An Integrative Computational Model of Multiciliary Beating

Abstract

The coordinated beating of motile cilia is responsible for ovum transport in the oviduct, transport of mucus in the respiratory tract, and is the basis of motility in many single-celled organisms. The beating of a single motile cilium is achieved by the ATP-driven activation cycles of thousands of dynein molecular motors that cause neighboring microtubule doublets within the ciliary axoneme to slide relative to each other. The precise nature of the spatial and temporal coordination of these individual motors is still not completely understood. The emergent geometry and dynamics of ciliary beating is a consequence of the coupling of these internal force-generating motors, the passive elastic properties of the axonemal structure, and the external viscous, incompressible fluid. Here, we extend our integrative model of a single cilium that couples internal force generation with the surrounding fluid to the investigation of multiciliary interaction. This computational model allows us to predict the geometry of beating, along with the detailed description of the time-dependent flow field both near and away from the cilia. We show that synchrony and metachrony can, indeed, arise from hydrodynamic coupling. We also investigate the effects of viscosity and neighboring cilia on ciliary beat frequency. Moreover, since we have precise flow information, we also measure the dependence of the total flow pumped per cilium per beat upon parameters such as viscosity and ciliary spacing.

A 3D Motile Rod-Shaped Monotrichous Bacterial Model

“…The (IB) method has been employed in a variety of applications including the study of blood flow in the heart [82], blood vessels [102,93], deformation of blood cells [19], platelet aggregation and adhesion in blood clotting [46,43,47,103], signal transduction by cochlea [17,51], flow and transport in a renal arteriole [1], ameboid motion [18], swimming and microorganism motility [45,44,36,41,42,27], ciliary and sperm motility [33,32,108] as well as applications in developmental biology [37,90] and tumor growth [89,88,38].…”

Emergence of flagellar beating from the collective behavior of individual ATP-powered dyneins

“…4a. A similar two-filament approach has been taken by Fauci and coworkers [35,40,41]. We analyze this system using a two dimensional computational model in which an integral formulation for Stokes flow is implemented using the boundary element method to represent the fluid environment, while the microtubules and nexin links are represented by an assemblage of elastic beam elements.…”

“…The force-transduction of individual dynein molecules has been studied experimentally via optical-trap nanometry [23,[25][26][27][28] and their collective behavior has been analyzed through microtubule-motility assays [25,[29][30][31][32][33][34]. It has been generally accepted that the dyneins apply a sliding force during their working cycle leading to the generation of bending of the microtubules [8,10,[35][36][37]. Large deflections can be generated by the accumulation of successive sliding events, while the microtubules remain of fixed length [1].…”

“…Computational studies based on the curvature control hypothesis -given pre-existing curvatures along the axoneme length -predict steady oscillations and wave propagation only when there is a delay in the feedback loop from curvature to (de)-activation of the dyneins [8,9,15,[35][36][37][39][40][41].…”

“…Existing theoretical models [8,9,14,15,[35][36][37][39][40][41][42][43] are mostly based on geometry-controlled activation and deactivation of dynein forces, in which the inherent physical parameters of the dynein ATP-cycle are not accounted for.…”