CAPÍTULO I: PLANTEAMIENTO DEL PROBLEMA, ANTECEDENTES
1.2 ANTECEDENTES DE LA INVESTIGACIÓN
1.2.5 RIESGO EN LAS MICROFINANZAS
The table and figures referred to in this section are given on pages 62-71.
2.2.3.1 Oxygens
2.2.3.1 (a) R Values
The carboxyl oxygens (-O') favour an interatomic separation distance (R) of 2.8Â (Fig.2.4(b)) from the reference arginine group as indicated by the single prominent
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peak in the plot of the normalized frequency versus R distribution |(Fig.2.4(b)). In contrast, fairly broad R distributions ranging from 2.8 to 4.0Â are observed for the other oxygen types (Fig.2.4(a,c,d)). These plots indicate that the carboxyl oxygens (-O'), for the most part, solely form hydrogen bond contacts with the atoms o f the arginine whilst the other oxygen atom types form both hydrogen bonds and van der Waals interactions with the arginine. A total of 67% of carboxyl oxygens are found at separation distances o f less than 3.2Â from an arginine atom compared to 43% of all other oxygen types.
2.2.3.1 (b) 0 Values
The oxygen atom types have non-random
0
distributions as indicated by the low p values in 'Table 2.5 W ith the exception o f the carbonyl oxygens (= 0 ), the oxygens exhibit a preference to lie in the plane of the guanidinium group (0
= 0-20°). As deduced from the R plots all four oxygen types engage in hydrogen bonding interactions with the arginine atoms, and the preference for the coplanar atom- sidechain arrangement is probably a reflection of the geometrical constraints of such interactions. It is interesting to note that the carbonyl oxygens (= 0 ) are the only oxygen type not confined to the plane. This may be an artifact o f the small number o f examples of this atom type. It was also deduced from the R plots that three out of the four oxygen types engage in van der Waals interactions with the arginine atoms, the 0 plots however indicate that the hydrogen bonding interactions are more common than the van der Waals interactions - see Figures 2.5(a)-(d).Atomic Environments o f Arginine Sidechains Within Proteins
2.2.3.1 (c) (|) Values
Inspection o f the (|) distribution reveals that all oxygen types tend to cluster in certain preferred regions. Firstly, for the carboxyl oxygens (-0 ) inspection of their c|) profiles (Fig.2.6(b)) together with the corresponding contour plot (Fig.2.13) reveal that these atom types cluster in three regions around the arginine sidechain. The smaller o f these regions is where an oxygen might form hydrogen bonds with the N H l and NH2 atoms of the arginine The two larger groupings are on either side o f the CD atom of the arginine (corresponding to (|)~+300° & +60°). In contrast, the carbonyl and hydroxyl oxygens (= 0 & -OH) are less clustered in ^ space but do show a slight preference for the (|)= +60° region (Figs.2.6(b),(c)). It is thought that there are two main influences causing the -OH atoms to pack in that region. The first is the inclination for the apolar aromatic group to which the -OH is bound in the tyrosine (73% o f the interactions involve tyrosine) to interact with the ‘apolar tail end of the rigid group’ (the tail end is attached to the CD atom). The second is the inclination of the -OH to participate in hydrogen bonding; hence the necessity to be close to the NH2 atom. As for the (j) space occupied by the carbonyl oxygens (= 0 ) - this probably occurs as a result of these atoms types being excluded from other (|) regions as other atoms types can form more favourable interactions with the arginine in those regions. The (|) distribution for the backbone oxygens (=0B ) is strikingly different with a large peak centred around (|)=0°, which falls off sharply as the value o f (|) increases. This may be a consequence of the rigid nature of the protein backbone o f which these atoms are a part and the local nature o f these arginine-atom interactions (See Fig. 2.6(d)).
2.2.3.2 Carbons
2.2.3.2 (a) R Values
The arginine-carbon interactions can be divided into three groups on the basis o f their R plots. The first group consists of carbon atoms which participate in mainly van der Waals type interactions with the atoms of the sidechain of arginine. This group
contains the methyl carbons (-CH3), carbonyl carbons (=CP-) and both types of aromatic carbons (=CA & =CHA) - See Figs.2.7(a)-(d). The R plots o f these carbon atoms have bell-shaped profiles. The bell-shaped profile pertaining to the carbonyl cu b o n s is reminiscent of the R plot of the carboxyl oxygens to which 73% o f these carbons are attached to.
The second group comprises those carbons which pack at distances longer than those expected for a van der Waals contact. These include the carbon types aliphatic, backbone and backbone C a carbons (>CH-, =CB and >CHB) (Figs.2.7(e)-(g)). All of these carbon types are comparatively inaccessible because of their substituents and therefore unable to form good contacts. The third group contains the polar, apolar and neutral carbon types (CH2P, CH2A & CH2N). These carbon types form a large proportion of very close interactions at separation distances less than the van der W aals contact distance (Figs.2.7(h)-(j)). This is quite a surprising result, but a possible explanation for this may be that the van der Waals radii obtained from Richards
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those(1974) are for extended carbon atoms so they do not accurately reflect the radii of these atoms. A common theme of the R plots of the atoms in the second and third groups is the broadness of their distributions which range in value from 3.0Â and 4.8Â.
2.2.3.2 (b) 0 Values
On the basis of the 0 plots and the values we can divide the carbons into three groups:
• Carbons which prefer to lie in the plane of the guanidinium {e.g. carbonyl and backbone carbons or =CP- & =CB) - see Fig.2.8(a & b).
• Carbons which display a random 0 distribution. These are the backbone C a , neutral and polar carbons (=CB, CH2N & CH2P) - see figs.2.8(b, c & e).
• Carbons which prefer to stack over the plane of the guanidinium. These include apolar (CH2A), aromatic carbons (both =CA & =CHA), carbon CH3 (-CH3) and aliphatic CH (>CH-) carbons. (Figs.2.8(e-i)). Fig.2.14 is a contour plot showing the arg-aromatic carbon distribution.
Atomic Environments of Arginine Sidechains Within Proteins
The most likely reasons ’ why the aromatic carbons distribute themselves as they do are discussed in Chapter 4, Section 4.4.4. The unexpected 0 distributions of the ‘other carbons in this last grouping’, however, is not very easy to explain. It may be the case that these carbon types are excluded from other regions as a result of more favourable interactions formed between the other atom types and the arginine in those regions.
2.2.3.2 (c) (|) Values
The carbons can also be divided into three groups on the basis o f their ^ profiles. • The first group comprises the carbonyl and backbone carbons (=CP- & =CB). The (j) profiles of these atoms are very similar to those of the oxygens to which they are covalently attached. These oxygens are involved in hydrogen bonding interactions with the arginine (Figs.2.9(a,b)).
• The second group consists o f aromatic carbons and those carbon atoms not a part o f polar sidechains. These include the aromatic (=CA & =CHA), aliphatic CH atoms (>CH-), carbon CH3 (-CH3) and apolar (CH2A) carbons. Their (j) profiles are characterized by the peaks in the 0° to 90° range and the 340° to 360° range. The (j) profiles of these atoms can be described as random because although we see peaks in two angular ranges, the presence o f the CD atom in the arginine sidechain means that the (|) distribution will be biased with a greater number of examples expected in the (|) =0° to 90° range (Fig.2.9(c)-(g)).
• The third group comprises the atoms which adopt an even (|) distribution. These include the polar, neutral and backbone C a atoms (CH2P, CH2N & >CHB). As one would expect the (j) distribution to be biased in the (])=0° to 90° range, it can be said that this region is not popular for these atoms. These atoms are probably constrained as they are within polar sidechains which are involved in hydrogen bonding (Figs.2.9(h-j)).
2.2.3.3 Nitrogens and Sulphurs
for completeness, though with the exception of the backbone nitrogens (>NHB), there
are comparatively few . o f these atom types.