Instrumental analysis of scanning force microscopy for nanostructured biomaterials: Applications to cartilage

Instrumental analysis was used to provide new capabilities for scanning force microscopy (SFM) investigations of nanoscale biomaterials. Both imaging and force measurements were considered.; For SFM imaging, we formulated the first general purpose reconstruction technique that can accurately recover biomolecular dimensions from tip broadened data. SFM probes used in biomolecule imaging are first calibrated using the blind reconstruction algorithm, modified to be more accurate at length scales of a few nanometers. The calibrated probe geometry is then used to simulate images from molecular models that are compared with the experimental SFM image data in a nonlinear regression loop. Using simulated and experimental images of the cartilage proteoglycan aggrecan we show that the reconstructed model has lateral dimensions commensurate with transmission electron microscopy data. The model can be used to infuse image analysis with a priori information that describes relevant structures of the molecule or surface under study. We demonstrate this using a model that connects tertiary structures of aggrecan, measured by SFM, with primary structure information obtained from cDNA analysis. Aggrecan data was analyzed with a focus on recent information regarding its catabolism by aggrecanase. The distribution of lengths, with a maximum of 450 nm and mean of 300 nm, suggested that a large fraction of molecules in vivo exist in a partially catabolized state. Comparing the length distribution with current models regarding the degradation of aggrecan by aggrecanase, our results suggest that 48% of aggrecan molecules are cleaved at either the E(1480)-(1481)G or E(1667)-(1668)G aggrecanase cleavage sites.; For SFM force measurements, we increased the range and bandwidth possible in viscous (i.e. liquid) environments using high-speed digitization and a dynamical cantilever model. We first showed that a multimodal beam model was necessary to reconstruct forceseparation curves from high-bandwidth measurements of tip motion in the snap-to-contact. We then analyzed the model and showed that even when the underlying force-separation is arbitrarily nonlinear, the reconstruction can be solved using linear transformations. This is in contrast to previous techniques that used low-order expansions or complicated nonlinear solvers. The reconstruction problem is ill-posed but we show that useful solutions can be obtained using Tikhonov regularization and L-curve analysis. We demonstrated the utility of the technique by performing one of the only measurements of single colloid interactions where the characteristic size of the colloid was smaller than the length scale for the interaction. This experimentally demonstrated the limitations of the Derjaguin approximation and agreed with theoretical predictions that the Derjaguin approximation overestimates the force on small particles. Replacing the Derjaguin approximation with surface element integration provided a significantly better description of the experimental data. The study should be useful for future investigations of polymers, biological molecules, and other nanoscale colloids where the Derjaguin approximation does not apply.