A self-consistent cell flux expression for simultaneous chemotaxis and contact guidance in tissues

During wound healing, both chemotaxis and contact guidance can contribute to the migration of blood and tissue cells to the wound. In order to understand the wound healing process, we must thus understand how cells respond to both these simultaneous directional cues, which are not necessarily coaligned. Although chemotaxis and contact guidance have been studied individually, the interaction between them has not been addressed. We extend a stochastic cell movement model, developed by Dickinson and Tranquillo (1995) [6] for individual cues, for simultaneous chemotaxis and contact guidance by a two-parameter perturbation analysis in terms of the two associated cues, a chemotactic factor gradient and aligned tissue fibers. We present results from analysis of the first-order perturbation, which includes the cell flux expression heuristically proposed by others, but reveals paradoxical results for other indices of cell movement, such as the mean-squared displacement. We then present second-order perturbation results that resolve these paradoxical results. Finally, we relate these results to a continuum mechanical model developed by Barocas and Tranquillo (1997) [3] that predicts fiber alignment due to cell traction induced tissue contraction. Received: 30 April 1999 / Revised version: 30 October 1999 / Published online: 14 September 2000