Multiscale developments of the cellular potts model

Multiscale Modeling and Simulation

Volumn 10, Issue 2, 2012, Pages 342-382

  Scianna, M ^a   Preziosi, L ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Cellular Potts model; Hybrid model; Multiscale model

Indexed keywords

BIOLOGICAL PHENOMENA; CELL-BASED; CELLULAR POTTS MODELS; COMPLEX INTERACTION; CONTINUOUS MODELS; EXPERIMENTAL DATA; HYBRID FRAMEWORK; HYBRID MODEL; INTERNAL STATE; MESOSCOPICS; MICROSCOPIC DYNAMICS; MULTISCALE MODELS; MULTISCALE PROBLEM; MULTISCALES; QUANTITATIVE AGREEMENT;

MATHEMATICAL MODELS;

POTTS MODEL;

EID: 84865676266     PISSN: 15403459     EISSN: 15403467     Source Type: Journal    
DOI: 10.1137/100812951     Document Type: Article

References (100)

1. M. S. Alber, M. A. Kiskowski, J. A. Glazier, and Y. Jiang, On cellular automation approaches to modeling biological cells, in Mathematical Systems Theory in Biology, Communication and Finance, J. Rosenthal and D. S. Gilliam, eds., Springer-Verlag, New York, 2004, pp. 1-40.
2. B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson, Molecular Biology of the Cell, 3rd ed., Garland Science, New York, 1994.
3. A. R. A. Anderson, M. A. J. Chaplain, and K. A. Rejniak, eds., Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interactions, Birkhäuser, Basel, 2007.
4. P. B. Armstrong and D. Parenti, Cell sorting in the presence of cytochalasin b, J. Cell Biol., 55 (1972), pp. 542-553.
5. D. Baird, Q. Feng, and R. A. Cerione, The Cool-2/alpha-Pix protein mediates a Cdc42-Rac signaling cascade, Curr. Biol., 15 (2005), pp. 1-10. (Pubitemid 40084695)
6. A. Balter, R. M. H. Merks, N. J. Poplawski, M. Swat, and J. A. Glazier, The Glazier-Graner-Hogeweg model: Extensions, future directions, and opportunities for further study, in Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interactions, A. R. A. Anderson et al., eds., Birkhäuser, Basel, 2007, pp. 151-167.
7. A. L. Bauer, T. L. Jackson, and Y. Jiang, A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis, Biophys. J., 92 (2007), pp. 3105-3121. (Pubitemid 46684572)
8. A. B. Bortz, M. H. Kalos, and J. L. Lebowitz, A new algorithm for Monte Carlo simulation of Ising spin systems, J. Comput. Phys., 17 (1975), pp. 10-18.
9. T. Bosse, J. Ehinger, A. Czuchra, S. Benesch, A. Steffen, X. Wu, K. Schloen, H. H. Niemann, G. Scita, T. E. B. Stradal, C. Brakebusch, and K. Rottner, Cdc42 and PI 3K drive Rac-mediated actin polymerization downstream of c-Met in distinct and common pathways, Mol. Cell. Biol., 27 (2007), pp. 6615-6628. (Pubitemid 47483616)
10. V. Brinkmann, H. Foroutan, H. Sachs, K. M. Weidner, and W. Birchmeier, Hepatocyte growth factor/scatter factor induces a variety of tissue specific morphogenic programs in epithelial cells, J. Cell Biol., 131 (1995), pp. 1573-1586.
11. H. M. Byrne, M. R. Owen, T. Alarcon, J. Murphy, and P. K. Maini, Modelling the response of vascular tumours to chemotherapy: A multiscale approach, Math. Models Methods Appl. Sci., 16 (2006), pp. 1219-1241. (Pubitemid 44576651)
12. W. Cai, S. L. Rook, Z. Y. Jiang, N. Takahara, and L. P. Aiello, Mechanisms of hepatocyte growth factor-induced retinal endothelial cell migration and growth, Investigative Ophthalmology and Visual Science, 41 (2000), pp. 1885-1893. (Pubitemid 30354364)
13. F. P. Cercato, J. C. M. Mombach, and G. G. H. Cavalheiro, High performance simulations of the Cellular Potts model, in Proceedings of the 20th International Symposium on High-Performance Computing in an Advanced Collaborative Environment, IEEE, Washington, DC, 2006, p. 28. (Pubitemid 44754650)
14. R. Chaturvedi, C. Huang, J. A. Izaguirre, S. A. Newman, J. A. Glazier, and M. S. Alber, A hybrid discrete-continuum model for 3-D skeletogenesis of the vertebrate limb, in Cellular Automata, Lecture Notes in Comput. Sci. 3305, Springer, New York, 2004, pp. 543-552. (Pubitemid 39742868)
15. R. Chaturvedi, C. Huang, B. Kazmierczak, T. Schneider, J. A. Izaguirre, T. Glimm, H. G. Hentschel, J. A. Glazier, S. A. Newman, and M. S. Alber, On multiscale approaches to three-dimensional modelling of morphogenesis, J. R. Soc. Interface, 2 (2005), pp. 237-253.
16. A. Chauviere, L. Preziosi, and C. Verdier, eds., Cell Mechanics: From Single Scaled-Based Models to Multiscale Modeling, Mathematical and Computational Biology Series, CRC Press, Boca Raton, FL, 2010.
17. N. Chen, J. A. Glazier, J. A. Izaguirre, and M. S. Alber, A parallel implementation of the cellular Potts model for simulation of cell-based morphogenesis, Comput. Phys. Commun., 176 (2007), pp. 670-681. (Pubitemid 46722711)
18. T. Cickovski, C. Huang, R. Chaturvedi, T. Glimm, H. G. E. Hentschel, M. S. Alber, J. A. Glazier, S. A. Newman, and J. A. Izaguirre, A framework for three-dimensional simulation of morphogenesis, IEEE/ACM Trans. Comput. Biol. Bioinform., 2 (2005), pp. 273-288.
19. B. A. Cipra, An introduction to the Ising-model, Amer. Math. Monthly, 94 (1987), pp. 937-959.
20. P. M. Comoglio and C. Boccaccio, Scatter factors and invasive growth, Semin. Cancer Biol., 11 (2000), pp. 153-165. (Pubitemid 32423290)
21. P. M. Comoglio and M. C. Stella, HGF: A multifunctional growth factor controlling cell scattering, Int. J. Biochem. Cell Biol., 31 (1999), pp. 1357-1362.
22. D. Dan, C. Mueller, K. Chen, and J. A. Glazier, Solving the advection-diffusion equations in biological contexts using the cellular Potts model, Phys. Rev. E Stat. Nonlin. Soft Matter Phys., 72 (2005), 041909.
23. A. De Luca, N. Arena, L. M. Sena, and E. Medico, Met overexpression confers HGFdependent invasive phenotype to human thyroid carcinoma cells in vitro, J. Cell. Physiol., 180 (1999), pp. 365-371. (Pubitemid 29334837)
24. M. F. Di Renzo, M. Oliviero, R. P. Narsimhan, S. Bretti, S. Giordano, E. Medico, P. Gaglia, P. Zara, and P. M. Comoglio, Expression of the Met/HGF receptor in normal and neoplastic human tissues, Oncogene, 6 (1991), pp. 1997-2003. (Pubitemid 21924039)
25. D. Drasdo and S. Hohme, Individual-based approaches to birth and death in avascular tumors, Math. Comput. Modelling, 37 (2003), pp. 1163-1175. (Pubitemid 36761623)
26. D. Drasdo, On selected individual-based approaches to the dynamics of multicellular systems, in Multiscale Modeling, W. Alt and M. Griebel, eds., Birkhäuser, Basel, 2005, pp. 169-203.
27. D. Drasdo and G. Forgacs, Modeling the interplay of generic and genetic mechanisms in cleavage, blastulation, and gastrulation, Dev. Dyn., 219 (2000), pp. 182-191.
28. C. J. Drake, A. LaRue, N. Ferrara, and C. D. Little, VEGF regulates cell behavior during vasculogenesis, Dev. Biol., 224 (2000), pp. 178-188. (Pubitemid 30661003)
29. S. Etienne-Manneville, Cdc42-The centre of polarity, J. Cell Sci., 117 (2004), pp. 1291-1300.
30. K. A. Fichthorn and W. H. Weinberg, Theoretical foundations of dynamical Monte Carlo simulations, J. Chem. Phys., 95 (1991), pp. 1090-1096.
31. F. M. Gabhann and A. S. Popel, Model of competitive binding of vascular endothelial growth factor and placental growth factor to VEGF receptors on endothelial cells, Am. J. Physiol. Heart Circ. Physiol., 286 (2004), pp. H153-H164. (Pubitemid 38049475)
32. C. Giverso, M. Scianna, L. Preziosi, N. Lo Buono, and A. Funaro, Individual cell-based model for in-vitro mesothelial invasion of ovarian cancer, Math. Model. Nat. Phenom., 5 (2010), pp. 203-223.
33. J. A. Glazier, A. Balter, and N. J. Poplawski, Magnetization to morphogenesis: A brief history of the Glazier-Graner-Hogeweg model, in Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interactions, A. R. A. Anderson, M. A. J. Chaplain, and K. A. Rejniak, eds., Birkhäuser, Basel, 2007, pp. 79-106.
34. J. A. Glazier and F. Graner, Simulation of the differential adhesion driven rearrangement of biological cells, Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics, 47 (1993), pp. 2128-2154.
35. F. Graner and J. A. Glazier, Simulation of biological cell sorting using a two dimensional extended Potts model, Phys. Rev. Lett., 69 (1992), pp. 2013-2017.
36. E. Gusatto, J. C. M. Mombach, F. P. Cercato, and G. H. Cavalheiro, An efficient parallel algorithm to evolve simulations of the cellular Potts model, Parallel Process. Lett., 15 (2005), pp. 199-208. (Pubitemid 41144029)
37. H. G. E. Hentschel, T. Glimm, J. A. Glazier, and S. A. Newman, Dynamical mechanisms for skeletal pattern formation in the vertebrate limb, Proc. Biol. Sci., 271 (2004), pp. 1713-1722. (Pubitemid 39107992)
38. H. N. Higgs and T. D. Pollard, Activation by Cdc42 and PIP2 of Wiskott-Aldrich syndrome protein (WASp) stimulates actin nucleation by Arp2/3 complex, J. Cell Biol., 150 (2000), pp. 1311-1320.
39. P. Hogeweg, Evolving mechanisms of morphogenesis: On the interplay between differential adhesion and cell differentiation, J. Theoret. Biol., 203 (2000), pp. 317-333. (Pubitemid 30662930)
40. J. Howard, Mechanics of Motor Proteins and the Cytoskeleton, Sinauer Associates, Sunderland, MA, 2001.
41. Y. Jiang, Cellular Pattern Formation, Ph.D. thesis, University of Notre Dame, South Bend, IN, 2004.
42. B. N. Kholodenko, Four-dimensional organization of protein kinase signaling cascades: The roles of diffusion, endocytosis and molecular motors, J. Exp. Biol., 206 (2003), pp. 2073-2082. (Pubitemid 36761810)
43. E. Ising, Beitrag zur theorie des ferromagnetismus, Z. Physik, 31 (1925), p. 253.
44. N. Lahat, M. Sheinfeld, E. Sobel, A. Kinarty, and Z. Kraiem, Divergent effects of cytokines on human leukocyte antigen-DR antigen expression of neoplastic and nonneoplastic human thyroid cells, Cancer, 69 (1992), pp. 1799-1807.
45. K.-C. Lee, Rejection-free Monte Carlo technique, J. Phys. A, 28 (1995), p. 4835.
46. E. Lesko and M. Majka, The biological role of HGF-MET axis in tumor growth and development of metastasis, Front. Biosci., 13 (2008), pp. 1271-1280. (Pubitemid 351594710)
47. J. S. Lowengrub, H. B. Frieboes, F. Jin, Y.-L. Chuang, X. Li, P. Macklin, S. M. Wise, and V. Cristini, Nonlinear modelling of cancer: Bridging the gap between cells and tumours, Nonlinearity, 23 (2010), pp. R1-R91.
48. L. Ma, C. Janetopoulos, L. Yang, P. N. Devreotes, and P. A. Iglesias, Two complementary, local excitation, global inhibition mechanisms acting in parallel can explain the chemoattractant-induced regulation of PI (3,4,5)P3 response in Dictyostelium cells, Biophys. J., 87 (2004), pp. 3764-3774. (Pubitemid 39602884)
49. A. W. Mahoney, B. G. Smith, N. S. Flann, and G. J. Podgorski, Discovering novel cancer therapies: A computational modeling and search approach, in IEEE Conference on Computational Intelligence in Bioinformatics and Bioengineering, IEEE, Washington, DC, 2008, pp. 233-240.
50. P. K. Maini, L. Olsen, and J. A. Sherratt, Mathematical models for cell-matrix interactions during dermal wound healing, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 12 (2008), pp. 2021-2029.
51. A. F. M. Mar'ee, V. A. Grieneisen, and P. Hogeweg, The cellular Potts model and biophysical properties of cells, tissues and morphogenesis, in Single-Cell-Based Models in Biology and Medicine, Mathematics and Biosciences in Interactions, A. R. A. Anderson, M. A. J. Chaplain, and K. A. Rejniak, eds., Birkhäuser, Basel, 2007, pp. 107-136.
52. A. F. M. Mar'ee and P. Hogeweg, How amoeboids self-organize into a fruiting body: Multicellular coordination in Dictyostelium discoideum, Proc. Natl. Acad. Sci. USA, 98 (2001), pp. 3879-3883. (Pubitemid 32249865)
53. A. F. M. Mar'ee, A. Jilkine, A. Dawes, V. A. Grieneisen, and L. Edelstein-Keshet, Polarization and movement of keratocytes: A multiscale modelling approach, Bull. Math. Biol., 68 (2006), pp. 1169-1211. (Pubitemid 44195545)
54. N. I. Markevich, M. A. Tsyganov, J. B. Hoek, and B. N. Kholodenko, Long-range signaling by phosphoprotein waves arising from bistability in protein kinase cascades, Mol. Sys. Biol., 2 (2006), 61.
55. A. M. Mongiovi, J. Huff, M. A. Jelinek, A. Follenzi, G. Gaudino, J. T. Parsons, P. M. Comoglio, and E. Medico, The tyrosine kinase receptors Ron and Sea control "scattering" and morphogenesis of liver progenitor cells in vitro, Mol. Biol. Cell, 7 (1996), pp. 495-504.
56. R. M. H. Merks and J. A. Glazier, Dynamic mechanisms of blood vessel growth, Nonlinearity, 19 (2006), pp. C1-C10. (Pubitemid 41806747)
57. R. M. H. Merks, S. V. Brodsky, M. S. Goligorksy, S. A. Newman, and J. A. Glazier, Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling, Dev. Biol., 289 (2006), pp. 44-54. (Pubitemid 41804087)
58. R. M. H. Merks, E. D. Perryn, A. Shirinifard, and J. A. Glazier, Contact-inhibited chemotactic motility: Role in de novo and sprouting blood vessel growth, PLoS Comput. Biol., 4 (2008), e1000163.
59. R. M. H. Merks and P. Koolwijk, Modeling morphogenesis in silico and in vitro: Towards quantitative, predictive, cell-based modeling, Math. Model. Nat. Phenom., 4 (2009), pp. 149-171.
60. N. Metropolis, A. Rosenbluth, M. N. Rosenbluth, A. H. Teller, and E. Teller, Equation of state calculations by fast computing machines, J. Chem. Phys., 21 (1953), pp. 1087-1092.
61. A. Mochizuki, Pattern formation of the cone mosaic in the zebrafish retina: A cell rearrangement model, J. Theoret. Biol., 215 (2002), pp. 345-361. (Pubitemid 34948569)
62. J. C. M. Mombach and J. A. Glazier, Single cell motion in aggregates of embryonic cells, Phys. Rev. Lett., 76 (1996), pp. 3032-3035. (Pubitemid 126639059)
63. J. C. M. Mombach, R. M. C. De Almeida, G. L. Thomas, A. Upadhyaya, and J. A. Glazier, Bursts and cavity formation in Hydra cells aggregates: Experiments and simulations, Phys. A, 297 (2001), pp. 495-508. (Pubitemid 32705114)
64. J. C. M. Mombach, R. M. C. De Almeida, and G. L. Iglesias, Mitosis and growth in biological tissues, Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics, 48 (1993), pp. 598-608.
65. J. Moreira and A. Deutsch, Pigment pattern formation in zebrafish during late larval stages: A model based on local interactions, Develop. Dynam., 232 (2005), pp. 33-42. (Pubitemid 40070856)
66. N. B. Ouchi, J. A. Glazier, J. P. Rieu, A. Upadhyaya, and J. Sawada, Improving the realism of the cellular Potts model in simulations of biological cells, Phys. A, 329 (2003), pp. 451-458.
67. R. Pedeux, D. Ythier, and A. Duperray, Cell motility and tumor suppressor genes, in Cell Mechanics: From Single Scale-Based Models to Multiscale Modeling, Mathematical and Computational Biology Series, A. Chauvier, L. Preziosi, and C. Verdier, eds., CRC Press, Boca Raton, FL, 2010, pp. 67-88.
68. T. D. Pollard and G. G. Borisy, Cellular motility driven by assembly and disassembly of actin filaments, Cell, 112 (2003), pp. 453-465. (Pubitemid 36263079)
69. N. J. Poplawski, A. Shirinifard, M. Swat, and J. A. Glazier, Simulation of single-species bacterical-biofilm growth using the Glazier-Graner-Hogeweg model and the CompuCell3D modeling environment, Math. Biosci. Eng., 5 (2008), pp. 355-388.
70. N. J. Poplawski, M. Swat, J. S. Gens, and J. A. Glazier, Adhesion between cells, diffusion of growth factors, and elasticity of the AER produce the paddle shape of the chick limb, Phys. A, 373 (2007), pp. 521-532. (Pubitemid 44649275)
71. R. B. Potts, Some generalized order-disorder transformations, Proc. Cambridge Phil. Soc., 48 (1952), pp. 106-109.
72. S. M. Rafelski and J. A. Theriot, Crawling toward a unified model of cell motility: Spatial and temporal regulation of actin dynamics, Annu. Rev. Biochem., 73 (2004), pp. 209-239. (Pubitemid 39050368)
73. A. J. Ridley, H. F. Paterson, C. L. Johnston, D. Diekmann, and A. Hall, The small GTP-binding protein Rac regulates growth factor-induced membrane ruffling, Cell, 70 (1992), pp. 401-410.
74. A. J. Ridley, Rho GTPases and cell migration, J. Cell Sci., 114 (2001), pp. 2713-2722. (Pubitemid 32785451)
75. B. M. Rubenstein and L. J. Kaufman, The role of extracellular matrix in glioma invasion: A cellular Potts model approach, Biophys. J., 95 (2008), pp. 5661-5680.
76. N. J. Savill and P. Hogeweg, Modelling morphogenesis: From single cells to crawling slugs, J. Theoret. Biol., 184 (1997), pp. 118-124.
77. N. J. Savill and J. A. Sherratt, Control of epidermal stem cell clusters by Notch-mediated lateral induction, Dev. Biol., 258 (2003), pp. 141-153. (Pubitemid 36627662)
78. M. Scianna, R. M. H. Merks, L. Preziosi, and E. Medico, Individual cell-based models of cell scatter of ARO and MLP-29 cells in response to hepatocyte growth factor, J. Theoret. Biol., 260 (2009), pp. 151-160.
79. M. Scianna, A multiscale hybrid model for pro-Angiogenic calcium signals in a vascular endothelial cell, Bull. Math. Biol., to appear.
80. M. Scianna, L. Munaron, and L. Preziosi, A multiscale hybrid approach for vasculogenesis and related potential blocking therapies, Prog. Biophys. Mol. Biol., 106 (2011), pp. 450-462.
81. G. Serini, D. Ambrosi, E. Giraudo, A. Gamba, L. Preziosi, and F. Bussolino, Modeling the early stages of vascular network assembly, EMBO J., 22 (2003), pp. 1771-1779. (Pubitemid 36460134)
82. A. Shirinifard, J. S. Gens, B. L. Zaitlen, N. J. Poplawski, M. Swat, and J. A. Glazier, 3D multi-cell simulation of tumor growth and angiogenesis, PLoS ONE, 4 (2009), e7190.
83. J. Starruss, T. Bley, L. Søgaard-Andersen, and A. Deutsch, A new mechanism for collective migration in Myxococcus Xanthus, J. Stat. Phys., 128 (2007), pp. 269-286.
84. M. S. Steinberg, Reconstruction of tissues by dissociated cells. Some morphogenetic tissue movements and the sorting out of embryonic cells may have a common explanation, Science, 141 (1963), pp. 401-408.
85. M. S. Steinberg, Does differential adhesion govern self-Assembly processes in histogenesis? Equilibrium configurations and the emergence of a hierarchy among populations of embryonic cells, J. Exp. Zool., 173 (1970), pp. 395-433.
86. M. Stoker, E. Gherardi, M. Perryman, and J. Gray, Scatter factor is a fibroblast-derived modulator of epithelial cell mobility, Nature, 21 (1987), pp. 239-242. (Pubitemid 17071053)
87. K. Szczur, H. Xu, S. Atkinson, Y. Zheng, and M.-D. Filippi, Rho GTPase CDC42 regulates directionality and random movement via distinct MAPK pathways in neutrophils, Blood, 108 (2006), pp. 4205-4213. (Pubitemid 44913295)
88. L. Tamagnone and P. M. Comoglio, Control of invasive growth by hepatocyte growth factor (HGF) and related scatter factors, Cytokine Growth Factor Rev., 8 (1997), pp. 129-142. (Pubitemid 27299141)
89. C. Tomatis, A. Fiorio Pla, and L. Munaron, Cytosolic calcium microdomains by arachidonic acid and nitric oxide in endothelial cells, Cell Calcium, 41 (2007), pp. 261-269. (Pubitemid 46179176)
90. L. Trusolino and P. M. Comoglio, Scatter-factor and semaphorin receptors: Cell signalling for invasive growth, Nat. Rev. Cancer, 2 (2002), pp. 289-300. (Pubitemid 37328782)
91. S. Turner and J. A. Sherratt, Intercellular adhesion and cancer invasion: A discrete simulation using the extended Potts model, J. Theoret. Biol., 216 (2002), pp. 85-100. (Pubitemid 34748059)
92. T. Walther, H. Reinsch, A. Grosse, K. Ostermann, A. Deutsch, and T. Bley, Mathematical modeling of regulatory mechanisms in yeast colony development, J. Theoret. Biol., 229 (2004), pp. 327-338. (Pubitemid 38844937)
93. N. Wang, J. D. Tytell, and D. E. Ingber, Mechanotransduction at a distance: Mechanically coupling the extracellular matrix with the nucleus, Nat. Rev. Mol. Cell Biol., 10 (2009), pp. 75-82.
94. K. M. Weidner, J. Behrens, J. Vandekerckhove, and W. Birchmeier, Scatter factor: Molecular characteristics and effect on the invasiveness of epithelial cells, J. Cell Biol., 111 (1990), pp. 2097-2108.
95. S. A.Wright, S. J. Plimpton, T. P. Swiler, R. M. Fye, M. F. Young, and E. A. Holm, Potts-model grain growth simulations: Parallel algorithms and applications, SAND Report 97-1925, Sandia National Laboratories, Albuquerque, NM, 1997.
96. Z. Xu, J. Lioi, J. Mu, M. M. Kamocka, X. Liu, D. Z. Chen, E. D. Rosen, and M. S. Alber, A multiscale model of venous thrombus formation with surface-mediated control of blood coagulation cascade, Biophys. J., 98 (2010), pp. 1723-1732.
97. Z. Xu, N. Chen, S. Shadden, J. E. Marsden, M. Kamocka, E. D. Rosen, and M. S. Alber, Study of blood flow impact on growth of thrombi using a multiscale model, Soft Matter, 5 (2009), pp. 769-779.
98. Z. Xu, N. Chen, M. M. Kamocka, E. D. Rosen, and M. S. Alber, A multiscale model of thrombus development, J. R. Soc. Interface, 5 (2008), pp. 705-722. (Pubitemid 351882148)
99. Y. Zhang and G. F. Vande Woude, HGF/SF-Met signaling in the control of branching morphogenesis and invasion, J. Cell. Biochem., 88 (2003), pp. 408-417. (Pubitemid 36119916)
100. V. P. Zhdanov and B. Kasemo, Simulation of the growth and differentiation of stem cells on a heterogeneous scaffold, Phys. Chem. Chem. Phys., 6 (2004), pp. 4347-4350.