Particle tracking model of electrophoretic morphogen movement reveals stochastic dynamics of embryonic gradient

Some developmental events rely on an electrophoretic force to produce morphogenetic gradients. To quantitatively explore the dynamics of this process, we constructed a stochastic model of an early phase of left-right patterning: serotonin movement through the gap junction-coupled blastomeres of the Xenopus embryo. Particle-tracking simulations showed that a left-right gradient is formed rapidly, quickly reaching a final stable level. The voltage difference was critical for producing a morphogen gradient of the right steepness; gap junctional connectivity and morphogen mass determined the timing of the gradient. Endogenous electrophoresis drives approximately 50% of the particles across more than one cell width, and approximately 20% can travel across half the embryo. The stochastic behavior of the resulting gradients exhibited unexpected complexity among blastomeres' morphogen content, and showed how spatiotemporal variability within individual cells resulted in robust and consistent gradients across the embryonic left-right axis. Analysis of the distribution profile of gradient gain values made quantitative predictions about the conditions that result in the observed background level of laterality defects in unperturbed frog embryos. This work provides a general model that can be used to quantitatively analyze the unexpectedly complex dynamics of morphogens in a wide variety of systems.