Emergence of Collective Dynamics in Systems of Motile Cilia

Abstract

Motile cilia are fascinating structures, evolved very early in eukaryotes, and highly conserved throughout organisms of very different complexity. They generate the transport of fluid by periodic beating, through remarkably organized behaviour in space and time (e.g. collective waves). This allows simple unicellular organisms to swim, and allows transport of fluid in the airways and within the brain in humans.It is not understood how these spatiotemporal patterns emerge, and what sets their properties. Individual cilia are nonequilibrium systems with many degrees of freedom. We have reduced these to fewer parameters, representing the effective force laws that drive oscillations, and paralleled with nonlinear phase oscillators studied in physics. At this level, the beating cilia become sources for a velocity field, which can be approximated (in the far field) by the Oseen tensor, or taking into account the presence of solid boundaries if necessary. This becomes a more tractable (albeit still non-linear and entirely not trivial) system on which to try and understand the emergence of collective dynamical states, and how the macroscopic characteristics are linked to the microscopic cilia parameters.This presentation will report on insight gained by studying synthetic model phase oscillators, where colloidal particles are driven by optical traps (this keeps the length and time-scales of the living system, including the important role of thermal noise). The complex structural details of the cilia are coarse-grained into the details of how the colloidal particles are driven. We explore experimentally various colloidal models, finding in each case the conditions for optimal coupling. The applicability of this approach to biological data is illustrated by successfully mapping the behaviour of cilia in the alga Chlamydomonas onto the coarse-grained model, and linking the dynamics in a many-oscillator system to embryonic tissue development.