A continuous-time model of centrally coordinated motion with random switching

TL;DR

This paper develops a continuous-time Markov process model for centrally coordinated cell motion with random switching, analyzing its long-term behavior and validating results through numerical simulations.

Contribution

It introduces a simplified zero-relaxation model for cell motion, proves its well-posedness, and derives formulas for steady-state distribution and expected velocity.

Findings

Model is well-posed as a pure jump-type Markov process

Steady-state distribution for cell motion is characterized

Explicit formula for expected cell velocity is validated

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.