Extracellular Matrix Based Regulation of a Cytokine Gradient at the Growth Plate

1. Extracellular Matrix Based Regulation of a Cytokine Gradient at the Growth Plate Jonathan Behr David Berry BEH.400J Project Presentation Hereditary Multiple Exostoses Diastrophic Dysplasia

2. Outline • Goals • Introduction • GAG interaction with cytokines • Model system: Long bone growth • Methods • Model formulation • Model implementation • Results • Proposed experiments to test model • Conclusions

3. 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

4. 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

5. Model System: The Growth Plate In endochondral ossification, the formation of calcified bone is separated from mesenchymal condensation by the development of a cartilage anlage that regulates bone growth Resting Chondrocytes Proliferating Chondrocytes Prehypertrophic Chondrocytes Hypertrophic Chondrocytes Trabecular Bone Human cartilage during endochondrial ossification stained with H&E and alcian blue at 40x magnification. (Wheater’s Functional Histology) Human cartilage during endochondrial ossification stained with H&E and alcian blue at 120x magnification. (Wheater’s Functional Histology)

6. 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)

7. Assumptions: Geometry • Cylindrical geometry, radial symmetry • radial dimension >> z direction • Model as 1-D problem in z • Isotropic environment in hypertrophic zone

8. 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

9. H H 5ng/ml base H H H H H H H H H H H H H H H H H H bFGF Modified from Lander et al. (2002) Model Cartoon

10. Model Equations

11. Implementation • 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

12. Base Parameters from Literature

13. 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

14. Base Case Results, 3D

15. Concentrations Increasing Time Distance Base Case Results, 2D

16. Example of Faster Kinetics

17. Example of Longer Gradient

18. Example of Unstable Gradient

19. Steady State Dependence on“External” Parameters

20. Chondrodysplasia punctata • Acrocephalosyndactyly syndrome • Achondroplasia Steady State Dependence on “Cellular” Parameters

21. Steady State Dependence on“ECM” Parameters Most Important Results!

22. Kinetic Dependence on“ECM” Parameters This point takes >10 Years!!! • Hereditary multiple exostoses (HME) • Simpson-Golabi-Behmel syndrome (SGBS) • Diastrophic dysplasia Most Important Results!

23. Results: Sensitivity to parameters

24. Experiments: in vitro • Investigate and characterize base state/ parameters • Use chondrocyte cultures to better characterize cell-surface and ECM HSGAG using capillary electrophoresis • Identify ranges of binding sites using surface non-covalent affinity mass spectrometry. • Attempt organ culture to measure in vivo parameters (Keiser, 2001, Nature Medicine)

25. 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)

26. 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

27. 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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