Misra, Sushil K., and Hamid Reza Salahi. “Estimation of Distance Distributions Between Gd3+ Ion Pairs with a Significant Zero-Field Splitting from Pulsed EPR DEER Data.” Applied Magnetic Resonance 54, no. 3 (March 1, 2023): 383–400.
DEER (Double Electron–Electron Resonance) kernel signals are calculated, using the double rotating-frames (DRF) technique, for the various distances, r, between two coupled Gd3+ ions, distributed randomly in a biological system. This is done numerically, using full diagonalization of the spin-Hamiltonian matrix, taking into account the zero-field splitting of the Gd3+ion with spin $$S=7/2$$. These kernel signals are then used to estimate the probabilities of the distance distribution, P(r), between the pairs of various Gd3+ ions. This is accomplished using Tikhonov regularization, as implemented in the software DeerAnalysis [Jeschke et al. Appl Magn Reson 30(3): 473–498, (2006)], with the kernel signals calculated here by the DRF technique for different r values. This procedure is successfully illustrated by applying it to calculate the probabilities, P(r) from the reported experimental four-pulse DEER data for a sample of Gd ruler 15 in D2O/glycerol-d8 (i) at Q-band [Doll et al. J Magn Reson 259: 153–162, 2015] and (ii) at W-band [Dalaloyan et al. Phys Chem Chem Phys 17(28): 18464–18476, (2015)]. These results are found to be about the same, within the RMSD maximum and minimum bounds, from those obtained using analytical kernel signals, valid for hard (infinite) pulses for spin ½, so that the ZFS is not included, at the lower frequency (~ 35 GHz) of Q-band. However, at the higher frequency of W-band (~ 95 GHz), there are found slight, but distinct, differences beyond the RMSD maximum/minimum bounds, in the P(r) values calculated by the two approaches. In application scenarios to the commonly investigated proteins, where the errors are large, the results obtained by the two approaches would be about the same, at least for the data obtained at Q- and W-bands, if not at higher frequencies.