An analysis of lamellar x-ray diffraction from disordered membrane multilayers with application to data from retinal rod outer segments.

Oriented multilayers containing a membrane pair within the unit cell potentially possess both lattice disorder and substitution disorder. Lattice disorder occurs when there is a lack of long-range order in the lattice spacings produced by a variation in the nearest neighbor distances between unit cells. A simple form of substitution disorder can arise from a variation in the separation of the two membranes within the unit cells in the multilayer. Lattice disorder produces a monotonically increasing width for higher order lamellar "reflections" while simple substitution disorder produces an incoherent intensity underlying the coherent intensity. A generalized Patterson function analysis has been developed for treating lamellar diffraction from lattice disordered multilayers. This analysis allows the identification of the autocorrelation function of the unit cell electron density profile and its subsequent deconvolution to provide the unit cell electron density profile. A recursive procedure has been developed for separating the incoherent intensity from the coherent intensity via a Gaussian probability model of the membrane intra-pair separation. In cases studied so far both disorders can be quantitatively accounted for and eliminated from interfering with the phasing of the coherent intensity or distorting the derived electron density profile. Lamellar X-ray diffraction data from intact retinal rods, using either film or position sensitive detectors, shows severe effects of both forms of disorder which have not been taken into account in past analysis of such data. We have applied our analysis to the data on dark adapted rod outer segments in electrophysiologically intact retinas of Chabre and Cavaggioni (unpublished). An electron density profile is derived at 25 A resolution. The lattice nearest neighbor spacing has a variation of +/- 19 A out of a 295 A repeat. The intra-unit cell membrane pair center to center distance of 88 A varies +/-8 A.