Differentiating Unimodal and Multimodal Distributions in Pulsed Dipolar Spectroscopy Using Wavelet Transforms

Site directed spin labeling has enabled protein structure determination using electron spin resonance (ESR) pulsed dipolar spectroscopy (PDS). Small details in a distance distribution can be key to understanding important protein structure-function relationships. A major challenge has been to differentiate unimodal and overlapped multimodal distance distributions. They often yield similar distributions and dipolar signals. Current model-free distance reconstruction techniques such as Srivastava-Freed Singular Value Decomposition (SF-SVD) and Tikhonov regularization can suppress these small features in uncertainty and/or error bounds, despite being present. In this work, we demonstrate that continuous wavelet transform (CWT) can distinguish PDS signals from unimodal and multimodal distance distributions. We show that periodicity in CWT representation reflects unimodal distributions, which is masked for multimodal cases. This work is meant as a precursor to a cross-validation technique, which could indicate the modality of the distance distribution.