1. Helen Byrne Computational Biology Group, Computer Science and OCCAM Helen.Byrne@maths.ac.uk Oxford, January 2012 MULTISCALE MODELLING OF COLONIC CRYPTS AND EARLY COLORECTAL CANCER

2. OUTLINE Motivation Subcellular model of Wnt signalling Multiscale modelling of CRC Continuum modelling Discussion

3. MOTIVATION

4. 1.Lung: 2.Breast: 3.Colon: 4.Stomach: 5.Prostate: 1 238 000 1 050 000 943 000 875 000 542 000 1 102 000 372 000 491 000 646 000 204 000 incidence mortality Worldwide each year Why CRC? Prevalence

5. NORMAL COLON

6. Crypts of Lieberkühn in the small intestine Limited number of cells (~700) Human crypts self-renew every 5-7 days Paul Appleton, Dundee Colorectal crypts

7. Absorptive columnar cell Mucinous Goblet cell NORMAL COLON

8. Why model CRC? Well-characterised sequence of mutations Fearon and Vogelstein (1990) “A genetic model for colorectal carcinogenesis” Cell 61, 759-767 Normal epithelium Late adenoma Hyper- proliferative epithelium Carcinoma Intermediate adenoma Early adenoma Metastasis APCK-RASDCC?Hypomethylationp53 Other alterations Note: progression to cancer is not unique!

9. GENETIC ALTERATIONS

10. Normal tissueDeformation Fission & budding Polyp formationAdenocarcinoma What should we model? COLORECTAL CANCER

11. 1. Proliferation of stem cells (bottom of crypt) 2. Progeny divides a few times (lower third of crypt) 3. Progeny starts migrating to the surface 4. Progeny differentiates (midcrypt region) 5. Senile cells are removed from the surface (midpoint between crypts) 1 5 4 2 3 What should we model? NORMAL CRYPT RENEWAL CYCLE How are these processes coordinated?

12. WNT SIGNALLING

13. Co-ordination of cell proliferation, migration and differentiation: WNT SIGNALLING Wnt factors Gene expression Proliferation Cell death Differentiation Response to Wnt signalling is mediated by -catenin and APC

14. 12% of CRCs have a mutation in β- catenin mutation, rendering β-catenin insensitive to APC complex 80% have a double APC mutation, rendering APC complex ineffective MUTATIONS IN THE WNT PATHWAY

15. Mutations in Wnt pathway early event in CRC Normal epithelium Late adenoma Hyper- proliferative epithelium Carcinoma Intermediate adenoma Early adenoma Metastasis APCK-RASDCC?Hypomethylationp53 Other alterations APC mutation  hyperproliferation and abnormal crypt morphology Initial ODE models of Wnt pathway focus on -catenin’s role in regulating production of target genes (Lee et al, PLoS Biology, 2003)

16. What level of detail? WNT SIGNALLING Simple model developed by Lee et al (2003) focuses on roles of Wnt and -catenin in regulating production of target genes … it is possible to generate many different models but it is often less obvious to know what level of detail to include

17. Trends in Cell Biology 15, 2005 Current Biology 15, 2005 Science 303, 2004

18. “Off” State β β-catenin APC-complex cell-cell adhesion complexes β β-catenin degradation TRANSCRIPTION DEGRADATION WNT-STIMULUS WNT SIGNALLING ADHESION

19. Expression of target genes β β-catenin-TCF complexes WNT SIGNALLING TRANSCRIPTION DEGRADATION WNT-STIMULUS ADHESION ? β β-catenin cell-cell adhesion complexes “On” State

20. β-catenin cadherin Expression of target gene Y APC complex β-catenin TCF HYPOTHESIS-I (purely competitive scenario) Van Leeuwen et al (2007) J Theor Biol 247: 77-102

21. β-catenin cadherin TCF Expression of target gene Y APC complex β-catenin TCF Wnt HYPOTHESIS-II (two molecular forms of β-catenin) Van Leeuwen et al (2007) J Theor Biol 247: 77-102

22. MODEL EQUATIONS Wnt-dependent terms highlighted

23. Hypothesis IHypothesis II (=32 hours) RESULTS 1 Effect of Wnt stimulation on gene expression Model Prediction: not possible to discriminate between hypotheses by measuring transcription levels Build ODE model that combines both hypotheses

24. Hypothesis I RESULTS 2 Effect of Wnt stimulation on cell-cell adhesion Model Prediction: may be possible to discriminate between hypotheses by measuring adhesion complexes

25. Hypothesis I: pure competition between nucleus and membrane At crypt base high levels of nuclear and membrane-bound - catenin Which model of Wnt signalling? Intracellular localisation of -catenin Hypothesis II: bias towards nucleus At crypt base, -catenin concentrated in nucleus Van Leeuwen et al, J theor Biol, 247 (2007) Generating testable predictions

26. (133 hours) RESULTS 4 Effect of E-cadherin upregulation (external Wnt stimulus present) Model prediction: upregulating E-cadherin increases proportion of adhesion complexes but does not affect transcription (at steady state)

27. MULTISCALE MODELLING OF COLORECTAL CANCER

28. 1. Proliferation of stem cells (bottom of crypt) 2. Progeny divides a few times (lower third of crypt) 3. Progeny starts migrating to the surface 4. Progeny differentiates (midcrypt region) 5. Senile cells are removed from the surface (midpoint between crypts) 1 5 4 2 3 NORMAL CRYPT RENEWAL CYCLE Above processes coordinated by Wnt signalling

29. Modelling CRC: MULTISCALE MODEL FRAMEWORK

30. Multiscale Model Framework: MECHANICAL MODEL (CELL SCALE) © Gary Mirams, Nottingham Meineke et al. (2001) Cell Prolif 34: 253-266

31. Multiscale Model Framework Multiscale Model Framework Mechanical Model F i (t) = ∑ j k ij [|r i (t) – r j (t)| – s ij (t)] u ij (t), r i (t + Δ t) = r i (t) + F i (t) Δ t / η i. where η i = drag coefficient of cell i k ij = spring constant between cells i and j Note: cell mechanics coupled to subcellular dynamics through drag and spring coefficients

32. Random cell-cycle time assigned to each daughter cell after division Cell cycle time determined by ODE (Wnt-dependent) cell-cycle model Differentiation occurs after fixed number of transit-cell generations Differentiation determined by extracellular Wnt gradient Cells simply “walk off” the 2D surface “Proper cell death” Movement determined by spring forces only Movement determined by spring forces and surface penalty function Meineke et al (2001) van Leeuwen et al (2009) van Leeuwen et al (2009) Normal cells only Normal and mutant cells

33. HEALTHY CRYPTS: ARE THEY MONOCLONAL?

34. Monoclonal conversion Pinned stem cells (Meineke et al, 2001) Unpinned stem cells (van Leeuwen et al, 2009) Are the stem cells pinned at the bottom of the crypt?

35. Greaves et al (2006) PNAS 103: 714-719 Taylor et al (2003) J Clin Invest 112: 1351-1360 Evidence for Monoclonal Crypts

36. Role of of geometry: Cylindrical vs projection

37. Colorectal crypts Monoclonal conversion Osborne et al (in prep)

38. EARLY CRC (LOSS OF APC): TOP-DOWN vs BOTTOM-UP?

39. Wnt gradient along crypt axis Mutant cells identical to normals, except Wnt pathway always activated Mutant cells washed out EXPANSION OF MUTANT CELLS EXPANSION OF MUTANT CELLS (LOSS OF APC )

40. Mutant cells: Wnt on & stronger cell- substrate drag Mutant cells persist Consistent with ‘bottom-up’ theory EXPANSION OF MUTANT CELLS EXPANSION OF MUTANT CELLS (LOSS OF APC )

41. Mutant cells: Wnt on & stronger drag Mutant cells persist & migrate downwards Supports ‘top- down’ invasion Invasion of mutant cells: ‘Bottom-Up’ or ‘Top-Down’?

42. Note: many simulations to determine probability that mutant cells persist

43. CONTINUUM MODELLING

44. 44 Continuum Model Key parameters: D – Relative viscosity k – Gross proliferation λ 1 – Wnt dependence 0 < D < 1  mutant cells more sticky or adherent than normal cells mutant cells proliferate independent of Wnt

45. 45 Continuum model results D=0.2 D=1.0

46. 46 Continuum model results Note: More time- consuming to generate equivalent figures for cell-based models Note: Difficult to determine whether crypt monoclonal using continuum model and to account for subcellular effects

47. CONCLUSIONS

48. CONCLUSIONS AND DISCUSSION Wnt signalling: subcellular level Competing roles of -catenin in transcription and adhesion Multiscale modelling of colonic crypts Predict conditions under which crypts become monoclonal Establish conditions under which ‘top-down’ and ‘bottom-up’ invasion may occur Use of multiscale modelling for Hypothesis testing Generating testable predictions

49. Sara-Jane Dunn INTERACTIONS WITH THE STROMA Basement membrane separates layer of proliferating epithelial cells from tissue stroma

50. Absorptive columnar and mucinous cells Multiscale Modelling: Future Work Model validation (in vitro, in vivo) Distinguish different cell types Crypt fission Polyp formation

51. ACKNOWLEDGEMENTS: Nottingham Oliver Jensen John King Ingeborg van Leeuwen Gary Mirams Alex Walter Oxford Sara-Jane Dunn Alex Fletcher David Gavaghan Matthew Johnston Sophie Kershaw Philip Maini Philip Murray James Osborne Pras Pathmanathan Joe Pitt-Francis Jonathan Whiteley

53. Dimensionless Equations