**Title:** Force-based models of cell-extracellular interaction

**Abstract:** In order to alter, predict, and ultimately control wound healing, developmental processes, and pathological conditions such as cancer, biologists need a better understanding of cell-cell and cell-extracellular interactions. These interactions have both force and biochemical components and are mediated by random processes; our research focuses on just the force component of the interactions. We model the force interactions as a system of differential equations representing the location of cell centers and membrane-bound interaction sites. Numerical simulations and analysis of the model indicate that when duration of the adhesion sites is a memoryless and force independent random process, the cell speed is independent of the force these adhesion sites exert on the cell. Furthermore, understanding the dynamics of the attachment and detachment of the adhesion sites is key to predicting cell speed. We introduce a differential equation describing the cell motion and then introduce a conjecture about the expected drift of the cell, the expected velocity relation conjecture. In order to better

understand the conjecture, we analyze it in the context of a related (but simpler) model of cell motion, and then numerically

compare the results for the simpler model and the full differential equation model. We also heuristically describe the relationship between the simplified and full models as well as provide a discussion of the biological significance of these results.