Beyond Turing: Reaction-diffusion mechanisms of embryonic self-organization

Developing embryos display a remarkable capacity for self-organization, generating diverse shapes, patterns and structures de novo. First conceived in the 1950s, Turing’s reaction-diffusion hypothesis proposes that this self-organization is driven by interacting and diffusing signalling molecules. Indeed, mathematical Turing models recapitulate patterning in silico. However, key limitations cast doubt on the relevance of Turing models in vivo. First, current models are highly simplified and extremely fragile, at odds with the highly reproducible nature of embryonic development. Second, Turing mechanisms form repetitive patterns (e.g., fingers), whereas many in vivo patterns do not repeat. Third, Turing patterns do not scale with tissue size unlike most embryos and tissues. We propose that these limitations arise because current models are too simple to capture the molecular complexity operating in vivo. Turing models thus represent only a small subset of the much larger class of in vivo reaction-diffusion mechanisms. Here, we will build biologically-aligned mathematical models to investigate reaction-diffusion systems with unprecedented levels of complexity and biological realism. Aided by new computational tools (Aim 1), we seek novel self-organizing mechanisms that are: highly robust (Aim 2); do not repeat (Aim 3); and scale to tissue size (Aim 4). Our pilot data already indicates that this will reveal new paradigms for pattern formation beyond Turing’s original hypothesis. Our models will be challenged by data from various biological systems, including published datasets as well as close collaborations with experimentalists, taking advantage of the increasing availability of high-resolution quantitative data. Our unique blend of expertise spans theoretical physics, experimental embryology, and computational biology, ideally positioning us to discover conceptually new mechanisms of pattern formation that allow embryos, tissues and organoids to self-organize.