期刊论文详细信息
JOURNAL OF DIFFERENTIAL EQUATIONS 卷:268
Results from a differential equation model for cell motion with random switching show that the model cell velocity is asymptotically independent of force
Article
Dallon, J. C.1  Evans, Emily J.1  Grant, Christopher P.1  Smith, W., V1 
[1] Brigham Young Univ, Dept Math, Provo, UT 84602 USA
关键词: Randomly switched equations;    Markov chain;    Expectation;    Discrete process;    Continuous process;   
DOI  :  10.1016/j.jde.2019.08.019
来源: Elsevier
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【 摘 要 】

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. (C) 2019 Elsevier Inc. All rights reserved.

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