From flocking to jamming in collective cell dynamics: a Vicsek-like model including contact forces

The goal of the present work is to propose an agent-based model that originally combines classical Vicsek-like polarity alignments and contact forces, as implemented in the framework developed by Maury and Venel in [Maury, Venel, 2011]. The description additionally incorporates velocity feedback on polarity and soft attraction-repulsion interactions. After carefully studying the well posedness of the model, we introduce a suitable discretization and perform an extensive range of numerical experiments to assess the impact of different modeling ingredients. The dynamical system is capable of recovering the order-disorder phase transition of the flock, as well as the jamming effect in high density regimes. As such, the developed framework can be seen as a promising theoretical tool that could contribute to improving the understanding of complex collective cell dynamics and emerging tissue flows.

💡 Research Summary

The paper introduces a novel two‑dimensional agent‑based model for collective cell dynamics that merges three key ingredients: (i) Vicsek‑type polarity alignment, (ii) hard‑contact constraints à la Maury‑Venel, and (iii) a soft attraction‑repulsion potential. Each cell is represented as a rigid disk of radius R₀ with state variables position Xᵢ(t), velocity Vᵢ(t) and unit polarity vector Pᵢ(t). The desired velocity is composed of a self‑propulsion term c Pᵢ and a force term γ Fᵢ, where Fᵢ derives from a short‑range polynomial potential W(r)=−κ(r²/2−r³/6R_c) acting within a “comfort zone” R_c. To enforce non‑overlap, the raw velocity c P + γ F is projected onto the admissible velocity set C_X, defined by non‑penetration constraints between cells and with the domain boundary. This projection yields contact forces that can be interpreted as a normal cone inclusion, turning the dynamics into a differential inclusion.

Polarity dynamics follow a Vicsek‑like rule: each cell relaxes its polarity toward the local average polarity \bar Pᵢ (within interaction radius R_point) with rate μ, while simultaneously aligning to its own velocity direction Vᵢ/‖Vᵢ‖ with rate δ. Angular diffusion with coefficient D adds stochasticity, and a projection onto the tangent space of the unit circle guarantees unit norm. By converting the stochastic term to zero (D=0) for analysis, the authors rewrite the whole system as
\