Simulation of four-, five-, and six-pulse Double Quantum Coherence signals for nitroxide biradicals: Distance measurement in biological systems

Abstract

Algorithms are developed to calculate pulsed EPR (Electron Paramagnetic Resonance) signals, utilized for distance measurements in biological systems, using nitroxide biradicals, for the cases of: (i) four- (ii) five- and (iii) six-pulse double quantum coherence (DQC). The details of how to calculate the signals analytically and numerically are provided. It is shown that only onedimensional experiments are needed to determine the dipolar constant, from which the distance between the two nitroxides of the biradical can be extracted directly. The analytical expressions reveal that for the case of non-selective pulses the Fourier transforms of these three DQC pulse sequences exhibit two predominant peaks at ±d × 3 cos2 θ − 1 ; where d = 2 3D, with D being the dipolar-coupling constant and θ being the orientation of the dipolar axis with respect to the external magnetic field. It is shown here that the DQC signal is broadened by relaxation only for the four-pulse sequence, but not for the five- and six-pulse sequences. The rigorous numerical algorithm developed here is shown to produce very good agreement of the simulated signals with the published experimental signals for four-, five-, and six- pulse DQC sequences. It is discussed that the two-dimensional Fourier transform of the six-pulse signal, calculated in terms of the dipolar and echo times, gives information about the dipolar constant when analyzed along the dipolar axis, whereas its variation along the echo-axis provides information on the frequency-swept ESR spectrum of the two nitroxides