Peptides dihedral angle

Amino acids are combined (linked together) through peptide bonds (-C-N-) (Figure 8.1) the peptide bond formed is planar (flat), due to the delocalisation of electrons that form the partial double bond, restricting rotation about the bond. The rigid peptide dihedral angle, co (the bond between C and N), is always close to 180°. The dihedral angles phi (the bond between N and Ca) and psi (the bond between Ca and C) can only have a number of possible values, and so effectively control the protein s three-dimensional structure. 

Two simple shape descriptors use local properties of special bonds to characterize a macromolecular structure. These are the helical content and the distribution of peptidic dihedral angles (the Ramachandran diagram). 

If peptide residues are converted to peptoid residues, the conformational heterogeneity of the polymer backbone is likely to increase due to cis/trans isomerization at amide bonds. This will lead to an enhanced loss of conformational entropy upon peptoid/protein association, which could adversely affect binding thermodynamics. A potential solution is the judicious placement of bulky peptoid side chains that constrain backbone dihedral angles. 

Tab. 2.2 Comparison of backbone dihedral angles between 3i4-helical j8-peptides 2 and 66...

Peptides built from y-amino acids with L-amino acid-derived chirahty centers form a right-handed (P)-2.6i4 hehx of ca. 5 A pitch with both ethane bonds in a -y)-synclinal conformation (mean values for dihedral angles 9 and 82 of central residues 2-5 in compounds 141 are 72.5 and 64.3°, respectively Fig. 2.36 A and B Tab. 2.8). 

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.

Fig. 3 Protonation states, isomerism and mesomerism of the HBI chromophore (p-hydroxybenzi-lidene-imidazolinone). The chromophore is shown in its most stable Z ( cw ) conformation, conventionally associated to a 0° value of the dihedral angle t, while the E ( trans ) conformation corresponds to t = 180°. For model compound HBDI (4 -hydroxy-benzylidene-2,3-dimethyl-imidazolinone), Ri = R2 = CH3, for chromophore in GFP, Ri, and R2 stand for the peptidic main chains toward N-terminus and C-terminus, respectively, (a) Possible protonation states of HBI (a) neutral, (b) anionic, (c) enolic, (d) cationic, and (e) zwitterionic. (b) Two resonance structures of the anionic form of HBI...

The characteristic properties of peptides result from the presence of a chain of several or many amide bonds. A first problem is that of numbering, and here Fig. 6.1 taken from the IUPAC-IUB rules may help. A second and major aspect of the structure of peptides is their conformational behavior. Three torsion angles exist in the backbone (Fig. 6.2). The dihedral angle co (omega) describes rotation about C-N,

rotation about N-C , and ip (psi) describes rotation about C -C. Fig. 6.2 represents a peptide in a fully extended conformation where these angles have a value of 180°. 

In addition to the backbone angles discussed above, the conformational hyperspace of peptides also includes the dihedral angles of the residue side... 

Now that about 70 different disulfides have been seen in proteins and more than 20 of those have been refined at high resolution, it is possible to examine disulfide conformation in more detail, as it occurs in proteins. Many examples resemble the left-handed small-molecule structures extremely closely Fig. 46 shows the Cys-30-Cys-115 disulfide from egg white lysozyme. The x > Xs and x dihedral angles and the Ca-Ca distance can be almost exactly superimposed on Fig. 45 the only major difference is in Xi All of the small-molecule structures have Xi close to 60°. Figure 47 shows the Xi values for halfcystines found in proteins. The preferred value is -60° (which puts S-y trans to the peptide carbonyl), while 60° is quite rare since it produces unfavorable bumps between S-y and the main chain except with a few specific combinations of x value and backbone conformation. 

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. 

In proteins, specific combinations of the dihedral angles c ) and / (see p. 66) are much more common than others. When several successive residues adopt one of these conformations, defined secondary structures arise, which are stabilized by hydrogen bonds either within the peptide chain or between neighboring chains. When a large part of a protein takes on a defined secondary structure, the protein often forms mechanically stable filaments or fibers. Structural proteins of this type (see p. 70) usually have characteristic amino acid compositions. 

The most important secondary structural elements of proteins are discussed here first. The illustrations only show the course of the peptide chain the side chains are omitted. To make the course of the chains clearer, the levels of the peptide bonds are shown as blue planes. The dihedral angles of the structures shown here are also marked in diagram D1 on p. 67. 

Miller also explored the ASD of glycerol derivatives through an enantioselective acylation process which relies on the use of a pentapeptide-catalyst which incorporates an A-terminal nucleophilic 3-(l-imidazolyl)-(5)-alanine residue [171], Most recently, Miller has probed in detail the role of dihedral angle restriction within a peptide-based catalyst for ferf-alcohol KR [172], site selective acylation of erythromycin A [173], and site selective catalysis of phenyl thionoformate transfer in polyols to allow regioselective Barton-McCombie deoxygenation [174],... 

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... 

Figure 3 The collapse of the peptide Ace-Nle30-Nme under deeply quenched poor solvent conditions monitored by both radius of gyration (Panel A) and energy relaxation (Panel B). MC simulations were performed in dihedral space 81% of moves attempted to change angles, 9% sampled the w angles, and 10% the side chains. For the randomized case (solid line), all angles were uniformly sampled from the interval —180° to 180° each time. For the stepwise case (dashed line), dihedral angles were perturbed uniformly by a maximum of 10° for 4>/ / moves, 2° for w moves, and 30° for side-chain moves. In the mixed case (dash-dotted line), the stepwise protocol was modified to include nonlocal moves with fractions of 20% for 4>/ J/ moves, 10% for to moves, and 30% for side-chain moves. For each of the three cases, data from 20 independent runs were combined to yield the traces shown. CPU times are approximate, since stochastic variations in runtime were observed for the independent runs. Each run comprised of 3 x 107 steps. Error estimates are not shown in the interest of clarity, but indicated the results to be robust.

Fitzgerald, J.E., Jha, A.K., Sosnick, T.R., Freed, K.F. Polypeptide motions are dominated by peptide group oscillations resulting from dihedral angle correlations between nearest neighbors. 

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