Abstract

Understanding cell motion facilitates the understanding of many biological processes such as wound healing and cancer growth. Constructing mathematical models that replicate amoeboid cell motion can help us understand and make predictions about real-world cell movement. We review a force-based model of cell motion that considers a cell as a nucleus and several adhesion sites connected to the nucleus by springs. In this model, the cell moves as the adhesion sites attach to and detach from a substrate. This model is then reformulated as a random process that tracks the attachment characteristic (attached or detached) of each adhesion site, the location of each adhesion site, and the centroid of the attached sites. It is shown that this random process is a continuous-time jump-type Markov process and that the sub-process that counts the number of attached adhesion sites is also a Markov process with an attracting invariant distribution. Under certain hypotheses, we derive a formula for the velocity of the expected location of the centroid.

Degree

College and Department

Physical and Mathematical Sciences; Mathematics

Rights

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