Two Torsion Angles

Conformational preferences have been studied for many other C Hs-X-CgHs fragments (X = CH2, CR2, C = 0, NH, NR, O, S, SO2) [42], as well as for nitrobenzenes with C(sp ) or N(sp ) substituents in ortho-position [43], If the terminal phenyl groups in the above examples are replaced by triptycyl-units, molecular analogs of bevel gear systems are obtained [44]. The conformational interconversion pathway mapped by bis(9-triptycyl)methane and related molecules follows almost ex- 

A similar study was performed on systems containing two or more t-butyl groups in close proximity [46]. It has been complemented by comparative empirical force-field calculations for propane, di-t-butylmethane and bis(9-triptycyl)methane and by a group theoretical analysis [47] along the lines given in Chapter 2 (Section 2.6.3). Some of the detail, not obtainable from crystal structure data alone, could be extracted from NMR-measurements on appropriately substituted bis(9-triptycyl) methane derivatives [48]. 

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Fig. 5.1 Variation in the energy of pentane with the two torsion angles indicated and represented as a contour diagram and isometric plot. Only the lowest-energy regions are shown.

In simple chemical systems, it is often possible to make a good first guess at the dominant reaction pathway [25-28]. An example of such a reaction is the chair-to-boat isomerization in cyclohexane. In that pathway, a clever combination of two torsion angles provides an excellent reaction coordinate for the isomerization reaction [29,30]. 

Many of the conformational properties of peptide systems, including protein conformation, can be approximated in terms of the local interactions encountered in dipeptides, where the two torsional angles 4> (N-C(a)) and < i (C(a)-C ) are the main conformational variables. N-acetyl N -methyl alanine amide, shown in Fig. 7.11, is a model dipeptide that has been the subject of numerous computational studies. 

As an example, this approach was applied to the calculation of the PMF for alanine dipeptide as a function of the two torsion angles

resulting free energy surface is shown in Fig. 4.5. Bilinear Qi elements were used to approximate the free energy. Control points were chosen such that there are four of them around each data point. This was done in order to increase the smoothness and quality of the reconstructed free energy. The position of the Q i nodes and control points is shown in Fig. 4.6. 

The CORCEMA-ST calculations on the initial bovine DHFR/TMP model already yielded a very low NOE R-factor of 0.076, and this was further improved (NOE R-factor = 0.055) with a very shght refinement of two torsion angles (ti... 

The geometrical parameters of 1 were based on the standard structures of hexopyranoses ( ). The glycosidic linkage is described by the two torsion angles... 

C-N-H and C-S-0 angles and the two torsion angles about C-N and C-S bonds. On the other hand, the bond lengths themselves may be used as variables, also, when their precise values are not known. The number of variables will still be substantially reduced, provided that the symmetry restrictions are maintained. 

Figure 5.1. Notation for torsion angles of biopolymer chains. Torsion angles ( and ift) that affect the main chain conformations of biopolymers are shown for polysaccharide (a), polypeptide (b), and polynucleotide (c) chains according to the IUBMB notation. The two torsion angles, and ij>, specified around the phosphodiesteric bonds of nucleic acids correspond to a and respectively. Reproduced from IUBMB at http //www.chem.gmw. ac.uk/iubmb.

Under the Execute menu select the Energy option. The two torsion angles selected should appear in the selection list (see Fig. 17.15.4). 

Notice that at an M-N distance of 2.14/2.16 A there is a break in the curve. Analyze the two structures by double clicking with the mouse on the corresponding lines in the Energy table. With the two torsion angles described above (torsion tl and torsion t2, see Fig. 17.16.5) it emerges that the structural change is to D leli conformation. A similar conformational interconversion occurs with the )3/e/3 conformer. 

The overlap population of Fe-S bonds was found to be explicitly dependent on the two torsion angles of Fe-S. The Fe-S torsion angle dependence of the overlap populations with variation of the two Fe-S torsion angles is shown in Fig. 8. The increase in the overlap populations for two restricted Fe-S bonds is reflected by the experimental data of shortening the Fe-S bond, whereas the other two Fe-S bonds having the normal torsion angle show the decrease in the overlap... 

To help remedy this deficiency the structures of a great variety of oligonucleotide stem/loop (hairpin) structures are being determined, most by NMR spectro-scopy. The sharp turns in the loops involve mostly rotation about the two torsion angles around the phosphorus atom of the third, from the 5 end, of the seven nucleotides. Base bulges on stems (Fig. 5-9) not only introduce kinks and bends in RNA stems but also provide well-defined hydrogen-bonded binding sites for proteins. Numerous branched three-way and more complex jrmctions provide other important motifs in folded RNA. ... 

Current methodologies allow the prediction of some organic molecules with no more than 20 non-H atoms in the asymmetric units, with rigid structure or with a limited amount of flexibility (no more than two torsion angles) and with no more than one molecule per asymmetric unit. All the methods involve three stages ... 

This notation will be explained by an example taken from the chemistry of nucleosides/nucleotides, by far the most important family of furanosides (see Section 3.4). The nucleosides are glycosidic combinations with a heterocyclic base and a /3-D-ribofuranosyl or 2-deoxy-)3-D-cryr/iro-pentofuranosyl residue. The example chosen is the synthetic nucleoside 5-iodouridine. We can observe two different conformations of this molecule in the crystalline form, close to 72 (2.41) and Tj (2.42), respectively. The maximum torsion angle is between the 2 and 3 positions. In order for P to be close to 0, we will therefore choose T2 = Oq (Fig. 2.10) and consequently for 0. .. 0, the values T3, T4, Tq, and Ti, respectively. Knowledge of the two torsion angles allows us to calculate and P. The P angle has the character of a phase and is a measure of the flattening of the... 

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