Dynamics of cilia length in left-right development

Abstract

Reduction in the length of motile cilia in the zebrafish left-right organizer (LRO), also known as Kupffer's vesicle, has a large impact on left-right development. Here we demonstrate through genetic overexpression in zebrafish embryos and mathematical modelling that the impact of increased motile cilia length in embryonic LRO fluid flow is milder than that of short cilia. Through Arl13b overexpression, which increases cilia length without impacting cilia beat frequency, we show that the increase in cilium length is associated with a decrease in beat amplitude, resulting in similar flow strengths for Arl13b overexpression and wild-type (WT) embryos, which were not predicted by current theory. Longer cilia exhibit pronounced helical beat patterns and, consequently, lower beat amplitudes relative to WT, a result of an elastohydrodynamic shape transition. For long helical cilia, fluid dynamics modelling predicts a mild (approx. 12%) reduction in the torque exerted on the fluid relative to the WT, resulting in a proportional reduction in flow generation. This mild reduction is corroborated by experiments, providing a mechanism for the mild impact on organ situs.

Keywords: cilia length; flow dynamics; left–right development.

Figure 1.

Developmental laterality defects imposed by longer cilia. (a) Cilia length increases with growing concentrations of injected messenger RNA for arl13b. (b,c) Wild-type AB zebrafish embryos at 72 hpf, non-injected (b), and injected with 400 pg arl13b-gfp mRNA (c). Scale bar, 1 mm. (d,e) Laterality of the internal organs: heart situs evaluated at 30 hpf (jogging) in live fish (d); and gut situs evaluated at 53 hpf in fixed embryos by in situ hybridization (e). Left—left jogging of the heart; right—right jogging of the heart; central—heart tube with no jogging; normal—left liver and right pancreas; reversed—right liver and left pancreas; central—abnormal liver and abnormal pancreas. Source data in http://dx.doi.org/10.5061/dryad.m541q [30].

Figure 2.

Predicted and observed flow patterns for long cilia. (a) Predicted flow map from WT embryos. (b) Predicted flow map to arl13b-injected embryos. The pseudocolour scale represents flow speed, where red represents high speed versus low speed in blue. (c,d) Experimental data for WT embryos shown as heat map of flow speed (c) and as a box plot for quantification (d). (e,f) Experimental data for arl13b-gfp overexpressed embryos (injected with 400 pg of arl13b-gfp mRNA per embryo) represented as a heat map of flow speed (e) based on the same dataset used to generate the box plot (f). The colour scale represents flow speed in µm s⁻¹, where red represents high speed versus low speed in blue. Box plots for instantaneous flow speed were based on measurements at different locations of the KV based on 243 tracks for seven WT embryos and 525 tracked native particles in a total of seven embryos overexpressing Arl13b-GFP. (g,h) Cilia beat frequency average in WT and Arl13b-GFP overexpressing embryos from a total of 30 motile cilia for each condition. Source data in http://dx.doi.org/10.5061/dryad.m541q [30].

Figure 3.

Elastic shape transitions in KV cilia as length increases. (a) Cilium beat diameter as a function of the length of the beat envelope as viewed from the side. The plot shows three distinct regions (I) cilia act as straight rods whirling in a conical beat, (II) beat helicity onsets, trailing the cilium tip through the fluid and (III) cilia in fully developed helical beat patterns. (b) Short cilia (I), exert a pure torque upon the fluid. As helicity onsets (II), a small force perpendicular to the beat plane is exerted. For fully developed helical beating (III), this force is larger. (c) Representative beat patterns used for the fluid mechanics study of WT (left) versus injected (right) embryos (n = 30 cilia used for arl13b-injected measurements and for WT). Source data in http://dx.doi.org/10.5061/dryad.m541q [30].