Results from a differential equation model for cell motion with random switching show that the model cell velocity is asymptotically independent of force

Autor:	Emily J. Evans, Christopher P. Grant, J. C. Dallon, William V. Smith
Rok vydání:	2019
Předmět:	Markov chain Differential equation Applied Mathematics 010102 general mathematics Dynamics (mechanics) Mathematical analysis Centroid Expected value Random walk 01 natural sciences 010101 applied mathematics LTI system theory Spring (device) 0101 mathematics Analysis Mathematics
Zdroj:	Journal of Differential Equations. 268:301-317
ISSN:	0022-0396
DOI:	10.1016/j.jde.2019.08.019
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::9c86313dc3fd09711343e19d9677ec19 https://doi.org/10.1016/j.jde.2019.08.019 Zobrazit plný text záznamu Full Text from ScienceDirect