Lateral Diffusion of Intramembrane Particles in a Biomembrane: Dependence of Rates on Intramembrane Particle Concentrations and Membrane Curvature
Authors: Sowers Arthur E. , Hackenbrock Charles R. 
Published: June 2020

We have previously described a new technique using freeze-fracture electron microscopy to measure the lateral diffusion coefficient of integral proteins in suspensions of spherical-shaped preparations of mitochondrial inner membranes. Freeze-fracture electron microscopy was used to determine the lateral distribution of individual integral proteins which appear as intramembrane particles (IMP). An electric current pulse was applied to a membrane suspension to generate an electrophoretic force which caused the IMP, originally randomly distributed, to migrate to form an IMP-rich patch (Fig. 1). When the current was withdrawn, the integral proteins returned by diffusion back to a random distribution. Membranes which were frozen at a known time, t, after cessation of the current pulse but before rerandomization was complete showed gradients in the lateral distributions of IMP. These gradients were quantitatively measured and related to a mathematical model for diffusion of particles on a spherical membrane. This mathematical model relates the time-dependent change in the particle gradient to the time-dependent rate of return to a random distribution. The lateral diffusion coefficient, D, of the IMP was calculated from the equation D = R2/2τ, where R = radius of the sphere and τ = length of the time constant in seconds.

Membrane suspensions were quick frozen at 2.0 sec after the end of the electric current pulse as described previously. Fractured membranes were micrographed at three known tilt angles to calculate the actual radius, R, of the sphere from the apparent radius of the dome formed by the intersection of the sphere with the ice surface. These three adjacent equal area square sample areas were drawn with their centers on a line parallel to the gradient (Fig. 2a). IMP in the sample areas were counted by placing an ink dot over each one on a transparent film laid over the micrograph (Fig. 2b). The measured IMP gradient for each membrane was superposed on a family of computer-generated curves to determine the time constant for the IMP concentration gradient of a given membrane (Fig. 3).

Quantitative analysis of the convex fracture faces of 22 membranes yielded data with the following ranges in values: a) radii of 0.22 to 1.15 μm, b) IMP concentrations of 2300 -6400 per μm, c) time constants of 1.12-2.75 sec, and d) diffusion coefficients of 1.3 x 10-10- 3.5 x 10-9cm2/ sec. When plotted as a function of membrane radius and as a function of IMP concentration, the diffusion coefficient is directly related to the membrane radius and inversely related to IMP concentrations (Fig. 4).

The data show a) an inverse correlation between D and IMP concentration and b) a direct correlation between D and radius of the membrane analyzed. The first observation suggests that the integral protein concentration in the membrane can have a marked influence on D. The second observation indicates that D has a strong relationship to membrane curvature, membrane total area, or both.