A fluid-structure interaction model that couples viscoelastic fluid motion induced by collective behavior of cilia to detailed axoneme mechanics is used to investigate bounds on cilia structure and mucus properties that determine effective fluid clearance. Dynein forcing is represented by a stochastic walker model that responds to local ATP concentrations provided by a biochemical network model. Cilium axonemes are modeled by large-deflection finite elements representing microtubules and viscoelastic springs representing connecting elements (nexins, radial spokes). Cilium motion is coupled to a viscoelastic fluid computation that models gel-like behavior of the mucus as well as possible Newtonian behavior of the periciliary fluid layer. Behavior of the viscoelastic fluid is prescribed at a microscopic level to avoid using continuum viscoelastic models of questionable validity. A lattice-based technique based upon a variational formulation of the Fokker-Planck equation is used to describe the viscoelastic fluid dynamics. A lattice Boltzmann method is applied to capture forcing of the viscoelastic mucus layer by concurrent airflow. The overall model exhibits natural formation of metachronal waves due to phase coupling of the dynein motion. Adjoint density analysis and uncertainty quantification techniques are applied to assess the stability of the transport induced by metachronal waves to perturbations in dynein walker rates, axoneme element rigidity, and mucus gel-formation process. The goal is not only to assess the robustness of the metachronal transport process, but also to identify elements within the overall transport mechanism that are most promising targets for pharmaceutical treatment of ciliary dysfunction.
Sperm are known to exhibit two distinct types of motility. One is characterized by constant amplitude, symmetrical waveforms. The other is characterized by asymmetrical waveforms, which are correlated with an increase in calcium concentration. The goal of this work is to model the undulatory swimming of sperm swimming in a viscous, incompressible fluid using the method of regularized Stokeslets. Varying waveforms will be considered via a preferred curvature function. Results showing emergent waveforms, swimming speeds, and trajectories will be compared to experimental data.
Many microorganisms swim by rotating one or many helical flagella, often propelling themselves through fluids that exhibit both viscous and elastic qualities in response to deformations. In an effort to better understand the complex interaction between the fluid and body in such systems, we have studied numerically the force-free swimming of a rotating helix in a viscoelastic (Oldroyd-B) fluid. The introduction of viscoelasticity can either enhance or retard the swimming speed depending on the body geometry and the properties of the fluid (through a dimensionless Deborah number). The results are compared to recent experiments on a rotating helix immersed in a Boger fluid. Our findings bridge the gap between studies showing situationally dependent enhancement or retardation of swimming speed, and may help to clarify phenomena observed in a number of biological systems.
Cilia in the Development of Left-right asymmetry
The ventricular system in the brain is lined by multiciliated cells. The motility of these ependymal cilia was analyzed in hy3-/- mice which carry a null mutation in Hydin and develop lethal hydrocephalus. Hy3-/- cilia lack a projection from the ciliary central pair and move with slightly reduced beat frequency and a greatly reduced beat amplitude. They lack the ability to generate fluid flow explaining the hydrocephalic phenotype of the mutant mice. The assembly of motile and non-motile cilia requires intraflagellar transport (IFT) but it remains largely unknown how IFT traffics ciliary precursors. Simultaneous in vivo imaging of IFT and cargoes revealed a complex pattern of IFT and non-IFT cargo movements, and unloading and assembly site docking events. Quantitative data on cargo frequency, assembly, and turn-over will provide a basis for future modeling of ciliary assembly and dynamics.
Since the pioneering studies of GI Taylor in the fifties, models have been used to gain understanding in the propulsion of microorganisms. Modern microfabrication techniques enable us to assemble very small scale devices emulating the motion of cilia. I will review the different strategies used in recent years towards the goal of fabricating micron scale artificial swimmers. In particular I will discuss the relative merits of self-assembly and micromolding. I will describle several sources of propulsive energy but most of the talk will be devoted to magnetically driven systems.
Blitz Session Talk (Rich Superfine)
Blitz Session (Arezoo Ardekani)
The beating of a cilium is an elegant example of an actuated elastic structure coupled to a surrounding fluid. Computational fluid dynamics enthusiasts will recognize that ciliary systems present many complications such as the interaction of groups of cilia, the influence of boundaries, and the coupling to fluids that have complex rheology and microstructures. Moreover, the ciliary beatform is an emergent feature of these mechanical considerations along with biochemical processes. We will present an overview of current CFD models of cilia, along with some recent progress in analyzing fluid mixing by cilia and modeling ciliary penetration of a mucus layer.
Microorganisms and the mechanical components of the cell motility machinery such as cilia and flagella operate in low Reynolds number conditions where hydrodynamics is dominated by viscous forces. The medium thus induces a long-ranged hydrodynamic interaction between these active objects, which could lead to synchronization, coordination and other emergent many-body behaviors. In my talk, I will examine these effects using minimal models that are simple enough to allow extensive analysis that sheds light on the underlying mechanisms for the emergent phenomena.