Quantification of the molar degree of folding/unfolding using a scaling model

The unfolded states in proteins and nucleic acids remain weakly understood despite their importance in folding processes; misfolding diseases (Parkinson's and Alzheimer's); natively unfolded proteins (as many as 30% of eukaryotic proteins, according to Fink); and the study of ribozymes. Research has been hindered by the inability to quantify the residual (native) structure present in an unfolded protein or nucleic acid. Here, a scaling model is discussed to quantify the molar degree of folding and to define the unfolded state. The scaling model can be applied to various analytic methods and to simulations. Examples are given using small-angle X-ray and neutron scattering. For instance, from pressure-induced unfolding of SNase, from acid-unfolded cytochrome c, and from folding of Azoarcus ribozyme. These examples quantitatively show three characteristic unfolded states for proteins, the statistical nature of a protein folding pathway, and the relationship between the extent of folding and chain size during folding for charge-driven folding in RNA.