Biological inferences from a mathematical model for malignant invasion.

Invasive cells show changes in adhesion, motility and the protease-antiprotease balance. In this paper the authors derive a model based on a continuum approach that describes the behaviour of the invasive cells. The invasive cells are studied in the context of their interaction with normal cells, noninvasive tumour cells, ECM proteins and the proteases. The authors briefly describe the methods of mathematical analysis used and then go on to highlight the biological inferences drawn from the mathematical analysis. Based on the results from the modelling the authors suggest that the movement of cells under the simultaneous effects of a haptotactic gradient and a concomitantly created chemotactic gradient is oscillatory both with respect to the speed of invasion and the wave profile of the invasive cells. They further demonstrate that the average speed of invasion can be computed as a measure of the phenotypic properties of the cell and the matrix. They use the model to suggest an intuitive explanation for the occurrence of noninvasion with high protease expression on the basis of chemotactic gradients that prevent invasion. The authors have studied the effect of the diffusivity of the protease on an invading cell and shown that increase in diffusivity initially results in enhanced invasion, but extreme increases in protease diffusivity can result in noninvasion.