Localized Reconstruction of Multimodal Distance Distribution from DEER Data of Biopolymers

Pulsed Dipolar ESR Spectroscopy (PDS) is a uniquely powerful technique to characterize the structural property of intrinsically disordered proteins (IDPs) and polymers and the conformational evolution of IDPs and polymers, e.g. during assembly, by offering the probability distribution of segment end-to-end distances. However, it is challenging to determine distance distribution P(r) of IDPs by PDS because of the uncertain and broad shape information that is intrinsic to the distance distribution of IDPs. We demonstrate here that the Srivastava-Freed Singular Value Decomposition (SF-SVD) point-wise mathematical inversion method along with wavelet denoising (WavPDS) can aid in obtaining reliable shapes for the distance distribution, P(r), for IDPs. We show that broad regions of P(r) as well as mixed narrow and broad features within the captured distance distribution range can be effectively resolved and differentiated without a priori knowledge. The advantage of SF-SVD and WavPDS is that the methods are transparent, requiring no adjustable parameters, the processing of the magnitude for the probability distribution is performed separately for each distance increment, and the outcome of the analysis is independent of the user's judgement. We demonstrate the performance and present the application of WavPDS and SF-SVD on model ruler molecules, model polyethylene glycol polymers with end-to-end spin labeling, and IDPs with pairwise labeling spanning different segments of the protein tau to generate the transparent solutions to the P(r)'s including their uncertainties and error analysis.