Antibody surface topography

To analyse patterns of surface topography, a fractal measure was used to identify the gross surface shapes which have, until now, been classified by eye: i.e. cavity, groove and planar[Webster et al., 1994]. The method reduces a three-dimensional molecular surface patch (of any size) to a two-dimensional composition profile which quantifies the relative amounts of concavity and convexity, and uses the fractal atomic density measure of Kuhn et al.kuhn:fractals to quantify local surface curvature. In Figure 2.6(a), the surface convexity/concavity composition profiles are shown for antibody-antigen interface surfaces; Figures 2.6(b) to (d) show the same profiles for the whole combining site surfaces (using our `contact' CDR definition, see Table 2.3).

**Figure 2.6:** Convexity/concavity composition profiles for antibody molecular surfaces. (a) Profiles for the 26 antibody-antigen interface surfaces. Data are grouped into antigen/interface size class (see Table 2.1 and Methods). Small antigens have more concave binding pockets whilst larger antigens have flatter binding surfaces (more points with fractal atomic density $\approx2.0$ ). (b) Profiles for the whole combining site surfaces (defined as the surface overlying `contact defined' CDR residues -- see text) for the 26 complexes (colours are as in (a)). (c) After clustering: whole combining site surfaces (see (b)) for all 45 complexed and uncomplexed antibodies. Line colours and descriptions refer to the four clusters determined for these data (see text). (d) Near-median representatives of each cluster in (c).
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