A Cellular Potts model simulating cell migration on and in matrix environments

Marco Scianna; Luigi Preziosi; Katarina Wolf

doi:10.3934/mbe.2013.10.235

Article Contents

2013, Volume 10, Issue 1: 235-261. Doi: 10.3934/mbe.2013.10.235

This issue Previous Article Mathematical analysis and simulations involving chemotherapy and surgery on large human tumours under a suitable cell-kill functional response Next Article On a mathematical model of tumor growth based on cancer stem cells

A Cellular Potts model simulating cell migration on and in matrix environments

1.
Department of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129, Torino
2.
Department of Mathematics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino
3.
Department of Cell Biology, Radboud University Nijmegen Medical Centre, 6500 HB Nijmegen

Received: April 30, 2012

Revised: June 30, 2012

Published: November 2012

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Abstract

Cell migration on and through extracellular matrix is fundamental in a wide variety of physiological and pathological phenomena, and is exploited in scaffold-based tissue engineering. Migration is regulated by a number of extracellular matrix- or cell-derived biophysical parameters, such as matrix fiber orientation, pore size, and elasticity, or cell deformation, proteolysis, and adhesion. We here present an extended Cellular Potts Model (CPM) able to qualitatively and quantitatively describe cell migration efficiencies and phenotypes both on two-dimensional substrates and within three-dimensional matrices, close to experimental evidence. As distinct features of our approach, cells are modeled as compartmentalized discrete objects, differentiated into nucleus and cytosolic region, while the extracellular matrix is composed of a fibrous mesh and a homogeneous fluid. Our model provides a strong correlation of the directionality of migration with the topological extracellular matrix distribution and a biphasic dependence of migration on the matrix structure, density, adhesion, and stiffness, and, moreover, simulates that cell locomotion in highly constrained fibrillar obstacles requires the deformation of the cell's nucleus and/or the activity of cell-derived proteolysis. In conclusion, we here propose a mathematical modeling approach that serves to characterize cell migration as a biological phenomenon in healthy and diseased tissues and in engineering applications.

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Mathematics Subject Classification: Primary: 92B05, 92C15; Secondary: 92C42, 92C17.

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