in that the is assumed to have the smoothest possible distribution of electron density. Contributions from side chains of varying size and disposition are subsumed in the smoothness assumption. Model ing by this procedure with data to 3 A resolution axially and 4 A resolution radially produced a model that is a gently bent, continuous IX-helix of 1 3 turns. The axis of approximately the first five turns is approximately parallel to the main virion axis (Figure 10 of Reference 81) . The overall shapes of the three models are similar, as indicated by the lattice diagram of Figure 4. Ff Subunit Structure Determination Opella and his coworkers ( 108) have undertaken to determine the structure of the Ff subunits by measuring the nuclear magnetic spin interaction tensors for all 49 peptide backbone planes in the molecule. The spin interaction data, including dipole-dipole spin coupling, chemical shift anisotropy, and quadrupole interactions, yield a limited set of orientation angles for each peptide plane relative to its neighbors and to the main structure axis. The data also provide information on radial positioning due to the dependence of dipole-dipole interactions on distance. The set Table 4 Structural parameters for the protein coats Parameter Ff Xf Pfl PO References Symmetry of helix Rise per subunit (A) 16.0-16.2b 2.85 2.78-3.05 2.78-2.96 37,80,8�88, 101, 112 Rotation per subunitC _30.00b _66.7° -65.9--66.r -66.7° 77,85,88, 101, 112, 157 Pitch of helix' (A) 16.0-16.2b 15.4 15.0-16.6 15.0-15.8 37,80,85,88,101, 112 Symmetry designationd CSS2.0 CISS.4 CISS.4-- CISS.46 CISS.4 75 Symmetry designation (2/10; 3/15) (2/11; 3/17) (2/11; 3.17) (2/11; 3/17) 91 Subunit IX-helix content and orientation CD amplitudesf 18,33, 138 [111208 (cm2 deg dmol-') -27,000 -18,000 -35,000 -31,000 [111m (em2 deg dmol-') -41,000 -15,000 -32,000 -38,000 % IX-Helix 80-100 40--6 5 80-100 80-100 Raman 1650 cm -I amide I band 136, 137, 139 Deconvolved components 1648 (0.92) 1646 (0.71) 1652 (1.0) 1645 (0.82) 1667 (0.08) 1658 (0.29) 1666 (0.08) % IX-Helix 92 71 100 82 Infrared 1650 em-I amide I band 43,44 % IX-Helix 95-100 90-100 Average a-helix inclination to axis Birefringence 20-30° 145 Infrared dichroism 37±W 30± 10° 43, 44 NMR _10° -0, 20° 29, 108 • Helical parameters observed by fiber diffraction for various experimental conditions of temperature, humidity, and chemical modification. b Ff possesses fivefold rotational symmetry (76, 77, 104); the translation and rotation per pentamer of subunits are listed. cThe rotation per is limited to a narrow range afvalues, even far large changes in experimental conditions (91). d Symmetry notation of Klug et al (63a) (see text and Reference 75). An alternative notation gives the number af subunits and the number of helical turns in the apparent structural repeat, such as 27u/5t = 5.4 ult or 7Iu/13t = 5.46 u/t far Pfl (8\). 'N otation developed in a theoretical treatment of the symmetries of the filamentous phages (see text and Reference 91). f See Figure 6. Ul IV 0 > - Crl ..., > t' DNA PACKING IN FILAMENTOUS PHAGE 525
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