Controlling cell motion and microscale flow with polarized light fields
DDraft
Controlling cell motion and microscale flow with polarized lightfields
Siyuan Yang, Mingji Huang, Yongfeng Zhao, and H. P. Zhang
1, 2, ∗ School of Physics and Astronomy and Institute of Natural Sciences,Shanghai Jiao Tong University, Shanghai 200240, China Collaborative Innovation Center of Advanced Microstructures, Nanjing 210093, China (Dated: February 9, 2021)
Abstract
We investigate how light polarization affects the motion of photo-responsive algae,
Euglena gra-cilis . In a uniformly polarized field, cells swim approximately perpendicular to the polarizationdirection and form a nematic state with zero mean velocity. When light polarization varies spa-tially, cell motion is modulated by local polarization. In such light fields, cells exhibit complexspatial distribution and motion patterns which are controlled by topological properties of the un-derlying fields; we further show that ordered cell swimming can generate directed transporting fluidflow. Experimental results are quantitatively reproduced by an active Brownian particle model inwhich particle motion direction is nematically coupled to local light polarization. a r X i v : . [ c ond - m a t . s o f t ] F e b atural microswimmers, such as bacteria and algae, can achieve autonomous motionby converting locally stored energy into mechanical work [1–15]. Such cellular motility isnot only an essential aspect of life but also an inspirational source to develop artificial mi-croswimmers, which propel themselves through self-generated fields of temperature, chemicalconcentration, or electric potential [1, 3–7, 12, 13]. Both natural and artificial microswim-mers have been used in a wide variety of applications [16–19].To properly function in a fluctuating heterogeneous environment, microswimmers needto adjust their motility in response to external stimuli [20–23]. For example, intensityand direction of ambient light can induce a variety of motility responses in photosyntheticmicroorganisms [24–38] and artificial microwimmers [39–45]; these responses have been fre-quently used to control microswimmer motion [27, 30, 34–36, 45–53]. Besides intensity anddirection, light polarization can also affect microswimmer motility and lead to polarotaxis: Euglena gracilis cells align their motion direction perpendicular to the light polarization,possibly to maximize the light absorption [54, 55]; artificial microswimmers consisting oftwo dichroic nanomotors move in the polarization direction [44]. These previous exper-iments have focused on uniform light fields [44, 54, 55]. The possibility to use complexpolarization patterns to control polarotactic microswimmers has not been explored.In this letter, we investigate
Euglena gracilis cell motion in various polarized light fieldsin a quantitative and systematic fashion. Our experiments show that while spatially uniformpolarization aligns cells into a global nematic state with no net motion, spatially varyingfields can induce both local nematic order and mean cell motion. Further, we show thatordered cell swimming motion generates fluid flow that can transport passive tracers. Usingthe experimental data of individual cells, we construct a model to describe the influenceof local light polarization on cell orientation dynamics and quantitatively reproduce allexperimental observations.
Experiments - Euglena gracilis are unicellular flagellated microorganisms with a rod-shaped body of a length ∼ µ m and a width ∼ µ m. As shown in Fig. 1(a) and Movie S1in the Supplemental Material [56], cells swim at a mean speed ∼ µ m/s (with a standarddeviation of µ m/s.), while rolling around their long axis at a frequency of 1-2 Hz [57]. Aphotoreceptor on Euglena cell surface, marked as a red dot in Fig. 1(b), senses surroundinglight and generate signals to modulate flagellar beating pattern [33, 58].In our experiments , Euglena culture is sealed in a disk-shaped chamber ( ∼ µ m in2 igure 1. Cell motion in a uniformly polarized light field. (a) Cell trajectories (color-coded bytime) plotted on an experimental snapshot. Light polarization is horizontal and cells tend to swimvertically in the targeted direction θ T . (b) shows a schematic for a cell (with a red eye-spot anda flagellum) which moves at a ϕ direction; a circular arrow indicates body rolling motion. (c)Probability distribution of cell motion direction ϕ . thickness and 24 mm in diameter), which is placed in an illuminating light path, as shownin Fig. S1 [56]. A collimated blue light beam is used to excite cell photo-responses; thedefault light intensity is 100 µ W/cm . Various polarized optical fields can be generatedby using different birefringent liquid crystal plates and by changing relative angles betweenoptical elements [59]. Cell motion is recorded by a camera mounted on a Macro-lens. Defaultsystem cell density ( ρ = ) is sufficiently low that we can use a standard particletracking algorithm [60] to measure position, orientation, and velocity of cells. The currentwork mainly focuses on steady state dynamics that is invariant over time. Uniformly polarized light field - Euglena photoreceptor contains dichroically oriented chro-moproteins which lead to polarization-dependent photo responses [33, 54, 55, 61]. As shownin Fig. 1(a), cells in a horizontally polarized field tend to orient and swim perpendicularlyto the polarization [54]; we denote such a targeted direction for cells as θ T . Quantitatively,we measure the j th cell’s location (cid:126)r j ( t ) , velocity (cid:126)v j , and velocity angle ϕ j , cf. Fig. 1(b).3 = 0 : : = 0 : : u m = s 100 m = s ; = ; ?3 T r (mm) u ExpSim r (mm) -40-200204060 v t ( m " s ! ) r (mm) ; = ; = 0 : :3 = 0 : :3 = 0 : :3 = 0 : : (a) (b)(c) (d)(e) (f) (g) Figure 2. Orientation, velocity, and cell density in axisymmetric light fields containing a k = +1 defect with θ = π/ (a,c) and θ = 3 π/ (b,d). In (a-b), targeted direction θ T and mean cellmotion direction φ u are shown by green and black lines, respectively, on nematic order parameter u (in color). In (c-d), mean cell velocity (cid:126)v is plotted on mean density (in color). In (a-d), topand bottom halves (separated by a white line) are experimental and numerical results, respectively.The inset of (b) defines three angles (see text). (e-g) Radial profiles of nematic order parameter u ,tangential velocity v t = (cid:126)v · ˆ φ , and cell density ρ for four fields. Over a square window (1.2 mm ), we define mean cell velocity as (cid:126)v = (cid:104) (cid:126)v j (cid:105) , where average (cid:104)·(cid:105) runs over all cells in the region during the measurement time; nematic order parameter andorientation angle are defined as u = |(cid:104) exp ( i (2 ϕ j )) (cid:105)| and φ u = Arg ( (cid:104) exp ( i (2 ϕ j )) (cid:105) ) , whereArg denotes the phase angle of a complex number. In uniform fields, cells are homogeneouslydistributed over space and form a global nematic state with a vanishing mean cell velocity: u ≈ . and (cid:126)v ≈ . Axisymmetric light field - We next investigate cell motion in light fields with spatiallyvarying polarization. In our experiments, the targeted direction field θ T ( (cid:126)r ) is designed to4ave the form of θ T ( (cid:126)r ) = kφ ( (cid:126)r ) + θ , where k is a winding number, φ = tan − ( y/x ) is thepolar angle, and θ is a spiral angle (cf. inset of Fig. 2(b)). When k = 1 , θ T ( (cid:126)r ) field isaxisymmetric as shown by short green lines in Fig. 2 (a-b) and θ controls the ratio betweenbend and splay strength.Cell motion in axisymmetric fields can be seen in Movies S2-S5 [56]. Quantitatively,mean nematic order parameter, cell velocity, and cell density are plotted in Fig. 2 andFig. S3 [56]. As shown in Fig. 2(e), nematic order parameter u increases from the defectcenter to the exterior of the illuminated region, where spatial gradients of θ T ( (cid:126)r ) are smalland cells closely follow θ T ( (cid:126)r ) . Cells in pure bend ( θ = π/ ) and mixed ( θ = 3 π/ ) lightfields also exhibit mean velocity; peak value in radial profiles in Fig. 2(f) is about µ m/s.Spatial distributions of cells depend on θ : while cells aggregate at the exterior boundaryfor θ = π/ , Fig. 2(g) shows a relatively flat distribution with a small peak at r = 2 . mmfor θ = 3 π/ and cell aggregation near the defect center for other two θ conditions. Wealso systematically vary light intensity and system cell density; qualitatively similar resultsare shown in Figs. S4-S5 and Movie S7 in the Supplemental Material [56]. Deterministic model - Fig. 1 and Fig. 2 show that cells tend to align their motiondirection ϕ towards the local targeted direction θ T ( (cid:126)r ) . To quantify this nematic alignmentinteraction, we extract the time derivative of motion direction ˙ ϕ j from cell trajectories andfind that ˙ ϕ j is a function of the angular deviation ϕ j − θ T ( (cid:126)r j ) . We average the dependencefunction over all cells in a given experiment. Mean ˙ ϕ in Fig. 3(a) can be adequately describedby the following equation: ˙ ϕ = − A sin (2 ( ϕ − θ T )) + C. (1)Fitting data in Fig. 3(a) leads to a nematic interaction strength A = 0 . rad/s [62]and a constant angular velocity C = − . rad/s for default light intensity; parameter A increases with light intensity, and C shows a weak dependence, as shown in Fig. S4(e) [56].Small negative C value indicates that cells have a weak preference to swim clockwise; suchchirality has been reported before [36] and is likely caused by the symmetry breaking fromhandedness of cell body rolling and directionality of the illuminating light, cf. Fig. S1 [56].This weak chirality explains the non-zero mean cell velocity in an achiral light field in Fig.2(c) ( θ = π/ ). To describe cell translational motion in our model, we assume all cells have5 r ( mm ) : : : ' d p ( r ; ' d ) -3 ExpSim p -3 : : : ' d r=3mmr=5mmr=8mm0 : /4 : /2 3 : /4 : ' ! T -0.03-0.02-0.0100.010.02 _ ' ( r a d " s ! ) = 0 : :3 = 0 : :3 = 0 : :3 = 0 : : : : : : D ( r a d " s ! ) -3 = 0 : : 3 = 0 : : . mm . mm (a)(b) (c)(d) (e)(f) (g) Figure 3. (a) Mean angular velocity ˙ ϕ versus the angular deviation ϕ − θ T in in axisymmetriclight fields. Inset shows effective diffusivity D measured in different fields θ . (b-g) Deterministictrajectory and probability distribution in axisymmetric fields with θ = π/ (b, d, f) and θ = 3 π/ (c, e, g). (b-c) Cell trajectories from the deterministic model plotted on the targeted field. SeeFig. S8 [56] for more trajectories. (d-e) Experimentally measured probability p ( r, ϕ d ) (color) andcomputed phase trajectories (black lines). Stable and neutrally stable fixed points are colored inred. Fixed points in (d) is outside of the experimentally measured range ( r < . µ m). (f-g)Profiles of p ( r, ϕ d ) at three radii. Dashed lines in (d-g) mark targeted direction θ T . the same speed v ◦ = 60 µ m/s and update cell’s position with a velocity ˙ (cid:126)r = v ◦ (cos ϕ ˆ x + sin ϕ ˆ y ) . (2)In axisymmetric fields, particle dynamics from Eqs. (1-2) can be described by two vari-ables: the radial coordinate r and the angular deviation from the local polar angle ϕ d = ϕ − φ .6e solve the governing equations for these quantities (cf. the Supplemental Material [56])and compute particle trajectories in ( r, ϕ d ) phase plane, as shown dark lines in Fig. 3(d-e).Fixed point in the phase plane is identified at r ∗ = (cid:12)(cid:12)(cid:12) v ◦ C − A sin 2 θ (cid:12)(cid:12)(cid:12) and ϕ ∗ d = π (if C > A sin 2 θ )or ϕ ∗ d = − π (if C < A sin 2 θ ); it is stable if cos 2 θ < , neutrally stable if cos 2 θ = 0 , andunstable if cos 2 θ > . At stable and neutrally stable fixed points, particle moves alongcircular trajectories, cf. the violet trajectory in Fig. 3(b). Around neutrally stable fixedpoints, there is a family of closed trajectories in ( r, ϕ d ) phase plane; in real space, suchtrajectories appear to be processing ellipses around the defect center, cf. yellow trajectoriesin Fig. 3(c) and Fig. S8(c) [56]. Langevin model - Cell motion contains inherent noises, which may arise from flagellumdynamics or cell-cell interactions. To account for this stochasticity, we add a rotational noiseterm √ Dξ ( t ) to Eq. (1), which becomes Eq. (S1) [56]; ξ ( t ) represents Gaussian whitenoise with zero-mean (cid:104) ξ ( t ) ξ (0) (cid:105) = δ ( t ) and D is an effective rotational diffusivity. Withthis noise term, Eq. (S1) and Eq. (2) constitute a Langevin model of an active Brownianparticle whose orientation is locally modulated by the light polarization, i.e. θ T . Thecorresponding Fokker-Planck equation can be written down for the steady-state probabilitydensity, p ( (cid:126)r, ϕ ) , of finding a particle at a state ( (cid:126)r, ϕ ) . For uniformly polarized field, theprobability distribution p ( ϕ ) can be analytically solved and fitted to data in Fig. 1(c),yielding an estimation of D/A = 0 . rad for this experiment.We then consider axisymmetric fields. Probability density p ( r, ϕ d ) is experimentallymeasured and Fig. 3 (d-e) show high value around stable/neutrally stable fixed points. Thishighlights the importance of fixed points: their radial positions determine cell distributionsin Fig. 2(c-d) and they appear at either ϕ ∗ d = + π or ϕ ∗ d = − π , which breaks the chiralsymmetry and leads to a non-zero mean velocity. p ( r, ϕ d ) measured in two other cases of θ are shown in Fig. S3 [56]. To quantitatively reproduce measured p ( r, ϕ d ) , we numericallyintegrate the Langevin model: parameters A and C values extracted from Fig. 3(a) areused and the effective angular diffusivity D is tuned to fit experimental measurements, seeinset of Fig. 3(a). Our numerical results agree well with experiments for probability densityprofiles in Fig. 3 (f-g) and for radial profiles in Fig. 2 (e-g). Transport of passive particles - Ordered swimming of
Euglena cells in Fig. 2 can collec-tively generate fluid flow [63], which we use hollow glass spheres (50 µ m) on an air-liquidinterface to visualize. Tracer trajectories from an experiment are shown in the top half7 mm m = s r (mm) -505 v t ( m " s ! ) = 0 : :3 = 0 : :3 = 0 : : ExpSim
Figure 4. Trajectories of passive tracers (top panel, from experiments) and flow field (bottompanel, from the dipole model) driven by
Euglena in a light field with k = +1 and θ = π/ .An experimental snapshot is shown in the background. The inset shows radial profiles of tracerstangential velocities in three axisymmetric ( k = 1 ) light fields. of Fig. 4 and particles spiral counter-clock-wisely towards the center with a peak speedabout 5 µ m/s. To compute the generated flow, we represent swimming cells as force-dipoles[64, 65]: a dipole in a state ( (cid:126)r, ϕ ) generate flow velocity (cid:126)w ( (cid:126)r s ; (cid:126)r, ϕ ) (including contributionsfrom a force-dipole [64] and its image [66, 67]) at a location on the surface (cid:126)r s . Then, fora given light field, the Langevin model is used to simulate the motion of N cells and tofind the probability distribution of cells p ( (cid:126)r, ϕ ) . Finally, we compute the total flow as: (cid:126)W ( (cid:126)r s ) = N (cid:82) p ( (cid:126)r, ϕ ) (cid:126)w ( (cid:126)r s ; (cid:126)r, ϕ ) d (cid:126)r d ϕ , see Sec. II(F) in the Supplemental Material [56] fordetails. This approach generates flow fields (cf. bottom half and inset of Fig. 4) that areconsistent with measured tracer velocities, see also Fig. S6 [56]. Discussion - Our setup can also generate nonaxisymmetric light fields with integer wind-ing numbers. Fig. 5 shows that cells in a k = − field form dense and outgoing bandsin regions where θ T is close to be radial; these observations can be explained by stableradial particles trajectories in Fig. S9 (also Movie S6) [56]. The Langevin model is usedto investigate light fields with half-integer defects and multiple defects [68]; results of cell8 mm u m/s ; = ; (a) (b) Figure 5. Orientation (a) and velocity/density (b) in a light fields containing a k = − defect with θ = π/ . In (a), targeted direction θ T and mean cell motion direction φ u are shown by green andblack lines, respectively, on nematic order parameter u (in color). In (b), mean cell velocity (cid:126)v isplotted on mean density (in color). Top and bottom panels are experimental and numerical results,respectively. dynamics and transporting flow in Figs. S12 and S13 [56] demonstrate that our idea of localorientation modulation can be used as a versatile and modular method for system control.Local orientation modulation has been previously implemented by embedding rod-shapedbacteria in nematic liquid crystal with patterned molecular orientation [69–73]. In thisbio-composite system, while cell orientation is physically constrained by aligned molecules,bacteria swimming can in return disrupt the molecular order; this strong feedback weakensthe controlling ability of the imposed pattern and leads to highly complex dynamics [69–73].By contrast, our method relies on biological responses , instead of physical interactions, toachieve orientation control, and Euglena motion has no effect on the underlying light field.Such a one-way interaction leads to a much simpler system and may help us to achieve moreaccurate control. Furthermore, our method works on cells in their natural environment andrequires no elaborate sample preparation. This factor and the spatio-temporal tunability oflight fields [68] make our method flexible and easy to use.Sinusoidal term in Eq. (1) is the simplest harmonic for nematic alignment. The same termhas been observed in dichroic nano-particle systems [44, 74] and is related to the angulardependence of dichroic light absorption. These nano-particle systems usually require verystrong ( ∼ W/cm -MW/cm ) light stimulus to operate. By contrast, biological response in Euglena greatly amplifies the light signal and functions in the range of 100 µ W/cm ; thishigh sensitivity significantly reduces the complexity to construct a controlling light field. Conclusion - To summarize, we have experimentally demonstrated that
Euglena motion9irection is strongly affected by the local light polarization and that cell dynamics in spatiallyvarying polarization fields is controlled by topological properties and light intensity of theunderlying fields. Our experiments also showed that ordered cell swimming, controlled bythe polarization field, can generate directed transporting fluid flow. Experimental resultshave been quantitatively reproduced by an active Brownian particle model in which particlemotion direction is nematically coupled to the local light polarization; fixed points andclosed trajectories in the model have strong impacts on system properties. These resultssuggest that local orientation modulation, via polarized light or other means, can be usedas a general method to control active matter and micro-scale transporting flow.
Acknowledgments -
We acknowledge financial support from National Natural ScienceFoundation of China (Grants No. 11774222 and No. 11422427) and from the Programfor Professor of Special Appointment at Shanghai Institutions of Higher Learning (GrantNo. GZ2016004). We thank Hugues Chaté and Masaki Sano for useful discussions and theStudent Innovation Center at Shanghai Jiao Tong University for support. ∗ [email protected][1] E. Lauga and T. R. Powers, Rep. Prog. Phys. , 096601 (2009).[2] S. Ramaswamy, Annual Review of Condensed Matter Physics , 323 (2010).[3] W. C. K. Poon, Physics of Complex Colloids, ed. C Bechinger, F Sciortino and P Ziherl, ,317 (2013).[4] I. S. Aranson, Phys. Usp. , 79 (2013).[5] W. Wang, W. Duan, S. Ahmed, T. E. Mallouk, and A. Sen, Nano Today , 531 (2013).[6] S. Sanchez, L. Soler, and J. Katuri, Angew. Chem. Int. Ed. , 1414 (2015).[7] J. Elgeti, R. G. Winkler, and G. Gompper, Rep. Prog. Phys. , 056601 (50 pp.) (2015).[8] C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, and G. Volpe, Giorgio and, Rev.Mod. Phys. , 045006 (2016).[9] O. D. Lavrentovich, Current Opinion in Colloid & Interface Science , 97 (2016).[10] A. Zottl and H. Stark, J. Phys.: Condens. Matter , 253001 (2016).[11] A. E. Patteson, A. Gopinath, and P. E. Arratia, Current Opinion in Colloid & InterfaceScience , 86 (2016).
12] J. Zhang, E. Luijten, B. A. Grzybowski, and S. Granick, Chem Soc Rev , 5551 (2017).[13] P. Illien, R. Golestanian, and A. Sen, Chem. Soc. Rev. , (2017).[14] B. Liebchen and H. Loewen, Acc Chem Res , 2982 (2018).[15] G. Gompper, R. G. Winkler, T. Speck, A. Solon, C. Nardini, F. Peruani, H. Lowen, R. Golesta-nian, U. B. Kaupp, L. Alvarez, T. Kiorboe, E. Lauga, W. C. K. Poon, A. DeSimone, S. Muinos-Landin, A. Fischer, N. A. Soker, F. Cichos, R. Kapral, P. Gaspard, M. Ripoll, F. Sagues,A. Doostmohammadi, J. M. Yeomans, I. S. Aranson, C. Bechinger, H. Stark, C. K. Hemelrijk,F. J. Nedelec, T. Sarkar, T. Aryaksama, M. Lacroix, G. Duclos, V. Yashunsky, P. Silberzan,M. Arroyo, and S. Kale, Journal of Physics-condensed Matter , 193001 (2020).[16] J. Wang, Lab. Chip , 1944 (2012).[17] W. Gao and J. Wang, ACS Nano , 3170 (2014).[18] J. X. Li, B. E. F. de Avila, W. Gao, L. F. Zhang, and J. Wang, Science Robotics , UNSPeaam6431 (2017).[19] Y. Alapan, O. Yasa, B. Yigit, I. C. Yasa, P. Erkoc, and M. Sitti, Annual Review of Control,Robotics, and Autonomous Systems, Vol 2 , 205 (2019).[20] A. M. Menzel, Physics Reports-review Section of Physics Letters , 1 (2015).[21] H. Stark, European Physical Journal-special Topics , 2369 (2016).[22] M. You, C. Chen, L. Xu, F. Mou, and J. Guan, Acc. Chem. Res. , 3006 (2018).[23] S. Klumpp, C. T. LefÈšvre, M. Bennet, and D. Faivre, Physics Reports , 1 (2019).[24] E. Mikolajczyk, P. L. Walne, and E. Hildebrand, Critical Reviews in Plant Sciences , 343(1990).[25] G. Jekely, Philosophical Transactions of the Royal Society B-biological Sciences , 2795(2009).[26] K. Drescher, R. E. Goldstein, and I. Tuval, Proc. Natl. Acad. Sci. U.S.A. , 11171 (2010).[27] L. Barsanti, V. Evangelista, V. Passarelli, A. M. Frassanito, and P. Gualtieri, Integr. Biol. ,22 (2012).[28] E. A. Kane, M. Gershow, B. Afonso, I. Larderet, M. Klein, A. R. Carter, B. L. de Bivort, S. G.Sprecher, and A. D. T. Samuel, Proc. Natl. Acad. Sci. U.S.A. , E3868 (2013).[29] X. Garcia, S. Rafai, and P. Peyla, Phys. Rev. Lett. , 138106 (2013).[30] A. Giometto, F. Altermatt, A. Maritan, R. Stocker, and A. Rinaldo, Proc. Natl. Acad. Sci.U.S.A. , 7045 (2015).
31] R. R. Bennett and R. Golestanian, Journal of the Royal Society Interface , 20141164 (2015).[32] R. M. W. Chau, D. Bhaya, and K. C. Huang, Mbio , e02330 (2017).[33] D.-P. Hader and M. Iseki, “Photomovement in euglena,” in Euglena: Biochemistry, Cell andMolecular Biology , edited by S. D. Schwartzbach and S. Shigeoka (Springer International Pub-lishing, Cham, 2017) pp. 207–235.[34] K. Ozasa, J. Won, S. Song, S. Tamaki, T. Ishikawa, and M. Maeda, PLoS One , 1 (2017).[35] J. Arrieta, A. Barreira, M. Chioccioli, M. Polin, and I. Tuval, Sci. Rep. , 3447 (2017).[36] A. C. H. Tsang, A. T. Lam, and I. H. Riedel-Kruse, Nat. Phys. , 1216 (2018).[37] J. Arrieta, M. Polin, R. Saleta-Piersanti, and I. Tuval, Phys. Rev. Lett. , 158101 (2019).[38] S. K. Choudhary, A. Baskaran, and P. Sharma, Biophys. J. , 1508 (2019).[39] L. Xu, F. Mou, H. Gong, M. Luo, and J. Guan, Chem. Soc. Rev. , (2017).[40] R. Dong, Y. Cai, Y. Yang, W. Gao, and B. Ren, Acc. Chem. Res. , 1940 (2018).[41] J. Wang, Z. Xiong, J. Zheng, X. Zhan, and J. Tang, Acc. Chem. Res. , 1957 (2018).[42] A. Aubret, M. Youssef, S. Sacanna, and J. Palacci, Nat. Phys. (2018).[43] D. P. Singh, W. E. Uspal, M. N. Popescu, L. G. Wilson, and P. Fischer, Adv. Funct. Mater. , 1706660 (2018).[44] X. Zhan, J. Zheng, Y. Zhao, B. Zhu, R. Cheng, J. Wang, J. Liu, J. Tang, and J. Tang, Adv.Mater. , 1903329 (2019).[45] F. A. Lavergne, H. Wendehenne, T. Bauerle, and C. Bechinger, Science , 70 (2019).[46] J. Arlt, V. A. Martinez, A. Dawson, T. Pilizota, and W. C. K. Poon, Nat. Commun. , 768(2018).[47] J. Dervaux, M. C. Resta, and P. Brunet, Nat. Phys. , 306 (2017).[48] T. Ogawa, E. Shoji, N. J. Suematsu, H. Nishimori, S. Izumi, A. Awazu, and M. Iima, PLoSOne , 1 (2016).[49] J. Stenhammar, R. Wittkowski, D. Marenduzzo, and M. E. Cates, Sci. Adv. , (2016).[50] J. Palacci, S. Sacanna, A. P. Steinberg, D. J. Pine, and P. M. Chaikin, Science , 936(2013).[51] G. Frangipane, D. Dell’Arciprete, S. Petracchini, C. Maggi, F. Saglimbeni, S. Bianchi, G. Vizs-nyiczai, M. L. Bernardini, and R. Di Leonardo, Elife , e36608 (2018).[52] C. Lozano, B. ten Hagen, H. Lowen, and C. Bechinger, Nat. Commun. , 12828 (2016).[53] A. Geiseler, P. Hanggi, F. Marchesoni, C. Mulhern, and S. Savel’ev, Phys. Rev. E , 012613 , 552 (1976).[55] D. P. Hader, Arch. Microbiol. , 179 (1987).[56] APS, “See supplemental material at [url] for detailed experimental procedure, additional ex-perimental results, analysis of the langevin model, description of dipole fluid model, and sup-porting videos.” (2020).[57] M. Rossi, G. Cicconofri, A. Beran, G. Noselli, and A. DeSimone, Proc. Natl. Acad. Sci. U. S.A. , 13085 (2017).[58] N. A. Hill and L. A. PLUMPTON, J. Theor. Biol. , 357 (2000).[59] S. Delaney, M. M. Sanchez-Lopez, I. Moreno, and J. A. Davis, Applied Optics , 596 (2017).[60] H. P. Zhang, A. Be’er, E. L. Florin, and H. L. Swinney, Proc. Natl. Acad. Sci. U. S. A. ,13626 (2010).[61] K. E. BOUND and G. TOLLIN, Nature , 1042 (1967).[62] H. Li, X.-q. Shi, M. Huang, X. Chen, M. Xiao, C. Liu, H. Chate, and H. P. Zhang, Proc NatlAcad Sci USA , 777 (2019).[63] A. J. T. M. Mathijssen, F. Guzman-Lastra, A. Kaiser, and H. Lowen, Phys. Rev. Lett. ,248101 (2018).[64] T. Ogawa, S. Izumi, and M. Iima, J. Phys. Soc. Jpn. , 074401 (2017).[65] D. Bardfalvy, S. Anjum, C. Nardini, A. Morozov, and J. Stenhammar, Physical Review Letters , 018003 (2020).[66] J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Prentice Hall, EnglewoodCliffs, NJ, 1965).[67] A. J. T. M. Mathijssen, D. O. Pushkin, and J. M. Yeomans, J. Fluid Mech. , 498 (2015).[68] C. Rosales-Guzman, B. Ndagano, and A. Forbes, Journal of Optics , 123001 (2018).[69] R. R. Trivedi, R. Maeda, N. L. Abbott, S. E. Spagnolie, and D. B. Weibel, Soft Matter ,8404 (2015).[70] C. H. Peng, T. Turiv, Y. B. Guo, Q. H. Wei, and O. D. Lavrentovich, Science , 882 (2016).[71] I. S. Aranson, Acc. Chem. Res. , 3023 (2018).[72] T. Turiv, R. Koizumi, K. Thijssen, M. M. Genkin, H. Yu, C. Peng, Q.-H. Wei, J. M. Yeomans,I. S. Aranson, A. Doostmohammadi, and O. D. Lavrentovich, Nat. Phys. (2020).[73] R. Koizumi, T. Turiv, M. M. Genkin, R. J. Lastowski, H. Yu, I. Chaganava, Q.-H. Wei, I. S. ranson, and O. D. Lavrentovich, Phys. Rev. Research , 033060 (2020).[74] L. Tong, V. D. Miljkovic, and M. Kall, Nano Lett. , 268 (2010)., 268 (2010).