Tissue properties and function arise from processes occurring at cellular and subcellular length scales. Therefore, the physical behavior of tissues (e.g., osmotic and mechanical properties, state of hydration, charge density) must all be characterized on distance scales below 100 nm. Understanding the interaction of polyelectrolytes with ions could help clarify the basic physics of ion binding as well as physical mechanisms affecting a large number of biological processes. In biology, osmotic pressure is particularly important in regulating and mediating various physiological processes. To help understand the nature of physical/chemical interactions in biomolecules and biomolecular assemblies, we have developed an experimental approach to study their structure (morphology) and thermodynamic properties simultaneously as a function of the length scale (spatial resolution) by combining macroscopic osmotic swelling pressure measurements and small-angle scattering measurements. Swelling pressure measurements probe the system in the large length scale range, thus providing information on the overall thermodynamic response. Small-angle neutron scattering (SANS) and small-angle X-ray scattering (SAXS) allow us to investigate biopolymer molecules in their natural environment and to correlate the changes in the environmental conditions (e.g., ion concentration, ion valance, pH, temperature) with physical properties such as molecular conformation and osmotic pressure. SANS and SAXS simultaneously provide information about the size of different structural elements and their respective contribution to the osmotic properties. Combining these measurements allows us both to separate the scattering intensity arising from thermodynamic concentration fluctuations from the intensity scattered by large static superstructures (e.g., aggregates), and to determine the length scales governing the macroscopic thermodynamic properties. This thermodynamic and structural information cannot be obtained by other techniques. Specifically, we have applied this approach to study the effect of multivalent cations, particularly calcium ions, on the structure of various model systems mimicking soft tissues. Divalent cations are ubiquitous in the biological milieu, yet existing theories do not adequately explain their effect on and interactions with charged macromolecules. Moreover, experiments to study these interactions are difficult to perform, particularly in solution, because above a low ion concentration threshold multivalent cations generally cause phase separation or precipitation of charged molecules. Since macroscopic phase separation does not occur in cross-linked gels, we have overcome this limitation by cross-linking our biopolymers, extending the range of ion concentrations over which the system remains stable and can be studied. In pilot studies, this new non-destructive procedure has been used 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 contribute to the osmotic concentration fluctuations. We have combined SANS and SAXS to estimate the osmotic modulus of hyaluronic acid solutions in the presence of monovalent and divalent counterions. We studied the diffusion processes in these solutions by dynamic light scattering and determined the osmotic modulus from the relaxation response. We developed an experimental procedure to determine the distribution of counterions around charged biopolymer molecules using anomalous small-angle X-ray scattering measurements. We analyzed a series of simple models of network elasticity that address essential physical aspects of rigid chain biopolymer systems. The extracellular matrix of cartilage provides a good example of such a rigid chain biological network. We found that in compression (or indentation which is essentially a compressive process) strain stiffening was dominant.
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