A maximum entropy analysis of protein orientations using fluorescence polarization data from multiple probes

Techniques have recently become available to label protein subunits with fl uorescent probes at predetermined orientation relative to the protein coord inates. The known local orientation enables quantitative interpretation of fluorescence polarization experiments in terms of orientation and motions o f the protein within a larger macromolecular assembly. Combining data obtai ned from probes placed at several distinct orientations relative to the pro tein structure reveals functionally relevant information about the axial an d azimuthal orientation of the labeled protein segment relative to its surr oundings. Here we present an analytical method to determine the protein ori entational distribution from such data. The method produces the broadest di stribution compatible with the data by maximizing its informational entropy . The key advantages of this approach are that no a priori assumptions are required about the shape of the distribution and that a unique, exact fit t o the data is obtained. The relative orientations of the probes used for th e experiments have great influence on information content of the maximum en tropy distribution. Therefore, the choice of probe orientations is crucial. In particular, the probes must access independent aspects of the protein o rientation, and two-fold rotational symmetries must be avoided. For a set o f probes, a "figure of merit" is proposed, based on the independence among the probe orientations. With simulated fluorescence polarization data, we t ested the capacity of maximum entropy analysis to recover specific protein orientational distributions and found that it is capable of recovering orie ntational distributions with one and two peaks. The similarity between the maximum entropy distribution and the test distribution improves gradually a s the number of independent probe orientations increases. As a practical ex ample, WIE distributions were determined with experimental data from muscle fibers labeled with bifunctional rhodamine at known orientations with resp ect to the myosin regulatory light chain (RLC). These distributions show a complex relationship between the axial orientation of the RLC relative to t he fiber axis and the azimuthal orientation of the RLC about its own axis. Maximum entropy analysis reveals limitations in available experimental data and supports the design of further probe angles to resolve details of the orientational distribution.