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Full-Text Articles in Physical Sciences and Mathematics
A Continuous Time Model Of Centrally Controlled Motion With Random Switching Terms, J. C. Dallon, L C. Despain, E J. Evans, C P. Grant, Willaim V. Smith
A Continuous Time Model Of Centrally Controlled Motion With Random Switching Terms, J. C. Dallon, L C. Despain, E J. Evans, C P. Grant, Willaim V. Smith
Faculty Publications
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 …
A Mathematical Model Of Amoeboid Cell Motion As A Continuous-Time Markov Process, Lynnae Despain
A Mathematical Model Of Amoeboid Cell Motion As A Continuous-Time Markov Process, Lynnae Despain
Theses and Dissertations
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 …
Cell Speed Is Independent Of Force In A Mathematical Model Of Amoeboidal Cell Motion With Random Switching Terms., J. C. Dallon, Emily J. Evans, Christopher Grant, William V. Smith
Cell Speed Is Independent Of Force In A Mathematical Model Of Amoeboidal Cell Motion With Random Switching Terms., J. C. Dallon, Emily J. Evans, Christopher Grant, William V. Smith
Faculty Publications
In this paper the motion of a single cell is modeled as a nucleus and multiple integrin based adhesion sites. Numerical simulations and analysis of the model indicate that when the stochastic nature of the adhesion sites is a memoryless and force independent random process, the cell speed is independent of the force these adhesion sites exert on the cell. Furthermore, understanding the dynamics of the attachment and detachment of the adhesion sites is key to predicting cell speed. We introduce a differential equation describing the cell motion and then introduce a conjecture about the expected drift of the cell, …