Looking inside an invasion wave of cells using continuum models: proliferation is the key.

Recently, a suite of cell migration assays were conducted to investigate the migration of neural crest (NC) cells along the gut during the development of the enteric nervous system (ENS). The NC cells colonise the gastro-intestinal tract as a rostro-caudal wave. Local behaviour was shown to be controlled by position relative to the leading edge of the wavefront. The assays involved chick-quail grafting techniques allowing the total invading population to be considered as a two-species system. A two-species continuum model with logistic proliferation and a migration mechanism is developed here to simulate the chick-quail graft experiments and provide a means of looking at the processes occurring within the invasion wave. Five migration mechanisms are considered--linear diffusion, two cases of nonlinear diffusion, chemokinesis and chemotaxis. The model results agree with the experimental observations, regardless of the specific type of migration mechanism. The results show that NC cell invasion is driven by proliferation and cell motility at the leading edge of the wave. Furthermore, logistic proliferation exerts the dominant control on the system. This observation is confirmed by analysing some simplified invasion models. Once the basic experiments were mathematically replicated, the mathematical models were used in turn to make some predictions that were yet to be experimentally tested. This involved conducting a sensitivity analysis of the system by interrupting the proliferation and/or migration ability of the leading edge. Numerical results show that the system is stable against these changes. Of the three experiments suggested, one was carried out and the experimental results were concordant with the theoretical predictions. The outcome of two other suggested experiments are predicted and left for future experimental validation.