Section 22.1.2.4. Graphical representations of shape and properties

With very large complexes, such as viruses, the surface features to be viewed are obvious at low resolution. In a very simple yet effective representation popularized by the laboratories of David Stuart and Jim Hogle, a Cα trace is `depth cued' (shaded) according to the distance from the centre of mass (Acharya et al., 1990; Fig. 1 for example). The impression of three dimensions probably results from the similarity of the shading to highlighting. The method is most effective for large complexes in which there are sufficient Cα atoms to give a dense impression of a surface.

In one of the earliest surface graphical representations, dots were drawn for each Connolly surface dot, using vector-graphics terminals. With the improved graphics capability of modern computers, dot representations have been replaced by ones in which solid polyhedra are drawn with a large enough number of small triangular faces such that the surface appears smooth. These representations are clearer, because atoms in the foreground obscure those in the background.

Depth and three-dimensional relationships are most easily represented by stereovision or rotation of objects in real time on a computer screen. Graphics engines for interactive computers compromise quality for the speed necessary for interactive response, but simple depth cueing (combined with motion or stereo) is sufficient for good 3D representation. For still and/or non-stereo images more common in publications, more sophisticated rendering is helpful and possible now that speed is not a constraint. In Raster3D (Merritt & Bacon, 1997), multiple-light-source shading and highlighting is added, with individual calculations for each fine pixel. These are dependent on the directions of the normals to the surface, which are calculated analytically for spherical surfaces. More complicated surfaces, input as connected triangles, have surfaces rendered raster, pixel by pixel, by interpolating between the surface-normal vectors at the vertices of the surrounding triangle. Together, this leads to a high-quality smooth image that conveys much of the three-dimensionality of molecular surfaces.

GRASP is currently perhaps the most popular program for the display of molecular surfaces. Readers are referred to the program documentation (Nicholls, 1992) or a paper that tangentially describes an early implementation (Nicholls et al., 1991). The molecular or accessible surface is determined by the marching-cube algorithm. The surface is filled using methods that make modest compromises on photorealistic light reflection etc., but take advantage of machine-dependent Silicon Graphics surface rendering to perform the display fast enough for interactive adjustment of the view.

The most powerful part of the program is the ability to colour according to properties mapped to the surface (see Fig. 22.1.2.2). These may be values of (say) electrostatic potential interpolated from a three-dimensional lattice. Much has been learned about many proteins from the potentials determined by solution of the Poisson–Boltzmann equation (Nicholls & Honig, 1991). The electrostatic complementarity of binding surfaces has often been readily apparent in ways that were not obvious from Coulombic calculations that ignore screening or from calculations and graphics representations that treat the charges of individual atoms as independent entities.

Figure 22.1.2.2 | top | pdf | GRASP example. The larger picture shows the molecular surface of arginine kinase (Zhou et al., 1998) with the domains and a loop moved to the open configuration seen in a homologous creatine kinase structure (Fritz-Wolf et al., 1996). The surface, coloured with positive charge blue and negative charge red, demonstrates that the active-site pocket (centre) is the most positively charged part of the structure. It complements the negatively charged phosphates of the transition-state analogue components that are shown, moved as a rigid body to the bottom right. They are shown in van der Waals representation, in which oxygens are red, carbons black and nitrogens blue.

Many other properties can be mapped to the surface. These include properties of the atoms associated with that part of the surface (such as thermal factors), curvature of the surface calculated from adjacent atoms (Nicholls & Honig, 1991), or distance to the nearest part of the surface of an adjacent molecule. GRASP is now used to illustrate complicated molecular structures, in part because it also supports the superimposition of other objects over the molecular surface. These include the representation of molecules with CPK spheres and/or bonds, and the representation of electrostatic potentials with field lines, dipole vectors etc.

Commercial packages use variants of the methods discussed above. For example, surfaces are drawn in the Insight II molecular modelling system using the Connolly dot algorithm (Molecular Structure Corporation, 1995).