Magnetotactic bacteria optimally navigate natural pore networks
- Department of Physics, Clark University, United States
Figures
Figure 1
Multicellular magnetotactic bacterial consortia are directed through an artificial pore network by an applied magnetic field.
(a) The trajectories (green lines) of several hundred consortia (black dots) are shown. While each consortium is composed of tens of individual bacteria, it grows and moves like a single organism. The black boundaries show the positions of the microfluidic pillars, which separate the pores. The applied magnetic field is μT, corresponding to . (b) Averaging the positions of consortia across all pores over the course of an experiment yields the probability density within a pore. The edges of the pore are highlighted in blue. A detailed description of how these probability distributions are measured is provided in Materials and methods. The magnetic field is μT and the scattering number . The black line shows a representative trajectory of a consortium, which passed through a pore in 5.6 s. (c) Weakening the magnetic field produces a wider distribution of positions, which extends from the northernmost wall to the passages to neighboring pores. This panel corresponds to the experiment in (a). A representative trajectory is shown for a consortium that escaped in 1.2 s. (d) At low magnetic field ( μT, ), consortia swim in roughly straight lines and are randomly reoriented by collisions with the walls. The black line shows the trajectory of a consortium that escaped to a southward pore after 7.4 s.
Figure 2 with 2 supplements
The speed of consortia through a pore space is maximized at a finite value of Sc.
(a) The rates at which consortia (white spots) move with () and against () the applied magnetic field are measured in a small network of pores. The trajectories—shown here as colored lines that dim over the course of 4 s—are reconstructed from the instantaneous positions of consortia. Consortia move less than a consortium radius between frames, which are recorded at 75 frames/s. The blue and red trajectories highlight two consortia that transition either in the direction of (blue) or in the negative sense (red). This image, taken at ( μT), is a still from Figure 2—video 1. (b) Tracking the motion of a total of 938 consortia at various magnetic fields provides . The reported values of Sc are measured for each group of consortia moments before it enters the pore space. The solid lines show the predicted relationship for simulated consortia. (c) The asymmetry in transition rates causes multicellular magnetotactic bacteria (MMB) to drift through the pore space in the direction of the magnetic field at speed . The solid line shows the predicted relationship. The theoretical curves in (b) and (c) require no fitting parameters. Their calculation from simulations is discussed in Materials and methods. The source data for the experiments and simulations can be found in Figure 2—source data 1 and Figure 2—source data 2, respectively. (d) The measured values of the drift velocity are well approximated by the predicted form of with no fit parameters. The horizontal error bars reflect both the uncertainty in the measured value of Sc and the uncertainty in arising from the finite number of simulations, which are discussed in Materials and methods.
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Figure 2—source data 1
Experimental data for transition rates of multicellular magnetotactic bacteria (MMB) between chambers.
The file includes the scattering number, the dimensionless transition rates , the dimensionless drift velocities for each experiment, and the associated uncertainty in all of these quantities.
- https://cdn.elifesciences.org/articles/104797/elife-104797-fig2-data1-v1.csv
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Figure 2—source data 2
Theoretical data for the transition rates between chambers.
The file includes the scattering number at which the simulation was conducted, the predicted dimensionless drift velocity, and the numerical uncertainty in this quantity.
- https://cdn.elifesciences.org/articles/104797/elife-104797-fig2-data2-v1.csv
Figure 2—video 1
Video of a small pore space in which are measured.
Figure 2a shows a still from this video. Consortia appear as white dots. Trajectories appear as colored lines. The blue line highlights a consortium that moves between pores in the direction of the magnetic field. The red trajectory moves between pores twice, once with the applied magnetic field and then against it. The applied magnetic field is and . The video is slowed to 80% of the true speed. Clickable link: https://youtu.be/SibUoIuCc2c.
Figure 2—video 2
A simulation of point-like consortia (red dots) moving between pores shows the equilibrium distribution and fluctuations at .
The magnetic field points to the right. As , simulated consortia accumulate mainly in the northernmost pore. These dynamics and the associated transition rates depend only on the scattering number. Simulations that calculate the first passage times between pores at 100 different values of Sc are used to produce the smooth curves in Figure 2b and c. Clickable link: https://youtu.be/a897UT0hZ2I.
Figure 3
Diverse magnetotactic taxa are able to optimally navigate the pore spaces of medium to coarse sand.
These organisms tune their swimming speeds, rotational hydrodynamic mobilities, and magnetic moments to the local geomagnetic field. A table of the phenotypic parameters shown here and their sources is provided in Appendix 1. (a) All taxa have scattering numbers that are similar to or slightly less than unity. By contrast, random phenotypes, which lack correlations between phenotypic variables, are characterized by large and widely distributed scattering numbers. That the measured values of Sc are anomalously narrowly distributed indicates selective pressure. The gray shaded region () shows the estimated range of scattering numbers that allow for efficient navigation. (b) The scaling analysis predicts that the rate that a species aligns with local geomagnetic field is proportional to the swimming speed. The solid line shows , which is the optimal value predicted in Figure 2c. The gray shaded region and legend are the same as in the first panel.
Figure 4
Schematic of a typical microfluidic photomask.
White regions correspond to 40 μm tall regions that are filled with seawater. The pink area shows the location where we place a spacer that creates a 1 ml void, called the vestibule. After filling the chamber with filtered seawater, an enrichment is inoculated into the vestibule. A 300 μT field pointed to the left directs consortia to accumulate near the red line, where Sc is measured. Reversing the magnetic field directs consortia into the pore network, which is highlighted here in blue. The scale bar is 1 mm.
Figure 5
The transition rates and the drift velocity are calculated from first passage times of simulated magnetotactic swimmers at various values of Sc.
(a) The probability that swimmers escape a pore in the positive sense in a time is exponentially distributed. The blue dots are the results of simulations. The blue line shows the best fit exponential. The red dots and line correspond to motion against the direction of the magnetic field. These data were simulated at . (b) The asymmetry in the transition rates causes swimmers to move through the pore space with an average speed , which is calculated for each simulation (black lines). The blue curve shows a most probable smooth function that approximates the results of the simulation. Only the smooth curves for are shown in Figure 2.
Figure 6
The trajectory of a consortium is shown in black.
At the start of the experiment, the consortium swims with velocity in the vertical direction and the applied magnetic field is pointed to the right. The red line shows the best fit to Equations 6 and 7, from which we measure γ and .
Appendix 1—figure 1
This companion figure to Figure 3 provides references for each data point.
Each number corresponds to the index on Appendix 1—table 1.
Author response image 1
Videos
Video 1
Multicellular magnetotactic bacteria move through an artificial pore space.
Each white dot shows a spherical consortium composed of tens of individual bacteria, which grow and move like a single multicellular organism. The red pillars show the separations between neighboring pores. The video is slowed to 80% of the true speed.
Video 2
At scattering number , trajectories of consortia (bright lines) are roughly straight between collisions.
The video is slowed to 80% of the true speed.
Tables
Appendix 1—table 1
The unidentified magnetotactic bacteria labeled MTB-(some integer) correspond to the organisms listed in Table 1 of Esquivel and De Barros, 1986.
| Index | Species | Ref. | |||||||
|---|---|---|---|---|---|---|---|---|---|
| 1 | M. bavaricum | 49 | 36 | 9×3 | 14.9 | 1.0 | 0.8 | 0.2 | Petersen et al., 1989; Spring et al., 1993 |
| 2 | MYC-1 | 54 | 141 | 1.7 | 1.8 | 20.9 | 2.0 | 0.3 | Pan et al., 2009 |
| 3 | M. magneticum AMB-1 | 47 | 44 | 3×0.9 | 0.4 | 23.5 | 0.5 | 0.5 | Nadkarni et al., 2013 |
| 4 | M. magneticum | 51 | 19 | 4.7×0.7 | 0.6 | 9.4 | 0.3 | 0.3 | Bahaj et al., 1996 |
| 5 | MTB-1 | 23 | 100 | 1 | 0.3 | 375.3 | 2.6 | 0.2 | Esquivel and De Barros, 1986 |
| 6 | MTB-2 | 23 | 50 | 2 | 0.5 | 42.2 | 0.5 | 0.5 | Esquivel and De Barros, 1986 |
| 7 | MTB-3 | 23 | 12 | 5×3 | 1.0 | 5.1 | 0.1 | 0.5 | Esquivel and De Barros, 1986 |
| 8 | MTB-5 | 23 | 40 | 5 | 2.4 | 1.9 | 0.1 | 1.9 | Esquivel and De Barros, 1986 |
| 9 | MTB-7 | 23 | 70 | 5 | 8.0 | 2.7 | 0.5 | 0.7 | Esquivel and De Barros, 1986 |
| 10 | MTB-8 | 23 | 30 | 18×10 | 54.0 | 0.1 | 0.1 | 1.3 | Esquivel and De Barros, 1986 |
| 11 | Magnetococcus | 23 | 85 | 1.3 | 8.2 | 6.2 | 1.2 | 0.4 | Acosta-Avalos et al., 2019 |
| 12 | Magnetoglobus | 51 | 75 | 5 | 7.4 | 2.5 | 0.9 | 0.4 | Petroff et al., 2022 |
| 13 | Magnetoglobus | 51 | 133 | 5 | 8.3 | 2.5 | 1.1 | 0.6 | This study |
| 14 | Magnetoglobus | 23 | 110 | 5.7 | 14.2 | 2.1 | 0.7 | 0.8 | Carvalho et al., 2021 |
| 15 | Uncultured MTB coccus | 23 | 84 | 1.5 | 1.4 | 122.0 | 3.9 | 0.1 | Carvalho et al., 2021 |
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Magnetotactic bacteria optimally navigate natural pore networks
eLife 14:RP104797.
https://doi.org/10.7554/eLife.104797.3
