Long-range morphogen gradient formation by cell-to-cell signal propagation

Morphogen gradients are a central concept in developmental biology. Their formation often involves the secretion of morphogens from a local source, that spread by diffusion in the cell field, where molecules eventually get degraded. This implies limits to both the time and length scales over which morphogen gradients can form which are set by diffusion coefficients and degradation rates. Towards the goal of identifying plausible mechanisms capable of extending the gradient range, we here use theory to explore properties of a cell-to-cell signaling relay. Inspired by the millimeter-scale Wnt-expression and signaling gradients in flatworms, we consider morphogen-mediated morphogen production in the cell field. We show that such a relay can generate stable morphogen and signaling gradients that emanate from a source of morphogen at a boundary. This gradient formation can be related to an effective diffusion and an effective degradation that result from morphogen production due to signaling relay. If the secretion of morphogen produced in response to the relay is polarized, it further gives rise to an effective drift. We find that signaling relay can generate long-ranged gradients in relevant times without relying on extreme choices of diffusion coefficients or degradation rates, thus exceeding the limits set by physiological diffusion coefficients and degradation rates. A signaling relay is hence an attractive principle to conceptualize long-ranged gradient formation by slowly diffusing morphogens that are relevant for patterning in adult contexts such as regeneration and tissue turn-over.