[Paper Review] A minimal model for structure, dynamics, and tension of monolayered cell colonies

Debarati Sarkar, Gerhard Gompper+1 more|arXiv (Cornell University)|Jun 8, 2020

Micro and Nano RoboticsPhysics and Astronomy59 references25 citations

TL;DR

This paper proposes a minimal active Brownian particle model with a long-range, broad-minimum attraction potential to capture the liquid-vacuum coexistence observed in monolayered cell colonies. The model reproduces fluid-like dynamics, cohesive edge behavior, tensile stress due to outward-polarized cell alignment, and collective cluster detachment under strong propulsion, with velocity alignment enhancing swirl-like motion and stress.

ABSTRACT

The motion of cells in tissues is an ubiquitous phenomenon. In particular, in monolayered cell colonies in vitro, pronounced collective behavior with swirl-like motion has been observed deep within a cell colony, while at the same time, the colony remains cohesive, with not a single cell escaping at the edge. Thus, the colony displays liquid-like properties inside, in coexistence with a cell-free "vacuum" outside. How can adhesion be strong enough to keep cells together, while at the same time not jam the system in a glassy state? What kind of minimal model can describe such a behavior? Which other signatures of activity arise from the internal fluidity? We propose a novel active Brownian particle model with attraction, in which the interaction potential has a broad minimum to give particles enough wiggling space to be collectively in the fluid state. We demonstrate that for moderate propulsion, this model can generate the fluid-vacuum coexistence described above. In addition, the combination of the fluid nature of the colony with cohesion leads to preferred orientation of the cell polarity, pointing outward, at the edge, which in turn gives rise to a tensile stress in the colony -- as observed experimentally for epithelial sheets. For stronger propulsion, collective detachment of cell clusters is predicted. Further addition of an alignment preference of cell polarity and velocity direction results in enhanced coordinated, swirl-like motion, increased tensile stress and cell-cluster detachment.

Motivation & Objective

• To understand how cell colonies maintain fluid-like internal dynamics while remaining cohesive at the edge, avoiding detachment despite strong collective motion.
• To resolve the paradox of strong adhesion preventing detachment while allowing fluidity, by introducing a modified interaction potential with a broad minimum.
• To explain the experimentally observed tensile stress in epithelial sheets, which arises from collective cell polarity alignment at the colony boundary.
• To investigate the conditions under which collective cell detachment occurs, particularly in the presence of velocity alignment and increased propulsion.
• To demonstrate that minimal physical models can reproduce complex biological phenomena like swirl-like motion and mechanical stress in collective cell migration.

Proposed method

• Adopts an active Brownian particle (ABP) model with self-propulsion, rotational diffusion, and Langevin dynamics for time evolution.
• Introduces a modified Lennard-Jones potential with an extended attractive basin (width ¯σ) to allow fluidity at strong adhesion, avoiding solidification.
• Incorporates a force-free regime between short-range repulsion and long-range attraction to enable both cohesion and mobility.
• Uses a Péclet number (Pe) to quantify the ratio of active to thermal forces, controlling the degree of collective motion.
• Adds velocity-alignment interactions between neighboring cells to promote coordinated, swirl-like motion and enhanced tensile stress.
• Employs stochastic simulations with Gaussian white noise for translational and rotational motion, with Drσ²/D = 3 to emphasize rotational over translational diffusion.

Experimental results

Research questions

• RQ1 How can a cell colony remain fluid-like internally while being cohesive at the edge, avoiding cell detachment?
• RQ2 What minimal physical model can reproduce the experimentally observed liquid-vacuum coexistence in monolayered cell colonies?
• RQ3 How does the combination of fluidity and cohesion lead to tensile stress in the colony, as observed in epithelial sheets?
• RQ4 What role does cell polarity alignment with velocity play in enhancing collective motion and promoting cluster detachment?
• RQ5 Under what conditions does collective detachment of cell clusters occur in the model?

Key findings

• The modified ABP model with a broad attractive well (increased ¯σ) enables liquid-vacuum coexistence, with the coexistence region expanding as ¯σ increases.
• For moderate propulsion (Pe ≈ 15), the model exhibits fluid-like dynamics with swirl-like motion and cohesive edges, matching experimental observations of MDCK colonies.
• Outward-polarized cell alignment at the colony edge generates tensile stress, consistent with experimental measurements in epithelial sheets.
• Stronger propulsion (Pe > 20) leads to collective detachment of cell clusters, with detachment threshold dependent on attraction strength and alignment.
• Velocity-alignment interactions significantly enhance coordinated swirl-like motion and increase tensile stress, with a negative minimum in the velocity correlation function Cvv(r) indicating long-range order.
• The model predicts that tensile stress and collective motion emerge from the interplay of fluidity, cohesion, and polarity alignment, without requiring complex biochemical signaling.