Keywords

randomly switched equations, Markov chain, expectation, velocity, discrete process, continuous process, exponential distribution, poisson distribution

Abstract

Numerical simulations suggest that average velocity of a biological cell depends largely on attachment dynamics and less on the forces exerted by the cell. We determine the relationship between two models of cell motion, one based on finite spring constants modeling attachment properties (a randomly switched differential equation) and a limiting case (a centroid model-a generalized random walk) where spring constants are infinite. We prove the main result of this paper, the Expected Velocity Relationship theorem. This result shows that the expected value of the difference between cell locations in the differential equation model at the initial time and at some elapsed time is proportional to the elapsed time. We also show that the relationship is time invariant. Numerical results show the model is consistent with experimental data.

Original Publication Citation

Journal of Differential Equations

Document Type

Peer-Reviewed Article

Publication Date

2019-12-15

Language

English

College

Physical and Mathematical Sciences

Department

Mathematics

University Standing at Time of Publication

Full Professor

Included in

Mathematics Commons

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