Ramachandran dihedral angle

Figure 2 Molecular representation of alanine dipeptide. The two Ramachandran dihedral angles are denoted with

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.

Figure 12 Time evolution of the Ramachandran dihedral angle during metadynamics (a) and evolution of the deposited bias over time (b).

Figure 14 RMSD from the two Cj and reference structures during the metadynamics run that uses the Ramachandran dihedral angle 4> as CV in metadynamics.

We revise here the last example to show how the diagnostics change when the CV is well chosen. As before, we adopt the 4> Ramachandran dihedral angle as a biased CV. 

An additional intricacy to be considered is that two variables are often coupled as in the case of the two Ramachandran dihedral angles 4> and T. These angles contain three atoms in common. Therefore, some sort of coupling should be introduced into the scheme to account for their interdependence. 

Make a plot of / (vertical axis) vs. (j) (horizontal axis) with /=0, ( )=0 in the middle and ranging from -180° to 180° for both variables. Put a point on your plot for each dihedral angle (in each conformer). You have constructed what is now known as a Ramachandran plot. 

Fig. 1. Conformational energy diagram for the alanine dipeptide (adapted from Ramachandran et al., 1963). Energy contours are drawn at intervals of 1 kcal mol-1. The potential energy minima for p, ofR, and aL are labeled. The dependence of the sequential d (i, i + 1) distance (in A) on the 0 and 0 dihedral angles (Billeter etal., 1982) is shown as a set of contours labeled according to interproton distance at the right of the figure. The da (i, i + 1) distance depends only on 0 for trans peptide bonds (Wright et al., 1988) and is represented as a series of contours parallel to the 0 axis. Reproduced from Dyson and Wright (1991). Ann. Rev. Biophys. Chem. 20, 519-538, with permission from Annual Reviews.

Figure 7 Dihedral angles, atoms, and bonds of a proline ring. Adapted from R. Balasubramanian A. V. Lakshminarayanan M. N. Sabesan G. Tegoni K. Venkatesan G. N. Ramachandran, Int J. Protein Res. 1971, 3, 25-33.

The favoured dihedral angles for protein main chains were derived from energy considerations of steric clashes in peptides giving the well known Ramachandran plot (Ramachandran and Sasisekharan, 1968). These phi/psi combinations characterize the elements of secondary structure. Accurate main chain models can be constructed from spare parts, that is short pieces of helices, sheets, turns, and random coils taken from highly refined structures, provided a series of C-alpha positions can be established from the electron density map... 

A Ramachandran plot of the dihedral angles and is shown in Fig. 6b. The outline of the allowed area is taken from Fig. 38a in Ramachandran and Sasisekharan (72a). The only residue well outside of this contour is 60. 

Structural Properties of Crystalline ALBP. A Ramachandran plot of the main chain dihedral angle and Tr is shown in Fig. 8.6. In the refined model, 13 residues have positive angles, 9 of which belong to glycine residues. There are 11 glycine residues in ALBP, all associated with good quality electron density. 

Fig. 1.2.1. Conventions for naming the dihedral angles , if/, co, and / illustrated by a model dipeptide. Only certain backbone dihedral angles Ramachandran space, and % (chi space) are populated by each amino acid. 

Finally, the structure of the thermodynamically favored isomer of [l2(OCH3)2Ti2]2- was deduced from conformational analysis of X-ray structural data of some of the complexes using Ramachandrarfs method. The dihedral angles and T of the amino acid residues observed in the X-ray structures were determined and were correlated in a Ramachandran diagram. 

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 10.1 Basic polypeptide geometry. The upper panel shows a short peptide sequence of three amino acids joined by two peptide bonds. A relatively rigid planar structure, indicated by dashed lines, is formed by each peptide bond. The relative positions of two adjacent peptide bond planes is determined by the rotational dihedral angles

Ramachandran plot. Because of steric hindrance, only certain combinations of the main-chain dihedral angles

protein fold may force some residues to assume unallowed functional significance for some active site residues. However, if more than a few percent of aU the residues have [Pg.619]

Only certain , y conformation pairs are observed. This is usually described in terms of the Ramachandran diagram, as shown in Figure 5.8, with as the horizontal axis and y as the vertical axis. In Figure 5.8, the experimentally determined backbone dihedral angles for the alanine, glycine, and proline residues of 699 proteins are depicted. There are three basic... 

---