EPR spectra of spin labels in lipid bilayers

Assuming a probability function $\mathrm{P(\theta )\alpha }\exp \mathrm{\{(-q/RT)}{\cos }^2\mathrm{\Theta \}}$ 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 D_trans = 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 D_trans = 3.6 × 10⁻⁸ cm² sec⁻¹.