Mathematical model of morphogen electrophoresis through gap junctions

Abstract

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.

Electrical dimensions in cell science

“…Gradients of 20 mV were measured, with cells on the left side of the midline being depolarised with respect to those on the right side (Levin et al, 2002). This induces an intracellular gradient of voltage within the syncytium, which in turn (through electrophoresis) establishes a gradient of serotonin within cells of the midline, and this is thought to regulate left-right determination (Adams et al, 2006;Esser et al, 2006). This is clear evidence that an EF can establish intracellular gradients of relevant signalling molecules.…”

H+ pump-dependent changes in membrane voltage are an early mechanism necessary and sufficient to induceXenopustail regeneration

“…biophysical controls of pattern formation (Adams et al, 2006;Esser et al, 2006), we sought to gain mechanistic insight into the control of regeneration by ion flows in the Xenopus larval tail. Our physiological, genetic and cell-biological data show that H + flux (driven endogenously by the V-ATPase pump) underlies profound changes in membrane voltage, is necessary for initiating regeneration of the tail and correct neuronal patterning in the new tissue, and is sufficient to rescue both regeneration and axonal patterning in regeneration-refractory contexts.…”

Gradients in Planarian Regeneration and Homeostasis

“…Although diffusion has been considered the main mechanism by which morphogens establish a gradient, active processes for the transport of morphogens have recently been proposed based on novel molecular data (Pfeiffer et al 2000;Ibañes et al 2006), which would enable long-range transmission of morphogenetic signals. One of these mechanisms is the direct transport of small and specific molecules through the cells using gap-junctional connections (Esser et al 2006). Several innexins, the main components of invertebrate gap junctions, have been characterized from planarians (Nogi and Levin 2005;Oviedo and Levin 2007).…”