Dimensions, energetics, and denaturant effects of the protein unstructured state.

Determining the energetics of the unfolded state of a protein is essential for understanding the folding mechanics of ordered proteins and the structure-function relation of intrinsically disordered proteins. Here, we adopt a coil-globule transition theory to develop a general scheme to extract interaction and free energy information from single-molecule fluorescence resonance energy transfer spectroscopy. By combining protein stability data, we have determined the free energy difference between the native state and the maximally collapsed denatured state in a number of systems, providing insight on the specific/nonspecific interactions in protein folding. Both the transfer and binding models of the denaturant effects are demonstrated to account for the revealed linear dependence of inter-residue interactions on the denaturant concentration, and are thus compatible under the coil-globule transition theory to further determine the dimension and free energy of the conformational ensemble of the unfolded state. The scaling behaviors and the effective θ-state are also discussed.