DNA structure models deduced from X-ray and physicochemical data for Pfl, Xf, and fd viruses have two antiparallel chains wound in helices of approximately 15 A pitch with the phosphates near the structure axes and the bases directed outward. The models, which differ for each virus, are used to interpret ultraviolet absorbance and fluorescence data in terms of DNA protein interactions.
The capsids of the spherical viruses all show underlying icosahedral symmetry, yet they differ markedly in capsomere shape and in capsomere position and orientation. The capsid patterns presented by the capsomere shapes, positions, and orientations of three viruses (papilloma, SV40, and N beta V) have been generated dynamically through a bottom-up procedure which provides a basis for understanding the patterns. A capsomere shape is represented in two-dimensional cross-section by a mass or charge density on the surface of a sphere, given by an expansion in spherical harmonics, and referred to herein as a morphological unit (MU). A capsid pattern is represented by an icosahedrally symmetrical superposition of such densities, determined by the positions and orientations of its MUs on the spherical surface. The fitness of an arrangement of MUs is measured by an interaction integral through which all capsid elements interact with each other via an arbitrary function of distance. A capsid pattern is generated by allowing the correct number of approximately shaped MUs to move dynamically on the sphere, positioning themselves until an extremum of the fitness function is attained. The resulting patterns are largely independent of the details of both the capsomere representation and the interaction function; thus the patterns produced are generic. The simplest useful fitness function is sigma 2, the average square of the mass (or charge) density, a minimum of which corresponds to a "uniformly spaced" MU distribution; to good approximation, the electrostatic free energy of charged capsomeres, calculated from the linearized Poisson-Boltzmann equation, is proportional to sigma 2. With disks as MUs, the model generates the coordinated lattices familiar from the quasi-equivalence theory, indexed by triangulation numbers. Using fivefold MUs, the model generates the patterns observed at different radii within the T = 7 capsid of papilloma and at the surface of SV40; threefold MUs give the T = 4 pattern of Nudaurelia capensis beta virus. In all cases examined so far, the MU orientations are correctly found.
The relations between the protein coats and DNAs of the four filamentous bacteriophages fd, Xf, Pf1, and Pf3 are considered. These viruses have similar morphologies, yet show a diversity of detailed structure, having different protein coat symmetries (helical and rotational), different coat protein sizes (44-50 amino acids per subunit) and sequences, different nucleotide axial translations (2.3-5.5 A), and different ratios of nucleotides per coat protein subunit (integers 1.0 and 2.0, and nonintegers approximately 2.4). These divergences are all reconciled quantitatively by means of two theoretical concepts: the pitch connection and the restricted pitch connection. The pitch connection relates protein and DNA surface lattices with arbitrary, nonintegral nucleotide/subunit ratios in a nonrandom way. The restricted pitch connection selects a preferred set of n/s values. Both relations are derived formally in a mathematical appendix. The available structural data are explained, including the fd DNA pitch indicated by x-ray diffraction photos and the similar DNA morphologies of Xf and fd. Predictions are made for the existence of nonclassical inverted DNA structures (I-DNA) in Pf1 and Pf3.
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