# A population dynamics model of cell-cell adhesion incorporating population pressure and density saturation

## TL;DR

This paper develops an improved continuum model for cell-cell adhesion that captures sharp invasion fronts and intermingling of different cell types, aligning well with experimental observations and applicable to tissue growth.

## Contribution

It introduces a novel model incorporating localized repulsion and nonlocal attraction, enhancing the ability to simulate sharp fronts and cell intermingling in tissue growth.

## Key findings

- Model captures sharp invasion fronts and cell intermingling.
- Quantitative agreement with experimental data.
- Explores effects of cell-cell repulsion on tissue dynamics.

## Abstract

We discuss several continuum cell-cell adhesion models based on the underlying microscopic assumptions. We propose an improvement on these models leading to sharp fronts and intermingling invasion fronts between different cell type populations. The model is based on basic principles of localized repulsion and nonlocal attraction due to adhesion forces at the microscopic level. The new model is able to capture both qualitatively and quantitatively experiments by Katsunuma et al. (2016) [J. Cell Biol. 212(5), pp. 561--575]. We also review some of the applications of these models in other areas of tissue growth in developmental biology. We finally explore the resulting qualitative behavior due to cell-cell repulsion.