Closing the Loop on Morphogenesis: A Mathematical Model of Morphogenesis by Closed-Loop Reaction-Diffusion

Abstract

Morphogenesis, the establishment and repair of emergent complex anatomy by groups of cells, is a fascinating and biomedically-relevant problem. One of its most fascinating aspects is that a developing embryo can reliably recover from disturbances, such as splitting into twins. While this reliability implies some type of goal-seeking error minimization over a morphogenic field, there are many gaps with respect to detailed, constructive models of such a process being used to implement the collective intelligence of cellular swarms. We describe a closed-loop negative-feedback system for creating reaction-diffusion (RD) patterns with high reliability. It uses a cellular automaton to characterize a morphogen pattern, then compares it to a goal and adjusts accordingly, providing a framework for modeling anatomical homeostasis and robust generation of target morphologies. Specifically, we create a RD pattern with N repetitions, where N is easily changeable. Furthermore, the individual repetitions of the RD pattern can be easily stretched or shrunk under genetic control to create, e.g., some morphological features larger than others. Finally, the cellular automaton uses a computation wave that scans the morphogen pattern unidirectionally to characterize the features that the negative feedback then controls. By taking advantage of a prior process asymmetrically establishing planar polarity (e.g., head vs. tail), our automaton is greatly simplified. This work contributes to the exciting effort of understanding design principles of morphological computation, which can be used to understand evolved developmental mechanisms, manipulate them in regenerative medicine settings, or embed a degree of synthetic intelligence into novel bioengineered constructs.Comment: 20 pages, 3 tables, 5 figure