The critical determinants of the speed of an invading cell front are not well known. We performed a "wound-healing'' experiment that quantifies the migration of human peritoneal meosthelial cells over components of the extracellular matrix. We interpreted the results in the context of Fisher's equation, which includes terms for modelling random cell motility and proliferation. The model predicts that, after a short transient, the invading cell front will move as a travelling wave at constant speed. This is consistent with the experimental findings. We use the model to derive a relationship between the rate of cell proliferation and the cell diffusion coefficient. The model may be useful in analyzing the invasive capacity of cancer cells, for example, as well as predicting the efficacy of growth factors in tissue reconstruction, including the development of monolayer sheets of cells in skin engineering or the repair of injured corneas using grafts of cultured cells. See publications 166, 168.

Least-squares straight line fits for typical data sets. Also plotted are the positions of the computed wave front assuming different threshold values (u) defining the front: experimental data (blue line), least-squares fit (green line), u = 0.5 (red line), u = 0.1 (yellow line), u = 0.01 (pink line). Distance units are 0.25 mm. (A) Control, (B) collagen IV. [Reproduced with permission from publication 168]

Typical human peritoneal mesothelial cell front 10 h after wounding. [Reproduced with permission from publication 168].

** Work carried out in collaboration with S. McElwain and D. Leavesley