Abstract
We hypothesize that a population of migrating cells can form patterns when changes in local strains owing to relative cell motions induce changes in cell motility. That the mechanism originates in competing rates of motion distinguishes it from mechanisms involving strain energy gradients, e.g. those generated by surface energy effects or eigenstrains among cells, and diffusion-reaction mechanisms involving chemical signalling factors. The theory is tested by its ability to reproduce the morphological characteristics of enamel in the mouse incisor. Dental enamel is formed during amelogenesis by a population of ameloblasts that move about laterally within an expanding curved sheet, subject to continuously evolving spatial and temporal gradients in strain. Discrete-cell simulations of this process compute the changing strain environment of all cells and predict cell trajectories by invoking simple rules for the motion of an individual cell in response to its strain environment. The rules balance a tendency for cells to enhance relative sliding motion against a tendency to maintain uniform cell-cell separation. The simulations account for observed waviness in the enamel microstructure, the speed and shape of the 'commencement front' that separates domains of migrating secretory-stage ameloblasts from those that are not yet migrating, the initiation and sustainment of layered, fracture-resistant decussation patterns (cross-plied microstructure) and the transition from decussating inner enamel to non-decussating outer enamel. All these characteristics can be correctly predicted with the use of a single scalar adjustable parameter.