A multi-scale, discrete-cell simulation of organogenesis: Application to the effects of strain stimulus on collective cell behavior during ameloblast migration

Abstract

A multi-scale strategy is presented for simulating organogenesis that uses a single cell response function to define the behavior of individual cells in an organ-scale simulation of a large cell population. The response function summarizes detailed information about the behavior of individual cells in a sufficiently economical way that the organ-scale model can be commensurate with the entire organ. The first application demonstrates the effects of strain stimulus on the migration of ameloblasts during enamel formation. Ameloblasts are an attractive study case because mineralization preserves a complete record of their migratory paths. The response function in this case specifies the motions of cells responding to strain stimuli that propagate through the population. The strain stimuli are related to the curvature of the surface from which the ameloblasts migrate (the dentin–enamel junction or DEJ). A single unknown rate parameter is calibrated by an independent datum from the human tooth. With no remaining adjustable parameters, the theory correctly predicts aspects of the fracture-resistant, wavy microstructure of enamel in the human molar, including wavelength variations and the rate of wave amplitude damping. At a critical value of curvature of the DEJ, a transition in the ordering of cells occurs, from invariant order over the whole population to self-assembly of the population into groups or gangs. The prediction of an ordering transition and the predicted critical curvature are consistent with gnarled enamel in the cusps of the human molar. The calibration of the model using human data also predicts waves in the mouse incisor and an ordering transition at the chimpanzee cingulum. Widespread compressive strain is predicted late in the migration for both the human molar and mouse incisor, providing a possible signal for the termination of amelogenesis.