Geodesic
A Hybrid Model to Test the Importance of Mechanical Cues Driving Cell Migration in Angiogenesis
A. Stéphanou1 ; S. Le Floc’h2 ; A. Chauvière1
1 UJF-Grenoble 1, CNRS, Laboratory TIMC-IMAG/DyCTiM, UMR 5525, 38041 Grenoble, France
2 Université de Montpellier II, CNRS, LMGC, UMR 5508, 34095 Montpellier cedex 5, France
Mathematical modelling of natural phenomena, Tome 10 (2015) no. 1, pp. 142-166 Cet article a éte moissonné depuis la source EDP Sciences

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Many studies are stressing the crucial importance of the mechanical component in angiogenesis, but still, very few models really integrate mechanics. In this paper, we propose to investigate the importance of mechanical cues for cell migration in the context of angiogenesis. We propose a hybrid continuous-discrete model that describes the individual migration of contracting cells on an elastic matrix of fibres. The matrix is described as a continuum whereas the cells are described as discrete elements. We also take into account the degradation of the matrix by proteases. The Young’s modulus characterizing the matrix rigidity depends on the local and time-dependent density of matrix fibres. Our results show that acting on the mechanics, specifically on the cell traction force intensity and on the matrix rigidity, can significantly alter cell migration and angiogenesis. First, there is a limited range of traction force intensities for which a vascular network can be obtained. Second, the matrix rigidity plays a role, but only in a very specific range, compatible with the underlying biological process. Alteration of the matrix due to cell degradation appears too small to induce significant changes in cell migration trajectories.
DOI : 10.1051/mmnp/201510107

A. Stéphanou 1 ; S. Le Floc’h 2 ; A. Chauvière 1

1 UJF-Grenoble 1, CNRS, Laboratory TIMC-IMAG/DyCTiM, UMR 5525, 38041 Grenoble, France
2 Université de Montpellier II, CNRS, LMGC, UMR 5508, 34095 Montpellier cedex 5, France 
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A. Stéphanou; S. Le Floc’h; A. Chauvière. A Hybrid Model to Test the Importance of Mechanical Cues Driving Cell Migration in Angiogenesis. Mathematical modelling of natural phenomena, Tome 10 (2015) no. 1, pp. 142-166. doi: 10.1051/mmnp/201510107

[1] F. Amyot, A. Small, H. Boukari, K. Camphausen, A. Gandjbakhche Microvasc. Res. 2009 87 95

[2] A.R.A. Anderson, M.A.J. Chaplain Bull. Math. Biol. 1998 857 900

[3] A.L. Bauer, T.L. Jackson, Y. Jiang Biophys. J. 2007 3105 3121

[4] Y. Cai, K. Gulnar, H. Zhang, J. Cao, S. Xu, Q. Long Acta Mech. Sin. 2009 889 895

[5] J.P. Capp. Nouveau regard sur le cancer, pour une révolution des traitements. Ed. Belin (2012), ISBN 978-2-7011-5614-9.

[6] A. Chauvière, T. Hillen, L. Preziosi Net. Het. Med. 2007 333 357

[7] A. Chauvière, L. Preziosi. Mathematical framework to model migration of cell population in extracellular matrix. (2010) Cell Mechanics: From single-scale based models to multiscale modeling Taylor Francis Group, Chapman Hall/CRC, ISBN 978142009454.

[8] A. Das, D. Lauffenburger, H. Asada, R.D. Kamm Phil. Trans. R. Soc. A 2010 2937 2960

[9] G.E. Davis, D.R. Senger Circ. Res. 2005 1093 1107

[10] J.T. Daub, R.M.H. Merks Bull. Math. Biol. 2013 1377 1399

[11] L.T. Edgar, J.B. Hoying, U. Utzinger, C.J. Underwood, L. Krishnan, B.K. Baggett, S.A. Maas, J.E. Guilkey, J.A. Weiss J. Biomech. Eng. 2014 021001

[12] L.T. Edgar, S.C. Sibole, C.J. Underwood, J.E. Guilkey, J.A. Weiss Comp. Meth. Biomech. Biomed. Eng. 2013 790 801

[13] L.T. Edgar, C.J. Underwood, J.E. Guilkey, J.B. Hoying, J.A. Weiss PLOS ONE 2014

[14] J. Folkman, C. Haudenschild Nature 1980 551 556

[15] H. Gerhardt Organogenesis 2008 241 246

[16] M.J. Holmes, B.D. Sleeman J. Theor. Biol. 2000 95 112

[17] D.E. Ingber Sem. Canc. Biol. 2008 356 364

[18] P. Katira, R.T. Bonnecaze, M.H. Zaman Front. Oncol. 2013 145

[19] Y. Kim, M.A. Stolarska, H.G. Othmer Prog. Biophys. Mol. Biol. 2011 353 379

[20] E. Kniazeva, A.J. Putnam Am. J. Physiol. Cell Physiol. 2009 C179 C187

[21] L.D. Landau M. Lifshitz. Theory of Elasticity. London: Pergamon, 1959.

[22] J.R. Lange, B. Fabry Exp. Cell Res. 2013 2418 2423

[23] D. Manoussaki, S.R. Lubkin, R.B. Vernon, J.D. Murray Acta Biotheor. 1996 271 282

[24] R.M.H. Merks, S.V. Brodsky, M.S. Goligorsky, S.A. Newman, J.A. Glazier Dev. Biol. 2006 44 54

[25] F. Milde, M. Bergdorf, P. Koumoutsakos Biophys. J. 2008 3146 3160

[26] J.D. Murray C.R. Biologies 2003 239 252

[27] P. Namy, J. Ohayon, P. Tracqui J. theor. Biol. 2004 103 120

[28] L. Narunsky, R. Oren, F. Bochner, M. Neeman Pharm. Therap. 2014 192 208

[29] Z.K. Otrock, R.A.R. Mahfouz, J.A. Makarem, A.I. Shamseddine Blood Cells Mol. Dis. 2007 212 220

[30] M.Z. Pindera, H. Ding, Z. Chen J. Math. Biol. 2008 467 495

[31] M.J. Plank, B.D. Sleeman, P.F. Jones J. theor. Biol. 2004 435 454

[32] P. Roca-Cusachs, R. Sunyer, X. Trepat Curr. Opin. Cell Biol. 2013 543 549

[33] D.K. Schlüter, I. Ramis-Conde, M.A.J. Chaplain Biophys. J. 2012 1141 1151

[34] M. Scianna, L. Munaron, L. Preziosi Prog. Biophys. Mol. Biol. 2011 450 62

[35] M. Scianna, C.G. Bell, L. Preziosi J. theor. Biol. 2013 174 209

[36] D.W. Siemann Cancer Treat. Rev. 2011 63 74

[37] F. Spill, P. Guerrero, T. Alarcon, P.K. Maini, H.M. Byrne. Mesoscopic and continuum modelling of angiogenesis. J. Math. Biol., (2014).

[38] A. Stéphanou, G. Meskaoui, B. Vailhé, P. Tracqui Microvasc. Res. 2007 182 190

[39] A. Stéphanou, S.R. Mcdougall, A.R.A. Anderson, M.A.J. Chaplain Math. Comp. Mod. 2006 96 123

[40] A. Tosin, D. Ambrosi, L. Preziosi Bull. Math. Biol. 2006 1819 1836

[41] C. Valero, E. Javierre, J.M. García-Aznar, M.J. Gómez-Benito Biochem. Model. Mechanobiol. 2013 349 360

[42] M. Van Dijk, S.A. Göransson, S. Strömblad Exp. Cell Res. 2013 1663 1670

[43] R.S. Varga. Matrix iterative analysis. Second ed. (of 1962 Prentice Hall edition), Springer-Verlag, (2002).

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