Model‐Independent fluorescence polarization for measuring order in a biological assembly

In the first part of this paper, we developed a model‐independent method of describing the order in the arrangement of elements in a general, anisotropic, time‐independent biologic structure, where elemental order is reported by dipolar (e.g., fluorescent) probes. This method begins with the description of the elemental order of a biologic assembly as an arbitrary angular distribution of molecular frames, with one frame fixed in each element of the structure. The angular distribution is then expanded in a complete set of orthonormal angular functions and the moments of the series expansion are related to observable quantities. These moments describe the physical properties of the elemental order of the system without a model and without reference to the method of observation. The method is developed here for fluorescence polarization measurements, when each elemental subunit is specifically fluorescence‐labeled, and the elemental order is reported by the polarization of the emission from the fluorescent probe after polarized excitation. This approach establishes the theoretical limitations of the fluorescence polarization technique for determining elemental order in a system and indicates analytical and experimental strategies for obtaining all the order information in the observed signal. A version of this method has been successfully applied to the study of the order of arrangement of the myosin cross‐bridge in intact muscle fibers [Burghardt, Ando, and Borejdo (1983) Proc. Natl. Acad. Sci. USA 80, 7515–7519]. These results are discussed briefly in this paper. In the second part of this paper we extend the model‐independent analysis to the time‐dependent, anisotropic system where the fluorescence‐labeled elements are undergoing restricted rotational motion. The model‐independent analysis is used to measure the angular potential that restricts the rotational motion of the elements. The method does not require time‐resolved measurements.