Mathematical model of morphogen electrophoresis through gap junctions.

Gap junctional communication is important for embryonic morphogenesis. However, the factors regulating the spatial properties of small molecule signal flows through gap junctions remain poorly understood. Recent data on gap junctions, ion transporters, and serotonin during left-right patterning suggest a specific model: the net unidirectional transfer of small molecules through long-range gap junctional paths driven by an electrophoretic mechanism. However, this concept has only been discussed qualitatively, and it is not known whether such a mechanism can actually establish a gradient within physiological constraints. We review the existing functional data and develop a mathematical model of the flow of serotonin through the early Xenopus embryo under an electrophoretic force generated by ion pumps. Through computer simulation of this process using realistic parameters, we explored quantitatively the dynamics of morphogen movement through gap junctions, confirming the plausibility of the proposed electrophoretic mechanism, which generates a considerable gradient in the available time frame. The model made several testable predictions and revealed properties of robustness, cellular gradients of serotonin, and the dependence of the gradient on several developmental constants. This work quantitatively supports the plausibility of electrophoretic control of morphogen movement through gap junctions during early left-right patterning. This conceptual framework for modeling gap junctional signaling -- an epigenetic patterning mechanism of wide relevance in biological regulation -- suggests numerous experimental approaches in other patterning systems.