Values for and significance of order parameters and "cone angles" of fluorophore rotation in lipid bilayers

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Abstract
A rigid formalism was developed for the calculation of the order parameter S for fluorescence probes embedded in environments that hinder the motions of the probes and for calculation of a cone angle of gluorophore rotation from the order parameters. The motions of the fluorescence probes 1,6-diphenylhexa-1,3,5-triene (DPH) and 1-[4-(trimethylamino)phenyl]-6-phenylhexa-1,3,5-triene (TMA-DPH) embedded in lipid bilayers were then analyzed in terms of the order parameter and the cone angle. Order parameters for such fluorescence can only be compared to the average order parameter over a segment of a fatty acyl chain or of membrane thickness. Also, because the bilayer may be perturbed by the fluorophore at regions distant from the immediate location of the probe, these averaged order parameters cannot be easily compared to those calculated from NMR data but are more readily compared to order parameters and a dynamical parameter which would afford a calculation of membrane microviscosity. A Gaussian angular freedom parameter or cone angle of fluorophore motion was calculated from the order parameters and shows in a geometric sense the limitations imposed on the angular displacements of TMA-DPH as compared to DPH.

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