title: A continuous-time model of centrally coordinated motion with random switching.
abstract: This paper considers differential problems with random switching, with specific applications to the motion of cells and centrally coordinated motion. Starting with a differential-equation model of cell motion that was proposed previously, we set the relaxation time to zero and consider the simpler model that results. We prove that this model is well-posed, in the sense that it corresponds to a pure jump-type continuous-time Markov process (without explosion). We then describe the model's long-time behavior, first by specifying an attracting steady-state distribution for a projection of the model, then by examining the expected location of the cell center when the initial data is compatible with that steady-state. Under such conditions, we present a formula for the expected velocity and give a rigorous proof of that formula's validity. We conclude the paper with a comparison between these theoretical results and the results of numerical simulations.
authors.affiliation: Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA.
authors.forename: J C
authors.initials: JC
authors.lastname: Dallon
authors.affiliation: Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA.
authors.forename: Lynnae C
authors.initials: LC
authors.lastname: Despain
authors.affiliation: Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA. ejevans@math.byu.edu.
authors.forename: Emily J
authors.identifier: 0000-0003-3467-6650
authors.initials: EJ
authors.lastname: Evans
authors.affiliation: Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA.
authors.forename: Christopher P
authors.initials: CP
authors.lastname: Grant
authors.affiliation: Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA.
authors.forename: W V
authors.initials: WV
authors.lastname: Smith
mesh_terms: D002465:Cell Movement; D003198:Computer Simulation; D008390:Markov Chains; D008954:Models, Biological; D013997:Time Factors
keywords: Differential equations; Markov process; Random switching