Simulations of particle tracking in the oligociliated mouse node and implications for left-right symmetry breaking mechanics

Abstract

The concept of internal anatomical asymmetry is familiar; usually in humans the heart is on the left and the liver is on the right, however how does the developing embryo know to produce this consistent laterality? Symmetry breaking initiates with left-right asymmetric cilia-driven fluid mechanics in a small fluid-filled structure called the ventral node in mice. However the question of what converts this flow into left-right asymmetric development remains unanswered. A leading hypotheses is that flow transports morphogen containing vesicles within the node, the absorption of which results in asymmetrical gene expression. To investigate how vesicle transport might result in the situs patterns observed in wildtype and mutant experiments, we extend the open source Stokes flow package, NEAREST, to consider the hydrodynamic and Brownian motion of particles in a mouse model with flow driven by one, two, and 112 beating cilia.Three models for morphogen-containing particle released are simulated to assess their compatibility with observed results in oligociliated and wildtype mouse embryos: uniformly random release, localised cilium stress induced release, and localised release from motile cilia themselves. Only the uniformly random release model appears consistent with the data, with neither localised-release model resulting in significant transport in the oligociliated embryo.

Passively parallel regularized stokeslets

“…The same computation with the Nyström method ( N = Q = 3456) yielded a 5% error and required 350 seconds. Other early applications of the nearest-neighbour discretization by our group have included the diffusion tensor of a macromolecular structure [ 51 ], cell motility [ 31 ] and embryonic nodal flow [ 32 ].…”

“…To investigate this problem, we recently modelled the enclosed embryonic node of the mouse using NEAREST [ 32 ], with a biologically realistic 112 beating cilia, with particular focus on how the calculated flow can transport particles potentially needed for chemical signalling. The large number of beating cilia, and non-planar boundaries in this problem, means that long time scale computational simulation of particle transport is particularly challenging for most existing methods.…”

“…Taking the forces calculated for the 39 979 scalar d.f. from the previous work [ 32 ], we calculate the time required to track a set of 1, 10 and 100 particles for 1000 beat cycles of the 112 cilia. A sketch of the euciliated mouse node is shown in figure 5 a , with the paths of 10 particles shown in figure 5 b , time requirements in figure 5 c and relative speed increase in figure 5 d .…”

“…Algorithms vary greatly in how they improve in performance on parallel processing architectures in general, and GPU hardware in particular. We therefore assess what effect this has on the computational cost of the method by benchmarking against previous work [ 31 , 32 ], as well as providing new simulations of multiple undulatory swimmers and investigating whether sperm-like swimmers are capable of driving particle transport through an enclosed channel.…”

Chemosensing versus mechanosensing in nodal and Kupffer's vesicle cilia and in other left–right organizer organs

“…These NVPs moving in the nodal fluid, if they contained a morphogen, might act as described for a dissolved morphogen above, except that owing to their far greater mass, they would not undergo molecular diffusion, but only dispersion. This would effectively allow for their asymmetric LR accumulation, and possibly even for slow flows [13]. NVPs might still be chemosensed by cilia at either side of the node and there might still be an LR imbalance owing to the direction of fluid flow (figure 2).…”