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Figure 6
(A) Possible traveling wave solutions in a computational model of a cilia carpet. Left: Cilia are arranged on a triangular lattice (gray dots), with three-dimensional cilia beat pattern from Paramecium (not to scale, cilia length 10 ?m). Three example wave solutions are highlighted: in-phase beating, symplectic wave, dexioplectic wave. Wave fronts are indicated by black lines and the wave direction by an arrow, while the color code of cilia base points represents cilia phase. Right: Visualization of the set of all possible wave solutions as function of wave vector k=(kx,ky), where the distance from the origin encodes the wavelength of the wave as ? = 2? / |k| and the directional angle ? encodes the direction of the wave relative to the direction of the effective stroke of the cilia beat. Example waves from left panel are highlighted as colored dots. (B) Pumping rate Q per cilium computed for different wave solutions, with each wave represented by a color-coded dot as in hexagon plot of panel A (normalized by pumping rate Qrand ? 7.87 ?m3/ms for cilia beating with random phase relationship). (C) Direction of cilia-generated flow (averaged over one beat cycle) for different wave solutions relative to the direction of the effective stroke of the cilia beat; note that the range of the color bar spans only 10?. Mean ± standard deviation is shown in the upper right corner. (D) Pumping rate per cilium for four selected wave solutions as indicated in hexagon plot of panel (A) as function of a noise strength ? (see text for details). Dashed line indicates mean pumping rate for cilia beating with random phase relationship (Qrand). (E) Critical density ? of a cilia carpet below which steric interactions between cilia arise for different wave solutions; density ? is normalized relative to a critical density for cilia beating with random phase relationship, ?rand = 0.015 ?m?2.
Metachronal coordination enhances fluid pumping and reduces steric interactions, but does not affect fluid flow direction.