Values for and Significance of Order Parameters and "cone Angles" of Fluorophore Rotation in Lipid Bilayers

A rigid formalism has been 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 fluorophore 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 nuclear magnetic resonance data but are more readily compared to order parameters of electron spin resonance probes. There is no defined mathematical relation between the order parameter and a dynamical parameter which would afford a calculation of membrane "microviscosity". A Gaussian angular freedom parameter or cone angle of fluorophore motion has been 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.