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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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.
References
Marchetti, M. C. et al. Hydrodynamics of soft active matter. Rev. Mod. Phys. 85, 1143–1189 (2013).
Doostmohammadi, A., Ignes-Mullol, J., Yeomans, J. M. & Sagues, F. Active nematics. Nat. Commun. 9, 1–13 (2018).
Zhou, S., Sokolov, A., Lavrentovich, O. D. & Aranson, I. S. Living liquid crystals. Proc. Natl Acad. Sci. USA 111, 1265–1270 (2014).
Smalyukh, I. I., Butler, J., Shrout, J. D., Parsek, M. R. & Wong, G. C. L. Elasticity-mediated nematiclike bacterial organization in model extracellular DNA matrix. Phys. Rev. E 78, 030701 (2008).
Kumar, A., Galstian, T., Pattanayek, S. K. & Rainville, S. The motility of bacteria in an anisotropic liquid environment. Mol. Cryst. Liq. Cryst. 574, 33–39 (2013).
Mushenheim, P. C. et al. Effects of confinement, surface-induced orientation and strain on dynamic behavior of bacteria in thin liquid crystalline films. Soft Matter 11, 6821–6831 (2015).
Peng, C., Turiv, T., Guo, Y., Wei, Q.-H. & Lavrentovich, O. D. Command of active matter by topological defects and patterns. Science 354, 882–885 (2016).
Genkin, M. M., Sokolov, A., Lavrentovich, O. D. & Aranson, I. S. Topological defects in a living nematic ensnare swimming bacteria. Phys. Rev. X 7, 011029 (2017).
Genkin, M. M., Sokolov, A. & Aranson, I. S. Spontaneous topological charging of tactoids in a living nematic. New J. Phys. 20, 043027 (2018).
Sokolov, A., Mozaffari, A., Zhang, R., de Pablo, J. J. & Snezhko, A. Emergence of radial tree of bend stripes in active nematics. Phys. Rev. X 9, 031014 (2019).
Aditi Simha, R. & Ramaswamy, S. Hydrodynamic fluctuations and instabilities in ordered suspensions of self-propelled particles. Phys. Rev. Lett. 89, 058101 (2002).
Voituriez, R., Joanny, J. F. & Prost, J. Spontaneous flow transition in active polar gels. Europhys. Lett. 70, 404–410 (2005).
Giomi, L., Bowick, M. J., Mishra, P., Sknepnek, R. & Marchetti, M. C. Defect dynamics in active nematics. Phil. Trans. R. Soc. A 372, 20130365 (2014).
Thampi, S. P., Golestanian, R. & Yeomans, J. M. Vorticity, defects and correlations in active turbulence. Phil. Trans. R. Soc. A 372, 20130366 (2014).
Srivastava, P., Mishra, P. & Marchetti, M. C. Negative stiffness and modulated states in active nematics. Soft Matter 12, 8214–8225 (2016).
Putzig, E., Redner, G. S., Baskaran, A. & Baskaran, A. Instabilities, defects, and defect ordering in an overdamped active nematic. Soft Matter 12, 3854–3859 (2016).
Green, R., Toner, J. & Vitelli, V. Geometry of thresholdless active flow in nematic microfluidics. Phys. Rev. Fluids 2, 104201 (2017).
Maitra, A. et al. A nonequilibrium force can stabilize 2D active nematics. Proc. Natl Acad. Sci. USA 115, 6934–6939 (2018).
Li, H. et al. Data-driven quantitative modeling of bacterial active nematics. Proc. Natl Acad. Sci. USA 116, 777–785 (2019).
Wu, K. T. et al. Transition from turbulent to coherent flows in confined three-dimensional active fluids. Science 355, eaal1979 (2017).
Ramaswamy, S. The mechanics and statistics of active matter. Annu. Rev. Condens. Matter Phys. 1, 323–345 (2010).
Kumar, N., Zhang, R., de Pablo, J. J. & Gardel, M. L. Tunable structure and dynamics of active liquid crystals. Sci. Adv. 4, eaat7779 (2018).
Joshi, A., Putzig, E., Baskaran, A. & Hagan, M. F. The interplay between activity and filament flexibility determines the emergent properties of active nematics. Soft Matter 15, 94–101 (2019).
Peng, C. et al. Patterning of lyotropic chromonic liquid crystals by photoalignment with photonic metamasks. Adv. Mater. 29, 1606112 (2017).
Volovik, G. E. & Lavrentovich, O. D. The topological dynamics of defects—boojums in nematic drops. Zh. Eksp. Teor. Fiz. 85, 1997–2010 (1983).
Zhou, S. et al. Dynamic states of swimming bacteria in a nematic liquid crystal cell with homeotropic alignment. New J. Phys. 19, 055006 (2017).
Aharoni, A. Introduction to the Theory of Ferromagnetism Vol. 8 (Oxford Univ. Press, 1996).
Sanchez, T., Chen, D. T. N., Decamp, S. J., Heymann, M. & Dogic, Z. Spontaneous motion in hierarchically assembled active matter. Nature 491, 431–434 (2012).
Be’er, A. & Ariel, G. A statistical physics view of swarming bacteria. Mov. Ecol. 7, 1–17 (2019).
Saintillan, D. & Shelley, M. J. Instabilities and pattern formation in active particle suspensions: kinetic theory and continuum simulations. Phys. Rev. Lett. 100, 178103 (2008).
Guillamat, P., Ignés-Mullol, J. & Sagués, F. Control of active liquid crystals with a magnetic field. Proc. Natl Acad. Sci. USA 113, 5498–5502 (2016).
Guillamat, P., Ignés-Mullol, J. & Sagués, F. Taming active turbulence with patterned soft interfaces. Nat. Commun. 8, 1–8 (2017).
Cahn, J. W. & Hilliard, J. E. Free energy of a nonuniform system. 3. Nucleation in a 2-component incompressible fluid. J. Chem. Phys. 31, 688–699 (1959).
Blow, M. L., Thampi, S. P. & Yeomans, J. M. Biphasic, lyotropic, active nematics. Phys. Rev. Lett. 113, 248303 (2014).
Sokolov, A., Zhou, S., Lavrentovich, O. D. & Aranson, I. S. Individual behavior and pairwise interactions between microswimmers in anisotropic liquid. Phys. Rev. E 91, 013009 (2015).
Trivedi, R. R., Maeda, R., Abbott, N. L., Spagnolie, S. E. & Weibel, D. B. Bacterial transport of colloids in liquid crystalline environments. Soft Matter 11, 8404–8408 (2015).
Valeriani, C., Li, M., Novosel, J., Arlt, J. & Marenduzzo, D. Colloids in a bacterial bath: simulations and experiments. Soft Matter 7, 5228–5238 (2011).
Wu, X. L. & Libchaber, A. Particle diffusion in a quasi-two-dimensional bacterial bath. Phys. Rev. Lett. 84, 3017–3020 (2000).
Tinevez, J. Y. et al. TrackMate: an open and extensible platform for single-particle tracking. Methods 115, 80–90 (2017).
Schindelin, J. et al. Fiji: an open-source platform for biological-image analysis. Nat. Methods 9, 676–682 (2012).
Shribak, M. & Oldenbourg, R. Techniques for fast and sensitive measurements of two-dimensional birefringence distributions. Appl. Opt. 42, 3009–3017 (2003).
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).
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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.
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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. 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. 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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DOI: https://doi.org/10.1038/s41567-020-0793-0
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