversing species that exhibit asymmetric swimming speeds, paving the way to study signaling dynamics in other run-reversing bacterial species.

Materials and methods

Key resources table
Reagent type (species)
or resource
DesignationSource or referenceIdentifiersAdditional information
Cell line (H. pylori)PMSS1Ottemann LabArnold et al., 2011
Chemical compound, drugBrucella BrothMillipore SigmaB3051
Chemical compound, drugColumbia agarThermo Scientific OxoidCM0331
Chemical compound, drugDefibrinated Horse BloodHemostat LaboratoriesDHB100
Chemical compound, drugFetal Bovine SerumGibco10438
Chemical compound, drugPolymixin-B sulfateAlfa AesarJ6307403
Chemical compound, drugVancomycin hydrochlorideSigma AldrichV1130
Chemical compound, drugβ-CyclodextrinSigma AldrichC4767
Chemical compound, drugUreaFisher ScientificBP169

Strains and cell culturing

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All the work was done with H. pylori PMSS1. Cultures of microaerophilic H. pylori were grown in an incubator with controlled temperature and CO2 environment (Benchmark Incu-Shaker Mini CO2). The incubator was maintained at 10% CO2, 37°C. Fresh colonies were streaked out before each experiment on Columbia agar plates supplemented with 2.5 units/mL Polymixin-B, 10 μg/mL Vancomycin, 2 mg/mL β-cyclodextrin, and 5% v/v defibrinated horse blood. Colonies appeared on the horse-blood agar plates within 3–4 days and were picked with the aid of sterilized cotton-tipped applicators. The cells were then inoculated in 5 mL of BB10 (90% Brucella Broth + 10% Fetal Bovine Serum) to grow overnight cultures. No antibiotics were added to the liquid cultures as per previous protocols (Machuca et al., 2017; Huang et al., 2017). Overnight cultures were grown for ~16 hr to an OD600∼0.25–0.5 and diluted to OD600∼0.1 in fresh BB10. The day cultures were grown to an OD600∼0.125–0.15 in the shaker incubator set at 170 rpm under 10% CO2 and at 37°C. Prior to imaging, the cells were diluted in a motility buffer (MB- 0.01 M phosphate buffer, 0.067 M NaCl, and 0.1 mM EDTA, pH∼7.0) at ~6–7% v/v (BB10/MB).

Motility assays

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Cells were imaged in a culture-dish (Delta T system, Bioptechs Inc) on a phase-contrast microscope (Nikon Optiphot) equipped with a 10X phase objective. The dish was kept covered with a lid that was not airtight and that allowed a part of the top liquid surface to be exposed to air. Videos were recorded with a CCD camera (IDS model UI-3240LE) at 45 frames per second. Unless otherwise specified, the objective was focused ~5–20 μm away from the bottom surface of the culture-dish. All experiments were performed at 37°C unless otherwise noted.

Temperature control

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The microscope was housed inside a temperature control chamber (ETS Model 5472, Electro-Tech Systems, Inc), which enabled precise control over the temperature during the experiments. The grown cultures were stored in flasks within the chamber. Prior to each measurement, ~50 μL of cells were diluted in ~1.3–1.5 mL of MB. The entire mixture was then transferred to the culture dish and covered with the lid. As the cell density was low (~4 × 106 cells/mL) and as the liquid surface was exposed to air, oxygen gradients were minimized; the cells remained motile in MB for over an hour.

In the case of the temperature variation experiments, the cells were visualized in the dish ~5–10 min after each change in the temperature. Once recording was completed, the contents of the culture dish were emptied. The dish was then flushed with ethanol followed by copious amounts of DI water outside the chamber. The dish was then reused for further experiments. The whole cycle was repeated each time the temperature was changed.

Chemoattractant response

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We filled the culture dish with 20 mM urea (Fisher Chemical) in MB at 37°C, which served as an attractant. In the control case, no urea was added to the MB in the dish. We pipetted 50 μL of the cell culture into the dish prior to imaging. Videos were recorded and analysis was performed on the videos once the hydrodynamic flows visually subsided (~30 s).

Data analysis

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The low cell density enabled us to employ particle-tracking methods to record the swimming trajectory of each cell (Ford et al., 2017). All the videos were analyzed with custom-written MATLAB codes based on centroid-detection-based particle-tracking routines (Crocker and Grier, 1996). The experimental data shown in Figure 3C,D and Figure 4 were obtained from two biological and multiple technical replicates. All other data were collected from five or more biological and multiple technical replicates.

CWbias calculations

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Recorded videos were visually scanned with ImageJ (NIH) to confirm the number of reversals for each cell. The distance traveled between any two reversals was identified as a segment and numbered (see Figure 1A). The speeds were binned as per the segments, yielding n+1 bins for n reversals. A reversal changes the mode of motility between the pusher and the puller mode. On the other hand, a 180° turn by the cell maintains the same mode. Each reversal was therefore confirmed visually to distinguish between reversals; 180° turns were rarely observed. In cells that swam near surfaces, the pusher and puller modes were readily determined as described in Figure 2. In cells that did not swim near surfaces, we compared the mean speeds, which alternated as shown in Figure 1D. All the alternating fast speed-bins were labeled as pushers; alternating low speed-bins were labeled as pullers. The video frames corresponding to the puller bins were labeled as puller frames.

To determine the CWbias, cells that were observed for at least 0.5 s were retained for analysis. CWbias was calculated as the fraction of the time that a cell swam in the puller (slower) mode, which corresponds to CW rotation of the filament. To do this, the number of frames in which the ith cell swam in the puller mode (i.e. puller frames), NiCW, was divided by the total frames over which the cell was observed, Ni, to yield:

CWbias,i=NiCWNi

The error associated with the calculation of CWbias,i values decreases with increasing Ni. But, different cells were observed for different durations; hence the CWbias,i values were allocated weights that corresponded to their respective durations: W˙i= Ni Ni. Mean bias was determined as:

CWbias= W˙iCWbias,i

Reversal frequency was determined in a similar manner.

Appendix 1

ΔcheY cells swim in the pusher mode only

Appendix 1—figure 1
Single-cell trajectories of a H. pylori PMSS1 ΔcheY mutant are indicated.

The cells swam in clockwise-only trajectories as shown: open green circles denote the start of a trajectory; filled red circles denote the end. This behavior was observed for n > 150 cells; here we show 38 cells.

Appendix 2

Estimation of dissociation constants

The rate constants for flagellar switching from CCW to CW (kCCWCW) and CW to CCW (kCWCCW) were estimated from the CWbias and the reversal frequencies, ω:

kCCWCW=ω21-CWbias
kCWCCW=ω2CWbias

As shown in Appendix 2—figure 1, both rate constants increased until the physiological temperature (37°C) was attained; the rates decreased thereafter. Reliable estimates of the rate constants could not be obtained at 25°C, owing to the low frequency of reversals at that temperature.

Following the model of Scharf et al., 1998, the ratio of the dissociation constant (K) to the concentration of the phosphorylated CheY (C) was calculated from:

lnKeq=-ΔG0kT+m.ln(KCCW/KCW)CC+K

where Keq=CWbias1-CWbias, and K is the weighted average of the dissociation constants, KCCW and KCW, for CheY-P binding to the CCW and CW conformations, respectively. We assumed KCCW/KCW = 4.7 from an earlier work in E. coli (Fukuoka et al., 2014). The standard free energy difference between the CW and CCW conformations in the absence of CheY-P, ΔG0, was estimated at the temperatures used in our work by extrapolating previous data (Turner et al., 1996). The number of CheY-P binding sites in the flagellar switch in H. pylori, was determined from the ratio of the sizes of the switch complexes in the two species (Qin et al., 2017): mH. pylori= mE. coli(DiameterE. coli switch DiameterH. pylori switch ) where mE. coli=34 (Lele et al., 2012).

Appendix 2—figure 1
The switching rates were estimated from the CWbias and the reversal frequencies reported in Figure 4B (main text).

The maximum kCWCCW and kCCWCW values were attained at 37°C (2.75 ± 0.20 s−1 and 1.43 ± 0.08 s−1). The standard error is indicated.

Appendix 3

Wait-times for pusher and puller modes

Appendix 3—figure 1
Variation in wait-times in the pusher and puller modes with CWbias.

Each point on the plot is calculated by averaging over the number of samples noted above the point.

Appendix 3—figure 2
Wait-time distributions for (A) pusher mode (n = 322 segments) and (B) puller mode (n = 196 segments).

Gamma-fits reveal that the mean ± variance in wait-times for the pusher mode is 0.38 ± 0.06 and that for the puller mode is 0.26 ± 0.02.

Appendix 4

Diffusion model for asymmetric swimmers

Appendix 4—figure 1
Cell alignment and position are defined by the vectors e and r.

Function h(t) alternates between −1 and 1 with each reversal. The Heaviside function, H(h), describes the magnitudes of the two swimming modes with the asymmetry parameter a.

The velocity of the bacterium is expressed as:

(1) drtdt=vt=v0 et ht 1+aHt

where the unit vector e(t) represents cell alignment. The state function h(t) describes the direction of swimming, and alternates between ht=1 and ht=-1 to indicate the two modes (Appendix 4—figure 1).

h(t)={1,pusher1,puller

A Heaviside function H(t) characterizes the difference in swimming speeds in the two modes:

H(t)= {1,h(t)=10,h(t)= 1

Thus, the magnitudes of the two speeds are, vpusher=(1+a)v0 and vpuller=v0, where a is the asymmetry parameter.

Rotational diffusion causes the cell to deviate from a straight line during a run (or reversal), described by dθdt=2Dθξ(t), where the white noise is characterized by ξ(t)=0, and ξ(t)ξ(t+τ)=δ(-τ). Dθ is the rotational diffusion coefficient.

The velocity autocorrelation is:

(2) v(t)v(t+τ)=v02e(t)e(t+τ)G(t,τ)

here,

(3) Gt,τ=htht+τ1+aHt1+aHt+τ

Also, ete(t+τ)=e-Dθτ (Mikhailov and Meinköhn, 1997; Schienbein and Gruler, 1993).

The value of G in time τ is influenced by the number of reversals, k, whether they are odd or even, and the initial mode of swimming at t (see Appendix 4—table 1).

Appendix 4—table 1
Value of G(t,τ) for different possibilities.

For odd or even number of reversals occurring between time t and t+τ, corresponding cases of initial and final values for state function h and Heaviside function H are considered. Substituting h and H values in (3), G is calculated for each case.

Number of reversalsh(t)h(t+τ)H(t)H(t+τ)G(t,τ)
Even11111+a2
Even−1−1001
Odd1−110-(1+a)
Odd−1101-(1+a)

Based on table 2, the average value of the correlation can be determined from the probabilities of k reversals, Pkht,ht+τ(t,τ).

(4) G(t,τ)=(1+a)2P01,1(t,τ)+1P01,1(t,τ)+[(1+a)2Peven1,1(t,τ)+1Peven1,1(t,τ)](1+a)[Podd1,1(t,τ)+Podd1,1(t,τ)]

Assuming that the probability of finding the cell in the two modes initially (at time t) is similar (CWbias ~ 0.5), the expression reduces to:

(5) Gt,τ=1+a2+12 P0t,τ+Pevent,τ-1+aPoddt,τ

The probability Peven represents the cumulative probability that the cell undergoes an even and non-zero number of reversals (k = 2, 4, 6,). Similarly, the probability Podd represents the cumulative probability that the cell undergoes an odd number of reversals (k = 1, 3, 5,).

To determine the probabilities, we extended an approach previously developed by Groβmann and co-workers for the case of an symmetric swimmer that stochastically reverses its direction of swimming (Großmann et al., 2016). Our experimental measurements suggested that the run-times obeyed a Gamma distribution (Figure 5A, main text):

Ωt=rMtM-1e-rtM-1!

where, M is the shape-parameter and 1/r is the scale-parameter. The probability of k = 0 reversals was then determined in the Laplacian space as (Großmann et al., 2016):

(6) P0(t,τ)P^0(s,u)=1u[1s11Ω^(s)Ω^(s)Ω^(u)us]

where,

(7) Ω^s=rr+s2

To determine Peven, a summation of the even probabilities (k =2, 4, 6, ) was obtained while accounting for the turning angle, :

Peven(t,τ)β^even(s,u)=k=2,4,6,1Ω^(u)u(Ω^(u))k11Ω^(s)Ω^(s)Ω^(u)usαk
(8) =αΥ(s,u)k=2,4,6,(αΩ^(u))k1
(9) Υ(s,u)=1Ω^(u)u11Ω^(s)Ω^(s)Ω^(u)us

The series summation reduces to:

(10) k=2,4,6,(αΩ^(u))k1=αΩ^(u)1(αΩ^(u))2

Here, α = |cos|. The turning angle, , randomizes the bacterial trajectory similar to rotational diffusion but only acts upon a reversal.

Similarly,

(11) Podd(t,τ)β^odd(s,u)=αΥ(s,u)k=1,3,5,(αΩ^(u))k1

The series summation reduces to:

(12) k=1,3,5,(αΩ^(u))k1=11(αΩ^(u))2

To estimate the long-time probabilities, the final value theorem was employed:

(13) P^k(t,τ)=lims0sP^k(s,u)

Substituting (Equation 6) and (Equation 7) in (Equation 13),

(14) P0(t,τ)=1uru2M(1Ω^(u))

Substituting (Equation 7, 8 and 9), and (Equation 10) in (Equation 13),

(15) Peven(t,τ)lims0sβ^even(s,u)=rMΩ^(u)u2α2(1Ω^(u))21α2Ω^(u)2

Similarly,

(16) Podd(t,τ)lims0sβ^odd(s,u)=rM1u2α(1Ω^(u))21α2Ω^(u)2

Combining Equations (14), (15), (16), and (5),

(17) G^(u)=(1+a)2+12 {1uru2M(1Ω^(u))+rMΩ^(u)u2α2(1Ω^(u))21α2Ω^(u)2}(1+a){rM1u2α(1Ω^(u))21α2Ω^(u)2}

For two-dimensions, the diffusion coefficient D is related to the average correlation over long-times as (Großmann et al., 2016):

D=v022G^(Dθ)

Finally, we obtain the following expression for the diffusion coefficient:

or,

(18) D=v022Dθ[(1+a)2+12 {1rMDθ(1rM(r+Dθ)M)+α2rMDθrM(r+Dθ)M((r+Dθ)MrM)2(r+Dθ)2Mα2r2M}(1+a){αrMDθ((r+Dθ)MrM)2(r+Dθ)2Mα2r2M}]

For a=0 (no asymmetry in speeds) and α=1 (180° reversals), equation 3.13 from Großmann et al., 2016 is recovered.

A Gamma fit to the experimentally-determined wait-time distributions yielded M = 3 (Figure 5A, main text), such that:

(19) D=v022Dθ[(1+a)2+12 {1ωDθ(1(3ω)3(3ω+Dθ)3)+|cos|2ωDθ(3ω)3(3ω+Dθ)3((3ω+Dθ)3(3ω)3)2(3ω+Dθ)6|cos|2(3ω)6}(1+a){|cos|ωDθ((3ω+Dθ)3(3ω)3)2(3ω+Dθ)6|cos|2(3ω)6}]

Here, the reversal frequency ω = r/M.

Appendix 5

Single-cell simulation

Each cell was initialized at the origin (x=0,y=0) at time t = 0 s. Cell movement was simulated as alternating runs and reversals over a total duration of ~ 350 s. At the beginning of each run (or reversal), the time interval τi for the run (or reversal) was sampled from a Gamma distribution that was generated based on fits to experimental measurements (Figure 5A, main text). Each ith time interval τi was then divided into n batches of equal durations, Δt. The time-step Δt was fixed at 10 ms. Any remainder, rem(τi,Δt)=ζ (<Δt), was allocated to an (n+1)th batch. Within each batch, the cell was assumed to travel in a straight line with a displacement given by:

εn=vnζ, where ζ = Δt for each of the n bins and ζ = τi - nΔt for the final n+1th bin.

(20) εn=ht+τivo1+aHt+τien× ζ

Here, h is either +1 or −1 for a given interval:

(21) h(t+τi)=h(t+τi+1) and |h(t+τi)|=1

The Heaviside function: H=1h=1 and H=0h=-1. The position vector is simply: en=cosθnδi+sinθnδj

The angle θn was updated in between batches to account for rotational Brownian motion:

(22) θn+1i=θni+(2Dθζ)0.5

The x and y positions over time were calculated from, xk=1kδi.εn, yk=1kδj.εn. A sample trajectory for one such interval consisting of n+1 = 71 batches is indicated in Appendix 5—figure 1A.

Appendix 5—figure 1
Simulation results.

(A) A representative cell trajectory as it engages in a simulated run. The total run interval, τ, was split into 71 batches. The trajectory is not a straight-line owing to Brownian motion. (B) Two simulated reversals are indicated. Black and green segments indicate pusher (v=vo1+a) and puller (v=vo) modes, respectively. (C) Bacterial movements became purely diffusive over long times (~ 100 s) as indicated by the linear dependence of MSD on lag time τ (log-log plot). The value of the diffusion coefficient was calculated at these long times.

The turn angle, , is the angle between the original direction just before and the new direction just after a reversal. The angle tends to randomize the bacterial random walk, in addition to Brownian motion. The turn angle is likely influenced by kinematic properties of the cell body and filaments, as well as the flexibility of the flagellar hook. To account for the turning angle, at the start of each time interval τi, the angle θ was updated as:

θ1i+1=θendi+(2Dθζ)0.5+i+1

Note that this update only occurred at the start of each interval; subsequent batch-updates for θ within the interval occurred as per equation 22. The angles i+1 were sampled from a distribution that was obtained from fits to the experimental data (Figure 1B, main text). A representative reversal with the turning angle is shown in Appendix 5—figure 1B.

Diffusion coefficients

The simulations were repeated for 1000 cells. Mean square displacements were calculated as:

MSDτ=xt+τ-xt2+yt+τ-yt2

The MSD versus the lag time τ became linear at long times (~100 s), indicating purely diffusive behavior (Appendix 5—figure 1C). The diffusion coefficient was calculated from the slope of MSD versus τ over these times (D = slope/4 for two-dimensional walk).

Simulated diffusion with varying asymmetry and CWbias

Following the scheme described above, we simulated movements of cells over varying CWbias. To vary the bias, the mean wait times in the pusher and puller modes were varied. The wait times were Gamma distributed and the sum of the intervals (τi,pusher and τi,puller) was fixed at 0.35 s. Diffusion coefficients were calculated by simulating 1000 cells each for the conditions a= 0, 0.25, 0.5, 0.75, and 1; for CWbias = 0.14, 0.25, 0.39, 0.48, 0.61, 0.75, and 0.86. Results are plotted in Figure 5D (main text).

Appendix 6

Swimming asymmetry away from bounding surfaces

Differences in swimming speeds in the pusher and puller modes have been reported for Vibrio alginolyticus, but only near surfaces (Magariyama et al., 2005). A similar asymmetry was observed in Pseudomonas putida in the bulk fluid (Theves et al., 2013). To determine if near-wall effects played a role in the speed asymmetry in H. pylori, we recorded motile cells in the bulk, away from surfaces. To determine if near-wall hydrodynamic effects influence the asymmetry in H. pylori, we focused the microscope objective ~200 μm in the bulk fluid and recorded motility away from any surfaces in a culture-dish (see Materials and methods). Appendix 6—figure 1 shows one such trajectory. We observed that swimming speeds in consecutive segments were anti-correlated, in a similar manner as trajectories near surfaces (refer to Figure 1 in the main text of the manuscript). Although this observation has been made for a small number of cells (n = 4 cells), this preliminary data suggests that the asymmetry is unlikely to be due to the presence of nearby surfaces.

Appendix 6—figure 1
Cells of H. pylori exhibit asymmetry ~200 μm away from surfaces.

(A) Trajectory of a representative cell is shown, where the segment-color changes upon each reversal. Beginning of the trajectory is denoted by a green circle, reversals are denoted by black circles. (B) Quantitatively determined speeds of the same cell. The shaded regions indicate alternating swimming modes. (C) Average speed for each segment along with the standard deviation is indicated in a chronological manner.

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Decision letter

  1. Agnese Seminara
    Reviewing Editor; Université Côte d'Azur, France
  2. Aleksandra M Walczak
    Senior Editor; École Normale Supérieure, France
  3. Christian Esparza-Lopez
    Reviewer

In the interests of transparency, eLife publishes the most substantive revision requests and the accompanying author responses.

Acceptance summary:

In this work, the authors measure the trajectory of hundreds of swimming H. pylori cells near a surface. Taking advantage of the hydrodynamic interactions of rotating flagella with a surface, they can identify the pusher and puller mode of locomotion and quantify the velocity in these two distinct modes of locomotion. The authors find that cells decrease the rotational bias in the presence of an attractant, similar to what observed in E. coli. While the reversal frequency has received much attention in H. pylori, these results demonstrate that rotational bias is critical to quantify the chemotactic output.

Decision letter after peer review:

[Editors’ note: the authors submitted for reconsideration following the decision after peer review. What follows is the decision letter after the first round of review.]

Thank you for submitting your work entitled "Anisotropic random walks reveal chemotaxis signaling output in run-reversing bacteria" for consideration by eLife. Your article has been reviewed by three peer reviewers, and the evaluation has been overseen by a Reviewing Editor and a Senior Editor. The reviewers have opted to remain anonymous.

Our decision has been reached after consultation between the reviewers. Based on these discussions and the individual reviews below, we regret to inform you that your work will not be considered further for publication in eLife.

The discussion reached the shared conclusion that the present work does not provide sufficiently novel insight to grant publication in eLife. The interesting technique to disentangle CW from CCW modes by taking advantage of interaction with the surface has been previously used (Magariyama et al., 2005; Raatz et al. Eur. Phys. J. 2015); previous work already showed that H. pylori swims faster in forward mode rather than in backward mode (Constantino et al., 2016); the steady state bias has been previously quantified with a different technique (Howitt et al., 2011). To enrich the results and provide biological insight for this problem the author may consider to quantify thoroughly how the bias is affected by chemoattractants and chemorepellents, in which case we would consider the manuscript as a new submission.

Reviewer #1:

Antani et al. describe precise speed measurements of Helicobacter pylori, a bacterium that is used as a model of chemotaxis and motility in mammalian hosts. A main finding is that H. pylori swim with a faster speed in pusher mode, and a slower speed in puller mode. The finding that H. pylori can swim in a pusher or puller mode was already reported and appropriately referenced, but the new part here is the speed differences and use of them. Modeling suggests this anisotropic speed behavior limits diffusive behavior at physiological temps, a very interesting finding. Overall, the paper is an elegant combination of careful microscopy and modeling to understand interesting microbial behavior.

Reviewer #2:

The paper "Anisotropic random walks reveal chemotaxis signaling output in run-reversing bacteria" is primarily an experimental study of the locomotion of the bacterium H. pylori. I should preface by saying that I work in biophysics/biomechanics but I am not a biologist.

The main idea in this paper is that it is difficult to perform the standard cell-tethering experiments done with E. coli to measure bias in the motor rotation because H. pylori is a polar lophotrichous cell with all flagellar filaments sticking out from one side of the cell. The authors measure in swimming H. pylori cells two clearly distinct modes of swimming, but it is not clear which one corresponds to CCW vs. CW rotation of the motors. So they had the idea, which I find clever, to use the fact that we know that different flagellar rotation directions leads to circular tracks with different directions near surfaces. Doing this, they can identify which mode is which: the CCW motor rotation (pusher mode) is about 1.5x faster than the CW motor rotation (puller mode).

It is a very clear and well-written paper; it focuses on a single issue and treats it very convincingly. The section on the effect of temperature is a bit more foreign to me (very biological) but the rest was both interesting and appears to be correct. I am very happy to recommend this for publication.

Reviewer #3:

Measurements of the swimming behavior of H. pylori and the following claims are presented:

1) H. pylori swims faster with the flagellated pole lagging than leading.

2) The rotational bias (fraction of time spent in one flagellar rotation state) can be extracted from the individual distribution of swimming speeds.

3) The bias in rotation direction reports on "chemotactic output".

4) Different forward and backward running speeds increase diffusive spreading in run-reverse motility.

5) Swimming speed and turning frequency vary with temperature.

Even if all claims were novel and supported, the resulting impact would not justify publication in eLife. However, only claim 2 and 5 are. Some of the findings have descriptive value of interest to a section of the microbiology community.

Substantive concerns

1) The H. pylori literature background and the context of the present work are insufficiently discussed, making it laborious to assess the novelty of the claims.

2) The central claim (3) that bias reports on "chemotactic output" rests on an assumption that is not supported and that seems less likely to be true than not, namely that H. pylori performs chemotaxis by modifying the bias in flagellar rotation direction like E. coli.

a) Many other polarly flagellated species chemotact by changing turning the frequency without substantial change in bias: V. alginolyticus (Xie, Lu, Wu. Biophys. J. 2015), P. aeruginosa: (Cai et al., mbio 2016), C. crescentus (Grognot et al., bioRxiv 2020).

b) H. pylori's polar flagella enable locomotion with either direction of rotation, whereas E. coli's peritrichous flagella only enable locomotion in one rotation state. Thus bias modification makes sense for E. coli, but not for H. pylori.

c) The existing H. pylori literature also focusses on the turning frequency.

d) To support their assumption, the authors refer to the fact that modifying the turning frequency by concentration does not yield chemotaxis. That is a logical fallacy – the point made in Appendix C of the cited source (Berg's "Random Walks in Biology") is that chemotaxis is achieved by modifying turning frequency in response to changes in chemical concentration, rather than absolute concentrations. It is not a statement on the effectiveness of bias modulation vs turning frequency modulation. If the authors are referring to a different section of the book, they should state explicitly which one.

e) The "similarity in rotational bias in the two species" is referred to as grounds for assuming similarity in chemotactic strategy. Not only is the bias not similar (H. pylori shows similar durations of CCW and CW intervals, while in E. coli the typical wildtype CW bias is around ~10-15% (Montrone et al., 1998, Liu et al., 2020 and many others – though Ford et al., 2018 from the authors' lab reports a higher value), the argument also does not hold.

f) Given the crucial importance of the assumption, solid experimental evidence for it should be presented. That could be e.g. data that show that the bias changes drastically when an attractant/repellent is added.

3) Claim 1 is not novel (see e.g. Constantino et al., Science Advances 2016).

4) Claim 4 is not novel (see Theves et al., 2013).

5) The Discussion contains a number of misrepresentations of the literature.

[Editors’ note: further revisions were suggested prior to acceptance, as described below.]

Thank you for submitting your article "Asymmetric random walks reveal that the chemotaxis network modulates flagellar rotational bias in Helicobacter pylori" for consideration by eLife. Your article has been reviewed by two peer reviewers, and the evaluation has been overseen by a Reviewing Editor and Aleksandra Walczak as the Senior Editor. The following individual involved in review of your submission has agreed to reveal their identity: Christian Esparza-Lopez (Reviewer #1).

The reviewers have discussed the reviews with one another and the Reviewing Editor has drafted this decision to help you prepare a revised submission.

We would like to draw your attention to changes in our revision policy that we have made in response to COVID-19 (https://elifesciences.org/articles/57162). Specifically, we are asking editors to accept without delay manuscripts, like yours, that they judge can stand as eLife papers without additional data, even if they feel that they would make the manuscript stronger. Thus the revisions requested below only address clarity and presentation.

Summary:

In this work, the authors measure the trajectory of hundreds of swimming H. pylori cells near a surface. Taking advantage of the hydrodynamic interactions of rotating flagella with a surface, they can identify the pusher and puller mode of locomotion and quantify the velocity in these two distinct modes of locomotion. The authors find that cells decrease the rotational bias in the presence of an attractant, similar to what observed in E. coli. While the reversal frequency has received much attention in H. pylori, these results demonstrate that rotational bias is critical to quantify the chemotactic output.

Revisions:

1) the authors state "a very low basal value of the CWbias is disadvantageous as it prevents a response to an attractant stimulus – the cells cannot respond to an attractant if the pre-stimulus bias is ~ 0.", and similarly "But, a very low basal value of the CWbias is disadvantageous as it prevents cells from responding to attractants.". Is this a well-known experimental fact? In which case it may be useful to add a citation. Or do the authors infer this from their own data? In which case I missed something.

2) I think it would be helpful to discuss in the main text the results shown in Figure 5D and E. In particular, for a given asymmetry, the coefficient of diffusion first goes down with CWbias then goes up again, so that for small asymmetries the coefficient of diffusion is similar at low (~0.1) and high (~0.9) CWbias. I guess the diffusion coefficient first goes down because the fraction of time spent in the slow mode increases, but then why does it go up again?

3) As I said above, I like the data shown in Figure 4C, which demonstrates that the reversal frequency is likely not a good descriptor for chemotaxis. From what I understand, we're in fact hiding two reversal frequencies in the reversal frequency: the one from puller to pusher, and the one from pusher to puller. As for the CWbias, it tells us about the fraction of time in CW swimming, but not about the time spent in CW swimming. So I'm wondering if there's not a time information missing in the CWbias. Have the authors tried to look at the two reversal frequencies separately? Maybe the frequency of switching from puller to pusher is a more complete description of the data? Or have the authors plotted the CWbias on the x axis, and on the y axis the reversal frequency of slow to fast mode, and the reversal frequency of fast to slow mode? Although I am not asking the authors to redo the analysis, I think if they already have looked at these ways of describing the data, it would be useful for the reader to know it, and potentially to have the corresponding graphs as supplementary material.

4) Figure 3C and 3D: what are the light gray bins? The legend only indicates white for control and dark gray for attractant.

https://doi.org/10.7554/eLife.63936.sa1

Author response

[Editors’ note: the authors resubmitted a revised version of the paper for consideration. What follows is the authors’ response to the first round of review.]

The discussion reached the shared conclusion that the present work does not provide sufficiently novel insight to grant publication in eLife. The interesting technique to disentangle CW from CCW modes by taking advantage of interaction with the surface has been previously used (Magariyama et al., 2005; Raatz et al. Eur. Phys. J. 2015); previous work already showed that H. pylori swims faster in forward mode rather than in backward mode (Constantino et al. Science Advances 2016); the steady state bias has been previously quantified with a different technique (Howitt et al., 2011). To enrich the results and provide biological insight for this problem the author may consider to quantify thoroughly how the bias is affected by chemoattractants and chemorepellents, in which case we would consider the manuscript as a new submission.

In the previous version of the manuscript, we discussed an assay that enabled us to track the probability of clockwise rotation (rotational bias) in the flagellar motor in H. pylori. In the revised work, we have used that assay as suggested by the editor/reviewers to perform studies on how the bias is modulated by the chemotaxis network in response to a chemoeffector. We report the following novel findings:

1) We have shown that H. pylori decrease the rotational bias of flagellar motors (CWbias) in response to a potent chemo-attractant, urea (Figure 3C in the revised manuscript). This is similar to how E. coli modulates rotational bias in response to chemo-attractants.

2) We observe that the default direction of rotation in H. pylori is counterclockwise (CCW) in the absence of CheY, a molecule that links the chemotaxis network to the flagellar motors (Figure 3B). In the presence of CheY-P, the rotational bias increases. This is true of E. coli as well.

3) The relationship between CWbias and the reversal frequency is unimodal (Figure 4C), similar to that observed in E. coli. This is the first systematic characterization of the dependence of reversal frequencies on the rotational bias in polar –flagellates to our knowledge

Significance and impact: The novel insights reported above suggest that the chemotaxis network in H. pylori modulates the flagellar rotational bias in a similar manner to E. coli. We have modified the title accordingly. These findings are significant for the following reasons:

1) Reviewer 3 had predicted that the chemotaxis network in H. pylori was not likely to modulate the rotational bias as E. coli does, as the former is a polar-flagellate whereas the latter is peritrichous. Reviewer 3 had predicted that H. pylori were likely to adopt a frequency-modulation strategy for chemotaxis, unlike E. coli. They also had predicted that the dependence of H. pylori reversal frequency on the bias would not be similar to E. coli.

Our new results directly contradict all these predictions (see detailed responses to reviewer 3). Based on the above results, it is evident that if H. pylori adopted the frequency-modulation strategy suggested by reviewer 3, the chemotaxis network would likely be rendered superfluous. Thus, our results challenge the current understanding and intuition regarding chemotaxis in polar-flagellates.

2) Reviewer 3 correctly pointed out that the H. pylori field focuses on reversal frequencies as measure of chemotaxis response. Our results explain why this focus is misleading and why the rotational bias is a better measure of the chemotaxis output. In the canonical model, the CWbias is indicative of the chemotaxis kinase activity – when CWbias is high, the activity is high and vice-versa (see Cluzel et al., 2000). The architecture of the chemotaxis network in H. pylori shares strong similarities with the canonical model- E. coli (Lertsethtakarn et al., 2011). As we have now shown, the flagellar switch-functions are also similar in the two species. As is clearly evident from Figure 4C, a decrease in reversal frequency can indicate that either the CWbias (kinase activity) has increased or that it has decreased. But attractant decrease kinase activity; repellents increase kinase activity. Hence, we propose that reversal frequencies should not be used to report chemotaxis kinase responses to chemoeffectors. Yet, previous work in H. pylori has relied on changes in reversal frequencies alone to characterize chemotaxis responses (Schweinitzer et al., 2008; Rader et al., 2011; Sweeney et al., 2012; Sanders et al., 2013; Collins et al., 2016; Machuca et al., 2017). Therefore, we call for a change in current approaches for characterizing flagellar responses in polar flagellates based on this result.

3) Our findings (1, 2, 3) suggest that H. pylori modulate flagellar responses similar to E. coli. This is backed by known similarities in the flagellar motor structure and the makeup of the chemotaxis network in the two species. Thus, our work provides key functional information that should guide ongoing and future studies of the flagellar motor and the chemotaxis receptors/auxiliary enzymes.

4) Considering that polar-flagellates (H. pylori) undergo displacement in both modes unlike the peritrichous E. coli, our findings raise major questions: what exactly is the role of the chemotaxis kinase in H. pylori chemotaxis? Is the forward mode indeed more suitable for exploration in polar-flagellates, as has been suggested by Xie, Lu, and Wu, Biophys J, 2015 for V. alginolyticus, or is that true only in the case of certain species? Hence, our work will inspire significant research in the future on the chemotaxis mechanisms in H. pylori and other polar-flagellates in the future.

5) Reviewer 3 referred to an alternate technique employed in two previous works on the asymmetry in swimming in H. pylori (Constantino et al., 2016 and Howitt et al., 2011). Owing to the limitation of this technique, these studies based conclusions (specific to asymmetry and bias) on sample sizes consisting of 1 wild-type cell (Constantino et al., 2016) and 8 wild-type cells (Howitt et al., 2011). In contrast, our method allowed us to derive conclusions regarding flagellar functions from hundreds of wild-type cells (100 – 900 cells). We believe our work will be valuable to researchers because it raises the standard for scientific rigor for H. pylori studies.

Considering the biomedical relevance of H. pylori, which infect more than half the world population and cause stomach cancers, our findings on chemotaxis signaling will appeal the broad audience that eLife targets.

Reviewer #1:

Antani et al. describe precise speed measurements of Helicobacter pylori, a bacterium that is used as a model of chemotaxis and motility in mammalian hosts. A main finding is that H. pylori swim with a faster speed in pusher mode, and a slower speed in puller mode. The finding that H. pylori can swim in a pusher or puller mode was already reported and appropriately referenced, but the new part here is the speed differences and use of them. Modeling suggests this anisotropic speed behavior limits diffusive behavior at physiological temps, a very interesting finding. Overall, the paper is an elegant combination of careful microscopy and modeling to understand interesting microbial behavior.

We thank the reviewer for the positive comments. We have clarified our main findings and its potential impact in the response above.

Reviewer #2:

The paper "Anisotropic random walks reveal chemotaxis signaling output in run-reversing bacteria" is primarily an experimental study of the locomotion of the bacterium H. pylori. I should preface by saying that I work in biophysics/biomechanics but I am not a biologist.

The main idea in this paper is that it is difficult to perform the standard cell-tethering experiments done with E. coli to measure bias in the motor rotation because H. pylori is a polar lophotrichous cell with all flagellar filaments sticking out from one side of the cell. The authors measure in swimming H. pylori cells two clearly distinct modes of swimming, but it is not clear which one corresponds to CCW vs. CW rotation of the motors. So they had the idea, which I find clever, to use the fact that we know that different flagellar rotation directions leads to circular tracks with different directions near surfaces. Doing this, they can identify which mode is which: the CCW motor rotation (pusher mode) is about 1.5x faster than the CW motor rotation (puller mode).

It is a very clear and well-written paper; it focuses on a single issue and treats it very convincingly. The section on the effect of temperature is a bit more foreign to me (very biological) but the rest was both interesting and appears to be correct. I am very happy to recommend this for publication.

We thank the reviewer for these positive comments. We have now provided context to the temperature experiments; they enabled us to extract the dependence of reversal frequency on rotational bias, which challenges one of the major predictions by reviewer 3. These and other main advances from our new work and its impact has been discussed in the response above. Also see responses to reviewer 3.

Reviewer #3:

Measurements of the swimming behavior of H. pylori and the following claims are presented:

1) H. pylori swims faster with the flagellated pole lagging than leading.

2) The rotational bias (fraction of time spent in one flagellar rotation state) can be extracted from the individual distribution of swimming speeds.

3) The bias in rotation direction reports on "chemotactic output".

4) Different forward and backward running speeds increase diffusive spreading in run-reverse motility.

5) Swimming speed and turning frequency vary with temperature.

We have listed the key findings and the impact from the revised work in our response to this reviewer and editor’s comments. We have significantly updated the text to clarify the main advances from our work based on reviewer 3 and other reviewers’ comments. These comments have considerably improved the impact of the work (in our opinion). We are grateful, thank you!

Even if all claims were novel and supported, the resulting impact would not justify publication in eLife.

We observed that H. pylori modulate the rotational bias similar to E. coli in response to a strong attractant (see Figure 3C, D), where the gray data indicates response to attractant and the white data indicates a control. We also show that the bias in H. pylori is zero in the absence of CheY (Figure 3B) and that the presence of CheY increases the bias, similar to E. coli (Figure 3A).

Although reviewer 3 had predicted that the reversal frequency versus rotational bias relationship would not be similar between the two species, our data suggest otherwise (Figure 4C). These results highlight the inaccuracies prevalent in current approaches in the field, which rely on quantification of the reversal frequencies in H. pylori for characterizing chemotaxis response (Schweinitzer et al., 2008; Rader et al., 2011; Sweeney et al., 2012; Sanders et al., 2013; Collins et al., 2016; Machuca et al., 2017). Also see Discussion section.

Finally, our observations of functional similarities in the chemotaxis signaling between the two species is significant as polar-flagellates such as H. pylori have the ability to reverse their paths. To chemotax, they likely rely on strategies that are currently unknown. Our findings call for investigations into the mechanisms of chemotaxis in this particular species, and possibly in others (see Discussion section).

However, only claim 2 and 5 are. Some of the findings have descriptive value of interest to a section of the microbiology community.

We are glad that the reviewer agrees that our method to extract rotational bias is novel. We now show how valuable the temperature experiments will be for all scientific communities interested in chemotaxis – these experiments helped discover the dependence of reversal frequencies on the rotational bias in H. pylori for the first time in a polar-flagellate (to our knowledge).

Substantive concerns

1) The H. pylori literature background and the context of the present work are insufficiently discussed, making it laborious to assess the novelty of the claims.

We believe that we had cited all the prominent literature relevant to chemotaxis in H. pylori including Constantino et al., 2016 and Howitt et al., 2011. We have now added several related works for chemotaxis in polar-flagellates. Specifically, we cite: Constantino et al., 2016; Howitt et al., 2011; Xie et al., 2015; Cai et al., 2015; and Morse et al., 2016. We would be happy to add other citations that we may have missed.

2) The central claim (3) that bias reports on "chemotactic output" rests on an assumption that is not supported and that seems less likely to be true than not, namely that H. pylori performs chemotaxis by modifying the bias in flagellar rotation direction like E. coli.

Our new experiments argue against this notion that H. pylori do not modify the flagellar bias similar to E. coli. We showed that:

1) In the absence of CheY, motors rotate CCW-only.

2) In the presence of CheY, the bias is higher (~ 0.35).

3) Treatment with attractant, which is expected to decrease the kinase activity, reduces the bias. The decrease in reversal frequency occurs as a consequence.

4) And the reversal frequency unimodally depends on the bias.

These are key similarities between E. coli and H. pylori. Our functional data are backed by the structural similarity in the motor and the architectural similarity in the chemotaxis network (see Discussion section for references).

a) Many other polarly flagellated species chemotact by changing turning the frequency without substantial change in bias: V. alginolyticus (Xie, Lu, Wu. Biophys. J. 2015), P. aeruginosa: (Cai et al., 2016), C. crescentus (Grognot et al., bioRxiv 2020).

Tang and co-workers reported that forward run durations in C. crescentus were prolonged (shortened) when the cell migrated up (down) an attractant gradient (Morse et al., 2016). This suggests that the C. crescentus modulates its rotational bias during chemotaxis. These results were challenged recently by the work of Grognot and Taute, which is unpublished at the time of our submission.

In the work of Xie et al., 2015, the flagellar motors in V. alginolyticus appeared to modulate their reversal frequency without a substantial change in bias. However, recent cryo-ET maps of V. alginolyticus motors suggest that the CW conformation is likely stabilized by CheY-P binding (Carroll et al., eLife, 2020). The latter result is consistent with the notion that CheY-P binding increases rotational bias, whereas the former is inline with the reviewer’s expectations.

In Cai et al., mBio, 2016, the authors assumed that the P. aeruginosa cells were tethered by their flagella to the glass surface despite eschewing anti-flagellin antibodies (see Discussion section). As explained in Chawla et al., 2020; Dominick and Wu, 2018; and Lele et al., 2016, these assumptions are not always valid in the absence of antibodies and can lead to errors in distinguishing CW and CCW turns of the motor. This in turn can lead to erroneous measurements of rotational bias.

As the foregoing discussion and response demonstrate, there is plenty of uncertainty in our opinion regarding the modulation of flagellar functions in polar-flagellated species.

b) H. pylori's polar flagella enable locomotion with either direction of rotation, whereas E. coli's peritrichous flagella only enable locomotion in one rotation state. Thus bias modification makes sense for E. coli, but not for H. pylori.

Our data (Figure 3A-C) argue against reviewer 3’s prediction that H. pylori are unlikely to modulate bias. The observation that the reversal frequency exhibits a unimodal dependence on the bias (Figure 4C) likely indicates that the reversal frequency also exhibits a unimodal dependence on CheY-P, similar to E. coli (see Figure 6B and Cluzel et al., 2000). Were H. pylori to adopt the frequency modulation strategy as suggested by reviewer 3, an increase as well as a decrease in CheY-P would cause a decrease in reversal frequency – meaning both attractant and repellents would induce the same flagellar response and therefore, H. pylori would be attracted to repellents as well. This would render the chemotaxis network superfluous.

These findings are impactful since they point to a strategy of chemotaxis signaling in H. pylori (and possibly other polar-flagellates) that is presently unknown.

c) The existing H. pylori literature also focusses on the turning frequency.

We agree. We urgently call for a revision of these current approaches in the light of our new findings (Figure 4C). A decrease in reversal frequency can lead to the false impression that the kinase activity has increased when in fact it has decreased and vice-versa (see Discussion section and Figure 6). On the other hand, a change in bias is likely to be more representative of the kinase activity. Given that our study challenges current approaches, we are hopeful that the reviewer will appreciate the impact of our work.

d) To support their assumption, the authors refer to the fact that modifying the turning frequency by concentration does not yield chemotaxis. That is a logical fallacy – the point made in Appendix C of the cited source (Berg's "Random Walks in Biology") is that chemotaxis is achieved by modifying turning frequency in response to changes in chemical concentration, rather than absolute concentrations. It is not a statement on the effectiveness of bias modulation vs turning frequency modulation. If the authors are referring to a different section of the book, they should state explicitly which one.

We agree that this was confusingly presented. Our point was that mere dependence of reversal frequencies on absolute chemical concentrations (or temperatures) is not sufficient for chemotaxis – this is mentioned in the cited source. Yet, current works (Schweinitzer et al., 2008; Rader et al., 2011; Sweeney et al., 2012; Sanders et al., 2013; Collins et al., 2016; Machuca et al., 2017), have quantified the effect of absolute concentrations on the steady-state reversal frequencies to characterize the response to chemicals. Based on our data, we propose that these approaches are inaccurate. We have modified the text to avoid confusion.

e) The "similarity in rotational bias in the two species" is referred to as grounds for assuming similarity in chemotactic strategy. Not only is the bias not similar (H. pylori shows similar durations of CCW and CW intervals, while in E. coli the typical wildtype CW bias is around ~10-15% (Montrone et al., 1998, Liu et al., 2020 and many others – though Ford et al., 2018 from the authors' lab reports a higher value), the argument also does not hold.

This is a misunderstanding; we never suggested in the original manuscript that the chemotactic strategy is similar between the two species. Our claim was:

“The bias was similar to that observed in E. coli (28, 29), suggesting that the basal chemotactic output in the two species is similar.”

The basal chemotactic output refers to kinase activity as well as the rotational bias, and is distinct from chemotaxis (navigation) strategy. We stand by this statement based on our work and that of others, where the bias was ~ 0.3-0.4 in E. coli: Block et al., 1982; Block et al., 1983; Segall et al., J Bacteriol, 1986; Sagawa et al., 2014; Stock et al., 1985. We have cited these works.

f) Given the crucial importance of the assumption, solid experimental evidence for it should be presented. That could be e.g. data that show that the bias changes drastically when an attractant/repellent is added.

We believe we have met this requirement.

3) Claim 1 is not novel (see e.g. Constantino et al., Science Advances 2016).

Although we did not claim in the original manuscript that we discovered asymmetric swimming in H. pylori, we regret that the description created this impression. We now discuss this finding in the Results.

We draw the reviewer’s attention to the actual data discussed by Constantino and co-workers, a study whose main focus was not on swimming speeds. To distinguish between the two modes in H. pylori, the authors attempted to visualize the flagella. However, they were able to demonstrate data for only 1 wild-type cell, where the flagellum is at least partially visible, in the entire manuscript (including supplementary text and video) –. The authors discussed the technical challenges with flagellar visualization, which likely limited sampling. The conclusions were based on their claim that the pole that carried the flagella exhibited rapid changes in contrast during cell movement, which made it unnecessary to view the flagella. However, the authors failed to rigorously support this claim – as mentioned, only 1 cell data was shown where a change in contrast is discernible. In our opinion, no conclusions can be made from such limited data. In the work of Howitt and co-workers, they drew conclusions regarding bias based on a sample size of 8 cells. In both studies, experiments were performed at room temperature.

In contrast, we relied on well-established hydrodynamic models to show that the pusher mode is faster. Our method is high-throughput allowing sample sizes ~ 100 to 900 cells. Finally, we have performed experiments at physiologically relevant temperatures (37°C) for H. pylori unlike these other works. Thus, our findings are relevant to the biomedical problems posed by H. pylori.

4) Claim 4 is not novel (see Theves et al., 2013 for P. putida).

Theves and co-workers found that their diffusion model for asymmetric swimmers (P. putida) was inaccurate as they made an unrealistic assumption that the wait-times were exponentially distributed. However, they did not derive the appropriate expressions for the diffusion coefficients with the more general, Γ distributed wait-times.

In our work, we have shown that H. pylori wait time intervals are Γ distributed and not exponentially distributed, hence Theves et al.’s model does not apply. To realistically model the diffuse spread, we developed a model that incorporated the more difficult-to-derive but general form of distributions (Γ distribution). We now clarify this in the main-text. Thus our derivation and models are an improvement over the previous work, as can be seen from the close agreement between simulations and models (Figure 5C).

[Editors’ note: what follows is the authors’ response to the second round of review.]

Revisions:

1) The authors state "a very low basal value of the CWbias is disadvantageous as it prevents a response to an attractant stimulus – the cells cannot respond to an attractant if the pre-stimulus bias is ~ 0.", and similarly "But, a very low basal value of the CWbias is disadvantageous as it prevents cells from responding to attractants.". Is this a well-known experimental fact? In which case it may be useful to add a citation. Or do the authors infer this from their own data? In which case I missed something.

The logic here is that if the pre-stimulus (basal) CWbias was already at its minimum value (=0), then further reduction upon stimulation with attractants is not possible. This would inhibit chemotaxis towards attractants. We clarify this in the main text as:

“However, a very low basal value of the CWbias is disadvantageous from a chemotaxis perspective. H. pylori appear to respond to attractants by reducing their CWbias (Figure 3C). They would lose their ability to respond to attractants if the pre-stimulus (basal) bias was close to its minimum value (=0)”.

Also:

“Thus, the preference for the faster pusher mode (lower CWbias) in H. pylori is advantageous as it helps them spread faster (Figure 5D). However, H. pylori appear to respond to attractants by reducing their CWbias (Figure 3C). A basal value ~ 0 would mean that the CWbias cannot be reduced further, preventing the cell from responding to attractants.”

2) I think it would be helpful to discuss in the main text the results shown in Figure 5D and E. In particular, for a given asymmetry, the coefficient of diffusion first goes down with CWbias then goes up again, so that for small asymmetries the coefficient of diffusion is similar at low (~0.1) and high (~0.9) CWbias. I guess the diffusion coefficient first goes down because the fraction of time spent in the slow mode increases, but then why does it go up again?

We agree and have provided additional insights regarding the diffusion coefficients in Figure 5D and E. For a symmetric swimmer (a=0), the displacement in a run tends to cancel out the displacement during a reversal, which minimizes the diffusivity at CWbias ~ 0.5. The net displacement (and therefore, the diffusivity) increases when the CWbias is less than or greater than 0.5. This is why the diffusivity is high at low CWbias, minimizes at CWbias ~ 0.5, and then increases again at high CWbias. As the asymmetry increases, the net displacement (and therefore the diffusivity) increases when the swimmer prefers the slower mode (CWbias > 0.5). However, the displacement (diffusivity) is much higher when the CWbias is lower – it is more advantageous to spend a greater fraction of the time in the faster mode. We clarify this in the text:

“As shown in Figure 5D, the simulated diffuse spread was low when cells covered similar distances in the forward and backward directions, thereby minimizing net displacement. This tended to occur for swimmers with low a values that swam for equal durations in the two directions (CWbias ~ 0.5). For any given a, the diffuse spread increased with the net displacement during a run-reversal, for example, when the swimmer preferred the slower mode much more than the faster mode. The net displacement, and hence, the spread tended to be the highest when the cells spent a greater fraction of the time swimming in the faster mode compared to the slower mode.”

3) As I said above, I like the data shown in Figure 4C, which demonstrates that the reversal frequency is likely not a good descriptor for chemotaxis. From what I understand, we're in fact hiding two reversal frequencies in the reversal frequency: the one from puller to pusher, and the one from pusher to puller. As for the CWbias, it tells us about the fraction of time in CW swimming, but not about the time spent in CW swimming. So I'm wondering if there's not a time information missing in the CWbias. Have the authors tried to look at the two reversal frequencies separately? Maybe the frequency of switching from puller to pusher is a more complete description of the data? Or have the authors plotted the CWbias on the x axis, and on the y axis the reversal frequency of slow to fast mode, and the reversal frequency of fast to slow mode? Although I am not asking the authors to redo the analysis, I think if they already have looked at these ways of describing the data, it would be useful for the reader to know it, and potentially to have the corresponding graphs as supplementary material.

We estimated the wait-times for the two modes (τpusher and τpusher) as a function of the bias as per reviewer request, and have included them in the supplementary information (Appendix 1—figure 3).

4) Figure 3C and 3D: what are the light gray bins? The legend only indicates white for control and dark gray for attractant.

There are only two types of data – white and dark gray. The light gray data showed the overlap between the bars in the histograms. We have fixed this by bringing the dark gray data in front of the white; the overlap can be discerned from horizontal lines within the gray bars in Figure 3C and 3D.

https://doi.org/10.7554/eLife.63936.sa2

Article and author information

Author details

  1. Jyot D Antani

    Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX 77843, United States
    Contribution
    Data curation, Software, Formal analysis, Validation, Investigation, Visualization, Methodology, Writing - original draft, Writing - review and editing
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-7402-983X
  2. Anita X Sumali

    Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX 77843, United States
    Contribution
    Formal analysis
    Competing interests
    No competing interests declared
  3. Tanmay P Lele

    1. Department of Biomedical Engineering, Texas A&M University, College Station, TX 77840, College Station, TX 77840, United States
    2. Department of Translational Medical Sciences, Texas A&M University, Houston, TX 77030, United States
    Contribution
    Conceptualization, Formal analysis, Writing - original draft
    Competing interests
    No competing interests declared
  4. Pushkar P Lele

    Artie McFerrin Department of Chemical Engineering, Texas A&M University, College Station, TX 77843, United States
    Contribution
    Conceptualization, Resources, Data curation, Software, Formal analysis, Supervision, Funding acquisition, Validation, Visualization, Methodology, Writing - original draft, Project administration, Writing - review and editing
    For correspondence
    plele@tamu.edu
    Competing interests
    No competing interests declared
    ORCID icon "This ORCID iD identifies the author of this article:" 0000-0002-2894-3487

Funding

Cancer Prevention and Research Institute of Texas (RP170805)

  • Pushkar P Lele

National Institute of General Medical Sciences (R01-GM123085)

  • Pushkar P Lele

Cancer Prevention and Research Institute of Texas (RR200043)

  • Tanmay P Lele

The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication.

Acknowledgements

We thank Professor Karen Ottemann for the PMSS1 strains, and Professor Michael Manson and Rachit Gupta for comments.

Senior Editor

  1. Aleksandra M Walczak, École Normale Supérieure, France

Reviewing Editor

  1. Agnese Seminara, Université Côte d'Azur, France

Reviewer

  1. Christian Esparza-Lopez

Publication history

  1. Received: October 11, 2020
  2. Accepted: January 12, 2021
  3. Version of Record published: January 25, 2021 (version 1)

Copyright

© 2021, Antani et al.

This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.

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