A model-independent description of the angular orientation distribution of elements in an ordered biological assembly is applied to the electron spin resonance (ESR) technique. As in a previous model-independent treatment of fluorescence polarization (Burghardt, T.P., 1984, Biopolymers, 23:2383-2406) the elemental order is described by an angular distribution of molecular frames with one frame fixed in each element of the assembly. The distribution is expanded in a complete orthonormal set of functions. The coefficients of the series expansion (the order parameters) describe the orientation distribution of the elements in the assembly without reference to a model and can be obtained from the observed spectrum. The method establishes the limitations of ESR in detecting order in the assembly by determining which distribution coefficients the technique can detect. A method of determining the order parameters from an ESR spectra, using a set of ESR basis spectra, is developed. We also describe a treatment that incorporates the actual line shape measured from randomly oriented, immobile elements. In this treatment, no model-dependent assumptions about the line shape are required. We have applied the model-independent analysis to ESR spectra from spin-labeled myosin cross-bridges in muscle fibers. The results contain detailed information on the spin-probe angular distribution and differ in interesting ways from previous model-dependent interpretations of the spectra
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