Mechanical and Civil Engineering Seminar

We explore the idea that strain stimulus can trigger collective response in large cell populations, breaking symmetry and providing a possible route to patterning. One study problem is the formation of the fracture-resistant microstructure in dental enamel by migrating ameloblasts [1]. Strain rate variations among the ameloblasts cause wavelike oscillations in their migratory paths, which become fixed features of enamel when the paths are mineralized. A strain-cue model predicts the wavelength of the oscillations using an independent model calibration. Strain variations can also trigger a transition to more complex patterns: the ameloblast population can spontaneously divide into groups, within each of which cells have an approximately common migration velocity, but with very different velocities from group to group. This can cause bandedness in the microstructure, which is observed in human (and other species ) enamel morphology. A second study problem is the formation of network structures in organs, e.g., nervous networks in the gut or vascular capillary networks [2]. The collective response of cells to strains associated with the invasion of an existing cell population by another type of cell generates the symmetry breaking that is necessary to stabilize the formation of branches (network elements) by the invaders. It also generates spontaneous sprouting. Simulations of the invasion of the gut by neural cells that are guided by strain cues correctly predict a number of aspects of the resulting nerve network (density, rate of branching, etc.). In both the innervation of the gut and amelogenesis, the governing physical parameter is the ratio of the migration velocity to the rate of relaxation of strained cells. Analysis of these rates for different organs and species reveals quantitative similarity between innervation of the mouse gut and human amelogenesis. The parameter calibration that accounts for enamel morphology in the ameloblast model provides a value for the relaxation rate of strains among the ameloblast population. Using the same relaxation rate for the host (invaded) cells in the model of innervation of the gut successfully predicts the characteristics of the nerve network formed in the mouse gut. This suggests that the relaxation mechanism in strained cell populations might be a pervasive factor in morphogenesis. The models outlined above achieve predictions of some aspects of organ morphology without explicit description of chemical signaling or the variations in the concentrations of chemical species. Such phenomena are of course implicit in any cell s response to strain stimulus. One point of the models is that in regard to the aspects of morphogenesis that have been addressed, strain stimulus can serve as the primitive signal, with chemical signaling following in a subsidiary role. 1 Cox, B.N., 2010 A multi-scale, discrete-cell simulation of organogenesis: Application to the effects of strain stimulus on collective cell behavior during ameloblast migration. Journal of Theoretical Biology. 262, 58-72. 2 Cox, B.N., 2011 A strain-cue hypothesis for biological network formation. Journal of the Royal Society, Interface. 2011(8), 377-394.