Optimal chemotactic navigation in disordered landscapes

Reviewer #1 (Public review):

In this manuscript, the authors study optimal chemotactic navigation of bacteria in disordered environments. Most previous work has studied bacterial chemotaxis in free liquid, but navigation in obstructed environments is gaining more attention. Here, the authors first used the classic swim plate assay to select E. coli for chemotaxis in soft agar at two agar concentrations. In the higher concentration, they observed that the population's migration speed increased and the mean run duration decreased over selection cycles. Importantly, the growth rate did not change, so the change in migration speed was due to improved chemotaxis. Then, using a strain in which they could control the mean run duration with an inducible promoter, they measured population migration speed as a function of mean run duration, observing a peak. In liquid, theory predicts a peak when the run duration is comparable to the time scale of rotational diffusion. Here, the peak is at a much shorter run duration, and the optimal run duration decreased with agar concentration. A key feature in previous studies of bacterial motion in obstructed environments has been the dynamics of cell trapping and escape via tumbling. By directly visualizing the flagella in single cells, the authors found that the majority of trap events in semisolid agar did not end with a tumble. This is important because it means that the peak in the migration speed has a different origin from the peak typically seen in the diffusion coefficient, which is due to a balance between longer runs and less time spent trapped. Instead, using a minimal theoretical model, the authors argue that the peak in the migration speed is due to a balance between longer runs, which improve chemotaxis, and having those runs terminate with a tumble rather than a trap event, because runs that end with trapping do not result in up-gradient bias. Qualitatively similar behavior is seen in simulations of a more complex model of chemotaxis.

Overall, we find the results to be significant and the evidence to be strong. We have some comments, which the authors need to address to improve/clarify their work:

(1) The authors' model predicts that, because cells spontaneously escape traps without tumbling, the diffusion coefficient should depend monotonically on mean run length even though the chemotaxis coefficient is non-monotonic. It would strengthen the paper if the authors could show this to be true in experiments. Part of the reason for this comment is that the flagella labeling experiments were done in agar that was rapidly cooled in a freezer and then thawed, whereas the migration experiments were performed in agar cooled at room temperature. Our (anecdotal) understanding is that the cooling rate dramatically affects the properties of the agar mesh. Verifying that diffusivity is monotonic in mean run length would therefore show that cells' spontaneous escape from traps is not an artifact of the cooling protocol.

(2) Two agar densities were used in their study (0.2%, 0.3%). As shown in Figure 1, while cells in the 0.3% agar showed significant improvements during the directed evolutionary experiments, the cells in 0.2% agar didn't. Correspondingly, the evolved average run time did not show significant changes in the 0.2% agar, but it decreased in the 0.3% agar. What is the reason for this difference? Does it mean the cells are already optimized for the 0.2% agar medium?

(3) Related to the previous comment, the comparison between Figure 1 and Figure 2 should be made clearer. In Figure 2, a peak performance at an intermediate run time is shown, with the optimal run time decreasing with the agar density. Qualitatively, this result, i.e., the existence of the peak performance, gives the evolution experiments shown in Figure 1 a nice explanation. However, quantitatively, the run times shown in Figures 1 and 2 are quite different. For example, for the 0.3% agar case, the change of run time decreases from ~0.6sec. in cycle-1 to ~0.4sec in cycle-40. However, in Figure 2, the optimal run time is ~0.9sec., which means that the migration speed would decrease if the run time is decreased from 0.6sec to 0.4sec. We understand this may only be considered as a qualitative result. However, it does raise the question of what the molecular mechanisms are that drive the directed evolution, which the authors should address.

(4) In Figure 3B, the distributions of speed in different media (liquid versus agar) for cells with bundled and split flagella are shown. While the distribution for the bundled flagella shows nicely the emergence of the trapped state (peak near zero speed), the distribution for the split flagella shows a significant shift of the distribution. Does this mean the agar medium also changes the tumble state significantly? In fact, we are puzzled by the observation that in bulk liquid, the run speed distribution for cells with split flagella seems to be quite similar to that of cells with bundled flagella, which might indicate problems in determining run speed.

(5) Finally, none of the points plotted have error bars. Error bars would allow the readers to evaluate i) whether the changes in mean run speed during selection are significantly resolved and ii) whether the peaks in the migration speeds are significantly resolved.

Reviewer #2 (Public review):

Summary:

The manuscript by Bai and colleagues investigates how Escherichia coli navigates and explores agar gels through chemotaxis and what parameters of bacterial swimming are tuned under selection pressure for rapid migration (i.e., reaching the edge of the agar plate quickly). Prior studies have examined related questions to a substantial degree. Examples include "Migration of Chemotactic Bacteria in Soft Agar: Role of Gel Concentration" (https://pmc.ncbi.nlm.nih.gov/articles/PMC3145277) and numerous other studies in this area (e.g., "Migration of bacteria in semi-solid agar" https://www.pnas.org/doi/10.1073/pnas.86.18.6973). From such studies has emerged the paradigm/model that reorientation (i.e., tumbling) is essential when bacteria navigate agar, which is considered a model for "complex" environments, because run-only bacteria become trapped in the agar matrix and are unable to migrate far. This new manuscript provides some evidence that this paradigm may be overly simplified or incomplete. As I understand it, the authors propose that migration is influenced to a greater extent by bias in the chemotactic run, where runs up attractant gradients are longer. The authors incorporate these data into a new model for chemotactic navigation and claim that this work establishes a general principle for how bacteria optimize active transport through complex environments.

I will first note to the editor and authors that I am not qualified to assess the detailed mathematics of the model, and my review therefore focuses on the biology and phenotypes described. Nevertheless, in my view, this manuscript, in its current form, has several important limitations. For each point, I provide suggestions for additional experiments that could strengthen the rigor of the work and clarify the claims.

Strengths:

A strength of this work is the use of microscopy and automated methods to characterize an extremely large number of bacterial cells, which strengthens the authors' claims. However, substantially greater detail on these approaches is needed for the analysis to be reproducible and to allow verification that the analyses were performed correctly.

Weaknesses:

Major concerns

(1) Claims are overly broad, and the experimental system is too artificial to support general conclusions about bacteria, chemotaxis, or evolution.

E. coli MG1655 is a longstanding model organism in the chemotaxis field, and agar chemotaxis assays are also widely used. However, the authors make very broad claims about how phenotypic changes observed during selection in 0.2% or 0.3% agar relate to bacterial chemotaxis and evolution more generally. In essence, the experimental foundation on which the authors build a complex theoretical framework is limited to a domesticated laboratory strain of E. coli and a highly artificial environment consisting of agar in a Petri dish. Although E. coli is well studied, its motility and taxis behaviors are not necessarily representative of bacteria across nature. In addition, natural environments are dynamic, and bacteria rarely experience stable gradients for extended periods, such as the 24-hour time-frame used here. The authors have also only focused on responses to attractant gradients with undefined complex growth media, and not assessed if this is also true for repellent gradients. This is important to consider because E. coli also generates repellent gradients (indole) that are not considered here. E. coli also generates AI-2, sensed as an attractant, that would be an opposing force for migration. For these reasons, it is not clear that the data and theory presented here generalize to diverse bacterial species, to natural environments, or to chemotaxis broadly.

The authors should acknowledge that further work is needed to generalise their findings by testing additional organisms, such as non-laboratory E. coli isolates, other enteric bacteria, and species with fundamentally different motility systems (e.g., Campylobacter jejuni). Further work could also expand beyond agar by examining chemotaxis in a biological matrix such as mucin, as well as testing responses to defined attractants and repellents.

(2) No genetic component is identified, so claims about evolution are not supported.

Evolution requires heritable genetic changes that produce phenotypes advantageous under a given selection pressure. The authors state that bacteria were selected for rapid migration and that this selection produced progressively more efficient migrators. However, no sequencing analyses of the evolved isolates were performed, no genetic changes were identified, and no mechanism underlying this phenotypic shift was described. Without identifying genetic alterations, they cannot substantiate the claim that evolution occurred. Whole-genome sequencing of the evolved isolates is necessary to determine whether specific mutations underlie the observed phenotypes.

(3) The predictive power of the model is not tested.

The authors develop a model with post-dictive capability, meaning the model reproduces behaviors similar to those observed in the data used to construct it. However, the manuscript does not demonstrate that the model has predictive power. Demonstrating predictive performance would substantially increase the value of the model. For example, the authors could perform an additional round of selection and predict the resulting bacterial behavior under a condition not used during model construction (such as a different agar concentration or predicting the behavior of different bacteria). Otherwise, the authors should tone down the claims.

(4) Limited novelty and impact of the environmental difference studied.

A central point of the manuscript is the difference between evolution in 0.2% versus 0.3% agar and how this difference relates to the proposed model. However, this represents a relatively minor change in the environment experienced by the bacteria. Developing an extensive theoretical framework and proposing that bacterial evolution is highly sensitive to these parameters based on this narrow experimental system may be premature. This would be addressed by the suggested broadening of experiments described above.

(5) The manuscript is too brief, and some data and methods are insufficiently described, particularly related to the machine learning analysis.

The manuscript addresses a complex topic, yet the main text, methods, and figures are very brief, which need not be the case. As a result, it is often difficult to understand exactly what was done and how the data support the authors' claims. More detailed descriptions of the experimental approaches and analyses are necessary.

One example is the machine learning approach used for cell tracking. This method is only briefly described, and no validation data are presented that would allow readers to evaluate whether the approach performs accurately. If the method is robust, it would be a powerful analytical tool, but the current description does not provide sufficient information to evaluate the reliability of the results. This issue is particularly important because the authors conclude that tumbles account for less than 3% of escape events, which contrasts with previous paradigms. Automated tracking methods can be susceptible to artifacts, and therefore, rigorous validation of the tracking pipeline, supported by appropriate figures and benchmark data, is essential.

Reviewer #3 (Public review):

The manuscript by Bai et al presents a study of the effect of trapping on the efficiency of chemotactic spreading. While the overall impression of the study is positive, there are multiple drawbacks that accumulate and together make the statement of the paper not fully justifiable. Below, I provide some detailed comments in chronological order, and indicate those of particular importance.

(1) On the first page of the Introduction, the authors use the following wording: "...how bacteria optimise their intrinsic motility parameters to maximise navigation efficiency". However, it is not shown or known whether they do. In the experiments, the authors fetch the bacteria at the far front and artificially select the ones with shorter run times. The ones at the front could be the effect of heterogeneity of the population rather than an adaptation. Moreover, the authors claim that the selective pressure is via trapping. But this can be due to a multitude of other factors that change with agar concentration, availability of nutrients, osmotic properties of water, etc.

(2) At the beginning of the results section, the authors claim that for both agar concentrations, they observe a progressive increase in chemotactic navigation. I do not see how the data for 0.2 % agar would correspond to that. Migration speed remains flat.

(3) (Important). The authors claim that the mean run speed remained constant. But this is definitely not true, as seen in the plots. The speed of modernity is increasing for both agar conditions. And here it is important to note that the chemotactic drift velocity is proportional to the square of run speed (which is not the case for the formulas in this paper, see comment below). Thus, even smaller changes in v_0 can result in a significant increase in the drift velocity.

(4) (Important). Tumble bias is also significantly increasing in 0.3 agar concentration. While it is not clear from the paper what exactly the tumble bias is, if it is related to the persistence of the turning angle, this also has a linear effect on the chemotactic drift velocity.

(5) (Important). When performing aTc dependence testing, the authors didn't report how other observables of swimming behaviour are changing.

(6) (Very important). I'm not sure that by interfering with Che-Z expression, one does not affect the whole chemotactic circuit, for example, by changing G (in terms of the model) and thus the optimality occurs not due to the agar concentration/traps but due to the perturbations in the circuit. Also, the effect of different % seems to be much more minor compared to the overall induced changes in spreading speed.

(7) (Very important). I was very confused by the statement of the authors about only 3% of traps being exited due to tumble. I don't think this is possible (in a way consistent with the suggested model). Mean free run times (Figure 1C) go down to 0.4 s. Duration of tumbles is 0.3s (Figure S2c), but the duration of traps is longer than tumbles (and a bit shorter than runs). So how can it be that a running cell gets into a trap and only in 3% cases it experiences a tumble? What would be the distribution of run durations if one combines pre-trap+trap_time+post_trap run time - would they still have a mean below 1s?? It really looks like the authors are not able to detect tumbles when bacteria are trapped. Or is there an active mechanism suppressing tumbles when in the trap?

(8) It is not clear what it means that post-tumble angles were uniformly distributed. Does this refer to only trap-associated tumbles? It is known that in the freely swimming e.coli the tumbling angles are not isotropic but have a preference for the forward direction. Is it different in agar conditions?

(9) (Very important) The authors assume an oversimplified model for the chemotactic drift based on biased random walks. As a result, the answer for chemotactic drift velocity has a wrong scaling with run speed. In the linear theory of chemotaxis by de Gennes, the scaling is v_0^2, while the authors use a linear relationship. Thus, the assumption of the simplified model is incorrect. The exact effect of the traps (where no tumbling is happening, and the directional memory is conserved) needs to be properly calculated, for example, in the same de Gennes framework. And I can't say what the result would be from the top of my head because the calculation is, in fact, not too trivial. Thus, the model used is oversimplified, and thus the fact that it shows a non-monotonous relationship with tau_f is of little predictive power.

Taken together, you see that all the key points that are used in the chain of the argument about the optimality are not rock solid and allow for alternative explanations. I think all those either need to be tested explicitly or at least clearly discussed, and the respective conclusions of the paper need to be rephrased. In my view, this work needs major revision.