Ion-polymer interactions have important consequences for the macroscopic mechanical/osmotic properties and the biological function of the tissue. Divalent cations, particularly calcium ions, are abundant in the biological milieu. In general, experiments to determine the interactions between ions and biopolymers are difficult to perform, because above a relatively low ion concentration multivalent cations cause phase separation (or precipitation) of the charged macromolecules. Since macroscopic phase separation does not occur in gels, we can overcome this limitation by cross-linking these polymers, i.e., extending the range of ion concentrations over which the systems can remain stable. In pilot studies, we used this new non-destructive procedure to investigate cross-linked gels of a model synthetic polymer, polyacrylic acid, and different biopolymers such as DNA and hyaluronic acid to determine the size of the structural elements that govern the osmotic concentration fluctuations. We combined SANS and SAXS to estimate the osmotic modulus of hyaluronic acid in the presence of both monovalent and divalent counterions. We also studied the dynamic properties (e.g., diffusion processes) of these systems by dynamic light scattering and determined the osmotic modulus from the relaxation response. We developed an experimental procedure to determine the distribution of counter-ions around charged biopolymer molecules using anomalous small-angle X-ray scattering measurements. We analyzed and compared a series of network elasticity models that address essential physical aspects of biopolymer systems. We are particularly interested in understanding the mechanisms of interactions of biologically important divalent cations like Ca+2 with negatively charged biopolymers. We believe that the study of water-ion-biopolymer interactions at a fundamental level is necessary to understanding of biological processes at the molecular, cellular and tissue length scales about which little is currently known. Better understanding of the structure and interactions among tissue components is also necessary to design and develop tissue models and novel tissue phantoms that mimic tissue behavior. For instance, we are developing a biomimetic model of cartilage ECM consisting of highly charged polyelectrolyte particles embedded in a crosslinked neutral gel. In this system charged particles mimic the behavior of proteoglycan assemblies and the neutral gel mimics the collagen matrix. We study the effect of the structural parameters on the macroscopic swelling and load bearing properties of this composite gel system. We systematically vary the properties of the polymeric components by changing the concentration and cross-link density of the dispersed particles in the continuous network. In addition, we can control the fixed charge density (FCD), by varying the degree of ionization of the charged groups on the polymer chains. Biomimetic phantoms with well-characterized physical (osmotic, mechanical, relaxation, etc.) are critically important in quantitative MRI to validate measurements and advanced MRI applications from bench to bedside (in vivo MRI histology). In the context of cartilage, the hierarchical bottlebrush organization of charged polymer molecules is of particular interest for understanding the biological function of the tissue, such as its load bearing ability and lubrication mechanism. In cartilage ECM the bottlebrush shaped aggrecan molecules are condensed on hyaluronic acid chains forming secondary bottlebrush structures. In collaboration with Prof. Xia (Department of Chemistry, Stanford University) we started a research collaboration to determine the physical properties of model bottlebrushes (neutralized polyacrylic acid polymers) having well controlled molecular architecture. We make systematic studies on a family of bottlebrush structures by varying (i) the length of the main chains (at constant length of the side chains) and (ii) the length of the side chains (at constant length of the main chains). The structural investigations are complemented by molecular dynamics modeling performed in collaboration with Dr. Jack Douglas (National Institute of Standard and Technology). These studies will reveal the role of the hierarchical bottlebrush organization of cartilage proteoglycans that gives rise to the unique mechanical properties of cartilage. Biomimetic studies provide vital insights to help understand how different factors (e.g., matrix stiffness, charge density) affect the macroscopic mechanical and swelling properties of tissues. For example, the knowledge obtained from systematic measurements on well-defined model systems is critically important to understand cartilage behavior and develop a realistic biomimetic cartilage model. Such information cannot be obtained from measurements made on biological tissues because their composition and physical properties cannot be independently and systematically varied. Biomimetic model systems have been shown in our hands to be extremely powerful means to calibrate and validate quantitative MRI measurements for microstructure imaging. We have developed a wide variety of NMR and MRI phantoms that possess various salient features of cell or tissue systems, providing 'ground truth' to test the validity of our models and experimental designs.
