Ramachandran angles

Fig. 2. Sketch of the polypeptide backbone illustrating the Ramachandran angles...

In between rounds of computerized refinement, maps were computed using IFobsls from the ALBP data set and acalcs from the current model [taken from IFcalcls computed by Eq. (5.15)]. The model was corrected where the fit to maps was poor, or where the Ramachandran angles and P were forbidden. Notice that the use of 2F0 — Fc and Fc — Fc maps [Eqs. (7.4) and (7.5)] is as... 

Fig. 9. Schematic drawing of alanine dipeptide with the Ramachandran angles, 4>, i ) depicted...

Proteins are polypeptides where the degrees of freedom are restrained by the establishment of H-bonds. In a polypeptide the Ramachandran angles d> and 4 of each peptide (amide) group, shown in Figure 2.4, adopt any value. In a protein they adopt well-defined values that allow the establishment of intrachain H-bonds. These H-bonds make the corresponding conformations more stable than other ones. Such stabilized conformations constitute... 

An alternative convention useful in analyzing geometry of the backbone chain entails the description of pseudobonds between successive C atoms (Oldfield and Hubbard, 1994), because they form dihedral angle involving four consecutive (T atoms. This formahsm captures concisely more characteristics of the space-curve traced by the main chain than do the Ramachandran angles. Thus it has become a standard representation in studies of protein folding (Skolnick et al., 1997). 

Drobny et al. have reported solid-state NMR experiments that provide information on the structures of surface-immobilised peptides. The peptides were covalently bound to alkanethiolates that are self-assembled as monolayers on colloidal gold nanoparticles. The secondary structure of the immobilised peptides was characterised by quantifying the Ramachandran angles (j) and /. 

Advancing techniques for obtaining laser light in the UV have opened the door to time-resolved resonance Raman studies of tyrosine, phenylalanine and tryptophan residues in proteins [41, 61-68]. UV resonance Raman appears to be a potentially powerful source of information on the secondary structure and the distribution of Ramachandran angles in polypeptides [69, 70], and provides a way of probing the S-C-C-S dihedral angle of cystine residues in proteins [71]. 

Fig. 5 Bonded structural parameters in AA and CG representations of a protein s backbone. The top panel evidences the angle y and dihedral co required to describe the relative position of consecutive C s along the protein backbone trace. The bottom panel highlights the connection between the angle y and the AA Ramachandran angles (p,

To illustrate the significance of CVs selection in MetaD and in other enhanced samphng schemes, the same calculation is now repeated but using the Ramachandran angle O as the CV. The a was chosen according to the same procedure oudined above to be 0.1 rad while keeping all the other parameters identical. 

In order to quantify the tendencies of these peptides to form secondary stmctures, it is useful to investigate the average a-helical and -strand content as a function of temperature. We define a residue as or-helical if its Ramachandran angles

6 (-150°, -90°) and 6 (90°, 150°). 

The angle pairs iji and <)/ are usually plotted against each other in a diagram called a Ramachandran plot after the Indian biophysicist G.N. Ramachandran who first made calculations of sterically allowed regions. Figure 1.7 shows the results of such calculations and also a plot for all amino... 

FIGURE 5.2 The peptide bond is shown in its usnal trans conformation of carbonyl O and amide H. The atoms are the oi-carbons of two adjacent amino acids joined in peptide linkage. The dimensions and angles are the average valnes observed by crystallographic analysis of amino acids and small peptides. The peptide bond is the light gray bond between C and N. (Adapted from Ramachandran, G. A., ct ai, 1974. Biochimica Biophysica Acta 359 298-302.)... 

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. 

Regions of ordered secondary structure arise when a series of aminoacyl residues adopt similar phi and psi angles. Extended segments of polypeptide (eg, loops) can possess a variety of such angles. The angles that define the two most common types of secondary structure, the a helix and the (5 sheet, fall within the lower and upper left-hand quadrants of a Ramachandran plot, respectively (Figure 5-1). 

Figure 5-1. Ramachandran plot of the main chain phi (< ) and psi (T) angles for approximately 1000 nonglycine residues in eight proteins whose structures were solved at high resolution. The dots represent allowable combinations and the spaces prohibited combinations of phi and psi angles. (Reproduced, with permission, from Richardson JS The anatomy and taxonomy of protein structures. Adv Protein Chem 1981 34 167.)...

PPII helix is illustrated in Figure 8a. It consists of a left-handed extended helical conformation in which the angles of the constituent residues are restricted to values around —78°, +146° corresponding to a region of the Ramachandran surface adjacent to the /3-region (Fig. 8b). This imparts a perfect threefold rotational symmetry to the structure... 

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 5.65 provides theoretical evidence that resonance-assisted H-bonding can serve as an effective mechanism for switching a methyl rotor from one preferred conformation to another, or for controlling the stiffness of torsional motions in alkylated amides. In particular, the torsional potentials of proteins (more specifically, the Ramachandran b angle at Ca) should be sensitive to N—H- O and related H-bonding interactions involving the amide backbone. In principle, this electronic... 

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