Journal of Mathematical Biology

, Volume 66, Issue 7, pp 1409–1462 | Cite as

A review of spatial computational models for multi-cellular systems, with regard to intestinal crypts and colorectal cancer development

  • Giovanni De Matteis
  • Alex Graudenzi
  • Marco Antoniotti
Article

Abstract

Colon rectal cancers (CRC) are the result of sequences of mutations which lead the intestinal tissue to develop in a carcinoma following a “progression” of observable phenotypes. The actual modeling and simulation of the key biological structures involved in this process is of interest to biologists and physicians and, at the same time, it poses significant challenges from the mathematics and computer science viewpoints. In this report we give an overview of some mathematical models for cell sorting (a basic phenomenon that underlies several dynamical processes in an organism), intestinal crypt dynamics and related problems and open questions. In particular, major attention is devoted to the survey of so-called in-lattice (or grid) models and off-lattice (off-grid) models. The current work is the groundwork for future research on semi-automated hypotheses formation and testing about the behavior of the various actors taking part in the adenoma–carcinoma progression, from regulatory processes to cell–cell signaling pathways.

Keywords

Cell sorting Crypt dynamics Colorectal cancer Cell adhesion Modeling Simulation 

Mathematics Subject Classification

MSC 37N25 MSC 92-08 MSC 92B05 MSC 92C15 MSC 92C17 MSC 92C42 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adams J, Cory S (2007) The bcl-2 apoptotic switch in cancer development and therapy. Oncogene 26: 1324–1337Google Scholar
  2. Adams J, Watt F (1989) Fibronectin inhibits the terminal differentiation of human keratinocytes. Nature 340: 307–309Google Scholar
  3. Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P (2007) Molecular Biology of the Cell, 5th edn. Garland Science, New YorkGoogle Scholar
  4. Andreu P et al (2005) Crypt-restricted proliferation and commitment to the paneth cell lineage following apc loss in the mouse intestine. Development 132: 1443–1451Google Scholar
  5. Andreu P et al (2008) A genetic study of the role of the wnt/-catenin signalling in paneth cell differentiation. Dev. Biol. 324: 288–296Google Scholar
  6. Armstrong P (1989) Cell sorting out: the self-assembly of tissues in vitro. Crit Rev Biochem Mol Biol 24: 119–149Google Scholar
  7. Armstrong P, Parenti D (1972) Cell sorting in the presence of cytochalasin b. J Cell Biol 55: 542–553Google Scholar
  8. Arvanitis D, Davy A (2008) Eph/eprhin signaling: networks. Genes Dev 22: 416–429Google Scholar
  9. Barker N et al (2007) Identification of stem cells in small intestine and colon by marker gene lgr5. Nature 449: 1003–1007Google Scholar
  10. Barker N, Ridgway R, van Es J, van de Wetering M, Begthel H, van den Born M, Danenberg E, Clarke A, Sansom O, Clevers H (2009) Crypt stem cells as the cells-of-origin of intestinal cancer. Nature 457: 608–611Google Scholar
  11. Baron M (2003) An overview of the notch signalling pathway. Semin Cell Dev Biol 14: 113–119Google Scholar
  12. Barrett T, Troup DB, Wilhite SE, Ledoux P, Evangelista C, Kim IF, Tomashevsky M, Marshall KA, Phillippy KH, Sherman PM, Muertter RN, Holko M, Ayanbule O, Yefanov A, Soboleva A (2010) NCBI GEO: archive for functional genomics data sets–10 years on. Nucleic Acids Res 39(Database): D1005–D1010Google Scholar
  13. Basso K et al (2005) Reverse engineering of regulatory networks in human b cells. Nature Genetics 37: 382–390Google Scholar
  14. Batlle E et al (2002) Beta-catenin and tcf mediate cell positioning in the intestinal epithelium by controlling the expression of ephb/ephrinb. Cell 111: 251–263Google Scholar
  15. Bienz M, Clevers H (2000) Linking colorectal cancer to wnt signaling. Cell 103: 311–320Google Scholar
  16. Bjerknes M (1996) Expansion of mutant stem cell populations in the human colon. J Theor Biol 178: 381–385. doi: 10.1006/jtbi.1996.0034 Google Scholar
  17. Bjerknes M, Cheng H (1981) The stem-cell zone of the small intestinal epithelium. ii. Evidence from paneth cells in the newborn mouse. Am J Anat 160: 165–175Google Scholar
  18. Boland C (2002) Heredity nonpolyposis colorectal cancer (hnpcc). In: Vogelstein B, Kinzler KW (eds) The Genetic Basis of Human Cancer, 2nd edn. McGraw-Hill, New York, pp 307–321Google Scholar
  19. Boman B, Fields J, Bonham-Carter O, Runquist O (2001) Computer modeling implicates stem cell overproduction in colon cancer initiation. Cancer Res 61: 8408–8411Google Scholar
  20. Booth C, Brady G, Potten C (2002) Crown control in crypts. Nat Med 8: 1360–1361Google Scholar
  21. Bourgin C, Murai K, Richter M, Pasquale E (2007) The epha4 receptor regulates dendritic spine remodeling by affecting 1-integrin signaling pathways. J Cell Biol 178: 1295–1307Google Scholar
  22. Brenner S (1999) Theoretical Biology in the Thurd Millenium. Philos Trans R Soc Lond B 354: 1963–1965Google Scholar
  23. Brown S, Riehl T, Walker M, Geske M, Doherty J, Stenson W et al (2007) Myd88-dependent positioning of ptgs2-expressing stromal cells maintains colonic epithelial proliferation during injury. J Clin Invest 117: 258–269Google Scholar
  24. Bunow B, Kernevez J, Joly G, Thomas D (1980) Pattern formation by reaction-diffusion instabilities: application to morphogenesis in drosophila. J Theor Biol 84: 629–649MathSciNetGoogle Scholar
  25. Burgess P et al (1997) The interaction of growth rates and diffusion coefficients in a three-dimensional mathematical model of gliomas. J Neuropathol Exp Neurol 56: 701–713Google Scholar
  26. Buske P, Galle J, Barker N, Aust G, Clevers H, Loeffler M (2011) A comprehensive model of the spatio-temporal stem cell and tissue organisation in the intestinal crypt. PLoS Comput Biol 7(1): e1001,045Google Scholar
  27. Casciari J, Sotirchos S, Sutherland R (1992) Variations in tumor cell growth rates and metabolism with oxygen concentration, glucose concentration, and extracellular ph. J Cell Physiol 151: 386–394Google Scholar
  28. CellML (2001) http://www.cellml.org
  29. Cerami EG, Bader GD, Gross BE, Sander C (2006) cPath: open source software for collecting, storing, and querying biological pathways. BMC Bioinformatics 7. doi: 10.1186/1471-2105-7-497
  30. Chen C et al (1997) Geometric control of cell life and death. Science 276: 1425–1428Google Scholar
  31. Christie GR, Nielsen PMF, Blackett SA, Bradley CP, Hunter PJ (2009) FieldML: concepts and implementation. Philos Trans R Soc 367: 1869–1884. doi: 10.1098/rsta.2009.0025 Google Scholar
  32. Chwalinski S, Potten C (1989) Crypt base columnar cells in ileum of bdf1 male mice-their numbers and some features of their proliferation. Am J Anat 186: 397Google Scholar
  33. Clevers H, Battle E (2006) Ephb/ephrinb receptors and wnt signaling in colorectal cancer. Cancer Res 66: 2–5Google Scholar
  34. Coussens L, Werb Z (2002) Inflammation and cancer. Nature 420: 860–867Google Scholar
  35. Crosnier C, Stamataki D, Lewis J (2006) Organizing cell renewal in the intestine: stem cells, signals and combinatorial control. Nat Rev Genet 7: 349–359Google Scholar
  36. Cuellar AA, Lloyd CM, Nielsen PF, Bullivant DP, Nickerson DP, Hunter PJ (2003) An overview of CellML 1.1, a biological mdel description language. Simulation Trans Soc for Model Simul Int 79(12): 740–747Google Scholar
  37. Dada JO, Spasić I, Paton NW, Mendes P (2010) SBRML: a markup language for associating systems biology data with models. Bioinformatics 26(7): 932–938Google Scholar
  38. Damiani C, Serra R, Villani M, Kauffman S, Colacci A (2011) Cell–cell interaction and diversity of emergent behaviours. IET Syst Biol 5(2): 137–144Google Scholar
  39. Davidson E et al (2002) A genomic regulatory network for development. Science 295: 1669Google Scholar
  40. Deroanne C, Vouret-Craviari V, Wang B, Pouysségur J (2003) Ephrina1 inactivates integrin-mediated vascular smooth muscle cell spreading via the rac/pak pathway. J Cell Sci 116: 1367–1376Google Scholar
  41. Di Garbo A, Johnston MD, Chapman SJ, Maini PK (2010) Variable renewal rate and growth properties of cell populations in colon crypts. Phys Rev E 81(6): 061909. doi: 10.1103/PhysRevE.81.061909 Google Scholar
  42. D’Onofrio A, Tomlinson I (2007) A nonlinear mathematical model of cell turnover, differentiation and tumorigenesis in the intestinal crypt. J Theor Biol 244: 367–374MathSciNetGoogle Scholar
  43. Dover R, Potten C (1988) Heteogeneity and cell cycle analyses from time-lapse studes of human keratinocytes in vitro. J Cell Sci 89: 359–364Google Scholar
  44. Drasdo D (2000) Buckling instabilities in one-layered growing tissues. Phys Rev Lett 84(19): 4244–4247Google Scholar
  45. Dubois M, Demè B, Gulik-Krzywicki T, Dedieu JC, Vautrin C, Dèsert S, Perez E, Zemb T (2001) Self-assembly of regular hollow icosahedra in salt-free catanionic solutions. Nature 411: 672–675. doi: 10.1038/35079541 Google Scholar
  46. Dubois M, Lizunov V, Meister A, Gulik-Krzywicki T, Verbavatz JM, Perez E, Zimmerberg J, Zemb T (2004) Shape control through molecular segregation in giant surfactant aggregates. Proc Natl Acad Sci USA 101: 15082–15087Google Scholar
  47. Egeblad M, Nakasone E, Werb Z (2010) Tumors as organs: complex tissues that interface with the entire organism. Dev Cell 18: 884–901Google Scholar
  48. Falcone J, Chopard B, Hoekstra A (2010) MML: towards and multiscale modeling language. Procedia Comput Sci 1: 819–826Google Scholar
  49. Fearon E, Volgestein B (1990) A genetic model for colorectal tumorigenesis. Cell 61: 759–767Google Scholar
  50. Fevr T, Robine S, Louvard D, Huelsken J (2007) Wnt/beta-catenin is essential for intestinal homeostasis and mainteinance of intestinal stem cells. Mol Cell Biol 27: 7551–7559Google Scholar
  51. Fischer I et al (2005) Angiogenesis in gliomas: biology and molecular pathophysiology. Brain Pathol 15: 297–310Google Scholar
  52. Fotos J et al (2006) Automated time-lapse microscopy and high-resolution tracking of cell migration. Cytotechnology 51: 7–19Google Scholar
  53. Frank S (2007) Dynamics of cancer. Princeton University Press, PrincetonGoogle Scholar
  54. Free S et al (2005) Notch signals control the fate of immature progenitor cells in the intestine. Nature 435: 964–968Google Scholar
  55. Freyer J, Sutherland R (1986) Regulation of growth saturation and development of necrosis in emt6/ro multicellular spheroids by the glucose and oxygen supply. Cancer Res 46: 3504–3512Google Scholar
  56. Galiatsatos P, Foulkes W (2006) Familial adenomatous polyposis. Am J Gastroenterol 101: 385–398Google Scholar
  57. Galle J, Aust G, Schaller G, Beyer T, Drasdo D (2006) Individual cell-based models of the spatial-temporal organization of multicellular systemsóachievements and limitations. Cytometry Part A 69A(7): 704–710 doi: 10.1002/cyto.a.20287 Google Scholar
  58. Galle J, Hoffmann M, Aust G (2009) From single cells to tissue architecture: a bottom-up approach to modelling the spatio-temporal organisation of complex multi-cellular systems. J Math Biol 58: 261–283 doi: 10.1007/s00285-008-0172-4 MathSciNetMATHGoogle Scholar
  59. Galle J, Loeffler M, Drasdo D (2005) Modeling the effect of deregulated proliferation and apoptosis on the growth dynamics of epithelial cell populations in vitro. Biophys J 88: 62–75. doi: 10.1529/biophysj.104.041459 Google Scholar
  60. Galle J, Sittig D, Hanisch I, Wobus M, Wandel E, Loeffler M, Aust G (2006) Individual cell-based models of tumor-environment interactions: multiple effects of CD97 on tumor invasion. Am J Pathol 169(5): 1802–1811 doi: 10.2353/ajpath.2006.060006 Google Scholar
  61. Gene Ontology Consortium: (2006) The gene ontology (GO) project in 2006. Nucleic Acid Res (Database issue) 34: D322–D326Google Scholar
  62. Gerike T, Paulus U, Potten C, Loeffler M (1998) A dynamic model of proliferation and differentiation in the intestinal crypt based on a hypothetical intraepithelial growth factor. Cell Prolif 31:93–110. http://www.ncbi.nlm.nih.gov/pubmed/9745618 Google Scholar
  63. Gibson MA, Bruck J (2000) Efficient exact stochastic simulation of chemical systems with many species and many channels. J Phys Chem 104: 1876–1889Google Scholar
  64. Gierer A et al (1972) Regeneration of hydra from reaggregated cells. Nat New Biol 91: 98–101Google Scholar
  65. Gierer A, Meinhardt H (1974) Biological pattern formation involving lateral inhibition. Lect Math Life Sci 7: 163–183MathSciNetGoogle Scholar
  66. Gillespie DT (1976) A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J Comput Phys 22: 403–434MathSciNetGoogle Scholar
  67. Gillespie DT (1977) Exact stochastic simulation of coupled chemical reactions. J Phys Chem 2340–2361Google Scholar
  68. Glauche I, Cross M, Loeffler M, Roeder I (2007) Lineage specification of hematopoietic stem cells: Mathematical modeling and biological implications. Stem cells 25: 1791–1799Google Scholar
  69. Goss K, Groden J (2000) Biology of the adenomatous polyposis coli tumor suppressor. J Clin Oncol 18: 1967–1979Google Scholar
  70. Graner F, Glazier J (1992) Simulation of biological cell sorting using a two-dimensional extended potts model. Phys Rev Lett 69: 2013–2017Google Scholar
  71. Graner F, Glazier J (1993) Simulation of the differential adhesion driven rearrangement of biological cells. Phys Rev E 47:2128–2154. http://graner.net/francois/publis/glazier_rearrangement.pdf
  72. Graudenzi A, Caravagna G, De Matteis G, Mauri G, Antoniotti M (2012) A multiscale model of intestinal crypts dynamics. In: Proceedings of the Italian Workshop on Artificial Life and Evolutionary Computation, WIVACE 2012. ISBN: 978-88-903581-2-8Google Scholar
  73. Greenberg J, Hassard B, Hastings S (1978) Pattern formation and periodic structures in systems modeled by reaction-diffusion equations. Bull Am Math Soc 84: 1296–1327MathSciNetMATHGoogle Scholar
  74. Gregorieff A, Pinto D, Begthel H, Destree O, Kielman M, Clevers H (2005) Expression pattern of wnt signaling components in the adult intestine. Gastroenterology 129: 626–638Google Scholar
  75. Grindrod P (1991) Patterns and waves: theory and applications of reaction–diffusion equations. Oxford Applied Mathematics & Computing Science, OxfordMATHGoogle Scholar
  76. Hafner C et al (2005) Ephrin-b2 is differentially expressed in the intestinal epithelium in crohn’s disease and contributes to accelerated epithelial wound healing in vitro. World J Gastroenterol 11: 4024–4031Google Scholar
  77. Haga H et al (2005) Collective movemente of epithelial cells on a collagen gel substrate. Biophys J 88: 2250–2256Google Scholar
  78. Hanahan D, Folkman J (1996) Patterns and emerging mechanisms of the angiogenetic switch during tumorigenesis. Cell 86: 353–364Google Scholar
  79. Hanahan D, Weinberg RA (2011) Hallmarks of cancer: the next generation. Cell 144: 646–674Google Scholar
  80. Harrison NC (2010) BioCellSim 1.0 Simulation Software. http://pcwww.liv.ac.uk/~mf0u4027/biocellsim.html
  81. Hartsock A, Nelson W (2007) Adherens and tight junctions: structure, function and connections to the actin cytoskeleton. Biochim Biophys Acta. doi: 10.1016/j.bbamem.2007.07.012
  82. Haselwandter CA, Phillips R (2011) Elastic energy of polyhedral bilayer vesicles. Phys Rev E 83(6): 061,901. doi: 10.1103/PhysRevE.83.061901 Google Scholar
  83. Heckera M et al (2009) Gene regulatory network inference: data integration in dynamic models—a review. Biosystems 96: 86–103Google Scholar
  84. Hocker M, Wiedenmann B (1998) Molecular mechanisms of enteroendocrine differentiation. Ann NY Acad Sci 859: 160–174Google Scholar
  85. Hoehme S, Drasdo D (2010) A cell-based simulation software for multicellular systems. Bioinformatics 26(20): 2641–2642Google Scholar
  86. Hogeweg P (2000) Evolving mechanisms of morphogenesis: on the interplay between differential adhesion and cell differentiation. J Theor Biol 203(4): 317–333 doi: 10.1006/jtbi.2000.1087 Google Scholar
  87. Hogeweg P (2002) Computing an organism: on the interface between informatic and dynamic processes. Biosystems 64(1-3): 97–109 doi: 10.1016/S0303-2647(01)00178-2 Google Scholar
  88. Holmberg J et al (2006) Ephb receptors coordinate migration and proliferation in the intestinal stem cell niche. Cell 125: 1151–1163Google Scholar
  89. Honda H, Yamanaka H, Eguchi G (1986) Transformation of a polygonal cellular pattern during sexual maturation of the avian oviduct epithelium. J Embryol Exp Morphol 98: 1–19Google Scholar
  90. Huynh-Do U, Stein E, Lane AA, Liu H, Cerretti DP, Daniel TO (1999) Surface densities of ephrin-b1 determine ephb1-coupled activation of cell attachment through avb3 and a5b1 integrins. EMBO J 18: 2165–2173Google Scholar
  91. Ikushima H, Miyazono K (2010) Tgfbeta signaling: a complex web in cancer progression. Nat Rev Cancer 10: 415–424Google Scholar
  92. Ireland H, Houghton C, Howard L, Winton D (2005) Cellular inheritance of a cre-activated reporter gene to determine paneth cell longevity in the murine small intestine. Dev Dyn 233: 1332–1336Google Scholar
  93. Jass JR (2007) Classification of colorectal cancer based on correlation of clinical, morphological and molecular features. Histopathology 50: 113–130Google Scholar
  94. Jass JR, Whitehall VL, Young J, Leggett BA (2002) Emerging concepts in colorectal neoplasia. Gastroenterology 123: 862–876Google Scholar
  95. Jass JR, Young J, Leggett BA (2002) Evolution of colorectal cancer: change of pace and change of direction. J Gastroenterol Hepatol 17: 17–26Google Scholar
  96. Jemal A, Siegel R, Xu J, Ward E (2010) Cancer statistics 2010. CA Cancer J Clin 60: 277–300Google Scholar
  97. Jensen U, Lowell S, Watt F (1999) The spatial relationship between stem cells and their progeny in the basal layer of human epidermis: a new view based on whole-mount labelling and lineage analysis. Development 126: 2409–2418Google Scholar
  98. Jouanneau J, Tucker G, Boyer B, Vallés AJPT (1992) Epithelial cell plasticity in neoplasia. Cancer Cells 3: 525–529Google Scholar
  99. Kaneko K (2006) Life: an introduction to complex systems biology. Springer, BerlinMATHGoogle Scholar
  100. Kauffman S (1969) Homeostasis and differentiation in random genetic control networks. Nature 224: 177Google Scholar
  101. Kauffman S (1969) Metabolic stability and epigenesis in randomly constructed genetic nets. J Theor Biol 22: 437–467MathSciNetGoogle Scholar
  102. Kauffman S (1995) At home in the universe. Oxford University Press, OxfordGoogle Scholar
  103. Kaur P, Potten C (1986) Circadian variation in migration velocity in small intestinal epithelium. Cell Tissue Kinet 19: 591Google Scholar
  104. Kedinger M et al (1986) Fetal gust menschyme induces differentiation of cultured intestinal endonormal and crypt cells. Dev Biol 113: 474–483Google Scholar
  105. Kempf H, Bleicher M, Meyer-Hermann M (2010) Spatio-temporal cell dynamics in tumour spheroid irradiation. Eur Phys J D 60(1): 177–193Google Scholar
  106. Kinzler KW, Vogelstein B (1996) Lessons from hereditary colorectal cancer. Cell 87: 159–170Google Scholar
  107. Kinzler KW, Vogelstein B (2002) Colorectal tumors. In: Vogelstein B, Kinzler KW (eds) The genetic basis of human cancer, 2nd edn. McGraw-Hill, New YorkGoogle Scholar
  108. Kirouac D, Ito C, Csaszar E, Roch A, Yu M, Sykes E, Bader G, Zandstra P (2010) Dynamic interaction networks in a hierarchically organized tissue. Mol Syst Biol 6: 417Google Scholar
  109. Kitano H (2001) Foundations of systems biology. MIT Press, MassachusettsGoogle Scholar
  110. Kitano H (2002) Computational systems biology. Nature 206–210Google Scholar
  111. Koga S, Kuramoto Y (1980) Localized patterns in reaction-diffusion systems. Prog Theor Phys 63: 106–121Google Scholar
  112. Köhn D, Novère NL (2008) SED-ML - An XML Format for the Implementation of the MIASE Guidelines. In: Computational methods n systems biology. Lncs, vol. 5307. Springer, Berlin, pp 176–190Google Scholar
  113. Kohn K (1998) Functional capabilities of molecular network components controlling the mammalian g1/s cell cycle phase transition. Oncogene 16: 1065–1075Google Scholar
  114. Koinuma K, Shitoh K, Miyakura Y et al (2004) Mutations of braf are associated with extensive hmlh1 promoter methylation in sporadic colorectal carcinomas. Int J Cancer 108: 237–242Google Scholar
  115. Komarova N, Sengupta A, Nowak M (2003) Mutation-selection networks of cancer initiation: tumor suppressor genes and chromosomal instability. J Theor Biol 223: 433–450. doi: 10.1016/S0022-5193(03)00120-6 MathSciNetGoogle Scholar
  116. Komarova N, Wang L (2004) Initiation of colorectal cancer: where do the two hits hit?. Cell Cycle 3: 1558–1565. doi: 10.4161/cc.3.12.1186 Google Scholar
  117. Komarova N, Wodarz D (2004) The optimal rate of chromosome loss for the inactivation of tumor suppressor genes in cancer. Proc Natl Acad Sci USA 101: 7017–7021. doi: 10.1073/pnas.0401943101 Google Scholar
  118. Korinek V, Barker N, Moerer P, van Donselaar E, Huls G et al (1998) Depletion of epithelial stem-cell compartments in the small intestine of mice lacking tcf-4. Nat Genet 19: 379–383Google Scholar
  119. Kosinski C, Li V, Chan A, Zhang J, Ho C, Tsui W et al (2007) Gene expression patterns of human colon tops and basal crypts and bmp antagonists as intestinal stem cell niche factors. Proc Natl Acad Sci USA 104: 15418–15423Google Scholar
  120. Kullander K, Klein R (2002) Mechanisms and functions of eph and ephrin signaling. Nat Rev Mol Cell Biol 3: 475–486Google Scholar
  121. Kunz-Schughart L et al (2000) Proliferative activity and tumorigenic conversion: impact on cellular metabolism in 3-d culture. J Physiol Cell Physiol 278: 765Google Scholar
  122. Laird D (1996) The life cycle of a connexin: gap junction formation, removal, and degradation. J Bioenerg Biomembr 28: 311–318Google Scholar
  123. Landry J, Freyer J, Sutherland R (1981) Shedding of mitotic cells from the surface of multicell spheroids during growth. J Cell Physiol 106: 23–32Google Scholar
  124. Le Novère N, Bornstein B, Broicher A, Courtot M, Donizelli M, Dharuri H, Li L, Sauro H, Schilstra M, Shapiro B, Snoep JL, Hucka M (2006) BioModels Database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems. Nucleic Acids Res 34(Database issue): D689–D691Google Scholar
  125. Lee T et al (2002) Transcriptional regulatory networks in Saccharomyces cerevisiae. Science 298: 799–804Google Scholar
  126. Lemmon M, Schlessinger J (2010) Cell signaling by receptor tyrosine kinases. Cell 141: 1117–1134Google Scholar
  127. Lewis J (1998) Notch signalling: a short cut to the nucleus. Nature 393: 304–305Google Scholar
  128. Li C, Donizelli M, Rodriguez N, Dharuri H, Endler L, Chelliah V, Li L, He E, Henry A, Stefan MI, Snoep JL, Hucka M, Le Novère N, Laibe C (2010) BioModels database: an enhanced, curated and annotated resource for published quantitative kinetic models. BMC Syst Biol 4: 92Google Scholar
  129. Li Y et al (1994) The crypt cycle in mouse small intestinal epithelium. J Cell Sci 107: 3271–3279Google Scholar
  130. Lin G, Xu N, Xi R (2008) Paracrinewingless signalling controls selfrenewal of drosophila intestinal stem cells. Nature 455: 1119–1123Google Scholar
  131. Loeffler M, Potten C, Paulus U, Glatzer J, Chwalinski S (1988) Interstinal crypt proliferation. II. Computer modeling of mitotic index data provides further evidence for lateral and vertical cell migration in the absence of mitotic activity. Cell Tissue Kinet 21: 247–258Google Scholar
  132. Loeffler M, Stein R, Wichmann H, Potten C, Kaur P, Chwalinski S (1986) Intestinal cell proliferation. I. A comprehensive model of steady-state proliferation in the crypt. Cell Tissue Kinet 19: 627–645Google Scholar
  133. Logan C, Nusse R (2004) The wnt signaling pathway in development and disease. Annu Rev Cell Dev Biol 20: 781–810Google Scholar
  134. Lopez-Garcia CA, Klein M, Simons B, Winton D (2010) Intestinal stem cell replacement follows a patter of neutral drift. Science 330: 822–825Google Scholar
  135. Lowell S et al (2000) Stimulating of human epidermal differentiation by delta–notch signalling at the boundaries of stem-cells clusters. Curr Biol 10: 491–500Google Scholar
  136. Luebeck E, Moolgavkar S (2002) Multistage carcinogenesis and the incidence of colorectal cancer. Proc Natl Acad Sci USA 99: 15095–15100. doi: 10.1073/pnas.222118199 Google Scholar
  137. Macklin P et al (2009) Multiscale modeling and nonlinear simulation of vascular tumour growth. J Math Biol 58: 765–798MathSciNetGoogle Scholar
  138. Macklin P, Edgerton M, Thompson A, Cristini V (2010) MultiCellXML: an open XML data standard for multicell agent models. http://multicellxml.sourceforge.net
  139. Multiscale Applications on European e-Infrastructures (2010) http://www.mapper-project.eu
  140. Mardis E (2008) The impact of next-generation sequencing technology on genetics. Trends Genet 24: 133–141Google Scholar
  141. Marshman E, Booth C, Potten C (2002) The intestinal epithelial stem cells. Bioessays 24: 91–98Google Scholar
  142. Marshman F et al (2001) Caspase activation during spontaneous and radiation-induced apoptosis in the murine intestine. J Pathol 195: 285–292Google Scholar
  143. Martiel JL, Goldbeter A (1987) A model based on receptor desensitization for cyclic amp signaling in dictyostelium cells. Biophys J 52: 807–828 doi: 10.1016/S0006-3495(87)83275-7 Google Scholar
  144. Martone ME, Tran J, Wong WW, Sargis J, Fong L, Larson S, Lamont SP, Gupta A, Ellisman MH (2008) The Cell Centered Database project: an update on building community resources for managing and sharing 3D imaging data. J Struct Biol 161(3): 220–231Google Scholar
  145. Mathew JP, Taylor BS, Bader GD, Pyarajan S, Antoniotti M, Chinnaiyan AM, Sander C, Burakoff SJ, Mishra B (2003) From bytes to bedside: data integration and computational biology for translational cancer research. PLoS Comput Biol 102(18): 6245–6250. doi: 10.1371/journal.pcbi.0030012 Google Scholar
  146. McClay D, Ettensohn C (1987) Cell adhesion in morphogenesis. A. Rev Cell Biol 3: 319–345Google Scholar
  147. Medema JP, Vermulen L (2011) Microenvironmental regulation of stem cells in intestinal homeostasis and cancer. Nature 474(7351): 318–326Google Scholar
  148. Meineke F, Potten C, Loeffler M (2001) Cell migration and organization in the intestinal crypt using a lattice-free model. Cell Prolif 34(4): 253–266Google Scholar
  149. Meinhardt H, Gierer A (1974) Applications of a theory of biological pattern formation based on lateral inhibition. J Cell Sci 15: 321–346Google Scholar
  150. Merks RM, Brodsky SV, Goligorksy MS, Newman SA, Glazier JA (2006) Cell elongation is key to in silico replication of in vitro vasculogenesis and subsequent remodeling. Dev Biol 289(1): 44–54 doi: 10.1016/j.ydbio.2005.10.003 Google Scholar
  151. Merks RM, Glazier JA (2005) A cell-centered approach to developmental biology. Phys A Stat Mech Appl 352(1): 113–130 doi: 10.1016/j.physa.2004.12.028 Google Scholar
  152. Miao H, Burnett E, Kinch M, Simmon E, Wang B (2000) Activation of epha2 kinase suppresses integrin function and causes focal-adhesion-kinase dephosphorylation. Nat Cell Biol 2: 62–69Google Scholar
  153. Miao H, Strebhardt K, Pasquale E, Shen T, Guan J, Wang B (2005) Inhibition of integrin-mediated cell adhesion but not directional cell migration requires catalytic activity of ephb3 receptor tyrosine kinase. role of rho family small gtpases. J Biol Chem 2: 923–932Google Scholar
  154. Michaelis L, Menten M (1913) Die Kinetik der Invertinwirkung. Biochemische Zeitschrift 49: 333–369Google Scholar
  155. Mombach J, de Almeida R, Iglesias J (1993) Mitosis and growth in biological tissues. Phys Rev E 48: 598Google Scholar
  156. Morel D, Marcelpoil R, Brugal G (2001) A proliferation control network model: The simulation of two-dimensional epithelial homeostasis. Acta Biotheoretica 49: 219–234 doi: 10.1023/A:1014201805222 Google Scholar
  157. Mumm J, Kopan R (2000) Notch signaling: from the outside in. Dev Biol 228: 151–165Google Scholar
  158. Munemitsu S, Albert I, Souza B, Rubinfeld B, Polakis P (1995) Regulation of intracellular beta-catenin levels by adenomatous polyposis coli (apc) tumor-suppressor protein. Proc Natl Acad Sci USA 92: 3046–3050Google Scholar
  159. Nicol A, Garrod D (1979) The sorting out of embryonic cells in monolayer, the differential adhesion hypothesis and the non-specificity of cell adhesion. J Cell Sci 38: 249–266Google Scholar
  160. Nicol A, Garrod D (1982) Fibronectin, intercellular junctions and the sorting-out of chick embryonic tissue cells in monolayer. J Cell Sci 54: 357–372Google Scholar
  161. Nowak M, Komarova N, Sengupta A, Jallepalli P, Shih I, Vogelstein B, Lengauer C (2002) The role of chromosomal instability in tumor initiation. Proc Natl Acad Sci USA 99: 16226–16231. doi: 10.1073/pnas.202617399 Google Scholar
  162. Nowak M, Michor F, Iwasa Y (2003) The linear process of somatic evolution. Proc Natl Acad Sci USA 100: 14966–14969. doi: 10.1073/pnas.2535419100 Google Scholar
  163. Nowak MA, Komarova NL, Sengupta A, Jallepalli PV, Shih I, Vogelstein B, Lengauer C (2002) The role of chromosomal instability in tumor initiation. Proc Natl Acad Sci USA 99: 16226–16231Google Scholar
  164. Nucci M, Robinson C, Longo P, Campbell PSRH (1997) Phenotypic and genotypic characteristics of aberrant crypt foci in human colorectal mucosa. Hum Pathol 28: 1396–1407Google Scholar
  165. Oki E, Oda S, Maehara Y, Sugimachi K (1999) Mutated gene-specific phenotypes of dinucleotide repeat instability in human colorectal carcinoma cell lines deficient in dna mismatch repair. Oncogene 18: 2143–2147Google Scholar
  166. Olson E et al (2006) Gene regulatory networks in the evolution and development of the heart. Science 313: 1922Google Scholar
  167. Othmer H, Pate E (1980) Scale-invariance in reaction-diffusion models of spatial pattern formation. Proc Natl Acad Sci USA 77: 4180–4184Google Scholar
  168. Pasquale E (2005) Eph receptor signalling casts a wide net on cell behaviour. Nat Rev Mol Cell Biol 6: 462–475Google Scholar
  169. Paulus U, Loeffler M, Zeidler J, Owen G, Potten CS (1993) The differentiation and lineage development of goblet cells in the murine small intestinal crypt: experimental and modelling studies. J Cell Sci 106: 473–483Google Scholar
  170. Paulus U, Potten C, Loeffler M (1992) A model of the control of cellular regeneration in the intestinal crypt after perturbation based solely on local stem cell regulation. Cell Prolif 25: 559–578. doi: 10.1111/j.1365-2184.1992.tb01460.x Google Scholar
  171. Peixoto T, Drossel B (2009) Noise in random boolean networks. Phys Rev E 79: 036108–036117Google Scholar
  172. Pinto D, Gregorieff A, Beghtel H, Clevers H (2003) Canonical wnt signals are essential for homeostasis of the intestinal epithelium. Genes Dev 17: 1709–1713Google Scholar
  173. Pitt-Francis J, Pathmanathan P, Bernabeu MO, Bordas R, Cooper J, Fletcher AG, Mirams GR, Murray P, Osborne JM, Walter A, Chapman SJ, Garny A, van Leeuwen IM, Maini PK, RodrÌguez B, Waters SL, Whiteley JP, Byrne HM, Gavaghan DJ (2009) Chaste: a test-driven approach to software development for biological modelling. Comput Phys Commun 180(12): 2452–2471 doi: 10.1016/j.cpc.2009.07.019 MATHGoogle Scholar
  174. Poliakov A, Cotrina M, Wilkinson D (2004) Diverse roles of eph receptors and ephrins in the regulation of cell migration and tissue assembly. Dev Cell 7: 465–480Google Scholar
  175. Porter E, Bevins C, Ghosh D, Ganz T (2002) The multifaceted paneth cell. Cell Mol Life Sci 59: 156–170Google Scholar
  176. Potten C et al (1988) Scoring mitotic activity in longitudinal sections of crypts of the small intestine. Cell Tissue Kinet 21: 231Google Scholar
  177. Potten C, Gandara R, Mahida Y, Loeffler M, Wright N (2009) The stem cells of small intestinal crypts: where are they?. Cell Prolif 42: 731–750Google Scholar
  178. Potten C, Loeffler M (1990) Stem cells: attributes, cycles, spirals, pitfalls and uncertainties. lessons from the crypt. Development 110: 1001–1020Google Scholar
  179. Potten C, Morris R (1988) Epithelial stem cells in vivo. J Cell Sci 10: 45–62Google Scholar
  180. Potten CS, Booth C, Pritchard DM (1997) The intestinal epithelial stem cell: the mucosal governor. Int J Exp Pathol 78: 219–243Google Scholar
  181. Pradal C, Dufour-Kowalski S, Boudon F, Fournier C, Godin C (2008) Openalea: a visual programming and component-based software platform for plant modeling. Funct Plant Biol 35(9, 10):751–760. http://www-sop.inria.fr/virtualplants/Publications/2008/PDBFG08a Google Scholar
  182. Rajagopalan H, Nowak MA, Vogelstein B, Lengauer C (2003) The significance of unstable chromosomes in colorectal cancer. Nat Rev Cancer 3: 695–701Google Scholar
  183. Ramakrishnan N, Tadepalli S, Watson LT, Helm RF, Antoniotti M, Mishra B (2010) Reverse engineering dynamic temporal models of biological processes and their relationships. PNAS 107(28): 12511–12516Google Scholar
  184. Ratdke F, Clevers H (2005) Self-renewal and cancer of the gut: tho sides of a coin. Science 307: 1904–1909Google Scholar
  185. Reid JF, Gariboldi M, Sokolova V, Capobianco P, Lampis A, Perrone F, Signoroni S, Costa A, Leo E, Pilotti S, Pierotti MA (2009) Integrative approach for prioritizing cancer genes in sporadic colon cancer. Genes Chromosom Cancer 48(11): 953–962Google Scholar
  186. Reya T, Clevers H (2005) Wnt signalling in stem cells and cancer. Nature 434: 843–850Google Scholar
  187. Reya T, Morrison S, Clarke M, Weissman I (2001) Stem cells, cancer, and cancer stem cells. Nature 414: 105–111Google Scholar
  188. Roeder I, Braesel K, Lorenz R, Loeffler M (2007) Stem cell fate analysis revisited: Interpretation of individual clone dynamics in the light of a new paradigm of stem cell organization. J Biomed Biotechnol. doi: 10.1155/2007/84656
  189. Roeder I, Loeffler M (2002) A novel dynamic model of hematopoietic stem cell organization based on the concept of within-tissue plasticity. Exp Hematol 30: 853–861Google Scholar
  190. Rubinfeld B, Robbins P, EL Gamil M, Albert I, Porfiri E, Polakis P (1997) Stabilization of beta-catenin by genetic defects in melanoma cell lines. Science 275: 1790–1792Google Scholar
  191. Ruoslahti E (1997) Stretching is good for a cell. Science 276: 1345–1346Google Scholar
  192. Saito T, Masuda N, Miyazaki T, Kanoh K, Suzuki H, Shimura T, Asao T, Kuwano H (2004) Expression of epha2 and e-cadherin in colorectal cancer: correlation with cancer metastasis. Oncol Rep 11: 605–611Google Scholar
  193. Samson O et al (2004) Loss of apc in vivo immediately perturbs wnt signaling, differentiation and migration. Genes Dev 18: 1385–1390Google Scholar
  194. Samuel S, Walsh R, Webb J, Robins A, Potten C, Mahida Y (2009) Characterization of putative stem cells in isolated human colonic crypt epithelial cells and their interactions with myofibroblasts. Am J Physiol Cell Physiol 296: C296–C305Google Scholar
  195. Sancho E, Batlle E, Clevers H (2004) Signaling pathways in intestinal development and cancer. Annu Rev Cell Dev Biol 20: 695–723Google Scholar
  196. Sandersius S, Weijer C, Newman T (2011) Emergent cell and tissue dynamics from subcellular modeling of active bio-mechanical processes. Phys Biol 8: 045007Google Scholar
  197. Sato T et al (2011) Paneth cells constitute the niche for lgr5 stem cells in intestinal crypts. Nature 469: 415–418Google Scholar
  198. Savill NJ, Hogeweg P (1997) Modelling morphogenesis: from single cells to crawling slugs. J Theor Biol 184(3): 229–235 doi: 10.1006/jtbi.1996.0237 Google Scholar
  199. Savill NJ, Sherratt JA (2003) Control of epidermal stem cell clusters by notch-mediated lateral induction. Dev Biol 258(1): 141–153 doi: 10.1016/S0012-1606(03)00107-6 Google Scholar
  200. System Biology Markup Language (2002) http://www.smb-sbml.org/
  201. Schaff J (2011) SBML Spatial Geometry Extension Proposal. proposal at http://sbml.org
  202. Schaller G, Meyer-Hermann M (2005) Multicellular tumor spheroid in an off-lattice Voronoi-Delaunay cell model. Phys Rev E 71(5): 051910. doi: 10.1103/PhysRevE.71.051910 MathSciNetGoogle Scholar
  203. Schroder N, Gossler A (2002) Expression of notch pathway components in fetal and adult mouse small intestine. Gene Expr Patterns 2: 247–250Google Scholar
  204. Sekimura T, Kobuchi Y (1986) A spatial pattern formation model for dictyostelium discoideum. J Theor Biol 122: 325–338MathSciNetGoogle Scholar
  205. Serini G et al (2003) Modeling the early stages of vascular network assembly. EMBO J 22: 1771–1779Google Scholar
  206. Serra R, Villani M, Barbieri A, Kauffman S, Colacci A (2010) On the dynamics of random boolean networks subject to noise: attractors, ergodic sets and cell types. J Theor Biol 265: 185–193MathSciNetGoogle Scholar
  207. Shirinifard A, Gens JS, Zaitlen BL, Poplawski NJ, Swat M, Swat M, Swat M (2009) 3d multi-cell simulation of tumor growth and angiogenesis. PLoS ONE 4(10): e7190 doi: 10.1371/journal.pone.0007190 Google Scholar
  208. Siegert F, Weijer C (1992) Three dimensional scroll waves organise dictyostelium slugs. Proc Natl Acad Sci USA 89: 6433–6437Google Scholar
  209. Smallwood R, Holcombe W, Walker D (2004) Development and validation of computational models of cellular interaction. J Mol Histol 35: 659–665 doi: 10.1007/s10735-004-2660-1 Google Scholar
  210. The OBI Consortium: (2007) The OBO Foundry: coordinated evolution of ontologies to support biomedical data integration. Nature Biotechnol 25: 1251–1255Google Scholar
  211. Snippert H et al (2010) Intestinal crypt homeostasis results from neutral competition between symmetrically dividing lgr5 stem cells. Cell 143: 134–144Google Scholar
  212. Springer W, Barondes S (1978) Direct measurement of species specific cohesion in cellular slime molds. J Cell Biol 79: 937–942Google Scholar
  213. Steimberg M, Garrod D (1975) Observations on the sorting-out of embryonic cells in monolayer culture. J Cell Sci 18: 385–403Google Scholar
  214. Stein L (2004) Reactome site. http://www.reactome.org
  215. Steinberg M (1962) On the mechanism of tissue reconstruction by dissociated cells. i population kinetics, differential adhesiveness, and the absence of directed migration. Proc Natl Acad Sci USA 48: 1577–1582Google Scholar
  216. Sternfeld J (1979) Evidence for differential cellular adhesion as the mechanism of sorting out of various slime mold species. J Embryol Exp Morphol 53: 163–177Google Scholar
  217. Sulsky D, Childress S, Percus JK (1984) A model of cell sorting. J Theor Biol 106(3): 275–301 doi: 10.1016/0022-5193(84)90031-6 Google Scholar
  218. Takeuchi I, Kakutani T, Tasaka M (1988) Cell behavior during formation of prestalk/prespore pattern in submerged agglomerates of dictyostelium discoideum. Dev Genet 9: 607–614Google Scholar
  219. Takeuchi I, Tasaka M (1989) Formation of differentiation pattern in dictyostelium discoideum. Genome 31: 620–624Google Scholar
  220. Talmadge J, Fidler I (2010) Aacr centennial series: the biology of cancer metastasis: historical perspective. Cancer Res 70: 5649–5669Google Scholar
  221. Technau U, Holstein T (1992) Cell sorting during the regeneration of hydra from reaggregated cells. Dev Biol 151: 117–127Google Scholar
  222. Tepass U, Godt D, Winklbauer R (2002) Cell sorting in animal development: signalling and adhesive mechanisms in the formation of tissue boundaries. Curr Opin Genet Dev 12: 572–582Google Scholar
  223. The Cancer Genome Atlas. http://cancergenome.nih.gov/
  224. Thibodeau S, Bren G, Schaid D (1993) Microsatellite instability in cancer of the proximal colon. Science 260: 816–819Google Scholar
  225. Thirlwell C et al (2010) Clonality assessment and clonal ordering of individual neoplastic crypts shows polyclonality of colorectal adenomas. Gastroenterology 138: 1441–1454Google Scholar
  226. Thomas W, Yancey J (1988) Can retinal adhesion mechanisms determine cell-sorting patterns: a test of the differential adhesion hypothesis. Development 103: 37–48Google Scholar
  227. Toyota M et al (1999) Cpg island methylator phenotype in colorectal cancer. PNAS 96: 8681–8686Google Scholar
  228. Tsubouchi S (1983) Theoretical implications for cell migration through the crypt and the villus of labeling studies conducted at each position within the crypt. Cell Tissue Kinet 16: 441–456Google Scholar
  229. Turner S, Sherratt JA (2002) Intercellular adhesion and cancer invasion: a discrete simulation using the extended potts model. J Theor Biol 216(1): 85–100 doi: 10.1006/jtbi.2001.2522 MathSciNetGoogle Scholar
  230. Vajdic C, Leeuwen M (2009) Cancer incidence and risk factors after solid organ transplantation. Int J Cancer 125: 1747–1754Google Scholar
  231. van de Wetering M, Sancho E, Verweij C, de Lau W, Oving I et al (2002) The beta-catenin/tcf-4 complex imposes a crypt progenitor phenotype on colorectal cancer cells. Cell 111: 241–250Google Scholar
  232. van der Flier L et al (2009) Transcription factor achaete scute-like 2 constrol intestinal stem cell fate. Cell 136: 903–912Google Scholar
  233. van der Flier L, Clevers H (2009) Stem cells, self-renewal, and differentiation in the intestinal epithelium. Annu Rev Physiol 71: 241–260Google Scholar
  234. van Es J et al (2005) Notch/gamma-secretase inhibition turns proliferative cells in intestinal crypts and adenomas into goblet cells. Nature 435: 959–963Google Scholar
  235. van Es J, Jay P, Gregorieff A, van Gijn M, Jonkheer S, Hatzis P et al (2005) Wnt signaling induces maturation of paneth cells in intestinal crypt. Nat Cell Biol 7: 381–386Google Scholar
  236. van Es JH, van Gijn ME, Riccio OMv, Vooijs M, Begthel H, Cozijnsen M, Robine S, Winton DJ, Radtke F, Clevers H (2005) Notch/γ-secretase inhibition turns proliferative cells in intestinal crypts and adenomas into goblet cells. Nature 435: 959–963 doi: 10.1038/nature03659 Google Scholar
  237. van Leeuwen IM, Byrne HM, Jensen OE, King JR (2007) Elucidating the interactions between the adhesive and transcriptional functions of [beta]-catenin in normal and cancerous cells. J Theor Biol 247(1): 77–102 doi: 10.1016/j.jtbi.2007.01.019 Google Scholar
  238. van Leeuwen IMM, Byrne HM, Jensen OE, King JR (2006) Crypt dynamics and colorectal cancer: advances in mathematical modelling. Cell Prolif 39(3): 157–181 doi: 10.1111/j.1365-2184.2006.00378.x Google Scholar
  239. Villani M, Barbieri A, Serra R (2011) A dynamical model of genetic networks for cell differentiation. PLoS ONE 6(3): e17703 doi: 10.1371/journal.pone.0017703 Google Scholar
  240. Wagner A (2002) Estimating coarse gene network structure from large-scale gene gene perturbation data. Genome Res 12: 309–315Google Scholar
  241. Walker D, Southgate J, Hill G, Holcombe M, Hose D, Wood S, Mac Neil S, Smallwood R (2004) The epitheliome: agent-based modelling of the social behaviour of cells. Biosystems 76(1-3): 89–100 doi: 10.1016/j.biosystems.2004.05.025 Google Scholar
  242. Wang B (2011) Cancer cells exploit the eph-ephrin system to promote invasion and metastasis: tales of unwitting partners. Sci Signal 4(175): 128Google Scholar
  243. Wang M, Schaap P (1989) Ammonia depletion and dif trigger stalk cell differentiation in intact dictyostelium discoideum slugs. Development 105: 569–574Google Scholar
  244. Wehrle J et al (2000) Metabolism of alternative substrates and the bioenergetic status of emt6 tumor cell spheroids. NMR Biomed 13: 349–360Google Scholar
  245. Wilkinson DG (2003) Multiple roles of eph receptors and ephrins in neural development. Nat Rev Neurosci 2: 155–164Google Scholar
  246. Winton D, Ponder B (1990) Stem-cell organization in mouse small intestine. Proc Biol Sci 241: 13–18Google Scholar
  247. Winton DJ, Blount M, Ponder B (1988) A clonal marker induced by mutation in mouse intestinal epithelium. Nature 333: 463–466Google Scholar
  248. Witsch E, Sela M, Yarden Y (2010) Roles for growth factors in cancer progression. Physiology (Bethesda) 25: 85–101Google Scholar
  249. Wodarz A (1998) Mechanisms of wnt signaling in development. Annu Rev Cell Dev Biol 14: 59–88Google Scholar
  250. Wodarz D, Komarova N (2005) Computational biology of cancer: lecture notes and mathematical modeling. World Scientific Publishing, HackensackMATHGoogle Scholar
  251. Wong MH (2004) Regulation of intestinal stem cells. J Invest Dermatol Symp Proc 9: 224–228Google Scholar
  252. Wong SY, Chiam KH, Lim CT, Matsudaira P (2010) Computational model of cell positioning: directed and collective migration in the intestinal crypt epithelium. J R Soc Interf 7(Suppl 3): S351–S363. doi: 10.1098/rsif.2010.0018.focus Google Scholar
  253. Wright N, Alison M (1984) The biology of epithelial cell populations. Clarendon Press, OxfordGoogle Scholar
  254. Xu Q, Mellitzer G, Robinson V, Wilkinson D (1999) In vivo cell sorting in complementary segmental domains mediated by eph receptors and ephrins. Nature 399: 267–271Google Scholar
  255. Yen T, Wright N (2006) The gastrointestinal tract stem cell niche. Stem Cell Rev 2: 203–212Google Scholar
  256. Zheng X, Wise S, Cristini V (2005) Nonlinear simlation of tumor necrosis, neo-vascularization and tissue invasion via an adaptive finite-element/level-set method. Bull Math Biol 67: 211–259MathSciNetGoogle Scholar
  257. Zimmerman W, Weijer C (1993) Analysis of cell cycle progression during the development of dictyostelium and its relationship to differentiation. Dev Biol 160: 178–185Google Scholar
  258. Zipori D (2004) The nature of stem cells: state rather than entity. Nat Rev Genet 5: 873–878Google Scholar
  259. Zou J, Wang B, Kalo M, Zisch A, Pasquale E, Ruoslahti E (1999) An eph receptor regulates integrin activity through r-ras. Proc Natl Acad Sci 96: 13813–13818Google Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  • Giovanni De Matteis
    • 1
  • Alex Graudenzi
    • 2
  • Marco Antoniotti
    • 2
  1. 1.Department of Mathematics “F. Enriques”University of MilanMilanItaly
  2. 2.Department of Informatics, Systems and CommunicationUniversity of Milan BicoccaMilanItaly

Personalised recommendations