Identifying the Optimal Level of Regularization in Deer Data Analysis

Abstract

Double Electron-Electron Resonance (DEER) spectroscopy is an Electron Paramagnetic Resonance (EPR) experiment that accurately reports the distribution of distances, P(r), between two or more unpaired electrons over the range of about 10 to 160 ångströms. DEER is becoming increasingly important as a tool for structural biology due to its ability to elucidate protein conformational landscapes, as well as its amenability to complex samples such as membrane-bound proteins and large protein complexes. The spin-spin distance distribution, P(r), is most often inferred from the time-domain experimental data with a regularized least-squares method known as Tikhonov regularization. Although this method typically provides reliable estimates of P(r), it requires the input of a regularization parameter, α, which scales the magnitude of a penalty term with respect to the fitting error. This regularization parameter significantly affects the estimated P(r), so selecting its optimal value is crucial for accurate analysis of DEER data. The most popular procedure for selecting α in DEER data analysis is a graphical method called the L-curve criterion, which has empirical justification. However, to date, a systematic exploration of the many extant regularization parameter selection methods has not been carried out in the context of DEER data analysis. Here, we evaluate 16 methods, including the L-curve criterion, against a large, physically-derived test set of simulated DEER data. The test set of P(r)s was generated using a side-chain rotamer library in conjunction with a crystal structure (2LZM). This test set was then used to generate a large set of experimentally realistic simulated time-domain data.