The processes of wound healing and collective cell migration have been studied for decades. Intensive research has been devoted to understanding the mechanisms involved in wound healing, but the role of cell-substrate interactions is still not thoroughly understood. Here we probe the role of cell-substrate interactions by examining in vitro the healing of monolayers of human corneal epithelial (HCE) cells cultured on artificial extracellular matrix (aECM) proteins. We find that the rate of wound healing is dependent on the concentration of fibronectin-derived (RGD) cell-adhesion ligands in the aECM substrate. The wound closure rate varies nearly sixfold on the substrates examined, despite the fact that the rates of migration and proliferation of individual cells show little sensitivity to the RGD concentration (which varies 40-fold). To explain this apparent contradiction, we study collective migration by means of a dynamic Monte Carlo simulation. The cells in the simulation spread, retract, and proliferate with probabilities obtained from a simple phenomenological model. The results indicate that the overall wound closure rate is determined primarily by the rate at which cells cross the boundary between the aECM protein and the matrix deposited under the cell sheet.