Multi-Gaussian Monte Carlo Analysis of PELDOR Data in the Frequency Domain

Pulsed double electron–electron resonance technique (PELDOR or DEER) is often applied to study conformations and aggregation of spin-labelled macromolecules. Because of the ill-posed nature of the integral equation determining the distance distribution function, a regularization procedure is required to restrict the smoothness of the solution. In this work, we performed PELDOR measurements for new flexible nitroxide biradicals based on trolox, which is the synthetic analogue of α-tocopherol; spin-labelled trolox derivatives are investigated as potential anti-cancer drugs. We use regularization by an approximation of the solution with a sum of limited number of Gaussians, by varying their positions, widths and amplitudes. Their best-fitted values were found by a completely random Monte Carlo process. The use of the frequency-domain PELDOR data allowed diminution of the artifacts induced by spin–spin electron–nuclear and intermolecular electron–electron interactions. It was found that for the all biradicals studied, the use of three Gaussians was enough for good agreement with the experiments. The number of trials for obtaining satisfactory result was found to be quite reasonable, which is explained by presence of the singularity in the core of integral equation. The maxima of inter-spin distance distribution for different biradicals were found to vary between 1.5 and 2.3 nm, depending on the linkers between the Trolox core and nitroxides. The distance distributions around these positions reflect flexibility of the biradicals.