Continuous limit of a discrete stochastic model of cell migration
Abstract
We analytically derive the continuous limit of the Cellular Potts Model (CPM) for a one-dimensional cell subjected to constant and run-and-tumble driving forces. By coarse-graining the discrete lattice dynamics, we obtain the Fokker-Planck equations governing the cell's size and center-of-mass position. We show that in the low-force regime, the cell dynamics are accurately described by an overdamped Langevin equation. Beyond this regime, we expose intrinsic algorithmic artifacts, including a force-dependent diffusion coefficient, a non-linear force-velocity relationship, and the breakdown of the Einstein relation. We demonstrate that replacing the conventional Metropolis update rule with Glauber dynamics significantly mitigates these artifacts, broadening the physically valid parameter space. Our exact results bridge the gap between lattice-based simulations and continuous active matter models.
Related
- Disentangling discrete and continuous spectra of tidally forced internal waves in shear flow
- Delocalisation and scaling limit for the disordered long-range Discrete Gaussian Chain
- Binder migration across film consolidation and pore emptying in electrode drying: a continuous model validated against drying-rate, thickness, and schedule experiments
- On the coincidence of discrete and continuous definitions of Entanglement of Formation
- Adaptive metamaterial resonators: a discrete and continuous mechanism
BibTeX
@misc{despeignes2026continuous,
title = {{Continuous limit of a discrete stochastic model of cell migration}},
author = {Nino Despeignes and Marc Durand},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2606.03752},
eprint = {2606.03752},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.03752},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Continuous limit of a discrete stochastic model of cell migration
AU - Nino Despeignes
AU - Marc Durand
PY - 2026
DA - 2026/09/03
PB - arXiv
DO - 10.48550/arxiv.2606.03752
UR - https://arxiv.org/abs/2606.03752
AB - We analytically derive the continuous limit of the Cellular Potts Model (CPM) for a one-dimensional cell subjected to constant and run-and-tumble driving forces. By coarse-graining the discrete lattice dynamics, we obtain the Fokker-Planck equations governing the cell's size and center-of-mass position. We show that in the low-force regime, the cell dynamics are accurately described by an overdamped Langevin equation. Beyond this regime, we expose intrinsic algorithmic artifacts, including a force-dependent diffusion coefficient, a non-linear force-velocity relationship, and the breakdown of the Einstein relation. We demonstrate that replacing the conventional Metropolis update rule with Glauber dynamics significantly mitigates these artifacts, broadening the physically valid parameter space. Our exact results bridge the gap between lattice-based simulations and continuous active matter models.
ER -