AbstractA probability distribution of rate constants contained within an exponential-like saturation recovery (SR) electron paramagnetic resonance signal can be constructed using stretched exponential function fitting parameters. Previously (Stein et al. Appl. Magn. Reson. 2019.), application of this method was limited to the case where only one relaxation process, namely spin-lattice relaxations due to the rotational diffusion of the spin labels in the intact eye-lens membranes, contributed to an exponential-like SR signal. These conditions were achieved for thoroughly deoxygenated samples. Here, the case is described where the second relaxation process, namely Heisenberg exchange between the spin label and molecular oxygen that occurs during bimolecular collisions, contributes to the decay of SR signals. We have further developed the theory for application of stretched exponential function to analyze SR signals involving these two processes. This new approach allows separation of stretched exponential parameters, namely characteristic stretched rates and heterogeneity parameters for both processes. Knowing these parameters allowed us to separately construct the probability distributions of spin-lattice relaxation rates determined by the rotational diffusion of spin labels and the distribution of relaxations induced strictly by collisions with molecular oxygen. The later distribution is determined by the distribution of oxygen diffusion concentration products within the membrane, which forms a sensitive new way to describe membrane fluidity and heterogeneity. This method was validated in silico and by fitting SR signals from spin-labeled intact nuclear fiber cell plasma membranes extracted from porcine eye lenses equilibrated with different fractions of air.Statement of SignificanceMulti-exponential spin-lattice relaxation in complex membranous systems can be described by a stretched exponential function that provides a continuous probability distribution of relaxation rates rather than discreet relaxations from separate domains. The stretched exponential function has two fitting parameters, the characteristic spin-lattice relaxation rate (T1str−1) and the stretching parameter (β), obtained without any assumption about the number of membrane domains and their homogeneity. For membranes equilibrated with air, collisions with molecular oxygen provide an additional relaxation pathway for spin labels that depends on the oxygen-diffusion-concentration product in the vicinity of spin labels. This new approach allows separation of membrane fluidity and heterogeneity sensed by motion of lipid spin labels from those described by the translational diffusion of molecular oxygen.
Characterization of the Distribution of Spin–Lattice Relaxation Rates of Lipid Spin Labels in Fiber Cell Plasma Membranes of Eye Lenses with a Stretched Exponential Function