Structures, superposing

Tom Blundell has answered these questions by superposing the Ca atoms of the two motifs within a domain with each other and by superposing the Ca atoms of the two domains with each other. As a rule of thumb, when two structures superpose with a mean deviation of less than 2 A they are considered structurally equivalent. For each pair of motifs Blundell found that 40 Ca atoms superpose with a mean distance of 1.4 A. These 40 Ca atoms within each motif are therefore structurally equivalent. Since each motif comprises only 43 or 44 amino acid residues in total, these comparisons show that the structures of the complete motifs are very similar. Not only are the individual motifs similar in stmcture, but they are also pairwise arranged into the two domains in a similar way since superposition of the two domains showed that about 80 Ca atoms of each domain were structurally equivalent. 

Use models to solve this problem.) (a) Write a conformational structure for the most stable conformation of 1,2-diethyl-cyclohexane and write its mirror image, (b) Are these two molecules superposable (c) Are they interconvertible through a ring flip (d) Repeat the process in part (a) with OT-l,2-diethylcyclohexane. (e) Are these structures superposable (f) Are they interconvertible ... 

An experimental teclmique that is usefiil for structure studies of biological macromolecules and other crystals with large unit cells uses neither the broad, white , spectrum characteristic of Lane methods nor a sharp, monocliromatic spectrum, but rather a spectral band with AX/X 20%. Because of its relation to the Lane method, this teclmique is called quasi-Laue. It was believed for many years diat the Lane method was not usefiil for structure studies because reflections of different orders would be superposed on the same point of a film or an image plate. It was realized recently, however, that, if there is a definite minimum wavelengdi in the spectral band, more than 80% of all reflections would contain only a single order. Quasi-Laue methods are now used with both neutrons and x-rays, particularly x-rays from synclirotron sources, which give an intense, white spectrum. 

Figure 1 The basis of comparative protein structure modeling. Comparative modeling is possible because evolution resulted in families of proteins, such as the flavodoxin family, modeled here, which share both similar sequences and 3D structures. In this illustration, the 3D structure of the flavodoxin sequence from C. crispus (target) can be modeled using other structures in the same family (templates). The tree shows the sequence similarity (percent sequence identity) and structural similarity (the percentage of the atoms that superpose within 3.8 A of each other and the RMS difference between them) among the members of the family.

This structural similarity is also reflected in the amino acid sequences of the domains, which show 40% identity. They are thus clearly homologous to each other. The motif structures within the domains superpose equally well but their sequence homology is less, being around 30% between motifs 1 and 2 and 20 Xi between 3 and 4. This study, however, clearly shows that the topological description in terms of four Greek key motifs is also valid at the structural and amino acid sequence levels. 

Fig. 4.—The structure of topaz. The layers are to be superposed in the order abed, with d uppermost. The crosses are the traces of the corners of the unit of structure in the plane of the paper. Large circles represent oxygen, large double circles fluorine, small open circles aluminum, and small solid circles silicon ions.

The requirement for the existence of enantiomers is a chiral structure. Chirality is solely a symmetry property a rigid object is chiral if it is not superposable by pure rotation or translation on its image formed by inversion. Such an object contains no rotoinversion axis (or rotoreflection axis cf. Section 3.1). Since the reflection plane and the inversion center are special cases of rotoinversion axes (2 and 1), they are excluded. 

The CED-3 sub-family shows very similar three-dimensional structures. Figure 7.6 shows the superpositions of the Ca atoms. The structural backbones of the proteins within the family are closely superposed. 

Figure 5.19 tn// s-l,3-I)imethylcyclohexane does not have a plane of symmetry and exists as a pair of enantiomers. The two structures a and b) shown here are not superposable as they stand, and flipping the ring of either structure does not make it superposable on the other, (c) A simplified representation of (b). 

Mass spectrometry is used to identify unknown compounds by means of their fragmentation pattern after electron impact. This pattern provides structural information. Mixtures of compounds must be separated by chromatography beforehand, e.g. gas chromatography/mass spectrometry (GC-MS) because fragments of different compounds may be superposed, thus making spectral interpretation complicated or impossible. To obtain complementary information about complex mixtures as a whole, it may be advantageous to have only one peak for each compound that corresponds to its molecular mass ([M]+). Even for thermally labile, nonvolatile compounds, this can be achieved by so-called soft desorption/ionisation techniques that evaporate and ionise the analytes without fragmentation, e.g. matrix-assisted laser desorption/ionisation mass spectrometry (MALDI-MS). 

Fig. 8 Local transmission pictures in a superposed benzenoid structure. As the two rings change geometry from an eclipsed pseudo para geometry (upper left) through an eclipsed pseudo meta geometry to a slip-stacked structure to a single tunneling pathway, the transmission at the Fermi energy increases hy roughly a factor of ten. Reprinted with permission from G. C. Solomon et al. J. Am. Chem. Soc. (2010) 132, 7887-7889. Copyright 2011 American Chemical Society...

Figure 8.23 Illustration of chiral layer structure proposed for NOBOW high-temperature smectic banana phase is given. On left layer with (+) configuration is shown, while on right enantiomeric (—) configuration is illustrated. These mirror image fluid smectic layer configurations are not superposable.

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