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

Jose A Carrillo; Hideki Murakawa; Makoto Sato; Hideru Togashi; Olena Trush

doi:10.1016/j.jtbi.2019.04.023

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

J Theor Biol. 2019 Aug 7:474:14-24. doi: 10.1016/j.jtbi.2019.04.023. Epub 2019 May 3.

Authors

Jose A Carrillo¹, Hideki Murakawa², Makoto Sato³, Hideru Togashi⁴, Olena Trush⁵

Affiliations

¹ Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2AZ, UK. Electronic address: carrillo@imperial.ac.uk.
² Department of Applied Mathematics and Informatics, Ryukoku University, Seta Otsu 520-2194, Japan. Electronic address: murakawa@math.ryukoku.ac.jp.
³ Laboratory of Developmental Neurobiology, Graduate School of Medical Sciences, Mathematical Neuroscience Unit, Institute for Frontier Science Initiative, Kanazawa University, 13-1 Takaramachi, Kanazawa, Ishikawa 920-8640, Japan. Electronic address: makotos@staff.kanazawa-u.ac.jp.
⁴ Division of Molecular and Cellular Biology, Department of Biochemistry and Molecular Biology, Kobe University Graduate School of Medicine, 7-5-1, Kusunoki-cho, Chuo-ku, Kobe 650-0017, Japan. Electronic address: htogashi@med.kobe-u.ac.jp.
⁵ Laboratory of Developmental Neurobiology, Graduate School of Medical Sciences, Kanazawa University, 13-1 Takaramachi, Kanazawa, Ishikawa 920-8640, Japan. Electronic address: trush@stu.kanazawa-u.ac.jp.

PMID: 31059713
DOI: 10.1016/j.jtbi.2019.04.023

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). 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.

Keywords: Cell sorting; Cell-cell adhesion; Mathematical model.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Animals
Cell Adhesion / physiology*
Cell Communication / physiology*
Humans
Models, Biological*