Emergence of spatial patterns in a mathematical model for the co-culture dynamics of epithelial-like and mesenchymal-like cells

Marcello Delitala; Tommaso Lorenzi; Marcello Delitala; Tommaso Lorenzi

doi:10.3934/mbe.2017006

Mathematical Biosciences and Engineering

2017, Volume 14, Issue 1: 79-93. doi: 10.3934/mbe.2017006

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Emergence of spatial patterns in a mathematical model for the co-culture dynamics of epithelial-like and mesenchymal-like cells

Marcello Delitala ^{1
,
,},
Tommaso Lorenzi ²

1.
Department of Mathematical Sciences, Politecnico di Torino, Corso Duca degli Abruzzi 24,10129 Torino, Italy
2.
School of Mathematics and Statistics, University of St Andrews, North Haugh, St Andrews, Fife, KY16 9SS, United Kingdom

Received: 29 October 2015 Accepted: 23 May 2016 Published: 01 February 2017
MSC : Primary: 92B05; Secondary: 92C17

Accumulating evidence indicates that the interaction between epithelial and mesenchymal cells plays a pivotal role in cancer development and metastasis formation. Here we propose an integro-differential model for the co-culture dynamics of epithelial-like and mesenchymal-like cells. Our model takes into account the effects of chemotaxis, adhesive interactions between epithelial-like cells, proliferation and competition for nutrients. We present a sample of numerical results which display the emergence of spots, stripes and honeycomb patterns, depending on parameters and initial data. These simulations also suggest that epithelial-like and mesenchymal-like cells can segregate when there is little competition for nutrients. Furthermore, our computational results provide a possible explanation for how the concerted action between epithelial-cell adhesion and mesenchymal-cell spreading can precipitate the formation of ring-like structures, which resemble the fibrous capsules frequently observed in hepatic tumours.
- Mathematical modelling,
- epithelial-mesenchymal interactions,
- pattern formation,
- segregation patterns,
- ring patterns
Citation: Marcello Delitala, Tommaso Lorenzi. Emergence of spatial patterns in a mathematical model for the co-culture dynamics of epithelial-like and mesenchymal-like cells[J]. Mathematical Biosciences and Engineering, 2017, 14(1): 79-93. doi: 10.3934/mbe.2017006

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Abstract

Accumulating evidence indicates that the interaction between epithelial and mesenchymal cells plays a pivotal role in cancer development and metastasis formation. Here we propose an integro-differential model for the co-culture dynamics of epithelial-like and mesenchymal-like cells. Our model takes into account the effects of chemotaxis, adhesive interactions between epithelial-like cells, proliferation and competition for nutrients. We present a sample of numerical results which display the emergence of spots, stripes and honeycomb patterns, depending on parameters and initial data. These simulations also suggest that epithelial-like and mesenchymal-like cells can segregate when there is little competition for nutrients. Furthermore, our computational results provide a possible explanation for how the concerted action between epithelial-cell adhesion and mesenchymal-cell spreading can precipitate the formation of ring-like structures, which resemble the fibrous capsules frequently observed in hepatic tumours.

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