Active Flows and Deformable Surfaces in Development

Abstract

We review progress in active hydrodynamic descriptions of flowing media on curved and deformable manifolds: the state-of-the-art in continuum descriptions of single-layers of epithelial and/or other tissues during development. First, after a brief overview of activity, flows and hydrodynamic descriptions, we highlight the generic challenge of identifying the dependence on dynamical variables of so-called active kinetic coefficients-active counterparts to dissipative Onsager coefficients. We go on to describe some of the subtleties concerning how curvature and active flows interact, and the issues that arise when surfaces are deformable. We finish with a broad discussion around the utility of such theories in developmental biology. This includes limitations to analytical techniques, challenges associated with numerical integration, fitting-to-data and inference, and potential tools for the future, such as discrete differential geometry.

Theory of defect-mediated morphogenesis

“…In the past decade, the conceptual framework of active matter (3)-namely, materials whose building blocks can autonomously move and perform mechanical work-has enormously contributed to classify the arsenal of physical mechanisms behind force generation and collective migration in both eukaryotes and prokaryotes. However, how these physical mechanisms can be harnessed to achieve biological functionality remains a major open question at the crossroads between developmental biology and mechanics (4)(5)(6)(7).…”