The Role of Cell-Cell Adhesion in Wound Healing

Abstract

We present a stochastic model which describes fronts of cells invading a wound. In the model cells can move, proliferate, and experience cell-cell adhesion. We find several qualitatively different regimes of front motion and analyze the transitions between them. Above a critical value of adhesion and for small proliferation large isolated clusters are formed ahead of the front. This is mapped onto the well-known ferromagnetic phase transition in the Ising model. For large adhesion, and larger proliferation the clusters become connected (at some fixed time). For adhesion below the critical value the results are similar to our previous work which neglected adhesion. The results are compared with experiments, and possible directions of future work are proposed.

Towards a unified approach in the modeling of fibrosis: A review with research perspectives

“…The reader interested in a detailed description of other agent-based models for fibrosis-related diseases is referred to papers [118][119][120][121][122][123][124][125][126] and the references cited therein.…”

Generalized Cahn-Hilliard equation for biological applications

“…We review the discrete model for diffusion, proliferation, and cell-cell adhesion [1]. Consider a square twodimensional lattice in a channel geometry.…”

“…Without proliferation the model can be mapped into the Ising model, as we pointed out in [1]. In this mapping the adhesion parameter q is identified with 1 − exp(−J/k B T ) where T is the temperature, k B is Boltzmann's constant, and J is the coupling strength in the magnetic model, and the average density u is identified with (m + 1)/2, where m is the average magnetization.…”

“…This problem arises in models for wound healing [2] and tumor growth [3]. It is easy to formulate a discrete model for these processes [1]. However, proceeding to the continuum limit is non-trivial [4].…”

“…Next consider a discrete model which includes diffusion and cell-cell adhesion, but not proliferation. When a particle is picked at random, the probability to jump decreases with the number of nearest neighbors, to take into account cell-cell adhesion [1]. This scheme can be mapped into the Ising model [11,12], by identifying an empty site with spin down, and an occupied site with spin up.…”