Equivalent Radii and Ratios of Radii from Solution Properties as Indicators of Macromolecular Conformation, Shape, and Flexibility

Abstract

The equivalent radius for any solution property is the radius of a spherical particle having the same value of solution property as that of the macromolecule under consideration. Equivalent radii for different properties present a dependence on size and shape that are more similar than the values of the properties themselves. Furthermore, the ratios of equivalent radii of two properties depend on the conformation (shape or flexibility), but not on the absolute sizes. We define equivalent radii and their ratios, and describe their evaluation for some common models of rigid and flexible macromolecules. Using radii and ratios, we have devised procedures to fit macromolecular models to experimental properties, allowing the determination of the model parameters. Using these quantities, we can construct target functions for an equilibrated, unbiased optimization. The procedures, which have been implemented in public-domain computer programs, are illustrated for rigid, globular proteins, and the rodlike tobacco mosaic virus, and for semiflexible, wormlike heparin molecules.