Synthetic morphogenesis : space, time, and deformation

Abstract

Synthetic biology has presented engineers with a fascinating opportunity: can we understand the principles of our origins { animal embryonic development - by re-engineering it in the laboratory? I investigate, from an engineer's perspective, some of problems that arise in developing geometric form in a deformable substrate. More abstractly, I attack the problem of establishing spatial patterns, when rearranging and deforming parts of the system is inherent to the process. Deformable, foam-like cellular surfaces are developed as a model for embryonic epithelia (polarized cellular sheets), one of the principal tissue types in early animal development. I explore ways in which simple agent programs running within the individual cells can collectively craft large-scale structures. The mechanical properties of the substrate prove crucial to the patterning process. In such a distributed, heterogeneous substrate, little can be assumed about the progress of time. In one branch of my work, I develop patterning techniques where convergence is transparently and locally detectable, drawing insights from clockless digital circuits and casting the problem as distributed constraint propagation. In another branch of work, I avoid the problem of timing by making all patterns self- correcting. In self-correcting patterning, I attempt to understand "canalization" - how development is naturally robust to perturbations. I formulate a model for regional patterning, inspired by regeneration experiments in developmental biology, and using mathematical principles from classical models of magnetic domains and phase separation. The problem again becomes a form of distributed constraint propagation, now using soft constraints. I explore some of the resulting phenomena and then apply the mechanism to crafting surface geometries, where self-correction makes the process robust to both damage and self-deformation. I conclude with a look at how this naturally leads to an example of partial redundancy { multiple systems that partly but not completely overlap in function - yielding confusing responses to the effects of virtual knock-out experiments, reminiscent of the confusing behavior of knock-out experiments in biology.