Figures and data
Construction of sediment-mimicking obstacle channels:
Micro-computer tomography slices of sediment samples (a) are cropped out to ignore border effect due to the reconstruction and binarized (b). The binarized images are then fitted with circles (c) for statistical analysis (grain size distribution in d) and for construction of arrays of pillar-shaped obstacles (e). The images of irregular grains (b) and fitted circles (e) are used as masks to design microfluidic channels with obstacle arrays (f), in which the bacteria are injected in the middle channel (3.5 mm × 1.2 mm × 10 µm) where they encounter the obstacles.
Analysis of micro-computer tomography images of a sediment sample in water:
a) Slice of the sediment sample, b) cube from the center of the cuvette, c) and d) examples of water gaps rendered with the Amira software. e) Distribution of the smallest grain dimension (i.e., trabecular thickness analyzed with CTAn) with Gaussian fit a exp(−(x− µ)2/c2), µ = 3.83, c = 0.5903, corresponding to a mean sand grain diameter of 46 µm. f) Distribution of the water gap size (i.e., trabecular separation) with Gaussian fit a exp(−(x−µ)2/c2), µ = 42.94 µm, c = 28.66 µm. g) Percentage of sand over water as function of the distance from the bottom of the cuvette as obtained from 2D slices of the µCT images (yellow filled line) and for the equivalent fit with circles (yellow dashed line). The red points show the mean radius of the fitted circles (± standard error of the mean) in µm (right axis).
Swimming of magnetotactic bacteria through obstacle channels
A) View of a channel, in which the entrance (IN) and exit regions (OUT) are indicated, in which the bacterial density was monitored. Bacteria enter the IN region through an inlet that connects to a syringe containing bacteria. The magnetic field points to the left. B) Cumulative bacterial intensity (measuring the cumulative arrival of bacteria) in these two regions, for three different field strengths. C) Bacterial throughput, quantified by the ratio of the cumulative intensities in the OUT and IN regions as function of the magnetic field. The reduction of throughput by B = 500µT compared to B = 50µT is significant (Mann-Whitney test, p < 10−3), the increase between B = 0 and B = 50µT is weakly significant (p = 0.028), but agrees with the observation for a channel without obstacles in which the throughput increases monotonically with increasing field strength (Supporting Figure S5).
Sliding of bacteria on obstacle surfaces:
(a) Experimental trajectories of sliding bacteria (B = 0). (b) Trajectory of sliding particle in the simulation. The light blue region shows the spatial extent of the particle. Sliding is defined as motion in the sliding region (up to 2 µm from the surface, dotted line), provided that the particle also reaches the region where interactions with the obstacle take place (up to ≈ 0.6 µm from the surface, dashed line). The sliding distance is the distance covered tangentially to the surface. (c) Histogram of sliding distances as measured in the experiment (filled black circles) and the simulation (empty markers, for different values of the wall torque parameter α). We find good agreement for α = 0.2 µm.
Simulated motion of bacteria in an obstacle channel:
Heat maps of the time-averaged density of bacteria from simulations of 2000 bacteria for 30 min with a magnetic field B = 50 µT, pointing from left to right).. The blue map represents bacteria that did not arrive at the right end of the simulation box during the simulated time the red heat map represents those that did. The interplay between magnetic field and the channel’s geometry creates natural paths through the channel. These paths can include or end in traps, formed by overlapping obstacles (examples are indicated by the green boxes).
Effect of magnetic field strength on simulated swimming through obstacle channels:
(a) Motion of bacteria in a channel for different values of the field strength B (heat maps of the densities of arriving and non-arriving bacteria, blue and red, respectively, as in Figure 5) (b) Fraction ϕ of simulated bacteria that have arrived up to time t for different B. Circles mark the first-arrival times tf; crosses with thin lines mark total arrival fractions ϕtot. The curve for B = 500 µT remains at 0. (c) First-arrival times tf (top) and total arrival fraction ϕtot (bottom) as a function of the field strength B. With stronger fields, tf converges to the first-arrival time of a persistent swimmer in an empty channel (dashed grey line). ϕtot shows a peak at an intermediate (optimal) field strength, which can be explained by the interplay of two opposing effects that arise with stronger fields: effectively faster motion in the direction of the field and higher susceptibility to trapping. Blue data points show the results for the channel shown in a), gray lines show results in other channels.
Escape from traps: Simulation
(a) Trajectories of 100 bacteria escaping from the apex of a symmetric trap (B = 50 µT). The trap consists of two obstacles of radius 50 µm, in a distance of Δy = 100 µm. This results in a trap depth d = 50 µm. (b) Distribution of escape times of bacteria from the trap in (a). An exponential curve exp(−t/τ) (dashed line) is fitted to the data, with mean escape time τ = 22 s. (c) Dependence of the mean escape time τ on the field strength B for the trap in (a). An exponential curve τ0;1 exp 
Escape from trap: Experiment
The bacterial density in a trap (indicated by the yellow triangular area in the inset) is monitored over time. At the time points indicated by the arrows, the field strength is reduced (from 500 µT to 50 µT and from 50 µT to 0 µT, respectively), allowing the escape of trapped bacteria.
