EPR spectra of spin labels in lipid bilayers

Assuming a probability function P(θ)αexp{(−q/RT)cos2Θ} for the orientation of the chain segments in a lipid bilayer, a quantitative theory for the spin label spectra of such systems is developed. Only three parameters, namely two energy parameters q3 and q1 and the correlation time τ20 are required to yield perfect agreement between experimental and theoretical spectra for correlation times up to 3 × 10−9 sec. In calculating the EPR spectra pseudosecular and nonsecular contributions to the linewidth are included, since especially the former exert a distinct influence on the spectra. Also discussed are the effects of tilt angle and spread angle. The theory is applied to the anisotropic motion of the fatty acid spin label I (13.2) in a decanol‐sodium decanoate bilayer. Between 44 and 8°C the correlation time is found to increase exponentially from 1.0 × 10−10 to 4.0 × 10−10 sec with an activation energy of 6.84 kcal mole−1. The energy parameters q3 and q1, which determine the order parameters S3 and S1, remain constant in the same temperature range (q3 = −2.9 kcal mole−1; q1 = 1.7 kcal mole−1). The average orientation of the chain segment is perpendicular to the bilayer normal. Below 8°C a phase transition occurs and the chain segments become gradually tilted. At −8°C the correlation time has increased to 2.8 × 10−9 sec and the chains are now tilted by approximately 18° from the bilayer normal. From the correlation time the translational diffusion constant can also be deduced. At 21°C a value of Dtrans = 1.5 × 10−6 cm2 sec−1 is obtained for the lipid molecules in the decanol‐sodium decanoate bilayer. In vesicles of dimyristoyl‐L‐α‐lecithin at 21°C the analysis of the spectrum yields a correlation time of 2.5 × 10−9 sec and a diffusion constant of the lipid molecules of Dtrans = 3.6 × 10−8 cm2 sec−1.