University of Texas at Austin

Past Event: Oden Institute Seminar

Perspectives on the mathematics of patterning and morphogenesis with applications to developmental biology

Krishna Garikipati, Professor, Mechanical Engineering, and Mathematics; Director, Michigan Institute for Computational Discovery & Engineering, University of Michigan

3:30 – 5PM
Thursday Apr 12, 2018

POB 6.304

Abstract

A central question in developmental biology is how size and position are determined. The genetic code carries instructions on how to control these properties in order to regulate the pattern and morphology of structures in the developing organism. Transcription and protein translation mechanisms implement these instructions. However, this cannot happen without some manner of sampling of epigenetic information on the current patterns and morphological forms of structures in the organism. Any rigorous description of space- and time-varying patterns and morphological forms reduces to one among various classes of spatio-temporal partial differential equations. Reaction-transport equations represent one such class. Starting from simple Fickian diffusion, the incorporation of reaction, phase segregation and advection terms can represent many of the patterns seen in the animal and plant kingdoms. Morphological form, requiring the development of three-dimensional structure, also can be represented by these equations of mass transport, albeit to a limited degree. The recognition that physical forces play controlling roles in shaping tissues leads to the conclusion that (nonlinear) elasticity governs the development of morphological form. In this setting, inhomogeneous growth drives the elasticity problem. The combination of reaction-transport equations with those of elasto-growth makes accessible a potentially unlimited spectrum of patterning and morphogenetic phenomena in developmental biology. This perspective talk is a survey of the partial differential equations of mathematical physics that have been proposed to govern patterning and morphogenesis in developmental biology. Several numerical examples will be shown to illustrate these equations and the corresponding physics, with the intention of providing physical insight wherever possible. Bio Krishna Garikipati obtained his undergraduate degree from IIT Bombay in 1991, and his Masters and PhD in 1992 and 1996, respectively, from Stanford University. He joined the faculty at University of Michigan in 2000, where he has been a professor since 2012. Since 2016, he has been the Director of the Michigan Institute for Computational Discovery & Engineering (MICDE), which is the focus of research, education and outreach in computational science and engineering at University of Michigan. His work in computational science draws upon applications in biophysics, mathematical biology and materials physics. Of particular interest now are patterning and morphogenesis in developmental biology, and mechano-chemically driven phase transformations in materials. Data-driven modeling is a recent methodological interest, also. He has been awarded the Department of Energy Early Career Award for Scientists and Engineers, the Presidential Early Career Award for Scientists and Engineers, and the Alexander von Humboldt Foundation's Research Fellowship.

Event information

Date
3:30 – 5PM
Thursday Apr 12, 2018
Location POB 6.304
Hosted by Tan Bui-Thanh