Estimation of distance-distribution probabilities from pulsed electron paramagnetic resonance (EPR) data of two dipolar interaction coupled nitroxide spin labels using doubly rotating frames and least-squares fitting

Abstract

A method, based on the doubly rotating frame (DRF) technique to calculate the basis DEER (Double Electron–Electron Resonance) signals [Physica B: Condensed Matter, 625, 413,511 (2022)] accurately by numerical techniques over a range of $$r$$ values, where $$r$$ is the distance between the two nitroxides in a biradical in a biological system, has been exploited to calculate the probabilities of distance distribution, $$P\left( r \right),$$ by the use of Tikhonov regularization. It is demonstrated here by applying it to the data reported by Lovett et al. [J. Magn. Reson., 223, 98–106 (2012)] on a sample of bis-nitroxide nanowire, P1, in deuterated ortho-terphenyl solvent with 5% BnPy (d14-oTP/BnPy) in semi-rigid state. An improvement in the agreement of the calculated signal with respect to the experimental signal and thus in the probabilities of the distance distribution, $$P\left( r \right)$$, so obtained, is found, as compared to that obtained using the kernel signals based on analytical expressions