Last modified: 2016-05-23
Abstract
Pulsed dipolar electron spin resonance spectroscopy (PDS) has in recent years become an important tool for studying the dynamics and structural conformations of a protein complex. It allows one to measure long distances (1 − 9 nm, approximately) between spin labels, making it convenient to reveal the structural changes and dynamics of a large protein complex between different functional states. The determination of the inter-spin-label distance distribution from the PDS measurements involves an ill-posed inverse problem. A common method to extract the distance distribution from the PDS data has been the use of Tikhonov regularization. However, the determination of an optimal regularization parameter in the Tikhonov analysis has been a challenging task. Here we report our recent efforts concerning an improved strategy to obtain an optimal regularization parameter for solving the ill-posed problem. Basically, we used a Lanczos-based algorithm (JCP 2011, 134, p034112) to solve for eigenvalues of the kernel matrix of the problem in an iterative way. We show that the variations revealed in the iterative eigenvalues provide a robust criterion for selecting an optimal regularization parameter. Numerical and experimental demonstrations of this approach have been performed to quantify the improvements. This approach allows one to perform validation of the results obtained by the Tikhonov method and, therefore, improve accuracy in the PDS distance measurements for structural biology.