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However, the trend is much less clear when the whole antibody combining site is subjected to the same analysis; Figure 2.6(b) presents the surface convexity/concavity composition profiles for the molecular surfaces overlying the `contact defined' CDR residues (Table 2.3) for the 26 complexed antibody crystal structures. A number of the anti-hapten antibodies (green lines in Figure 2.6(b)) have the highest proportion of concave surface points, but there is considerable overlap between the profiles of medium and large antigen binding sites. The loss of distinction between the antigen classes is caused by the increase in noise resulting from the inclusion of random, non-interface surfaces in the calculations.
In order to eliminate the subjectivity of these observations we have performed cluster analysis on the full set of 45 whole combining site surface topography profiles from both complexed and uncomplexed structures. Using Ward's minimum variance method[Ward, 1963,Wishart, 1969], the topography composition profiles (as multi-dimensional vectors) cluster into four subclasses of roughly equal size. Figure 2.6(c) presents the profiles for the complexed and uncomplexed antibodies; the colours refer to the cluster membership of each surface. The near-centroid representatives of each cluster are shown in Figure 2.6(d). Descriptions of each cluster are based on their general shape properties: planar, ridged, concave and moderately concave.
Ridged-type combining site surfaces are characterised by a large proportion of convex surface in addition to concave surface points. Note that our strictly compositional surface analysis cannot describe contiguous features, such as long and narrow surface depressions which one would describe as a groove. We therefore use the term `ridged' although for practical purposes this is equivalent to the established `groove' classification.
Tables 2.1 and 2.2 show which topographic class (i.e. cluster) is assigned for each antibody in our data set. Tables 2.4 and 2.5 show the distributions of topographies by antigen type. For the complexed data set (Table 2.4) there is a good, but not perfect, correlation between antigen type and surface topography, supporting the cavity-groove-planar classification[Webster et al., 1994] in principle. While others have suggested three shape classes, our analysis shows that four classes fit the data better with both concave and moderately concave being predominantly hapten binders.
| antigen size | planar | ridged | moderately concave | concave |
| small | 1 | 0 | 3 | 6 |
| medium | 0 | 6 | 1 | 1 |
| large | 4 | 1 | 2 | 1 |
In an attempt to explain the occurrence of a number of outliers, including a planar anti-hapten antibody (AN02[Brunger et al., 1991]) and a concave-type anti-protein antibody (JE142[Prasad et al., 1988]), we assessed the relative contributions of interface and non-interface surfaces to the measure of combining site topography. Figure 2.6(a) highlights selected outliers from the whole combining site analysis (thick lines). The AN02 antibody-antigen interface has a fairly typical concave topography for a small antigen; its planar combining site classification arises because the non-interface combining site surface is so flat. In contrast, the interface between antibody JE142 and its protein antigen has a relatively large amount of concave surface (compared with other large antigens) and its concave-type combining site classification (planar is expected) is therefore only partly influenced by non-interface surface topography.