On the relationship between C-C and C-D order parameters and its use for studying the conformation of lipid acyl chains in biomembranes

We have used the order tensor method to establish relationships between carbon-carbon and carbon-deuterium order parameters (SCC and SCD, respectively) in saturated and unsaturated lipid acyl chains in biomembranes. We thus confirm the existence of a recursion relation between these order parameters ( - 2S(k)(CD) = S-k(CC) + S-k+1(CC)) as was; previously shown using Wigner matrices formalism [Douliez, Leonard, and Dufourc, Biophys. J. 68, 1727 (1995)]. This leads to the determination of S-k(CC) as a function of the position k along the chain having experimentally measured the corresponding S-k(CD). Making use of a mean field approach for computing the energy of chain conformers in the frame of the rotational isomeric model (RIS) we have also calculated S-CC and S-CD order profile for the sn-l chain of dipalmitoylphosphatidylcholine. A very good agreement is obtained between computational and predicted S-k(CC) values, reinforcing the validity of the recursion relation. A marked odd-even effect is evidenced on the S-CC order profile for positions near the polar head, as was previously experimentally reported for dimyristoylphosphatidylcholine. We propose that this effect reveals an average bent orientation of the beginning of the chain with respect to the normal of the bilayer. Finally, it is shown that our formalism can be applied to some extent to cis or trans unsaturated lipid.