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MULTISCALE MODELLING OF
COLONIC CRYPTS AND
EARLY COLORECTAL
CANCER
Helen Byrne
Computational Biology Group, Computer Science
and OCCAM
[email protected]
Oxford, January 2012
OUTLINE
•
Motivation
• Subcellular model of Wnt signalling
• Multiscale modelling of CRC
• Continuum modelling
• Discussion
MOTIVATION
Why CRC?
Prevalence
1.
2.
3.
4.
5.
Lung:
Breast:
Colon:
Stomach:
Prostate:
incidence
mortality
1 238 000
1 050 000
943 000
875 000
542 000
1 102
372
491
646
204
000
000
000
000
000
Worldwide each year
NORMAL COLON
Colorectal crypts
Paul Appleton, Dundee
•
•
•
Crypts of Lieberkühn in the small intestine
Limited number of cells (~700)
Human crypts self-renew every 5-7 days
NORMAL COLON
Absorptive
columnar cell
Mucinous
Goblet cell
Why model CRC?
Well-characterised sequence of mutations
APC
Normal
epithelium
Hypomethylation
Hyperproliferative
epithelium
Early
adenoma
K-RAS
Intermediate
adenoma
Fearon and Vogelstein (1990)
“A genetic model for colorectal carcinogenesis”
Cell 61, 759-767
DCC?
Late
adenoma
p53
Other
alterations
Carcinoma
Metastasis
Note: progression to
cancer is not unique!
GENETIC ALTERATIONS
What should we model?
COLORECTAL CANCER
Normal tissue
Polyp formation
Deformation
Fission & budding
Adenocarcinoma
What should we model?
NORMAL CRYPT RENEWAL CYCLE
5
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)
How are these processes coordinated?
3
4
2
1
WNT SIGNALLING
Co-ordination of cell proliferation, migration and differentiation:
WNT SIGNALLING
Response to Wnt signalling is
mediated by b-catenin and APC
MUTATIONS IN THE WNT PATHWAY
• 12% of CRCs have
a mutation in βcatenin mutation,
rendering β-catenin
insensitive to APC
complex
• 80% have a double
APC mutation,
rendering APC
complex ineffective
Mutations in Wnt pathway
early event in CRC
APC
Normal
epithelium
Hypomethylation
Hyperproliferative
epithelium
Early
adenoma
K-RAS
Intermediate
adenoma
Initial ODE models of Wnt pathway
focus on b-catenin’s role in
regulating production of target genes
(Lee et al, PLoS Biology, 2003)
DCC?
p53
Late
adenoma
Other
alterations
Carcinoma
Metastasis
APC mutation 
hyperproliferation and abnormal
crypt morphology
Simple model developed by Lee et al (2003)
What level of detail?
focuses on
rolesSIGNALLING
of Wnt and b-catenin in
WNT
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
Trends in Cell Biology 15, 2005
Current Biology 15, 2005
Science 303, 2004
WNT SIGNALLING
ADHESION
“Off” State
β-catenin
WNT-STIMULUS
APC-complex
DEGRADATION
TRANSCRIPTION
cell-cell
adhesion
complexes
β-catenin
degradation
WNT SIGNALLING
ADHESION
“On” State
WNT-STIMULUS
?
β-catenin
cell-cell
adhesion
complexes
DEGRADATION
TRANSCRIPTION
β-catenin-TCF
complexes
Expression of
target genes
HYPOTHESIS-I
(purely competitive scenario)
APC
complex
β-catenin
β-catenin
TCF
β-catenin
Expression of
target gene
Y
β-catenin
cadherin
Van Leeuwen et al (2007) J Theor Biol 247: 77-102
HYPOTHESIS-II
(two molecular forms of β-catenin)
TCF
APC
complex
β-catenin
β-catenin
Wnt
β-catenin
β-catenin
TCF
β-catenin
Expression of
target gene
Y
β-catenin
cadherin
Van Leeuwen et al (2007) J Theor Biol 247: 77-102
MODEL EQUATIONS
Wnt-dependent terms
highlighted
RESULTS 1
Effect of Wnt stimulation on gene expression
Hypothesis II
Hypothesis I
(=32 hours)
Build ODE model that combines
both hypotheses
Model Prediction: not possible to
discriminate between hypotheses
by measuring transcription levels
RESULTS 2
Effect of Wnt stimulation on cell-cell adhesion
Hypothesis I
Model Prediction: may be possible to discriminate
between hypotheses by measuring adhesion complexes
Which model of Wnt signalling?
Intracellular localisation of b-catenin
Generating
testable
predictions
Hypothesis I: pure competition
between nucleus and membrane
• At crypt base high levels of
nuclear and membrane-bound bcatenin
•
Hypothesis II: bias towards
nucleus
• At crypt base, b-catenin
concentrated in nucleus
•
Van Leeuwen et al, J theor Biol, 247 (2007)
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)
(133 hours)
MULTISCALE MODELLING
OF COLORECTAL CANCER
NORMAL CRYPT RENEWAL CYCLE
5
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
3
4. Progeny differentiates
(midcrypt region)
5. Senile cells are removed from the surface
(midpoint between crypts)
Above processes coordinated by Wnt signalling
4
2
1
Modelling CRC:
MULTISCALE MODEL FRAMEWORK
Multiscale Model Framework:
MECHANICAL MODEL (CELL SCALE)
© Gary Mirams, Nottingham
Meineke et al. (2001) Cell Prolif 34: 253-266
Multiscale Model Framework
Mechanical Model
Fi(t) = ∑j kij [|ri(t) – rj(t)| – sij(t)] uij(t),
ri(t + Δ t) = ri(t) + Fi(t) Δ t / ηi .
where
ηi = drag coefficient of cell i
kij = spring constant between
cells i and j
Note: cell mechanics coupled to subcellular
dynamics through drag and spring coefficients
Meineke et al (2001)
van Leeuwen et al (2009)
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
Normal cells only
Normal and mutant cells
HEALTHY CRYPTS:
ARE THEY MONOCLONAL?
Monoclonal conversion
Are the stem cells pinned at the bottom of the crypt?
Pinned stem cells
(Meineke et al, 2001)
Unpinned stem cells
(van Leeuwen et al, 2009)
Evidence for Monoclonal Crypts
• Greaves et al (2006) PNAS 103: 714-719
• Taylor et al (2003) J Clin Invest 112: 1351-1360
Role of of geometry:
Cylindrical vs projection
Colorectal crypts
Monoclonal conversion
Osborne et al (in prep)
EARLY CRC (LOSS OF APC):
TOP-DOWN vs BOTTOM-UP?
EXPANSION OF MUTANT CELLS
(LOSS OF APC )
• Wnt gradient
along crypt axis
• Mutant cells
identical to
normals, except
Wnt pathway
always activated
• Mutant cells
washed out
EXPANSION OF MUTANT CELLS
(LOSS OF APC )
• Mutant cells: Wnt
on & stronger cellsubstrate drag
• Mutant cells
persist
• Consistent with
‘bottom-up’ theory
Invasion of mutant cells:
‘Bottom-Up’ or ‘Top-Down’?
• Mutant cells:
Wnt
on & stronger drag
• Mutant cells
persist & migrate
downwards
• Supports ‘topdown’ invasion
Invasion of mutant cells:
‘Bottom-Up’ or ‘Top-Down’?
Note: many
simulations to
determine
probability that
mutant cells
persist
CONTINUUM MODELLING
Continuum Model
Key parameters:
D – Relative viscosity
k – Gross proliferation
λ1 – Wnt dependence
• 0 < D < 1  mutant
cells more sticky or
adherent than normal cells
• mutant cells proliferate
independent of Wnt
44
Continuum model results
D=1.0
D=0.2
45
Continuum model results
Note: More timeconsuming to
generate
equivalent figures
for cell-based
models
Note: Difficult to
determine
whether crypt
monoclonal using
continuum model
and to account
for subcellular
46
effects
CONCLUSIONS
CONCLUSIONS AND DISCUSSION
• Wnt signalling: subcellular level
• Competing roles of b-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
INTERACTIONS WITH THE STROMA
Basement membrane separates layer of
proliferating epithelial cells from tissue stroma
Sara-Jane Dunn
Multiscale Modelling: Future Work
Absorptive columnar
and mucinous cells
Crypt fission
• Model validation (in vitro, in vivo)
• Distinguish different cell types
• Crypt fission
Polyp formation
ACKNOWLEDGEMENTS:
Oxford
Nottingham
Sara-Jane Dunn
Alex Fletcher
Oliver Jensen
David Gavaghan
John King
Matthew Johnston
Ingeborg van Leeuwen
Sophie Kershaw
Gary Mirams
Philip Maini
Alex Walter
Philip Murray
James Osborne
Pras Pathmanathan
Joe Pitt-Francis
Jonathan Whiteley
Dimensionless Equations