The rise of synthetic biology has presented engineers with an
unprecedented, fascinating opportunity: can we come to understand the
principles of our own origins -- animal embryonic development -- by
re-engineering it in the laboratory? I have been investigating from
an engineer's perspective some of algorithmic challenges that arise in
developmental patterning, and in particular, in the problem of
patterning geometric form in a deformable substrate. In such a
system, rearranging and deforming the parts of the system, both
geometrically and topologically, is inherent part of patterning.
Simultaneous patterning and deformation is unavoidable.
I developed a 3D computational model for deformable cellular surfaces,
as an abstraction of embryonic epithelia, one of the principal forms
of tissue in early animal development. With this model, I explore
several ways in which extremely simple agent programs running within
the individual cells can collectively craft large-scale structures.
In many cases, the mechanical properties of the substrate are a
crucial partner in the patterning process.
In attempt to better tackle simultaneous patterning and deformation, I
investigate the problem of self-correcting patterning. I pose a model
for self-correcting regional patterning inspired by regeneration
experiments in developmental biology, summarized in Mittenthal's Rule
of Normal Neighbors. The problem, interestingly, becomes a form of
distributed constraint propagation. I explore some of the phenomena
entailed by such a patterning mechanism and then apply it to the
problem of crafting surface geometries, where the inherently
self-correcting pattern helps to make the patterning process robust to
the self-deformation it entails. As a side-effect, the resulting
structures not only reliably break symmetry and develop but also
Thesis Supervisor: Gerald Jay Sussman