Hydrodynamic synchronization in cilia carpets and its robustness to noise and perturbations

Motile cilia are hair-like cell appendages that actively bend themselves, thus driving the surrounding fluid in motion. For many microorganisms, such as unicellular Paramecium, cilia are essential for their motility. Higher animals, including mammals, utilize cilia for transporting fluids. For example, in humans, large collections of cilia, called cilia carpets, remove mucus and pathogens from the airways. Cilia constitute an example of biological oscillators that can spontaneously synchronize their beat in the form of metachronal waves, i.e., traveling waves of cilia phase. These waves may arise purely by hydrodynamic interactions between the cilia and supposedly enhance fluid transport. Our goal is to theoretically understand how the properties of individual cilia, e.g., cilia beat pattern, determine the emergent behavior, e.g., the direction of the metachronal wave. Additionally, we address the robustness of hydrodynamically-induced synchronization with respect to intrinsic active fluctuations of the cilia beat and disorder of intrinsic cilia frequencies. Both of these effects are not yet well understood. In this thesis, we studied metachronal synchronization in cilia carpets using a theoretical physicist’s toolbox. First, we proposed a novel multi-scale modeling framework Lagrangian Mechanics of Active Systems (LAMAS) to describe fluid-structure interactions for active elastic structures, such as cilia. We quantified hydrodynamic interactions between cilia using detailed hydrodynamic simulations with a realistic cilia beat pattern. In the dynamical simulations for N = 2 cilia, we found that cilia would synchronize either in-phase or anti-phase, depending on their relative positions. For a lattice of N ≫ 1 cilia, we found the emergence of metachronal waves, many of which are locally stable. Nevertheless, just a single wave has a predominantly large basin of attraction, i.e., it is likely to be selected from a random initial condition. In the presence of noise, synchronization abruptly breaks up beyond a characteristic noise strength. Likewise, for cilia with non-identical intrinsic frequencies, synchronization is lost beyond a characteristic level of frequency disorder. In large cilia carpets, noise excites long-wavelength perturbations, whose relaxation times are proportional to the square of the system length. Thus, in large systems, we predict locally synchronized domains, instead of the global synchronization