Ramachandran space

Fig. 1.2.1. Conventions for naming the dihedral angles , if/, co, and / illustrated by a model dipeptide. Only certain backbone dihedral angles [Pg.19]

In a general case the second residue of the classic type IT turn (the position occupied in the lipase turn by the nucleophilic serine) adopts the so-called e conformation within the Ramachandran space [the nomenclature is again that of Efimov (1986), extended by Sibanda et al., (1989)]. This secondary structure of the nucleophile is preserved among all the structurally characterized members of the lipase-esterase suf>erfamily (see Section IV,B). Although unusual, it has been observed several times in other protein structures (for a discussion, see De-rewenda and Derewenda, 1991). In RmL the interatomic distances between C/8 of Ser-144 and other atoms of the turn are very short (N of Leu-145, 2.85 A C of His-143, 2.77 A O of His-143, 2.81 A). Similar... 

Salvador et al using DFT have calculated 21, that is all possible /, V and homo- and hetero-nuclear couplings, for a trialanine peptide as a function of dihedral backbone angles over the full Ramachandran space and found many of them to be functions of both the ( ) and v / dihedrals. 

Clearly, one of the reason of these kind of quandaries in estabfishing the dihedral dependences of the J-couplings is the lack of experimental data on significant parts of the conformational space. The backbone conformations typically populate the allowed regions of the Ramachandran space, and the... 

Figure 5.8 B3LYP/D95 H ) couplings over the whole Ramachandran space of...

Figure 5.9 B3LYP/D95 J(N,C ) couplings over the whole Ramachandran space of the central residue in Ac-Ala3-NH2 model. Adapted from Ref. [123] with permission from the PCCP Owner societies.

In Co,-based CG representations of backbone chains, the two-dimensional Ramachandran space is reduced to one bending parameter (angle y in Fig. 5). The most common secondary structure elements a-helices and p-sheets correspond to two well-separated values of y ( 90° for the a-helix and between 120° and 140° for the p-sheet). This simple example is sufficient to explain how a CG potential that aims at exploring thermodynamically accessible protein conformations and/or folding events cannot use a simple harmonic approximation for the angular terms, but it requires more complicated functional forms allowing multiple minima. 

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.)...

R denotes the region of the conformational space of the Ramachandran plot occupied by the given residue ne, nonallowed for nonglycine residues. 

Early SBCR models were reviewed by Ramachandran and Chaudhari (5) and by Deckwer (9). They require hold-up correlations as an input and do not compute flow patterns. The most complete and useful of these models applied to the Fischer-Tropsch (F-T) conversion of synthesis gas in a SBCR is that of Prakash and Bendale (79). They sized commercial SBCR for DOE. They gave syngas conversion and production as a function of temperature, pressure and space velocity. Input parameters with considerable uncertainty that influenced production rates were the gas hold-up, the mass transfer coefficient and the dispersion coefficient. Krishna s group (77) extended such a model to compute product distribution using a product selectivity model. Air Products working with Dudukovic measured dispersion coefficients needed as an input into such model. The problem with this approach is that the dispersion coefficients are not constant. They are a function of the local hydrodynamics. 

Several studies have used automatic clustering methods in 0, y/ coordinate space to search for recurring loop conformations [25, 26, 27], If one considers all the possible Ramachandran regions theoretically accessible to each residue, less than one quarter of all possible conformers of a heptapeptide fragment are observed [28]. Indeed, Jones and Thirup [25] found that protein loops can usually be constructed from a small number of fragments of known structure. 

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