Collective oscillatory behaviour is ubiquitous in nature1, having a vital role in many biological processes from embryogenesis2 and organ development3 to pace-making in neuron networks4. Elucidating the mechanisms that give rise to synchronization is essential to the understanding of biological self-organization. Collective oscillations in biological multicellular systems often arise from long-range coupling mediated by diffusive chemicals2,5,6,7,8,9, by electrochemical mechanisms4,10, or by biomechanical interaction between cells and their physical environment11. In these examples, the phase of some oscillatory intracellular degree of freedom is synchronized. Here, in contrast, we report the discovery of a weak synchronization mechanism that does not require long-range coupling or inherent oscillation of individual cells. We find that millions of motile cells in dense bacterial suspensions can self-organize into highly robust collective oscillatory motion, while individual cells move in an erratic manner, without obvious periodic motion but with frequent, abrupt and random directional changes. So erratic are individual trajectories that uncovering the collective oscillations of our micrometre-sized cells requires individual velocities to be averaged over tens or hundreds of micrometres. On such large scales, the oscillations appear to be in phase and the mean position of cells typically describes a regular elliptic trajectory. We found that the phase of the oscillations is organized into a centimetre-scale travelling wave. We present a model of noisy self-propelled particles with strictly local interactions that accounts faithfully for our observations, suggesting that self-organized collective oscillatory motion results from spontaneous chiral and rotational symmetry breaking. These findings reveal a previously unseen type of long-range order in active matter systems (those in which energy is spent locally to produce non-random motion)12,13. This mechanism of collective oscillation may inspire new strategies to control the self-organization of active matter14,15,16,17,18 and swarming robots19.
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We thank Y. Li and W. Zuo from our laboratory for building the microscope stage temperature control system, L. Xu (The Chinese University of Hong Kong) for providing silicone oil, H. C. Berg (Harvard University) for providing the bacterial strains, and J. Näsvall and J. Bergman (Uppsala University) for providing the mRFP plasmid. This work was supported by the Research Grants Council of Hong Kong SAR (RGC numbers 2191031 and 2130439 and CUHK Direct Grant numbers 3132738 and 3132739 to Y.W.), the National Natural Science Foundation of China (NSFC number 21473152, to Y.W.; NSFC number 11635002 to H.C. and X.S.; NSFC numbers 11474210, 11674236 and 91427302 to X.S.), and the Agence Nationale de la Recherche (project Bactterns, to H.C.).
Extended data figures
Turbulent collective motion of E. coli cells in a colony prior to the onset of collection oscillation
This phase-contrast video is played in real time at 10 frames per second, with the real elapsed time indicated in the video control bar. Cells display a disordered state with collective motion at small spatial scales (~10 µm) taking the form of transient jets and vortices.
This phase-contrast video is played in real time at 15 frames per second, with the real elapsed time indicated in the video control bar. Two silicone oil tracers appeared as dark spots near the center of field of view, and they underwent synchronized oscillation in elliptical trajectories. This video is associated with Fig. 1 (panel a-c) and Extended Data Figure 2. The last frame of this video is associated with Fig. 1a.
This video (associated with Fig. 2e) is played in real time at 15 frames per second, with the real elapsed time indicated in the video control bar. The cells seen here were fluorescent (strain HCB1737 mRFP), and they were mixed with non-fluorescent cells at a ratio of 1:99. Individual cells moved in an erratic manner while the entire population was undergoing collective oscillation. Red trace indicates the trajectory of a cluster consisting of immotile cells that can serve as a flow tracer. The cluster is in fact larger than shown in the video because some cells in it are non-fluorescent.
Collective oscillation near the boundary of an area of cells immobilized by the photosensitizing effect of FM4-64
This phase-contrast video (associated with Extended Data Figure 7c,d) is played in real time at 15 frames per second, with the real elapsed time indicated in the video control bar. The area of light illumination to excite FM 4-64 is of diameter ~160 μm, and the boundary of this area is near the bottom of the field of view. The collective oscillation of cells was almost unaffected by the light-immobilized area beyond a distance of ~50 μm away from the boundary.
Individual particles in the system show erratic trajectories (some particles are marked in different colors) while the whole system shows regular global oscillations of the mean velocity. The red trajectories are the time integration of average velocity of the system. This video is associated with Figure 4a.
The system is of size 1536μm x 192μm. The particles are colored according to their moving directions relative to x-axis (see colormap). White particles are ten randomly chosen particles for easy visibility. Elliptic trajectories are generated by the integration of local average flow velocity in a domain of size 150 μm x 150 μm. This video is associated with Figure 4c.
This video is associated with Figure 4d. Here the system has stronger flows perpendicular to the travelling wave direction. The colormap in the unit of μm/s represents the intensity of the speed of flows.
The video is associated with Extended Data Figure 8. Particles are colored according to their moving direction relative to x-axis (see colormap). White particles are randomly chosen and marked for easy visibility. The system still maintains travelling wave state with the deactivation zone present. Particle motion inside the deactivation zone is driven by small residual oscillatory flows governed by the Stokes equation.
About this article
Nature Communications (2018)