X-ray Scattering Study of Pike Olfactory Nerve: Intensity of the Axonal Membrane, Solution of the Phase Problem and Electron Density Profile

Synchrotron radiation X-ray scattering experiments were performed on unmyelinated pike olfactory nerves. The difference between the meridional and the equatorial traces of the 2-D spectra yielded the 1-D equatorial intensity of the macromolecular components oriented with respect to the nerve: axonal membranes, microtubules and other cytoskeletal filaments. These 1-D spectra display a diffuse band typical of bilayer membranes and, at small s, a few sharper bands reminiscent of microtubules. All the spectra merge at large s. The intensity of the axonal membrane was determined via a noise analysis of the nerve-dependent spectra, involving also the notion that the thickness of the membrane is finite. The shape of the intensity function indicated that the electron density profile is not centrosymmetric. The knowledge of intensity and thickness paved the way to the electron density profile via an ab initio solution of the phase problem. An iterative procedure was adopted: (i) choose the lattice D of a 1-D pseudo crystal, interpolate the intensity at the points sh = h/D, adopt an arbitrary set of initial phases and compute the profile; (ii) determine the phases corresponding to this profile truncated by the thickness D/2; (iii) repeat the operation with the updated phases until a stable result is obtained. This iterative procedure was carried out for different D-values, starting in each case from randomly generated phases: stable results were obtained in less than 10,000 iterations. Most importantly, for D in the vicinity of 200 A, the overwhelming majority of the profiles were congruent with each other. These profiles were strongly asymmetric and otherwise typical of biological membranes.