The Motile-Units model: Interacting spins model of cell polarization and motility
Abstract
We introduce a coarse-grained interacting-spin model for two-dimensional cell motility, in which the cell perimeter is discretized into stochastic binary spins that switch between active and inactive states. Each perimeter spin represents a "motile-unit" that is a source of protrusive force and retrograde flow when active. Long-range interactions between the motile-units arise through a polarity cue advected by the collective actin retrograde flow, providing a minimal realization of spontaneous symmetry breaking and self-propulsion. The model exhibits three dynamical phases, a random walk phase, persistent random walk phase, and an intermittent bistable phase characterized by run-and-tumble migration. Additional nearest-neighbor interactions modulate speed and persistence without altering the overall phase structure. Owing to its simplicity, the framework naturally incorporates external cues, reproducing chemotactic migration, steering by localized optogenetic activation, and directional decision-making (symmetry breaking) under competing stimuli. The model introduces a new class of active-particle model in which both speed and polarity emerge from internal stochastic spin dynamics, rather than being imposed as particle-level variables, offering a framework for the study of cell migration and extends the scope of active-matter physics.
Related
- The polarization behavior of a system of two interacting identical spins 1/2 in adiabatically varying magnetic field
- Gap-Protected Heisenberg-Limited Squeezing with Locally Interacting Multi-Level Spins
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- Dielectric response of the antiferromagnetic multiferroics with cycloidal equilibrium for the polarization related to the noncollinear spins
- Mechanisms of spatial pattern transition in motile bacterial collectives
BibTeX
@misc{ron2026motileunits,
title = {{The Motile-Units model: Interacting spins model of cell polarization and motility}},
author = {Jonathan E. Ron and Nir S. Gov},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.20587},
eprint = {2609.20587},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.20587},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - The Motile-Units model: Interacting spins model of cell polarization and motility
AU - Jonathan E. Ron
AU - Nir S. Gov
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2609.20587
UR - https://arxiv.org/abs/2609.20587
AB - We introduce a coarse-grained interacting-spin model for two-dimensional cell motility, in which the cell perimeter is discretized into stochastic binary spins that switch between active and inactive states. Each perimeter spin represents a "motile-unit" that is a source of protrusive force and retrograde flow when active. Long-range interactions between the motile-units arise through a polarity cue advected by the collective actin retrograde flow, providing a minimal realization of spontaneous symmetry breaking and self-propulsion. The model exhibits three dynamical phases, a random walk phase, persistent random walk phase, and an intermittent bistable phase characterized by run-and-tumble migration. Additional nearest-neighbor interactions modulate speed and persistence without altering the overall phase structure. Owing to its simplicity, the framework naturally incorporates external cues, reproducing chemotactic migration, steering by localized optogenetic activation, and directional decision-making (symmetry breaking) under competing stimuli. The model introduces a new class of active-particle model in which both speed and polarity emerge from internal stochastic spin dynamics, rather than being imposed as particle-level variables, offering a framework for the study of cell migration and extends the scope of active-matter physics.
ER -