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Published on: May 10, 2012
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A continuous-time model of centrally coordinated motion with random switching
J C Dallon1, Lynnae C Despain1, Emily J Evans2
1Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA.
Journal of Mathematical Biology
|July 11, 2016
Summary
This study simplifies cell motion models, proving a new model is well-posed. It analyzes long-term cell behavior and derives a formula for expected velocity, validated by simulations.
Area of Science:
- Mathematical modeling
- Cellular dynamics
- Stochastic processes
Background:
- Previous differential-equation models of cell motion.
- Simplification of models by setting relaxation time to zero.
Purpose of the Study:
- To analyze a simplified differential-equation model for cell motion.
- To prove the model is well-posed as a continuous-time Markov process.
- To investigate the long-time behavior and derive a formula for expected velocity.
Main Methods:
- Mathematical analysis of differential equations with random switching.
- Proof of well-posedness for a pure jump-type continuous-time Markov process.
- Analysis of steady-state distributions and expected cell location.
- Derivation and rigorous proof of a formula for expected velocity.
Main Results:
- The simplified cell motion model is proven to be well-posed.
- An attracting steady-state distribution is identified for a projection of the model.
- A formula for the expected velocity of the cell center is derived and rigorously proven.
- Theoretical results are compared with numerical simulations.
Conclusions:
- The simplified model accurately represents cell motion dynamics.
- The derived formula for expected velocity is mathematically sound.
- The study provides a robust framework for analyzing coordinated cell motion.
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