Volvox Inversion Mechanics Project Proposal Solid Mechanics ES240

The genus Volvox is comprised of several species of communal multcellular chlorophytes which exhibit a series of interesting morphogenetic events during their developmental cycle. In Volvox carteri, the inversion event is interesting in that after several rounds of cell division from a single cell, the glycoprotein lled, spheroidal plakea completely inverts itself thorough of series of highly coordinated genetic, kinetic and mechanical interactions[4, 3, 7, 5]. This dramatic coming of age of the adult colony is beginning to be understood from a developmental viewpoint, with descriptive data on the phenomena for both wild-type and mutants, as well as the distribution of relevant gene products now available. Herein, I examine the experimental data, and propose a mathematical model to describe this process, taking into consideration both the chemical kinetics and the tissue mechanics of the colony. The resulting system of coupled equations is solved in an approximated geometry of the mature gonidia, using the nite element method (FEM). Results are compared with the observed data, as well as exact solutions for idealized parametrization.