Restatement of order parameters in biomembranes: calculation of C-C bond order parameters from C-D quadrupolar splittings

Abstract

An expression for the C-C bond order parameter, SCC, of membrane hydrocarbon chains has been derived from the observed C-D bond order parameters. It allows calculation of the probability of each of the C-C bond rotamers and, consequently, the number of gauche defects per chain as well as their projected average length onto the bilayer normal, thus affording the calculation of accurate hydrophobic bilayer thicknesses. The effect of temperature has been studied on dilauroyl-, dimyristoyl-, and dipalmitoylphosphatidylcholine (DLPC, DMPC, DPPC) membranes, as has the effect of cholesterol on DMPC. The salient results are as follows: 1) an odd-even effect is observed for the SCC versus carbon position, k, whose amplitude increases with temperature; 2) calculation of SCC, from nonequivalent deuterons on the sn-2 chain of lipids, SCC2, leads to negative values, indicating the tendency for the C1-C2 bond to be oriented parallel to the bilayer surface; this bond becomes more parallel to the surface as the temperature increases or when cholesterol is added; 3) calculation on the sn-2 chain length can be performed from C1 to Cn, where n is the number of carbon atoms in the chain, and leads to 10.4, 12.2, and 13.8 A for DLPC, DMPC, and DPPC close to the transition temperature, TC, of each of the systems and to 9.4, 10.9, and 12.6 for T-TC = 30-40 degrees C, respectively; 4) separation of intra- and intermolecular motions allows quantitation of the number of gauche defects per chain, which is equal to 1.9, 2.7, and 3.5 for DLPC, DMPC, and DPPC near TC and to 2.7, 3.5, and 4.4 at T-TC = 30-40 degrees C, respectively. Finally, the validity of our model is discussed and compared with previously published models.