A. Microfluidic device used in the experiment (top view). B. Thirty bacterial trajectories selected from the data of 44-μm-wide lane in gradient assays. These represent a subset of the trajectories analyzed in panel C. C. The relationship between Δx and nΔt calculated from all trajectories in the lanes with a width of 44 μm. The black dots represent the gradient assay (∇c=0.05 μM/μm) with a total of 3206 tracks from 6 movies, while the gray dots represent no gradient (∇c=0) with a total of 4755 tracks from 10 movies. The light-yellow and light-blue shadows represent the standard error of the mean (SEM) of different trajectories in the gradient assays and the control assays, respectively. Linear fitting was performed to obtain Vd = 1.6 ± 0.3 μm/s (black solid line) and Vd = 0.2 ± 0.2 μm/s (gray solid line) for gradient and control assays respectively. Error in drift velocity represents standard deviation.

A. Schematic drawing of three typical motion states. B. Trajectories for three typical motion states. Red dots represent the start of each trajectory. C. Calculating the rotational exponent for each trajectory, γR, by fitting the mean-squared orientational displacement ⟨MSOD⟩. Dots were experimental data calculated from the tracks in Fig. 2B. Solid lines were fitting results with . The fitted γR values are 0, 0.77, and 1.80 for gray, brown, and black tracks, respectively. D. Relationship between the rotational exponent γR and the mean y position of the bacterial trajectories. Errors denote SEM. Red and purple shaded area represent the region 3 μm from the LSW and RSW, respectively. Green shaded area represents the MA region. E&F. Normalized distribution of tumble angle for tracks along the sidewalls (E) and in the MA region (F). Red solid lines are fitting results with an exponential function: y = a ∗ exp (x/b). G. Distribution of bacteria along the y-axis in the lanes with a width of 44 μm. The shades of different colors denote the same meaning as in Fig. 2D. H. Drift velocity of bacterial cells in the three regions. I. Proportions of bacterial trajectories in the three regions. Errors are standard deviations (SD).

A. The drift velocity for the experiments in lanes of different widths. The error in drift velocity is the standard deviation. B. The distribution of the radius of circular swimming from 382 trajectories in the MA regions. The peak value of the radius is ∼10 μm. C. The swimming speed of cells in lanes with different widths. The mean swimming speeds and standard deviations for lanes with widths of 6 μm, 8 μm, 10 μm, 15 μm, 25 μm, and 44 μm are 22.7 ± 8.7 μm/s, 25.4 ± 7.7 μm/s, 27.1 ± 7.9 μm/s, 21.9 ± 7.8 μm/s, 22.1 ± 7.7 μm/s, and 22.6 ± 7.5 μm/s, respectively.

A. Mean drift velocities in the LSW, MA, and RSW regions of lanes with different widths. The errors are SD. B. The proportion of bacterial cells in the LSW, MA, and RSW regions of lanes with different widths. Errors represent SD. C. The proportion of RSW-UG (cells swimming up-gradient in the RSW) and RSW-DG (cells swimming down-gradient in the RSW) for lanes with different widths.

Simulation of bacterial chemotaxis on the surface of lanes.

A. The relationship between drift velocity Vd of cells with 10 μm-radius circular swim and the lane width w. Errors denote SEM. B. The proportion of bacterial trajectories in the LSW, MA, and RSW regions of lanes with different widths, for cells with 10 μm-radius circular swim. C. The drift velocity Vd of cells with different radii of circular swim in lanes of different widths. D. The relationship between circular swim radius and lane width for optimal chemotaxis (maximal drift velocity) in Fig. 5C. The widths were extracted by fitting the peak value of w in Fig. 5A with a gaussian function. The red solid line represents a linear fit. The slope is 0.66 ± 0.03. Errors denote SD.

Geometrical analysis of optimal lane width for chemotaxis.

A. Case 1: 0 < w ≤ r. B. Case 2: r < w ≤ 2r. C. Case 3: w > 2r. The red arrows denote the velocity direction. The black solid lines represent the sidewalls. Dashed circles are trajectories. The up-gradient direction is along the positive x-axis. The green shade areas label the swim direction of cells that can swim up-gradient in the RSW. D. Relationship between probability (P) of cells swimming up-gradient in the RSW and m, where m = w/r. Red shaded area denotes m for maximal P, m ∈ (0.7,0.8).