Continuum Model of Collective Cell Migration in Wound Healing and Colony Expansion

Abstract

Collective cell migration plays an important role during wound healing and embryo development. Although the exact mechanisms that coordinate such migration are still unknown, experimental studies of moving cell layers have shown that the primary interactions governing the motion of the layer are the force of lamellipodia, the adhesion of cells to the substrate, and the adhesion of cells to each other. Here, we derive a two-dimensional continuum mechanical model of cell-layer migration that is based on a novel assumption of elastic deformation of the layer and incorporates basic mechanical interactions of cells as well as cell proliferation and apoptosis. The evolution equations are solved numerically using a level set method. The model successfully reproduces data from two types of experiments: 1), the contraction of an enterocyte cell layer during wound healing; and 2), the expansion of a radially symmetric colony of MDCK cells, both in the edge migration velocity and in cell-layer density. In accord with experimental observations, and in contrast to reaction-diffusion models, this model predicts a partial wound closure if lamellipod formation is inhibited at the wound edge and gives implications of the effect of spatially restricted proliferation.

A phenomenological model for chemico-mechanically induced cell shape changes during migration and cell–cell contacts

“…These models are useful on a tissue scale, where cells are not tracked, but rather cell densities are modeled. Some of these PDE models track the interface between for instance wound or tumor and the undamaged tissue, explicitly by incorporating a moving boundary problem (Adam 1999;Mi et al 2007;Arciero et al 2011;Schugart et al 2008;Xue et al 2009;Javierre et al 2008;Vermolen and Javierre 2009). Further, (Armstrong et al 2006;Gerisch and Chaplain 2006), some studies were performed based on the use of non-local (integral) terms in PDE's to simulate interfaces between different cell-types.…”

On the Mechanical Interplay Between Intra- and Inter-Synchronization During Collective Cell Migration: A Numerical Investigation

“…On the other hand, the cell layer may be represented as an incompressible fluid whose configuration is described by the density of cells and the velocity includes a growth term due to proliferation and apoptosis. Additionally, the adhesion forces of the layer sheet to the substrate and the stresses within the population are considered (Arciero et al 2011).…”

Computational Modeling of Inflammation and Wound Healing

“…20 In a two-dimensional continuum model, epithelial cells were represented as a compressible, nonviscous fluid, meaning individual cells were not tracked, but their density was. 19 The edge of this fluid progressed according to traction forces, causing the boundary of the fluid to move. Numerical solutions to this model were found using level sets.…”

“…[14][15][16] Equation-based models have been used to explore all phases of wound healing, from inflammation, 17,18 to wound closure, 19,20 to tissue remodeling. 21 This modeling framework, while extremely useful from a basic, mechanistic point of view, cannot be readily used to create tissue-realistic simulations that involve stochastic biological effects.…”

“…20 Such models have been used to infer which mechanisms, materials, and forces are critical to the wound-healing process. These equation-based models range from simple, equationbased models solved using level sets to represent and assess various stages of epithelial progression into a wound bed, 19 to more complex models that involve inflammatory and wound-healing mechanisms. 17,18,21 Such models have advanced our understanding of wound healing as it is supposed to work, suggested underlying pathological mechanisms, and tested therapies in silico.…”