Author response:

Response to Referee 1

We agree that convex walls increase the time that consortia remain trapped in pores at high magnetic fields. Since the non-monotonic behavior of the drift velocity with the Scattering number arises largely due to these long trapping times, we agree that experiments using concave pores are likely to show a peak drift velocity that is diminished or erased.

However, we disagree that a random packing of spheres or similar particles provides an appropriate model for natural sediment, which is not composed exclusively of hard particles in a pure fluid. Pore geometry is also influenced by clogging. Biofilms growing within a network of convex pillars in two-dimensional microfluidic devices have been observed to connect neighboring pillars, thereby forming convex pores. Similar pore structures appear in simulations of biofilm growth between spherical particles in three dimensions. Moreover, the salt marsh sediment in which MMB live is more complex than simple sand grains, as cohesive organic particles are abundant. Experiments in microfluidic channels show that cohesive particles clog narrow passageways and form pores similar to those analyzed here. Thus, we expect convex pores to be present and even common in natural sediment where clogging plays a role.

The concentration of convex pores in the experiments presented here is almost certainly much higher than in nature. Nonetheless, since magnetotactic bacteria continuously swim through the pore space, they are likely to regularly encounter such convexities. Efficient navigation of the pore space thus requires that magnetotactic bacteria be able to escape these traps. In the original version of this manuscript, this reasoning was reduced to only one or two sentences. That was a mistake, and we thank the reviewer for prompting us to expand on this point. As the reviewer notes, this reasoning is central to the analysis and should have been featured more prominently. In the final version, we will devote considerable space to this hypothesis and provide references to support the claims made above.

The reviewer suggests that the generality of this work depends on our finding a "positive correlation between the swimming speed and alignment [rate] based on parameters derived from literature." We wish to emphasize that, in addition to predicting this correlation, our theory also predicts the function that describes it. The black line in Figure 3 is not fitted to the parameters found in the literature review; it is a pure prediction.

Response to Referee 2

In the "Recommendations for the Authors," this reviewer drew our attention to a manuscript that absolutely should have been prominently cited. As the reviewer notes, our manuscript meaningfully expands upon this work. We are pleased to learn that the phenomena discussed here are more general than we initially understood. It was an oversight not to have found this paper earlier. The final version will better contextualize our work and give due credit to the authors. We sincerely appreciate the reviewer for bringing this work to our attention.

We disagree that the use of non-culturable organisms and our unrealistic array should be considered serious weaknesses. While any methodological choice comes with trade-offs, we believe these choices best advance our aims. First, the goal of our research, both within and beyond this manuscript, is to understand the phenotypes of magnetotactic bacteria in nature. While using pure cultures enables many useful techniques, phenotypic traits may drift as strains undergo domestication. We therefore prioritize studying environmental enrichments.

Clearly, an array of obstacles does not fully represent natural heterogeneity. However, using regular pore shapes allows us to average over enough consortium-wall collisions to enable a parameter-free comparison between theory and experiment. Conducting an analysis like this with randomly arranged obstacles would require averaging over an ensemble of random environments, which is practically challenging given the experimental constraints. Since we find good agreement between theory and experiment in simple geometries, we are now in a position to justify extending our theory to more realistic geometries. Additionally, we note that a microfluidic device composed of a random arrangement of obstacles would also be a poor representation of environmental heterogeneity, as pore shape and network topology differ between two and three dimensions.

Figures and data

The unidentified magnetotactic bacteria labeled MTB-(some integer) correspond to the organisms listed in Table 1 of S. Esquivel and De Barros (1986).