Research Program
Cell Surface Interactions

Objectives
1)   To develop experimental techniques for creating and maintaining steep gradients of mineralization inhibitors and promoters in hydrogels over small (<100 µm) length scales in a dynamic double diffusion system (DDS). To convert these gradients of proteins and/or small molecules into gradients of mineral density.

2)   To introduce articular chondrocytes into a DDS to study mineralization as a function of soluble and insoluble inhibitors produced by the cells.

3)   To develop theoretical tools with which to study the reaction-diffusion processes that define sharp gradients in extracellular chemistry and cellular phenotype.

Methods
1)      Double-Diffusion System (Estroff, Boskey). Carbonated apatite (Ca₁₀(PO₄)_6-x(CO₃)_x(OH)₂) crystals are grown in a gel (gelatin or agarose) by diffusion of Ca²⁺ and PO₄^3- from opposite ends of the gel (Fig. 1). Anodically etched nanoporous silicon is placed in the center of the tubes.

2)      Culture of Chondrocytes in 1-D gels (Bonassar, Estroff). Silicone tubes, rendered hydrophilic by plasma oxidation followed by treatment with an aminosilane, were filled with agarose gel containing a band of chondrocytes in the center (Fig. 2a). Cells were cultured for 5 days and then stained for dead and alive cells.

3)      Multi-Scale Kinetic Monte Carlo (MS-KMC) Computational Model (Stroock, Boskey, Estroff, Bonassar). The DDS is divided into discrete elements, and the macroscopic diffusion of ions is modeled using a finite difference method. Once Ca²⁺ and PO₄^3- encounter each other, the algorithm makes a scale change in order to evaluate the probability of diffusion of ions, nucleation, or crystal growth following the Kinetic Monte Carlo criteria.

Summary
During the past project period, we have been developing an in vitro model of the formation of the cartilage-bone tidemark by adapting a DDS to create a system containing chondrocytes and a defined zone of mineralization (Fig. 1). Our approach is three-pronged: 1) introduction of functionalized nano-porous silicon (pSi) membranes into the DDS to obtain control over the nucleation of nanocrystalline apatite; 2) modification of the DDS to support chondrocyte viability for at least 5 days (the length of the mineralization experiments); 3) development of a computational model of the reaction-diffusion proces-ses in the DDS. We have made progress in all three areas. By using hydrosilyation of the pSi to intro-duce functionality (e.g., carboxylic acids, hydroxyls, phosphates), we have demonstrated control over the size and morphology of the apatite nanocrystals grown on the surfaces. For integrating chondrocytes into the DDS, we have shown that the viability of chondrocytes in cylinders of agarose gels (3 cm long), contained within gas-permeable silicone tubing, is comparable to control disks of agarose (Fig. 2). This result indicates that gaseous diffusion and nutrient transport through the walls of the tubes, and along their lengthes, is sufficient to maintain cell viability. Having successfully tested the cell viability in all components of the DDS, individually, we are now ready in the coming year to integrate the tubes con-taining chondrocytes into the mineralizing system. Finally, we have successfully demonstrated that our MS-KMC model is a robust technique to model the high order crystallization process of nanocrystalline hydroxyapatite in the DDS (Fig. 3). This technique can validate and predict experimental observations, including the addition of an inhibitor or promoter of mineralization.

Accomplishments

• Optimization of a dynamic double diffusion system for studying the formation of carbonated apatite crystals in gelatin and agarose gels (Fig. 1).
• Demonstration of chondrocyte viability in agarose gels contained within gas permeable silicone tubing, suitable for incorporation into the double diffusion set-up (Fig. 2).
• Development of a Kinetic Monte Carlo model for the reaction-diffusion processes occurring in the dynamic double diffusion set-up (Fig. 3).