Calculation of EPR Spectra of Samples with Anistropic Line Width: A New Efficient Algorithm

Abstract

Calculation of Electron Paramagnetic Resonance (EPR) spectra is essential part of studying proteins by spin labeling method, and studying metalloenzymes by EPR as well. Solution of inverse EPR problem by fitting model parameters to experimental data involves multiple calculations, so the performance of this elementary step is critical. In case of powder spectrum of disordered samples (like ones frozen at 77K), usual algorithm integrates over the space of orientations, calculating corresponding resonance positions. Resulting ‘stick’ spectrum is then convolved with line shape function (Lorentzian or Gaussian). If the line width does not depend on orientation (i.e., isotropic), Fast Fourier Transform (FFT) can be applied to calculate the convolution efficiently, but in typical case of anisotropic line width it is no more applicable. Program espect presented here uses algorithm that circumvents this limitation, making it possible to use FFT in case of arbitrary anisotropy of line width tensor. This leads to up to 100 times reduction of computational time required to calculate single spectrum. It is achieved by splitting the range of line widths into equal intervals, calculation of sub-spectra in each interval, and then using cubic interpolation to find the target spectrum approximation.