Amino acid side chains torsion angles

Murphy et al. [34,45] have parameterized and extensively tested a QM/MM approach utilizing the frozen orbital method at the HF/6-31G and B3LYP/6-31G levels for amino acid side chains. They parameterized the van der Waals parameters of the QM atoms and molecular mechanical bond, angle and torsion angle parameters (Eq. 3, Hqm/mm (bonded int.)) acting across the covalent QM/MM boundary. High-level QM calculations were used as a reference in the parameterization and the molecular mechanical calculations were performed with the OPLS-AA force... 

A large number of chemical and physical properties, manifest in the amino acid side chains, have been thoroughly examined by many investigators. Attempts have been made to correlate these properties with their relatedness among protein sequences. What is most relevant is how these side chains interact with the backbone and with one another and what roles they each play within particular types of secondary and tertiary structure. The parametric description of residue environments with the help of solvent accessibility, secondary structure, backbone torsion angles, pairwise residue-residue distances, or Ca positions is the comparison between amino acid types at protein sequence positions and residue locations in structural templates. A recent review has evaluated and quantified the extent to which the amino acid type-specific distributions of commonly used environment parameters discriminate with respect to the 20 amino acid types (Sunyaev et al., 1998). Some of the important amino acid properties and residue environments are discussed below. 

Fig. 7.1 Protein building blocks. (A) The polypeptide chain, with a closeup showing the chemical form of the backbone , to which the side chains R , R +i,..., are attached. The (C=0) and (N-H) groups are linked by the peptide bond, which has a partial double bond character, making the (C=0)-(N-H) peptide group stiff and approximately planar. The torsion angles tj) and tfr, around single bonds, are soft. (B) The side chains R , R +i,..., can be any of the twenty common amino acid side chains, shown here labeled by their conventionial three-letter abbreviations (see also text). The horizontal axis corresponds roughly to the polarity of the sidechain the vertical axis corresponds to size. Reprinted from Thomas Simonson (2003) Electrostatics and dynamics of proteins. Reports on progresses in physics, vol 66, pp 737-787 with kind permission of lOP Pubhshing...

Mimicking a p-tum consists in constraining correctly four torsional angles (4>,4>2, P, P2) and four bonds (bonds a-d, cf. Fig. 2.3.3). Bonds a and d direct the entry and the exit of the peptide chain through the turn, respectively, whereas bonds b and c are responsible for the spatial dispositon of the amino acid side chains at position i+1 and i+2 of a turn. The torsional angles determine the backbone geometry of the turn and consequently the shape of the turn hydrogen... 

Hence, the set of incremental coefficients ACq is included in the fitting process. The authors used this formulation within a self-consistent fitting approach [81] to obtain very accurate amino acid-specific Karplus parameters for the six vicinal -couplings that probe the side-chain torsion angle x by making use of six additional AC parameters. In a subsequent study, the results were further improved by introducing an additional sine term to account for asymmetry effects. 

Fig. 2. (A) Backbone and side chain torsional angles (B) Newman projection of three staggered rotamers in L-amino acids.

Figure 1 Stylized representation of a portion of a polypeptide chain, indicating the nomenclature of the backbone torsion angles (p and p) and the side-chain torsion angle (x ) for the bonds emanating from the a carbon of an amino acid residue(/).

Torsion angles, in addition, may be used to designate the conformation of the side chains. These are denoted by x (x X working along the chain away from Ca). The steric interactions within the side chains in the trans form of the peptide bond (u> = 180°) are much more favorable than those in the cis form (w = 0°), where there may also be steric interference with side chains from residues i- -2. If the residue i+1 is proline, however, the cis and trans forms (Figure 12.25) have similar energies. Proline is the only amino acid taking part in a cis peptide that is normally encountered in proteins. 

The Sizes of Some Atoms Structure and Chemical Properties of Side Chain Groups of Amino Acids Approximate Torsion Angles for Some Regular Peptide Structures Classification of Protein Residues According to Their Tendencies to Form a Helix, P Structure, and P Turns... 

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