Dihedral angles <I> and

Figure 1 The principal sources of structural data are the NOEs, which give information on the spatial proximity d of protons coupling constants, which give information on dihedral angles < i and residual dipolar couplings, which give information on the relative orientation 0 of a bond vector with respect to the molecule (to the magnetic anisotropy tensor or an alignment tensor). Protons are shown as spheres. The dashed line indicates a coordinate system rigidly attached to the molecule.

Ramachandran pointed out that the folding of a protein depends on the conformation adopted by the two central cr-bonds of each amino acid and that this conformation can be described by using the dihedral angles and... 

Figure 4.8. Definition of the dihedral angles i/> and formed at grain-boundary grooves in the...

Figure 3 Representation of the free-energy landscape for alanine dipeptide as a function of the two Ramachandran dihedral angles and Each isoline accounts for 1 kcal/mol difference in free energy. The two main minima, namely, 7eq and 7ax> are labeled.

Fig. 19. Calculated coupling strength f (in cm-1, thin line) (Torri and Tasumi, 1998) and angle 0 (in degrees, thick line) between the two amide I transition dipoles as a function of the dihedral angles 0 and 0. From Woutersen and Hamm (2001)./. Chem. Phys. 114, 2727-2737, 2001, Reprinted with permission from American Institute of Physics.

Fig. 8. Plot of main chain dihedral angles and i/i experimentally determined for the glycines in 20 high-resolution protein structures.

With the exception of the terminal residues, every amino acid in a peptide is involved in two peptide bonds (one with the preceding residue and one with the following one). Due to the restricted rotation around the C-N bond, rotations are only possible around the N-C and C -C bonds (2). As mentioned above, these rotations are described by the dihedral angles ( ) (phi) and ]> (psi). The angle describes rotation around the N-C bond / describes rotation around Ca-C—i.e., the position of the subsequent bond. 

Fig.3 The dependences on the dihedral angles(< >,i /), of the isotropic chemical shielding constant for the L-alanine residue Cp- (a)and Ca-(b) carbons in peptides. Chemical shielding calculations were carried out using the GIAO-CHF method with 4-31G ab initio MO basis set. The 4-31G optimized geometries for the model molecules, N-acetyl-N -methyl-L-alanineamide, were employed.

The 13C chemical shift contour map for the Cp carbon of the L-alanine residue in peptides and polypeptides was made as a function of the dihedral angles(, W) by using the experimental data. Also, the corresponding calculated map was made by using the ab initio coupled Hartree-Fock method with the gauge included atomic orbitals(GIAO-CHF). From these results, it was found that the calculated map explains the chemical shift behavior of the a-helix and p-sheet forms in poly(L-alanine) and some proteins. This suggests that the calculated map is applicable to the structural analysis of proteins with complicated structure. 

Figure 3.1 Dihedral angles and i/r for tyrosyl dipeptide analogue (a-acetylamino-tyrosyl-N-methylamide, TDA).

Figure 18-1. Schematic of alanine dipeptide showing the dihedral angles (f> and i/r and the numbering used in the radial distribution functions of Figure 18-5...

Figure 17. Depiction of one of the dihedral angles (()> I between ligand SMS and trigonal SSS planes. As a structure distorts from TP to OCT geometry, the ligands twist and < > becomes <90°.

The middle panel of Figure 10-20 shows a comparison of the time-evolution of the c(6 )0(6)N(4)C(4) dihedral angle, 0, and AE. After about 50 fs, 0 starts to deviate significantly from zero bringing the system away from planarity. We notice that at the moment when AE is smallest (t 88 fs) the molecular structure is highly non-planar with 0 —18°. Furthermore, the peak in AE at about 106 fs coincides with a small absolute value of 0, i.e. near-planarity of the molecule. 

Side-chains were substituted to match the sequence of the Fv R45. We set up the dihedral angles x 1 and x2 (Table I) according to the highest probability found in the rotamer library established by Tuffery et al. (1991). Dihedral angles x3 and x4 were set to 180°. Consequently, each amino acid side chain displays the same starting conformation. 

Fig. 10. 3D plot and contour map for Vhccch in propane, calculated as a function of the dihedral angles ip, and ip3 by DFT/FPT at 30° intervals of the angles. 3D spline interpolations were used to create the graphs, which illustrate how the coupling constant changes sign, depending on the values of, i and, ... 

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