Mathematical Biosciences and Engineering, 2013, 10(1): 235-261. doi: 10.3934/mbe.2013.10.235.

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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

Cell migration on and through extracellular matrix is fundamental ina wide variety of physiological and pathological phenomena, and isexploited in scaffold-based tissue engineering. Migration isregulated by a number of extracellular matrix- or cell-derivedbiophysical parameters, such as matrix fiber orientation, pore size,and elasticity, or cell deformation, proteolysis, and adhesion. Wehere present an extended Cellular Potts Model (CPM) able toqualitatively and quantitatively describe cell migrationefficiencies and phenotypes both on two-dimensional substrates andwithin three-dimensional matrices, close to experimental evidence.As distinct features of our approach, cells are modeled ascompartmentalized discrete objects, differentiated into nucleusand cytosolic region, while the extracellular matrix iscomposed of a fibrous mesh and a homogeneous fluid. Our modelprovides a strong correlation of the directionality of migrationwith the topological extracellular matrix distribution and abiphasic dependence of migration on the matrix structure, density,adhesion, and stiffness, and, moreover, simulates that celllocomotion in highly constrained fibrillar obstacles requires thedeformation of the cell's nucleus and/or the activity ofcell-derived proteolysis. In conclusion, we here propose amathematical modeling approach that serves to characterize cellmigration as a biological phenomenon in healthy and diseased tissuesand in engineering applications.
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Keywords Cellular Potts model; extracellularmatrix; cell migration.

Citation: Marco Scianna, Luigi Preziosi, Katarina Wolf. A Cellular Potts model simulating cell migration on and in matrix environments. Mathematical Biosciences and Engineering, 2013, 10(1): 235-261. doi: 10.3934/mbe.2013.10.235

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