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X-ray diffraction data from polyoma capsid crystals were phased by refinement of low-resolution starting models to obtain a self-consistent structural solution. The unexpected result that the hexavalent morphological unit is a pentamer shows that specificity of bonding is not conserved among the protein subunits in the icosahedrally symmetric capsid.

Polyomavirus major capsid protein VP1, purified after expression of the recombinant gene in Escherichia coli, forms stable pentamers in low-ionic strength, neutral, or alkaline solutions. Electron microscopy showed that the pentamers, which correspond to viral capsomeres, can be self-assembled into a variety of polymorphic aggregates by lowering the pH, adding calcium, or raising the ionic strength. Some of the aggregates resembled the 500-A-diameter virus capsid, whereas other considerably larger or smaller capsids were also produced. The particular structures formed on transition to an environment favoring assembly depended on the pathway of the solvent changes as well as on the final conditions. Mass measurements from cryoelectron micrographs and image analysis of negatively stained specimens established that a distinctive 320-A-diameter particle consists of 24 close-packed pentamers arranged with octahedral symmetry. Comparison of this unexpected octahedral assembly with a 12-capsomere icosahedral aggregate and the 72-capsomere icosahedral virus capsid by computer graphics methods indicates that similar connections are made among trimers of pentamers in these shells of different size. The polymorphism in the assembly of VP1 pentamers can be related to the switching in bonding specificity required to build the virus capsid.

Models for the spatial distribution of protein, lipid and water in gap junction structures have been constructed from the results of the analysis of X-ray diffraction data described here and the electron microscope and chemical data presented in the preceding paper (Caspar, D. L. D., D. A. Goodenough, L. Makowski, and W. C. Phillips. 1977. 74:605-628). The continuous intensity distribution on the meridian of the X-ray diffraction pattern was measured, and corrected for the effects of the partially ordered stacking and partial orientation of the junctions in the X-ray specimens. The electron density distribution in the direction perpendicular to the plane of the junction was calculated from the meridional intensity data. Determination of the interference function for the stacking of the junctions improved the accuracy of the electron density profile. The pair-correlation function, which provides information about the packing of junctions in the specimen, was calculated from the interference function. The intensities of the hexagonal lattice reflections on the equator of the X-ray pattern were used in coordination with the electron microscope data to calculate the two-dimensional electron density projection onto the plane of the membrane. Differences in the structure of the connexons as seen in the meridional profiles and equatorial projections were shown to be correlated to changes in lattice constant. The parts of the junction structure which are variable have been distinguished from the invariant parts by comparison of X-ray data from different specimens. The combination of these results with electron microscope and chemical data provides low-resolution threedimensional representations of the structures of gap junctions.The structural variations detailed in the preceding paper (5) establish that we are looking at not one structure of the gap junction, but at a family of structures. By observing closely related states of a molecular assembly, it is often possible to infer something about the way that transitions occur between states. These molecular rearrangements may be significant in the functional activity of the structure. Furthermore, polymorphism provides a constraint on the interpretation of the diffraction patterns. For example, the connexon structure is likely to be similar in arrays with different lattice constants, although the intensities in the X-ray patterns may be quite different.