Global fit and structure optimization of flexible and rigid macromolecules and nanoparticles from analytical ultracentrifugation and other dilute solution properties

The calculation of hydrodynamic and other solution properties from structural information (size and shape or flexibility) of macromolecules and nanoparticles is feasible thanks to existing theories and computational tools. Here we review our recent advances in the inverse problem of extracting structural information from those properties. The concepts of equivalent radii and ratios of radii are particularly useful in global-fitting structural analysis, when one has to treat simultaneously with various properties, eventually for a series of samples. Based on the equivalent radii or their ratios, we define target functions that measure the adequacy of a given structure to fit a set of experimental properties. Structural determination is carried out by minimization of those target functions. We review a variety of examples. Some of them refer to the simple, yet important models like ellipsoids, cylinders and wormlike chains, whose structure is determined by optimization of the model parameters. In other, more complex cases, properties are calculated with computational tools like programs in the HYDRO suite. We have devised other tools to make the structure optimization from the results of those calculations in a quite direct, simple and systematic manner.