The mechanical properties of cartilage tissue depend largely on the macromolecules that make up its extracellular matrix (ECM). Aggrecan is the most abundant proteoglycan in articular cartilage. It is composed of a core protein with highly charged, densely packed glycosaminoglycan (GAG) side chains, which are responsible for ~ 50% of the equilibrium compressive stiffness of the tissue. Using atomic force microscopy (AFM) and high resolution force spectroscopy (HRFS), it is now possible to directly measure nanoscale interactions between ECM macromolecules in physiologically relevant aqueous solution conditions. In order to interpret these data and compare them to macroscopic tissue measurements, a combination of experiments and theoretical modeling must be used.

In this thesis, a new molecular-scale continuum Poisson-Boltzmann (PB)-based model was developed to predicthe intermolecular interactions between GAG macromolecules by taking into account nanoscale space varying electric potential and fields between neighboring GAGs. A rod-like charge density distribution describing the time averaged space occupied by a single GAG chain was formulated. The spacing and size of the rods greatly influenced the calculated force even when the total charge was kept constant. The theoretical simulations described HRFS experimental data of the normal interaction force between two surfaces chemically end-grafted with an array of GAGs ("brushes") more accurately than simpler models which approximate the GAG charge as a homogeneous volume or planar surface charge. Taken together, these results highlight the importance of nonuniform molecular-level charge distribution on the measured GAG interaction forces.

Normal interaction forces between aggrecan macromolecules weremeasured using contact mode AFM imaging and by HRFS. The aggrecan molecules were end-grafted to gold-coated substrates and probe tips to achieve brush-like layers at physiologically relevant densities. Both colloidal probe tips (2.5μm radius) and sharper probe tips (~ 25–50nm radius) were used. The measured normal forces were predominantly repulsive and showed a strong ionic strength dependence reflecting the importance of repulsivelectrostatic interactions. These aggrecan-aggrecan forces were much larger than those previously measured between brushes composed only of a single layer of GAG chains isolated from aggrecan molecules. The measured aggrecanormal force interactions were then compared to the predictions of the PB charged rod model for GAG electrostatic interactions and to measurements of the equilibrium compressive modulus of intact cartilage tissue. At near physiological bath conditions (0.1M NaCl), the PB electrostatic model closely predicted the values of the measured force for nanomechanical strains < 0.4, using model parameter values that were all fixed to their known values from the literature. At higher strains, the measured normal forces were higher than those predicted by the model, qualitatively consistent with the likelihood that other nonelectrostatic interactions were becoming more important. A compressive stiffness was also calculated from the measured aggrecan-aggrecan nanomechanical force data, and was found to be ~ 50% of the modulus of native intact cartilage. This is consistent with previous reports suggesting that aggrecan-associated electrostatic interactions account for approximately half of the tissue modulus.