A mathematical model of wound healing in bovine corneal endothelium

Abstract

We developed a mathematical model to describe healing processes in bovine corneal endothelial (BCE) cells in culture, triggered by mechanical wounds with parallel edges. Previous findings from our laboratory show that, in these cases, BCE monolayers exhibit an approximately constant healing velocity. Also, that caspase-dependent apoptosis occurs, with the fraction of apoptotic cells increasing with the distance traveled by the healing edge. In addition, in this study we report the novel findings that, for wound scratch assays performed preserving the basal extracellular matrix: i) the healing cells increase their en face surface area in a characteristic fashion, and ii) the average length of the segments of the cell columns actively participating in the healing process increases linearly with time. These latter observations preclude the utilization of standard traveling wave formalisms to model wound healing in BCE cells. Instead, we developed and studied a simple phenomenological model based on a plausible formula for the spreading dynamics of the individual healing cells, that incorporates original evidence about the process in BCE cells. The model can be simulated to: i) obtain an approximately constant healing velocity; ii) reproduce the profile of the healing cell areas, and iii) obtain approximately linear time dependences of the mean cell area and average length of the front active segments per column. In view of its accuracy to account for the experimental observations, the model can also be acceptably employed to quantify the appearance of apoptotic cells during BCE wound healing. The strategy utilized here could offer a novel formal framework to represent modifications undergone by some epithelial cell lines during wound healing.