Migration and orientation of endothelial cells on micropatterned polymers: A simple model based on classical mechanics

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June 2015, 20(4): 1059-1076. doi: 10.3934/dcdsb.2015.20.1059

Migration and orientation of endothelial cells on micropatterned polymers: A simple model based on classical mechanics

Julie Joie ^1, , Yifeng Lei ^2, , Marie-Christine Durrieu ^2, , Thierry Colin ^1, , Clair Poignard ^1, and Olivier Saut ^1,

1.	INRIA Bordeaux-Sud-Ouest, F-33400,Talence, France, France, France, France
2.	INSERM, IECB, UMR 5248, F-33600, Pessac, France, France

Received March 2013 Revised December 2014 Published February 2015

Abstract
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Understanding the endothelial cell migration on micropatterned polymers, as well as the cell orientation is a critical issue in tissue engineering, since it is the preliminary step towards cell polarization and that possibly leads to the blood vessel formation. In this paper, we derive a simple agent-based model to describe the migration and the orientation of endothelial cells seeded on bioactive micropatterned polymers. The aim of the modeling is to provide a simple model that corroborates quantitatively the experiments, without considering the complex phenomena inherent to cell migration. Our model is obtained thanks to a classical mechanics approach based on experimental observations. Even though its simplicity, it provides numerical results that are quantitatively in accordance with the experimental data, and thus our approach can be seen as a preliminary way towards a simple modeling of cell migration.

Keywords: agent-based model, Biomathematical modeling, cell migration, tissue engineering, differential equations..

Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35, 35Q9.

Citation: Julie Joie, Yifeng Lei, Marie-Christine Durrieu, Thierry Colin, Clair Poignard, Olivier Saut. Migration and orientation of endothelial cells on micropatterned polymers: A simple model based on classical mechanics. Discrete and Continuous Dynamical Systems - B, 2015, 20 (4) : 1059-1076. doi: 10.3934/dcdsb.2015.20.1059

References:

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[2]	M. Bagnat and K. Simons, Cell surface polarization during yeast mating, Proceedings of the National Academy of Sciences, 99 (2002), 14183-14188. doi: 10.1073/pnas.172517799.
[3]	C. Chen, M. Mrksich, S. Huang, G. Whitesides and D. Ingber, Geometric control of cell life and death, Science, 276 (1997), 1425-1428. doi: 10.1126/science.276.5317.1425.
[4]	T. Colin, M.-C. Durrieu, J. Joie, Y. Lei, Y. Mammeri, C. Poignard and O. Saut, Modeling of the migration of endothelial cells on bioactive micropatterned polymers, Mathematical biosciences and engineering, 10 (2013), 997-1015. doi: 10.3934/mbe.2013.10.997.
[5]	L. Dike, C. Chen, J. Tien, G. Whitesides and D. Ingber, Geometric control of switching between growth, apoptosis, and differentiation during angiogenesis using micropatterned substrates, In Vitro Cell. Dev. Biol., 35 (1999), 441-448. doi: 10.1007/s11626-999-0050-4.
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[7]	A. Folch and M. Toner, Microengineering of cellular interactions, Annu. Rev. Biomed. Eng., 2 (2000), 227-256.
[8]	R. J. Hawkins, O. Bénichou, M. Piel and R. Voituriez, Rebuilding cytoskeleton roads: Active-transport-induced polarization of cells, Physical Review E, 80 (2009), 040903(R). doi: 10.1103/PhysRevE.80.040903.
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[10]	Y. Ito, Surface micropatterning to regulate cell functions, Biomaterials, 20 (1999), 2333-2342. doi: 10.1016/S0142-9612(99)00162-3.
[11]	R. Jain, P. Au, J. Tam, D. Duda and D. Fukumura, Engineering vascularized tissue, Nat. Biotechnol., 23 (2005), 821-823. doi: 10.1038/nbt0705-821.
[12]	M. Kamei, W. Saunders, K. Bayless, L. Dye, G. Davis and B. Weinstein, Endothelial tubes assemble from intracellular vacuoles in vivo, Nature, 442 (2006), 453-456. doi: 10.1038/nature04923.
[13]	Y. Lei, Biochemical and Microscale Modification of Polymer for Endothelial Cell Angiogenesis, PhD thesis, Université Bordeaux 1, 2012.
[14]	Y. Lei, O. Zouani, L. Rami, C. Chanseau and M.-C. Durrieu, Modulation of lumen formation by microgeometrical bioactive cues and migration mode of actin machinery, Small, 9 (2013), 1086-1095. doi: 10.1002/smll.201202410.
[15]	Y. Lei, O. Zouani, M. Rémy, C. Ayela and M.-C. Durrieu, Geometrical microfeature cues for directing tubulogenesis of endothelial cells, PLoS ONE, 7 (2012), e41163. doi: 10.1371/journal.pone.0041163.
[16]	B. Lubarsky and M. Krasnow, Tube morphogenesis: Making and shaping biological tubes, Cell, 112 (2006), 19-28.
[17]	K. Madden and M. Snyder, Cell polarity and morphogenesis in budding yeast, Annual Reviews in Microbiology, 52 (1998), 687-744. doi: 10.1146/annurev.micro.52.1.687.
[18]	S. Marino, I. B. Hogue, C. J. Ray and D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, Journal of Theoretical Biology, 254 (2008), 178-196, URL http://www.sciencedirect.com/science/article/pii/S0022519308001896. doi: 10.1016/j.jtbi.2008.04.011.
[19]	C. Min and F. Gibou, A second order accurate projection method for the incompressible Navier-Stokes equations on non-graded adaptive grids, Journal of Computational Physics, 219 (2006), 912-929. doi: 10.1016/j.jcp.2006.07.019.
[20]	M. Morris, Factorial sampling plans for preliminary computational experiments, Technometrics, 33 (1991), 161-174. doi: 10.2307/1269043.
[21]	R. Nerem, Tissue engineering: The hope, the hype, and the future, Tissue Eng., 12.
[22]	D. Nicolau, T. T., H. Taniguchi, H. Tanigawa and S. Yoshikawa, Patterning neuronal and glia cells on light-assisted functionalized photoresists, Biosens. Bioelectron., 14 (1999), 317-324.
[23]	E. Phelps and A. Garcia, Engineering more than a cell: Vascularization strategies in tissue engineering, Curr. Opin. Biotechnol., 21 (2010), 704-709. doi: 10.1016/j.copbio.2010.06.005.
[24]	T.-H. Tsai, Simulations of endothelial cells clusters migration in angiogenesis, The SIJ Transactions on Computer Science Engineering & its Applications (CSEA), 1 (2013), 111-115.
[25]	R. Wedlich-Soldner, S. Altschuler, L. Wu and R. Li, Spontaneous cell polarization through actomyosin-based delivery of the cdc42 gtpase, Science, 299 (2003), 1231-1235, URL http://www.sciencemag.org/content/299/5610/1231.abstract. doi: 10.1126/science.1080944.
[26]	R. Wedlich-Soldner, S. Wai, T. Schmidt and R. Li, Robust cell polarity is a dynamic state established by coupling transport and gtpase signaling, The Journal of Cell Biology, 166 (2004), 889-900. doi: 10.1083/jcb.200405061.

show all references

References:

[1]	K. Anselme, P. Davidson, A. Popa, M. Liley and L. Ploux, The interaction of cells and bacteria with surfaces structured at the nanometre scale, Acta Biomaterialia, 6 (2010), 3824-3846. doi: 10.1016/j.actbio.2010.04.001.
[2]	M. Bagnat and K. Simons, Cell surface polarization during yeast mating, Proceedings of the National Academy of Sciences, 99 (2002), 14183-14188. doi: 10.1073/pnas.172517799.
[3]	C. Chen, M. Mrksich, S. Huang, G. Whitesides and D. Ingber, Geometric control of cell life and death, Science, 276 (1997), 1425-1428. doi: 10.1126/science.276.5317.1425.
[4]	T. Colin, M.-C. Durrieu, J. Joie, Y. Lei, Y. Mammeri, C. Poignard and O. Saut, Modeling of the migration of endothelial cells on bioactive micropatterned polymers, Mathematical biosciences and engineering, 10 (2013), 997-1015. doi: 10.3934/mbe.2013.10.997.
[5]	L. Dike, C. Chen, J. Tien, G. Whitesides and D. Ingber, Geometric control of switching between growth, apoptosis, and differentiation during angiogenesis using micropatterned substrates, In Vitro Cell. Dev. Biol., 35 (1999), 441-448. doi: 10.1007/s11626-999-0050-4.
[6]	D. Drasdo, S. Dormann, S. Hoehme and A. Deutsch, Cell-based models of avascular tumor growth, in Function and Regulation of Cellular Systems, Mathematics and Biosciences in Interaction, Birkhäuser Basel, (2004), 367-378, URL http://dx.doi.org/10.1007/978-3-0348-7895-1_37.
[7]	A. Folch and M. Toner, Microengineering of cellular interactions, Annu. Rev. Biomed. Eng., 2 (2000), 227-256.
[8]	R. J. Hawkins, O. Bénichou, M. Piel and R. Voituriez, Rebuilding cytoskeleton roads: Active-transport-induced polarization of cells, Physical Review E, 80 (2009), 040903(R). doi: 10.1103/PhysRevE.80.040903.
[9]	J. Irazoqui, A. Gladfelter and D. Lew, Scaffold-mediated symmetry breaking by cdc42p, Nat. Cell Biol., 5 (2003), 1062-1070. doi: 10.1038/ncb1068.
[10]	Y. Ito, Surface micropatterning to regulate cell functions, Biomaterials, 20 (1999), 2333-2342. doi: 10.1016/S0142-9612(99)00162-3.
[11]	R. Jain, P. Au, J. Tam, D. Duda and D. Fukumura, Engineering vascularized tissue, Nat. Biotechnol., 23 (2005), 821-823. doi: 10.1038/nbt0705-821.
[12]	M. Kamei, W. Saunders, K. Bayless, L. Dye, G. Davis and B. Weinstein, Endothelial tubes assemble from intracellular vacuoles in vivo, Nature, 442 (2006), 453-456. doi: 10.1038/nature04923.
[13]	Y. Lei, Biochemical and Microscale Modification of Polymer for Endothelial Cell Angiogenesis, PhD thesis, Université Bordeaux 1, 2012.
[14]	Y. Lei, O. Zouani, L. Rami, C. Chanseau and M.-C. Durrieu, Modulation of lumen formation by microgeometrical bioactive cues and migration mode of actin machinery, Small, 9 (2013), 1086-1095. doi: 10.1002/smll.201202410.
[15]	Y. Lei, O. Zouani, M. Rémy, C. Ayela and M.-C. Durrieu, Geometrical microfeature cues for directing tubulogenesis of endothelial cells, PLoS ONE, 7 (2012), e41163. doi: 10.1371/journal.pone.0041163.
[16]	B. Lubarsky and M. Krasnow, Tube morphogenesis: Making and shaping biological tubes, Cell, 112 (2006), 19-28.
[17]	K. Madden and M. Snyder, Cell polarity and morphogenesis in budding yeast, Annual Reviews in Microbiology, 52 (1998), 687-744. doi: 10.1146/annurev.micro.52.1.687.
[18]	S. Marino, I. B. Hogue, C. J. Ray and D. E. Kirschner, A methodology for performing global uncertainty and sensitivity analysis in systems biology, Journal of Theoretical Biology, 254 (2008), 178-196, URL http://www.sciencedirect.com/science/article/pii/S0022519308001896. doi: 10.1016/j.jtbi.2008.04.011.
[19]	C. Min and F. Gibou, A second order accurate projection method for the incompressible Navier-Stokes equations on non-graded adaptive grids, Journal of Computational Physics, 219 (2006), 912-929. doi: 10.1016/j.jcp.2006.07.019.
[20]	M. Morris, Factorial sampling plans for preliminary computational experiments, Technometrics, 33 (1991), 161-174. doi: 10.2307/1269043.
[21]	R. Nerem, Tissue engineering: The hope, the hype, and the future, Tissue Eng., 12.
[22]	D. Nicolau, T. T., H. Taniguchi, H. Tanigawa and S. Yoshikawa, Patterning neuronal and glia cells on light-assisted functionalized photoresists, Biosens. Bioelectron., 14 (1999), 317-324.
[23]	E. Phelps and A. Garcia, Engineering more than a cell: Vascularization strategies in tissue engineering, Curr. Opin. Biotechnol., 21 (2010), 704-709. doi: 10.1016/j.copbio.2010.06.005.
[24]	T.-H. Tsai, Simulations of endothelial cells clusters migration in angiogenesis, The SIJ Transactions on Computer Science Engineering & its Applications (CSEA), 1 (2013), 111-115.
[25]	R. Wedlich-Soldner, S. Altschuler, L. Wu and R. Li, Spontaneous cell polarization through actomyosin-based delivery of the cdc42 gtpase, Science, 299 (2003), 1231-1235, URL http://www.sciencemag.org/content/299/5610/1231.abstract. doi: 10.1126/science.1080944.
[26]	R. Wedlich-Soldner, S. Wai, T. Schmidt and R. Li, Robust cell polarity is a dynamic state established by coupling transport and gtpase signaling, The Journal of Cell Biology, 166 (2004), 889-900. doi: 10.1083/jcb.200405061.

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