Dimension conversion and scaling of disordered protein chains

To extract protein dimension and energetics information from single-molecule fluorescence resonance energy transfer spectroscopy (smFRET) data, it is essential to establish the relationship between the distributions of the radius of gyration (R-g) and the end-to-end (donor-to-acceptor) distance (R-ee). Here, we performed a coarse-grained molecular dynamics simulation to obtain a conformational ensemble of denatured proteins and intrinsically disordered proteins. For any disordered chain with fixed length, there is an excellent linear correlation between the average values of R-g and R-ee under various solvent conditions, but the relationship deviates from the prediction of a Gaussian chain. A modified conversion formula was proposed to analyze smFRET data. The formula reduces the discrepancy between the results obtained from FRET and small-angle X-ray scattering (SAXS). The scaling law in a coil-globule transition process was examined where a significant finite-size effect was revealed, i.e., the scaling exponent may exceed the theoretical critical boundary [1/3, 3/5] and the prefactor changes notably during the transition. The Sanchez chain model was also tested and it was shown that the mean-field approximation works well for expanded chains.