Collective spatial reorganization from arrest to peeling and migration through density-dependent mobility in internal-state coordinates

Abstract

Numerous problems in development, regeneration, and disease involve simultaneous evolution of both spatial organization and the internal state of the constituents in addition to local interactions and crowding. This motivates us to study a minimal model for interacting populations evolving in coupled spatial and internal-state coordinates. We focus on a specific transition of particular biological interest: the reorganization of dense collectives from compact or arrested states toward boundary-led peeling and migration. In our formulation, each particle carries a spatial position and a scalar internal state, and interacts through finite-range forces. Mobilities are defined on both spatial and internal-state coordinates with a density dependence, and are asymmetrically cross-coupled. We derive update equations for stochastic dynamics in the overdamped limit and perform numerical simulations. We find that mobility in internal-state coordinates alone provides an independent control axis for large-scale spatial reorganization. In particular, increasing the baseline internal-state diffusivity and tuning its density dependence drives a transition from arrested aggregates to a peeling-like regime with broad spatial excursions, strong outward radial bias, and edge-localized activity, while the baseline positional diffusivity is held fixed. The transition is accompanied by correlated broadening of spatial and internal-state displacements, systematic reorganization of radial density and density-curvature profiles, and a pronounced dependence on system size, consistent with the idea that growing aggregates can cross into a boundary-dominated migratory state. These results establish the utility of our approach and motivate a broader framework aimed at modeling state change, spatial redistribution, and neighborhood structure within a common formalism.