Kavli Affiliate: Boris I. Shraiman
| First 5 Authors: Dillon J. Cislo, Anastasios Pavlopoulos, Boris I. Shraiman, ,
| Summary:
How does growth encode form in developing organisms? Many different
spatiotemporal growth profiles may sculpt tissues into the same target 3D
shapes, but only specific growth patterns are observed in animal and plant
development. In particular, growth profiles may differ in their degree of
spatial variation and growth anisotropy, however, the criteria that distinguish
observed patterns of growth from other possible alternatives are not
understood. Here we exploit the mathematical formalism of quasiconformal
transformations to formulate the problem of "growth pattern selection"
quantitatively in the context of 3D shape formation by growing 2D epithelial
sheets. We propose that nature settles on growth patterns that are the
‘simplest’ in a certain way. Specifically, we demonstrate that growth pattern
selection can be formulated as an optimization problem and solved for the
trajectories that minimize spatiotemporal variation in areal growth rates and
deformation anisotropy. The result is a complete prediction for the growth of
the surface, including not only a set of intermediate shapes, but also a
prediction for cell displacement along those surfaces in the process of growth.
Optimization of growth trajectories for both idealized surfaces and those
observed in nature show that relative growth rates can be uniformized at the
cost of introducing anisotropy. Minimizing the variation of programmed growth
rates can therefore be viewed as a generic mechanism for growth pattern
selection and may help to understand the prevalence of anisotropy in
developmental programs.
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