Cell speed is independent of force in a mathematical model of amoeboidal cell motion with random switching terms

In this paper the motion of a single cell is modeled as a nucleus and multiple integrin based adhesion sites. Numerical simulations and analysis of the model indicate that when the stochastic nature 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 average velocity relation conjecture. Using Markov chain theory, we analyze our conjecture 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.