A Statistical Mechanical Study of Circularly Polarized Collective Motion of Micro-Swimmers in a Thin Liquid Film

Homogeneous cell populations are able to exhibit a rich variety of organized behavior, among which periodic oscillations. In many well-studied examples of collective motion in biology, cells communicate with each other through a chemical signal. Very recently, the Co-I’s group demonstrated noisy but robust synchronized motion of swarming bacteria confined in a thin layer of fluid [Nature 542, 210-214 (2017)]. The interplay between geometry, symmetry and hydrodynamics in the experimental setup is intriguing and poses new fundamental questions in active matter research.

We have recently developed a general linear response theory to study spontaneous oscillations in a communicating cell population. The theory takes input from single-cell measurements to predict collective motion. Of particular interest is the phase relationship between cellular activity and the perturbing signal. Cells that respond adaptively to a changing environment are phase-leading at low frequencies. This property can be leveraged to yield quantitative predictions on the emergence of collective behavior above a threshold cell density.

In the proposed work, we will follow the scheme outlined above to develop a detailed kinetic model of swarming bacteria in a thin liquid film. Experimentally, it has been shown that the fluid flow as well as the averaged bacterial motion is uniform over distances much greater than the size of individual cells. Therefore a mean-field Smoluchowski type description for the vertical profile of bacterial density and orientational distribution is appropriate. Our preliminary work on a minimal model identified a novel oscillatory instability as the cell density increases. The eigenmodes are the left and right polarized swarming motion in the plane, whose linear superpositiongives rise to the elliptical orbits observed in experiments. Improved models need to be introduced to treat confinement and surface effects more accurately. Statistical analysis of single-cell trajectories collected in Co-I’s lab will be performed to provide information about bacterial motion near the surface. Guided by general results from the linear response theory and symmetry, the research should yield fresh knowledge and insight towards the circularly polarized average motion in an active and highly noisy population that has remained elusive till now. More broadly, progress made in this project could inspire new approaches to self-organization of microswimmers in other biological contexts.