Proteins dihedral angles

Yang, D. W., Konrat, R., and Kay, L. E. (1997). A multidimensional NMR experiment for measurement of the protein dihedral angle psi based on cross-correlated relaxation between (H alpha-13C alpha) XH dipolar and 13C (carbonyl) chemical shift anisotropy mechanisms. J. Am. Chem. Soc. 119,11938-11940. 

Here we proposed a physically based approximation to get around this problem. We separate the coordinate set X into two domains X " and where slow and fast are with respect to the rate of approaching equilibrium. For example, we argue that the translation and rotation degrees of freedom of a bulk water molecule relax to equilibrium more rapidly than the protein dihedral angles of an amino acid i. 

In the above-mentioned example, the time scale of 100 picoseconds is probably in that range. It is significantly longer than the local orientation and translation relaxation of the water molecules but too short to allow complete relaxation of the protein dihedral angles. If such a time step, Af, is used in Ssdet calculation, it eliminates the need to follow the explicit dynamics of the water molecules. On this time scale, in a single step, the water molecules will already relax to equihbrium (with a frozen configuration of the slow protein). Their explicit dynamics will become irrelevant. 

Disulfides. The introduction of disulfide bonds can have various effects on protein stability. In T4 lyso2yme, for example, the incorporation of some disulfides increases thermal stability others reduce stability (47—49). Stabili2ation is thought to result from reduction of the conformational entropy of the unfolded state, whereas in most cases the cause of destabili2ation is the introduction of dihedral angle stress. In natural proteins, placement of a disulfide bond at most positions within the polypeptide chain would result in unacceptable constraint of the a-carbon chain. 

Einally, structural properties that depend directly neither on the data nor on the energy parameters can be checked by comparing the structures to statistics derived from a database of solved protein structures. PROCHECK-NMR and WHAT IE [94] use, e.g., statistics on backbone and side chain dihedral angles and on hydrogen bonds. PROSA [95] uses potentials of mean force derived from distributions of amino acid-amino acid distances. 

Q Zheng, R Rosenfeld, C DeLisi, DJ Kyle. Multiple copy sampling in protein loop modeling Computational efficiency and sensitivity to dihedral angle perturbations. Protein Sci 3 493-506, 1994. 

The structures of amino acids incorporated into polypeptides and proteins may be characterized by a pair of dihedral angles involving the so-called a carbon for each amino acid. 

As mentioned in the Introduction, in iron—sulfur proteins, the hyperfine shifts of the nuclei of the coordinating cysteines are essentially contact in origin (21, 22). In the case of [Fe4S4l (17) and [FegS4] (112) cluster, it has been shown that the hyperfine shift of the cysteinyl H/3 and Ca nuclei can be related to the value of the Fe-Sy-C/S-H/S/Ca dihedral angle (6) through a Karplus-type relationship of the form... 

Protein (cofactor) (assigned amino acids) % H assignment NOE Ri Fe-Sy-C)3-C dihedral angle mean (A) Number of conformers PDB entry... 

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. 

Fig. 7.17 Bend structure resulting from the HF/4-21G geometry refinement of a type-II bend of N-formyl pentaglycine amide. The torsional angles in this structure are not common in proteins due to the effects of the end groups on the dihedral angles in the bend.

The computational requirement of the aBB algorithm depends on the number of variables on which branching occurs. The most important variables are those variables that substantially influence the nonconvexity of the surface and the location of the global minimum. In the protein-folding problem, the backbone dihedral angles ( and ip) are the most influential variables. Therefore, in very large problems, to further reduce the dimensions of the problem, only these variables were involved in the optimization. 

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