Extracellular Matrix Based Regulation of a Cytokine Gradient

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

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

Project Goals n Quantitate how the physiochemical nature of the extracellular matrix modulates FGF 2 signaling n n FGF 2 must be localized to differentially signal for angiogenesis, chondrogenesis and osteogenesis Heparan sulfate glycosaminoglycans (HSGAGs) bind FGF 2 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 n HSGAG are one of several components of the ECM. n n n 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 n n n 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 anlage that regulates bone growth cartilage Proliferating Chondrocytes Prehypertrophic Chondrocytes Hypertrophic Chondrocytes Trabecular Bone Human cartilage during endochondrial ossification stained with H&E and alcian blue at 40 x magnification. stained with H&E and alcian blue at 120 x magnification. (Wheater’s Functional Histology)

Model System: The Growth Plate FGF 2 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 n Cylindrical geometry, radial symmetry n n n radial dimension >> z direction Model as 1 -D problem in z Isotropic environment in hypertrophic zone

Assumptions: Equations n Boundary conditions n Angiogenic side boundary: Constant influx of b. FGF n n Match so with base parameters, 5 ng/ml [b. FGF] at source at steady state Proliferating cartilage side: [b. FGF] 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 5 ng/ml base H H H H b. FGF Modified from Lander et al. (2002)

Model Equations

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 ode 15 s

Base Parameters from Literature Parameter Value Description Deff 0. 5 e-8 m 2/s Effective diffusivity in the ECM F 0 5 ng/ml (0. 278 n. M) S. S. concentration of b. FGF at “source” Htot 13 u. M 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 b. FGF source and proliferating chondrocytes kdeg 3. 5 e-5 /s Rate constant for degradation of free b. FGF kint 2 e-4 /s Rate constant for consumption of b. FGF due to receptor complex mediated internalization konh 4. 2 e 5 /(M*s) On rate for b. FGF·HS complex formation koffh 0. 01 /s Off rate for b. FGF·HS complex formation konr 1. 36 e 10 /(M*s) On rate for b. FGF·FGFR complex formation koffr 0. 18 /s Off rate for b. FGF·FGFR complex formation ε 0. 2 Volume fraction ECM v 4. 8 e-013 M/s In-flux of b. FGF at angiogenic boundary

Presentation of Results n n 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 [b. FGF] at x=0 Phase plots relating results to “normal” physiology

Base Case Results, 3 D

Concentrations Base Case Results, 2 D Increasing Time Distance

Example of Faster Kinetics

Example of Longer Gradient

Example of Unstable Gradient

Steady State Dependence on “External” Parameters

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

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

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

Results: Sensitivity to parameters Parameter Gradient Time to S. S. v + + kdeg + + kint + + Rtot + + Htot - + D + +

Experiments: in vitro n Investigate and characterize base state/ parameters n n n 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)

n Experiments: in vivo Validate model and model predictions n Test with exogenous delivery of saccharides and proteins. n n Heparin-alginate spheres could be used for FGF 2 or recombinant FGF 2 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 n n Expand to other relevant FGF family members: FGF 7, FGF 8 FGF 17, FGF 18. 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 n n n 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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