The Unreasonable Effectiveness of Reaction Diffusion in Vertebrate Skin Color Patterning

Abstract

In 1952, Alan Turing published the reaction-diffusion (RD) mathematical framework, laying the foundations of morphogenesis as a self-organized process emerging from physicochemical first principles. Regrettably, this approach has been widely doubted in the field of developmental biology. First, we summarize Turing's line of thoughts to alleviate the misconception that RD is an artificial mathematical construct. Second, we discuss why phenomenological RD models are particularly effective for understanding skin color patterning at the meso/macroscopic scales, without the need to parameterize the profusion of variables at lower scales. More specifically, we discuss how RD models ( a) recapitulate the diversity of actual skin patterns, ( b) capture the underlying dynamics of cellular interactions, ( c) interact with tissue size and shape, ( d) can lead to ordered sequential patterning, ( e) generate cellular automaton dynamics in lizards and snakes, ( f) predict actual patterns beyond their statistical features, and ( g) are robust to model variations. Third, we discuss the utility of linear stability analysis and perform numerical simulations to demonstrate how deterministic RD emerges from the underlying chaotic microscopic agents.