Simulation of fluid-structure interaction of cilia using immersed boundary (IB) method
Reference: Jihun Han, Charles S. Peskin, Spontaneous oscillation and fluid–structure interaction of cilia. Proceedings of the National Academy of Sciences, 115(17), (2018): 4417-4422.
Abstarct
The exact mechanism to orchestrate the action of hundreds of dynein motor proteins to generate wave-like ciliary beating remains puzzling and has fascinated many scientists. We present a 3D model of a cilium and the simulation of its beating in a fluid environment. The model cilium obeys a simple geometric constraint that arises naturally from the microscopic structure of a real cilium. This constraint allows us to determine the whole 3D structure at any instant in terms of the configuration of a single space curve. The tensions of active links, which model the dynein motor proteins, follow a postulated dynamical law, and together with the passive elasticity of microtubules, this dynamical law is responsible for the ciliary motions. In particular, our postulated tension dynamics lead to the instability of a symmetrical steady state, in which the cilium is straight and its active links are under equal tensions. The result of this instability is a stable, wave-like, limit cycle oscillation. We have also investigated the fluid–structure interaction of cilia using the immersed boundary (IB) method. In this setting, we see not only coordination within a single cilium but also, coordinated motion, in which multiple cilia in an array organize their beating to pump fluid, in particular by breaking phase synchronization.
1. Single ciliary beating: asymmetric beating (power-recovery strokes), reaching to the same limit cycle oscillation from different initial dynein tensions.
2. Multiple cilia in a diaplectic row (assumed to synchrony of cilia in orthoplectic row) with zero initial dynein tensions : Breaking the phase synchrony and pumping fluid.
3. Multiple cilia in an orthoplectic row (assumed to synchrony of cilia in diaplectic row) with random initial dynein tensions : phase synchronization.
