The determination of pair distance distributions by pulsed ESR using Tikhonov regularization

Pulsed ESR techniques with the aid of site-directed spin labeling have proven useful in providing unique structural information about proteins. The determination of distance distributions in electron spin pairs directly from the dipolar time evolution of the pulsed ESR signals by means of the Tikhonov regularization method is reported. The difficulties connected with numerically inverting this ill-posed mathematical problem are clearly illustrated. The Tikhonov regularization with the regularization parameter determined by the L-curve criterion is then described and tested to confirm its accuracy and reliability. The method is applied to recent experimental results on doubly labeled proteins that have been studied using two pulsed ESR techniques, double quantum coherence (DQC) ESR and double electron-electron resonance (DEER). The extracted distance distributions are able to provide valuable information about the conformational constraints in various partially folded states of proteins. This study supplies a mathematically reliable method for extracting pair distributions from pulsed ESR experimental data and has extended the use of pulsed ESR to provide results of greater value for structural biology.