Mathematical modeling of monoclonal conversion in the colonic crypt

Journal of Theoretical Biology

Volumn 300, Issue , 2012, Pages 118-133

  Fletcher, Alexander G ^a,b   Breward, Christopher J W ^a   Jonathan Chapman, S ^a  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF OXFORD   (United Kingdom)

Author keywords

Cancer; Crypt; Monoclonal conversion; Stem cells

Indexed keywords

BIOCHEMISTRY; CANCER; COMPARATIVE STUDY; EXPERIMENTAL STUDY; HYPOTHESIS TESTING; NUMERICAL MODEL; POPULATION MODELING; SIGNALING; STOCHASTICITY;

ARTICLE; CELL DIVISION; CELL MIGRATION; CELL MOTION; CELL POPULATION; CELL PROLIFERATION; CELL STRUCTURE; CELLULAR, SUBCELLULAR AND MOLECULAR BIOLOGICAL PHENOMENA AND FUNCTIONS; CONTROLLED STUDY; CRYPT CELL; HYPOTHESIS; IMMORTAL STEM CELL HYPOTHESIS; MATHEMATICAL MODEL; MONOCLONAL CONVERSION; PRIORITY JOURNAL; SIMULATION; STEM CELL; STEM CELL NICHE HYPOTHESIS; STOCHASTIC MODEL;

CELL CYCLE; CELL DIVISION; CELL MOVEMENT; CELL TRANSFORMATION, NEOPLASTIC; COLON; COLORECTAL NEOPLASMS; HUMANS; INTESTINAL MUCOSA; MODELS, BIOLOGICAL; NEOPLASTIC STEM CELLS; STOCHASTIC PROCESSES;

EID: 84856427171     PISSN: 00225193     EISSN: 10958541     Source Type: Journal    
DOI: 10.1016/j.jtbi.2012.01.021     Document Type: Article

References (53)

1. Alberts B., Johnson A., Lewis J., Raff M., Roberts K., Walter P. Molecular Biology of the Cell 2002, Garland Science. fourth ed.
2. Barker N., van Es J., Kuipers J., Kujala P., van den Born M., Cozijnsen M., Haegebarth A., Korving J., Begthel H., Peters P., Clevers H. Identification of stem cells in small intestine and colon by marker gene Lgr5. Nature 2007, 449:1003-1007.
3. Boman B.M., Fields J.Z., Bonham-Carter O., Runquist O.A. Computer modeling implicates stem cell overproduction in colon cancer initiation. Cancer Res. 2001, 61:8408-8411.
4. Brittan M., Wright N. Gastrointestinal stem cells. J. Pathol. 2002, 197:492-509.
5. Brittan M., Wright N. Stem cell in gastrointestinal structure and neoplastic development. Gut 2004, 53:899-910.
6. Cancer Research UK, 〈〉, 2010. http://info.cancerresearchuk.org/.
7. Cook H., Williams D., Thomas G. Crypt-restricted metallothionein immunopositivity in murine colon: validation of a model for studies of somatic stem cell mutation. J. Pathol. 2000, 191:306-312.
8. Dingli D., Traulsen A., Michor F. (A)symmetric stem cell replication and cancer. PLOS Comput. Biol. 2007, 3:482-487.
9. Drasdo D., Loeffler M. Individual-based models on growth and folding in one-layered tissues: intestinal crypts and early development. Nonlinear Anal. 2001, 47:245-256.
10. Drazin P. Nonlinear Systems 1992, Cambridge University Press.
11. Gaspar C., Fodde R. APC dosage effects in tumorigenesis and stem cell differentiation. Int. J. Dev. Biol. 2004, 48:377-386.
12. Giles R., van Es J., Clevers H. Caught up in a Wnt storm: Wnt signaling in cancer. Biochim. Biophys. Acta 2003, 1653:1-24.
13. Greaves L., Preston S., Tadrous P., Taylor R., Barron M., Oukrif D., Leedham S., Deheragoda M., Sasieni P., Novelli M., Jankowski J., Turnbull D., Wright N., McDonald S. Mitochondrial DNA mutations are established in human colonic stem cells, and mutated clones expand by crypt fission. Proc. Natl. Acad. Sci. USA 2006, 103:714-719.
14. Grimmett G., Stirzaker D. Probability and Random Processes 1992, Oxford University Press. second ed.
15. Halm D., Halm S. Secretagogue response of goblet cells and columnar cells in human colonic crypts. Am. J. Physiol. Cell Physiol. 2000, 278:212-233.
16. Ilyas M. Wnt signalling and the mechanistic basis of tumour development. J. Pathol. 2005, 205:130-144.
17. Johnston M., Edwards C., Bodmer W., Maini P., Chapman S. Mathematical modeling of cell population dynamics in the colonic crypt and in colorectal cancer. Proc. Natl. Acad. Sci. USA 2007, 104:4008-4013.
18. Kim K., Shibata D. Methylation reveals a niche: stem cell succession in human colon crypts. Oncogene 2002, 21:5441-5449.
19. Korinek V., Barker N., Moerer P., van Donselaar E., Huls G., Peters P., Clevers H. Depletion of epithelial stem-cell compartments in the small intestine of mice lacking Tcf-4. Nat. Genet. 1998, 19:379-383.
20. Lechler T., Fuchs E. Asymmetric cell divisions promote stratification and differentiation of mammalian skin. Nature 2005, 437:275-280.
21. Li Y.Q., Roberts S.A., Paulus U., Loeffler M., Potten C.S. The crypt cycle in mouse small intestinal epithelium. J. Cell Sci. 1994, 107:3271-3279.
22. Loeffler M., Grossmann B. A stochastic branching model with formation of subunits applied to the growth of intestinal crypts. J. Theor. Biol. 1991, 150:175-191.
23. Loeffler M., Stein R., Wichmann H.E., Potten C.S., Kaur P., Chwalinski S. Intestinal crypt proliferation. I. A comprehensive model of steady-state proliferation in the crypt. Cell Tissue Kinet. 1986, 19:627-645.
24. Loeffler M., Birke A., Pottern C. Somatic mutation, monoclonality and stochastic models of stem cell organization in the intestinal crypt. J. Theor. Biol. 1993, 160:471-491.
25. Loeffler M., Bratke T., Paulus U., Li Y.Q., Potten C.S. Clonality and life cycles of intestinal crypts explained by a state dependent stochastic model of epithelial stem cell organization. J. Theor. Biol. 1997, 186:41-54.
26. Marshman E., Booth C., Potten C. The intestinal epithelial stem cell. BioEssays 2002, 24:91-98.
27. McDonald S., Preston S., Greaves L., Leedham S., Lovell M., Jankowski J., Turnbull D., Wright N. Clonal expansion in the human gut: mitochondrial DNA mutations show us the way. Cell Cycle 2006, 5:808-811.
28. Meineke F., Potten C., Loeffler M. Cell migration and organization in the intestinal crypt using a lattice-free model. Cell Prolif. 2001, 34:253-266.
29. Norris J. Markov Chains 1997, Cambridge University Press.
30. Nowak M., Komarova N., Sengupta A., Jallepalli P., Shih I.-M., Vogelstein B., Langauer C. The role of chromosomal instability in tumor initiation. Proc. Natl. Acad. Sci. USA 2002, 99:16226-16231.
31. Okamoto R., Watanabe M. Molecular and clinical basis for the regeneration of human gastrointestinal epithelia. J. Gastroenterol. 2004, 39:1-6.
32. Park H., Goodlad R., Wright N. Crypt fission in the small intestine and colon. A mechanism for the emergence of G6PD locus-mutated crypts after treatment with mutagens. Am. J. Pathol. 1995, 147:1416-1427.
33. Paulus U., Potten C., Loeffler M. A model of the control of cellular regeneration in the intestinal crypt after perturbation based solely on local stem cell regulation. Cell Prolif. 1992, 25:559-578.
34. Pitt-Francis J., Pathmanathan P., Bernabeu M., Bordas R., Cooper J., Fletcher A., Mirams G., Murray P., Osborne J., Walter A., Chapman S., Garny A., van Leeuwen I., Maini P., Rodriguez B., Waters S., Whiteley J., Byrne H., Gavaghan D. Chaste: a test-driven approach to software development for biological modelling. Comput. Phys. Commun. 2009, 180:2452-2471.
35. Potten C.S., Loeffler M. Stem cells: attributes, cycles, spirals, pitfalls and uncertainties. Lessons from the crypt. Development 1990, 110:1001-1020.
36. Potten C.S., Booth C., Hargreaves D. The small intestine as a model for evaluating adult tissue stem cell drug targets. Cell Prolif. 2003, 36:115-129.
37. Preston S., Wong W., Chan A., Poulsom R., Jeffrey R., Goodlad R., Mandir N., Elia G., Novelli M., Bodmer W., Tomlinson I., Wright N. Bottom-up histogenesis of colorectal adenomas: origin in the monocryptal adenoma and initial expansion by crypt fission. Cancer Res. 2003, 63:3819-3825.
38. Reya T., Morrison S., Clarke M., Weissman I. Stem cells, cancer, and cancer stem cells. Nature 2001, 414:105-111.
39. Ro S., Rannala B. Methylation patterns and mathematical models reveal dynamics of stem cell turnover in the human colon. Proc. Natl. Acad. Sci. USA 2001, 98:10519-10521.
40. Roeder I., Lorenz R. Asymmetry of stem cell fate and the potential impact of the niche: observations, simulations, and interpretations. Stem Cell Rev. 2006, 2:171-180.
41. Ross M., Kaye G., Pawlina W. Histology: A Text and Atlas 2003, Lippincott Williams & Wilkins.
42. Sansom O., Reed K., Hayes A., Ireland H., Brinkmann H., Newton I., Batlle E., Simon-Assman P., Clevers H., Nathke I., Clarke A., Winton D. Loss of Apc in vivo immediately perturbs Wnt signaling, differentiation, and migration. Genes Dev. 2004, 18:1385-1390.
43. Schofield R. The relationship between the spleen colony-forming cell and the haemopoietic stem cell. Blood Cells 1978, 4:7-25.
44. Spradling A., Drummond-Barboa D., Kai T. Stem cells find their niche. Nature 2001, 414:98-104.
45. Tyson J., Chen K., Novák B. Network dynamics and cell physiology. Nat. Rev. Mol. Cell Biol. 2001, 2:908-916.
46. Tyson J., Csikász-Nagy A., Novák B. The dynamics of cell cycle regulation. BioEssays 2002, 24:1095-1109.
47. van de Wetering M., Sancho E., Verweij C., de Lau W., Oving I., Hurlstone A., van der Horn K., Batlle E., Coudreuse D., Haramis A., Tjon-Pon-Fong M., Moerer P., van den Born M., Soete G., Pals S., Eilers M., Medema R., Clevers H. The Β-catenin/TCF-4 complex imposes a crypt progenitor phenotype on colorectal cancer cells. Cell 2002, 111:241-250.
48. van Leeuwen I., Mirams G., Walter A., Fletcher A., Murray P., Osborne J., Varma S., Young S., Cooper J., Doyle B., Pitt-Francis J., Momtahan L., Pathmanathan P., Whiteley J., Chapman S., Gavaghan D., Jensen O., King J., Maini P., Waters S., Byrne H. An integrative computational model for intestinal tissue renewal. Cell Prolif. 2009, 42:617-636.
49. Williams E., Lowes A., Williams D., Williams G. A stem cell niche theory of intestinal crypt maintenance based on a study of somatic mutation in colonic mucosa. Am. J. Pathol. 1992, 141:773-776.
50. Winton D., Ponder B. Stem-cell organization in mouse small intestine. Proc. R. Soc. Lond. B 1990, 241:13-18.
51. Winton D., Blount M., Ponder B. A clonal marker induced by mutation in mouse intestinal epithelium. Nature 1988, 333:463-466.
52. World Health Organization, 〈〉, 2008. http://www.who.int/topics/ageing/en.
53. Yatabe Y., Tavaré S., Shibata D. Investigating stem cells in human colon by using methylation patterns. Proc. Natl. Acad. Sci. USA 2001, 98:10839-10844.