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Abstract
In tissues as diverse as amphibian skin and the human airway, the cilia that propel fluid are grouped in sparsely distributed multiciliated cells (MCCs). We investigate fluid transport in this "mosaic" architecture, with emphasis on the trade-offs that may have been responsible for its evolutionary selection. Live imaging of MCCs in embryos of the frog Xenopus laevis shows that cilia bundles behave as active vortices that produce a flow field accurately represented by a local force applied to the fluid. A coarse-grained model that self-consistently couples bundles to the ambient flow reveals that hydrodynamic interactions between MCCs limit their rate of work so that they best shear the tissue at a finite but low area coverage, a result that mirrors findings for other sparse distributions such as cell receptors and leaf stomata.
FIG. 1. Ectoderm of embryonic Xenopus laevis at tailbud stages. (a) Schematic side view of MCCs (red) intermixed with secreting cells. (b) Location of MCCs across the embryo (adapted from Refs. [22,23]) and cilia-driven flow (blue arrows). (c) Confocal image of cell membranes (stained by membrane-RFP), with MCCs segmented in red, in ventral region of skin.
Flow fields. (a) Lateral view of MCC showing (dashed) path of cilia tips and force F. (b) Experimental velocity field and vorticity in plane normal to skin near several MCCs. (c) Near an MCC, as in (b), with direction of cilia tip motion (black arrows) on ∂Ωc. (d) Estimated flow field u0 for an isolated MCC (blue arrows): Point forces (red arrows) are used to fit velocity near cilia tips. Lateral velocity at (e) x,y=(0,0) and (f) (±40μm, 0) in experiment (exp) and theory, with u0 driven by an isolated bundle and uc by a bundle exposed to endogenous flow ua (see also Figs. S2–S4 [29]).
FIG. 3. Response of cilia bundles to exogenous shear. (a),(b) Vorticity and velocity vectors before and during perfusion. (c) Velocities u(z;0) and u(z;˙γe), shear flow ˙γez, and sum Cu(z;0)+˙γez fitting u(z;˙γe), where C= F(˙γe)/F(0). (d) Variation with shear of estimated force F, velocity V and shear rate ˙θ=∂u(z)/∂z|ℓ measured above cilia tips, and rate of work W∝˙θV (overlapping ˙θ), normalized by values at ˙γe=0. Shaded regions are 95% confidence intervals of averages over 10 samples.
FIG. 4.
Collective efficiency of a distribution of point forces, in the space of coverage ϕ and dissipative coupling constant λ. Dashed lines trace optimization ridges of the extra forces per bundle Fa and Fw driving (a) flow in the outer region and (b) shear above nonciliated cells.
