Polar jets of swimming bacteria condensed by a patterned liquid crystal

Abstract

Active matter exhibits remarkable collective behaviour in which flows, continuously generated by active particles, are intertwined with the orientational order of these particles. The relationship remains poorly understood as the activity and order are difficult to control independently. Here we demonstrate important facets of this interplay by exploring the dynamics of swimming bacteria in a liquid crystalline environment with predesigned periodic splay and bend in molecular orientation. The bacteria are expelled from the bend regions and condense into polar jets that propagate and transport cargo unidirectionally along the splay regions. The bacterial jets remain stable even when the local concentration exceeds the threshold of bending instability in a non-patterned system. Collective polar propulsion and the different roles of bend and splay are explained by an advection–diffusion model and by numerical simulations that treat the system as a two-phase active nematic. The ability of prepatterned liquid crystalline medium to streamline the chaotic movements of swimming bacteria into polar jets that can carry cargo along a predesigned trajectory opens the door for potential applications in microscale delivery and soft microrobotics.

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Fig. 1: Experimental scheme of the cell with bacteria swimming in a patterned nematic DSCG.
Fig. 2: Trajectories, distribution and velocities of the bacteria in a dilute living nematic, \(\langle c \rangle \approx 0.3 \times 10^{14}\ {\mathrm{m}}^{-3}\), controlled by a periodic splay–bend director pattern.
Fig. 3: Emergence of the bacteria jet undulations in concentrated dispersion, \(\langle c \rangle\) ≈ 1.5 × 1014 m−3.
Fig. 4: Simulation results for the extensile living nematic (\(\alpha <0\)) based on the two-phase model.
Fig. 5: Cargo transport by the rectilinear and undulating bacterial jets.

Data availability

The data represented in Figs. 2d,g,h, 3a,c,d,i,j, 4b,d and 5g–i are available as Source Data Figs. 2–5. All other data that support the plots within this paper and other finding of this study are available from the corresponding author upon reasonable request.

Code availability

The code used to generate concentration and velocity distribution of bacteria can be accessed from https://github.com/turbikGitH/C-stripes-Bacteria-Code.git.

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Acknowledgements

We acknowledge valuable discussions with J. Toner, V. Vitelli and R. Green. We also thank S. Shiyanovskii and N. Aryasova who provided the Mathematica code for PolScope images analysis. This work was supported by NSF grants DMS-1729509 and CMMI-1663394 (plasmonic patterning). The research of I.S.A. was supported by the NSF grant PHY-1707900. K.T. was funded by the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement number 722497. A.D. was supported by a Royal Commission for the Exhibition of 1851 Research Fellowship and the Novo Nordisk Foundation (grant agreement number NNF18SA0035142).

Author information

Affiliations

Authors

Contributions

T.T., R.K. and C.P. performed the experiments, T.T. performed experimental data analysis, A.D. conceived the two-phase continuum model. K.T. developed and performed the two-phase continuum simulations with inputs from A.D. and J.M.Y. M.M.G. performed the advection–diffusion simulation, I.S.A. derived the analytical advection–diffusion model, H.Y. and Q.-H.W. provided the plasmonic photomask for patterned photoalignment, T.T. and O.D.L. wrote the manuscript with the input from all coauthors. O.D.L. conceived and supervised the project. All authors contributed to scientific discussions.

Corresponding author

Correspondence to Oleg D. Lavrentovich.

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The authors declare no competing interests.

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Peer review information Nature Physics thanks Jean Francois Joanny and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary text, Figs. 1–6, and legends for Supplementary Videos 1–10.

Supplementary Video 1

Bacterial polar jets focused by the patterned ‘C’ director field in the splay regions, moving from left to right. Bacteria moving in the opposite direction are realigned by experiencing a U-turn in bend regions. Contrast-enhanced bright-field microscope images.

Supplementary Video 2

Swimming bacteria in the uniformly aligned cell of 20 μm with the gradient of bacterial concentration. The lower part of the sample with an elevated concentration of bacteria exhibits a bend instability; in the upper part, the swimmers follow the rectilinear trajectories imposed by the uniform director.

Supplementary Video 3

Rectilinear jets experience undulations when the concentration of bacteria exceeds some threshold. The amplitude of undulations is stabilized by the underlying pre-imposed patterned director. Note that a small fraction of bacteria swim in the direction opposite to the jet. Contrast-enhanced bright-field microscope images.

Supplementary Video 4

Advection–diffusion simulation of bacterial jets and onset of their undulations. Left panel: variation of concentration of bacteria with time (shown by pseudocolours) and emergence of undulation as the concentration of bacteria increases; black ticks map the director of the passive nematic. Central and right panels: concentration (shown by pseudocoluors) and total bacterial velocity fields in the lab frame (shown by black arrows) for c+ and c populations of bacteria.

Supplementary Video 5

Two-phase simulation of jet formation by extensile swimmers in splay region. The high bacterial concentration is denoted by yellow; the depleted region is blue. The background liquid-crystal orientation is shown by red solid lines.

Supplementary Video 6

Two-phase simulation showing the undulating jet of extensile active fluid. The high bacterial concentration is denoted by yellow; the depleted region is blue. The undulation is stabilized by the underlying passive liquid crystal, marked by red solid lines.

Supplementary Video 7

Transport of single glass microspheres by the rectilinear bacterial jet moving from left to right in the splay region of the C-stripe patterned director.

Supplementary Video 8

Transport of a chain of six glass microspheres by the rectilinear bacterial jet moving from left to right in the splay region of the C-stripe patterned director.

Supplementary Video 9

Transport of microparticle by an undulating bacterial jet.

Supplementary Video 10

Snapshots of the bacteria jets at short, intermediate and long (>2 h) periods of time.

Source data

Source Data Fig. 2

Time average of bacterial concentration and theoretical fittings (Fig. 2d). Experimental bacterial velocity components along x and y axes obtained from PIV (Fig. 2g). Velocity components obtained from the advection–diffusion simulation (Fig. 2h).

Source Data Fig. 3

Parameters of the bacterial jet: amplitude, wavelength and width (Fig. 3a). Time evolution of bacterial concentration in the developing jet (Fig. 3c). Time evolution of total number of bacteria in the jet, excess of the jet’s contour length and average width of the jet (Fig. 3d). Maximum bacteria concentration as a function of normalized computational time (Fig. 3i). Distribution of bacterial concentration in the splay region at different computation times obtained from advection–diffusion simulation (Fig. 3j).

Source Data Fig. 4

Simulated concentration profiles for pushers focusing into unidirectional jets within splay regions (Fig. 4c). The steady-state amplitude of the undulation as a function of the dimensionless activity (Fig. 4d).

Source Data Fig. 5

Trajectories of colloidal particles carried by the rectilinear jet (Fig. 5g). Instantaneous horizontal velocity component of colloidal particles carried by the rectilinear jet (Fig. 5h). Mean squared displacement (MSD) along the x and y axes of the single colloid being transported by the jet (Fig. 5i).

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Turiv, T., Koizumi, R., Thijssen, K. et al. Polar jets of swimming bacteria condensed by a patterned liquid crystal. Nat. Phys. 16, 481–487 (2020). https://doi.org/10.1038/s41567-020-0793-0

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