Fluid-dynamical basis of the embryonic development of left-right asymmetry in vertebrates

Abstract

Experimental work in developmental biology has recently shown in mice that fluid flow driven by rotating cilia in the node, a structure present in the early stages of growth of vertebrate embryos, is responsible for determining the normal development of the left-right axis, with the heart on the left of the body, the liver on the right, and so on. The role of physics, in particular, of fluid dynamics, in the process is one of the important questions that remain to be answered. We show with an analysis of the fluid dynamics of the nodal flow in the developing embryo that the leftward flow that has been experimentally observed may be produced by the monocilia driving it being tilted toward the posterior. We propose a model for morphogen transport and mixing in the nodal flow and discuss how the development of left-right asymmetry might be initiated.

Fig. 1.

(a) Anterior-posterior, dorsal-ventral, and left-right axes provide a coordinate system for the vertebrate body plan. When only one or two of the axes are defined, the result is achiral; the mirror image is the same as the original. But when the final, left-right axis is added, two chiral forms now exist. (b) Ventral and posterior sketch views of the node of the mouse embryo, and its rotating monocilia, showing also the experimentally observed leftward nodal flow.

Fig. 2.

(a) Vortical flow structure produced by a single rotlet. (b) Rectangular array of rotlets with axes vertical, showing cellular structure of vortices with a general circulation only occurring at the edges. (c) Triangular array of rotlets with axes vertical, to correspond more closely with the shape of the node. As in b, a general circulation occurs only at the edges. (d) Result of tilting the rotlet axes: array of tilted rotlets with tilt angle α = 24°, showing directional flow above and below the array.

Fig. 3.

Views of the xy plane for α varying between 0 and 24°:0° (a), 8° (b), 16° (c), and 24° (d). For small α the flow is vortical, whereas for larger α it is increasingly linear. The small-α pictures are similar to what is seen in Inv mutant mice, whereas the larger-α cases correspond to experiments on normal mouse embryos.

Fig. 4.

(a) Sketch of how fluid will recirculate within the node in vivo with diffuse return flows above and below the more intense outward flow in the center. Also shown is the putative placement of morphogen sources (gray areas) at the left and right sides adjacent to the upper recirculatory vortex. (b and c) Numerical simulations of our model depicting the steady-state concentration of a morphogen with a finite lifetime within the node with normal (b) and Inv (c) mice. The color scale is as for a rainbow, with red the highest concentration and violet the lowest. (d and e) Graphs of the concentration of morphogen at the floor of the node in the simulations above with normal (d) and Inv (e) mice (arbitrary units).