SAXS Signatures of Conformational Heterogeneity and Homogeneity of Disordered Protein Ensembles

Abstract

An accurate account of disordered protein conformations is essential for deciphering the physico-chemical basis of biological functions of intrinsically disordered proteins and the folding-unfolding energetics of globular proteins. Physically, disordered ensembles of non-homopolymeric polypeptides are expected to be heterogeneous; i.e., they should differ from homogeneous ensembles of homopolymers that harbor a unique relationship between average values of end-to-end distance REE and radius of gyration Rg. It was posited recently, however, that small-angle X-ray scattering (SAXS) data on conformational dimensions of disordered proteins can be rationalized almost exclusively by homopolymer ensembles. Assessing this perspective, we used chain-model simulations to evaluate the discriminatory power of SAXS-determined molecular form factors (MFFs) with regard to homogeneous versus heterogeneous ensembles. We make no assumption about ensemble encodability. Accordingly, the heterogeneous ensembles we consider are not restricted to those entailed by simple interaction schemes. We found that MFFs of certain heterogeneous ensembles with more narrowly distributed REE and Rg deviates from MMFs of homogeneous ensembles, but the differences can be small. Interestingly, some heterogeneous ensembles with asphericity and REE drastically different from those of homogeneous ensembles can nonetheless exhibit practically identical MMFs, indicating that SAXS MMFs are far from affording unique characterizations of basic properties of conformational ensembles. Heteropolymeric variations of the REE--Rg relationship were further showcased using a pertubation theory of flexible polymers. Ramifications of our findings for interpretation of experimental data are discussed.