A Mechano-Diffusion Model of Morphogenesis

Mathematical Biology Seminar
Monday, April 24, 2023 - 3:15pm for 1 hour (actually 50 minutes)
Skiles 005
Benjamin Vaughan – University of Cincinnati - Department of Mathematical Sciences
Brandon Legried

Please Note: Hybrid version is available at: https://gatech.zoom.us/j/98003867540

Morphogenesis is the biological process that causes cells, tissues, or organisms to develop their shape. The theory of morphogenesis, proposed by Alan Turning, is a chemical model where biological cells differentiate and form patterns through intercellular reaction-diffusion mechanisms. Various reaction-diffusion models can produce a chemical pattern that mimics natural patterns. However, while they provide a plausible prepattern, they do not describe a mechanism in which the pattern is expressed. An alternative model is a mechanical model of the skin, initially described by Murray, Oster, and Harris. This model used mechanical interactions between cells without a chemical prepattern to produce structures like those observed in a Turing model. In this talk, we derive a modified version of the Murray, Oster, and Harris model incorporating nonlinear deformation effects. Since it is observed in some experiments that chemicals present in developing skin can cause or disrupt pattern formation, the mechanical model is coupled with a single diffusing chemical. Furthermore, it is observed that the interaction between tissue deformations with a diffusing chemical can cause a previously undescribed instability. This instability could describe both the pattern’s chemical patterning and mechanical expression without the need for a reaction-diffusion system.