Cilia, active hair-like appendages in biological cells serve many different functions. Cilia are present in lungs, intestines, and the inner ear where they serve specific functions by moving fluid.
Hundreds of dynein molecular motors drive the beating of a single cilium, producing wavelike bending.
Mathematical models can be used to study coordination of the dynein motors, by using a simple dynamical law that governs the tension of each dynein motor, along with a geometrical constraint based on the microstructure of the cilium.
The Immersed Boundary method, first proposed by Charles Peskin, facilitates the study of a cilium’s fluid-mediated interaction by immersing the model cilia in fluid.
The model demonstrates how the beat emerges spontaneously and shows how cilia interacts with fluid. Studies show remarkable tendency towards synchronization of nearby cilia regardless of initial conditions.
In this video, Charles Peskin (New York University), who first introduced the IB method, talks about the importance of cilia in the body, and how mathematical models can be used to study coordination of the dynein motors, which cause cilial motion.
More about Beating in Fluid:
Beating in Fluid: Mathematical Anatomy of the Heart
Beating in Fluid: Hearts and Cilia by the Immersed Boundary Method