Extracellular Matrix Based
Regulation of a Cytokine
Gradient at the Growth Plate
Jonathan Behr
David Berry
BEH.400J Project Presentation
Diastrophic Dysplasia
Hereditary Multiple
Exostoses
Outline


Goals
Introduction



Methods





GAG interaction with cytokines
Model system: Long bone growth
Model formulation
Model implementation
Results
Proposed experiments to test model
Conclusions
Project Goals

Quantitate how the physiochemical nature of the
extracellular matrix modulates FGF2 signaling




FGF2 must be localized to differentially signal for
angiogenesis, chondrogenesis and osteogenesis
Heparan sulfate glycosaminoglycans (HSGAGs) bind
FGF2
This process is important in development, and
errors therein can lead to a wide range of
abnormalities
An understanding of this system has applications
in treating these pathologies and in tissue
engineering
GAG Interaction with cytokines

HSGAG are one of several components of the
ECM.



HSGAG consist of a proteoglycan core and a
sugar chain with repeating units of a uronic
acid (glucuronic or iduronic with possible 2-O
sulfation) linked 1→4 to a glucosamine (with
possible 3,6, and N sulfation).
Variety in sequence and composition allows
for many potential interactions.
Roles of HSGAG in the ECM



Reservoir for proteins, preventing
degradation.
Impediment to diffusion. Non-specific binding
from high charge density
Co-factor for growth factor signaling by
facilitating ligand dimerization and/or
presentation to receptors.
Maeder, Scientific American
Model System: The Growth Plate
In endochondral ossification, the formation of calcified bone is
separated from mesenchymal condensation by the development of a
Resting Chondrocytes
cartilage anlage that regulates bone growth
Proliferating
Chondrocytes
Prehypertrophic
Chondrocytes
Hypertrophic
Chondrocytes
Trabecular Bone
Human
Humancartilage
cartilageduring
duringendochondrial
endochondrialossification
ossification
stained
stained
with H&E
with H&E
and alcian
and alcian
blue at
blue
40x
atmagnification.
120x
magnification.
(Wheater’s
(Wheater’s
Functional
Functional
Histology)
Histology)
Model System: The Growth Plate
FGF2 is secreted by the terminal hypertrophic chondrocytes and
acts on the proliferating chondrocytes, inhibiting their proliferation
and inducing their differentiation (Ornitz and Marie)
Assumptions: Geometry

Cylindrical geometry, radial symmetry



radial dimension >> z direction
Model as 1-D problem in z
Isotropic environment in hypertrophic zone
Assumptions: Equations

Boundary conditions

Angiogenic side boundary: Constant influx
of bFGF




Match so with base parameters,
5ng/ml [bFGF] at source at steady state
Proliferating cartilage side: [bFGF]
x(∞) = 0
Total receptor number at the cell
surface is constant
Rate constant for internalization of
complexes is constant
Model Cartoon
H
H
H
H H H
H
H
H
H
H
H
H
5ng/ml base
H
H
H
H
H
H
H
bFGF
Modified from Lander et al. (2002)
Model Equations
L  [bFGF]
LR  [bFGF  FGFR]
LH  [bFGF  HSGAG]
R tot  [FGFR]  [bFGF  FGFR]
H tot  [HSGAG]  [bFGF  HSGAG]
dL
d 2L
r
r
h
h
 D 2  kon
L( Rtot  LR)  koff
LR  kdeg L  kon
L( H tot  LH )  koff
LH
dt
dx
dLR
r
r
 kon
L( Rtot  LR)  koff
LR  kint LR
dt
dLH
h
h
 kon
L( H tot  LH )  koff
LH
dt
A  [bFGF]/R tot
B  [bFGF  FGFR]/R tot
H  [bFGF  HSGAG] / H tot
Implementation
1.
2.
3.
Built-in MATLAB BVP and PDE solvers failed
Created system of ODEs by discretizing space,
using central finite difference method on PDE
Solved system dynamically by using MATLAB
implicit variable order ODE solver ode15s
Base Parameters from Literature
Parameter
Value
Description
Deff
0.5e-8 m2/s
Effective diffusivity in the ECM
F0
5 ng/ml (0.278 nM)
S.S. concentration of bFGF at “source”
Htot
13 uM
Number density of HS binding sites (ECM and cell surface)
Rcell
1480
Number of FGFR per cell
rcell
10 um
Cell radius
L
7 cell diameters
Distance between bFGF source and proliferating chondrocytes
kdeg
3.5e-5 /s
Rate constant for degradation of free bFGF
kint
2e-4 /s
Rate constant for consumption of bFGF due to receptor complex mediated
internalization
konh
4.2e5 /(M*s)
On rate for bFGF·HS complex formation
koffh
0.01 /s
Off rate for bFGF·HS complex formation
konr
1.36e10 /(M*s)
On rate for bFGF·FGFR complex formation
koffr
0.18 /s
Off rate for bFGF·FGFR complex formation
ε
0.2
Volume fraction ECM
v
4.8e-013 M/s
In-flux of bFGF at angiogenic boundary
Presentation of Results




Distance where concentration threshold
(1 ng/ml) is crossed
Distance where receptor occupancy is less
than 10% (B<0.1)
Time to 80% of steady state [bFGF] at x=0
Phase plots relating results to “normal”
physiology
Base Case Results, 3D
Base Case: Ass0 = 2.9635e-010 M Threshold A at x = 51.4286 m 80% S.S. at t = 43 days
-10
x 10
[bFGF]
2
1
[bFGF*FGFR]/rtot
0
0
50
100
150
200
m
250
300
7
6
5
4
2
1
0
3
2
1
0
3
2
1
0
3
Threshold B at x = 108.5714 mtime (days)
1
0.5
0
0
50
100
150
-3
250
300
7
6
5
4
time (days)
m
x 10
[bFGF*HS]/htot
200
6
4
2
0
0
50
100
150
200
250
300
7
6
5
4
time (days)
Base Case Results, 2D
Base Case: Ass0 = 2.9635e-010 M Threshold A at x = 51.4286 m 80% S.S. at t = 43 days
-10
x 10
2
1.5
1
0.5
0
0
50
100
150
200
250
150
200
250
150
200
250
[bFGF*FGFR]/rtot
Threshold B at x = 108.5714 m
0.8
0.6
Increasing Time
0.4
0.2
0
0
50
100
0
50
100
0.012
[bFGF*HS]/htot
Concentrations
[bFGF]
2.5
0.01
0.008
0.006
0.004
0.002
0
m
Distance
Example of Faster Kinetics
[bFGF] Profiles For 10*base kdeg: Threshold A at x = 5.7143 m 80% S.S. at t = 5 days
-11
x 10
7
[bFGF]
6
5
4
3
2
1
0
0
50
100
150
200
250
150
200
250
150
200
250
[bFGF*FGFR]/rtot
Threshold B at x = 62.8571 m
0.8
0.6
0.4
0.2
0
0
50
100
50
100
-3
x 10
[bFGF*HS]/htot
3
2.5
2
1.5
1
0.5
0
0
m
Example of Longer Gradient
[bFGF]
Profiles For 10% base kdeg: Threshold A at x = 148.5714 m 80% S.S. at t = 554 days
x 10
-10
12
[bFGF]
10
8
6
4
2
0
0
50
100
150
200
250
150
200
250
150
200
250
[bFGF*FGFR]/rtot
Threshold B at x = 205.7143 m
0.8
0.6
0.4
0.2
0
0
50
100
0
50
100
[bFGF*HS]/htot
0.05
0.04
0.03
0.02
0.01
0
m
Example of Unstable Gradient
-8
x 10
[bFGF] Profiles For 10*v/rtot: Threshold Met At x = 280 m 80% S.S. at t = 34 days
[bFGF]
4
3
2
1
0
0
50
100
150
200
250
150
200
250
150
200
250
[bFGF*FGFR]/rtot
Threshold B at x = 280 m
0.8
0.6
0.4
0.2
0
0
50
100
0
50
100
[bFGF*HS]/htot
0.6
0.5
0.4
0.3
0.2
0.1
0
m
Steady State Dependence on
“External” Parameters
2
Phase Plane of Threshold Acceptability At the End of the Growth Plate
Fold Change From Base v
10
1
10
Pathological
0
10
Unnacceptable B
-1
10
Acceptable
-2
10
-2
10
-1
10
0
10
Fold Change From Base kdeg
1
10
2
10
Steady State Dependence on
“Cellular” Parameters
2
Phase Plane of Threshold Acceptability At the End of the Growth Plate
10
Fold Change From Base kint
Acceptable
1
10
Unacceptable B
0
10
-1
10
•Chondrodysplasia
punctata
•Acrocephalosyndactyly
syndrome
•Achondroplasia
Pathological
-2
10
-2
10
-1
10
0
10
Fold Change From Base Rtot
1
10
2
10
Steady State Dependence on
“ECM” Parameters
2
Phase Plane of Threshold Acceptability At the End of the Growth Plate
Fold Change From Base D
10
Pathological
1
10
Unacceptable B
0
10
Acceptable
-1
10
-2
10
-2
10
-1
10
0
10
Fold Change From Base Htot
1
10
Most Important Results!
2
10
Kinetic Dependence on
“ECM” Parameters
Plot of Time to 80% Steady State
This point takes
>10 Years!!!
4000
3500
3000
2500
2000
1500
1000
•Hereditary multiple
exostoses (HME)
•Simpson-Golabi-Behmel
syndrome (SGBS)
•Diastrophic dysplasia
500
0
2
10
2
1
10
10
1
10
0
10
0
10
-1
10
-1
10
-2
Fold Change From Base D
10
-2
10
Fold Change From Base htot
Most Important Results!
Results: Sensitivity to parameters
Parameter
Gradient
Time to S.S.
v
+
+
kdeg
+
+
kint
+
+
Rtot
+
+
Htot
-
+
D
+
+
Experiments: in vitro

Investigate and
characterize base state/
parameters



Use chondrocyte cultures
to better characterize cellsurface and ECM HSGAG
using capillary
electrophoresis
Identify ranges of binding
sites using surface noncovalent affinity mass
spectrometry.
Attempt organ culture to
measure in vivo
parameters
(Keiser, 2001, Nature Medicine)
Experiments: in vivo

Validate model and model
predictions

Test with exogenous
delivery of saccharides and
proteins.




Heparin-alginate spheres
could be used for FGF2 or
recombinant FGF2 mutant
delivery
Sodium chlorate to inhibit
sulfation of HSGAG
Knock-out mice/RNAi
Targeted delivery of GAG
modifying enzymes to
subsets of chondrocytes
Heparin release over time using alginate
(Edelman, 2000, Biomaterials)
Proposed future model directions




Expand to other relevant FGF family
members: FGF7, FGF8 FGF17, FGF18.
Complicate model by simulating growth
(moving source, semi-infinite domain)
Make predictions about sources of
pathologies with known phenotypes but
unknown causes
Use in silico testing to gauge potential
efficacy of treatments for growth plate
related pathologies
Conclusions





Our model is predictive of qualitative
physiological and pathological conditions at the
growth plate
Our model suggests that a previous assumption
that ECM binding could be lumped into an
“effective” diffusivity may be incorrect
Experimental testing and validation of the model
is required to determine quantitative accuracy
The model can suggest treatments for
pathologies
The model can be expanded to other systems
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