Section 3.3.3.2.6.  Bilder

This system (Diamond, 1980a,c, 1982b) runs on a minicomputer independent of any mainframe. It builds a polymer chain from a library of residues and adapts it by internal rotations and overall positioning in much the same way as previous systems described in this section. Like them, it can provide user-controlled bond rotations, but its distinctive feature is that it has an optimizer within the minicomputer which will determine optimal combinations of bond rotations needed to meet the user's declared objectives. Such objectives are normally target positions for atoms set by the user by visual reference to the density, using the method of Section 3.3.1.3.9, but they may include target values for angles. These latter may either declare a required shape that is to take precedence over positional requirements, which are then achieved as closely as the declared shape allows, or they may be in least-squares competition with the positional requests. The optimizer also recognizes the constraints imposed by chain continuity and enables an internal section of the main chain to be modified without breaking its connection to the rest of the molecule. Similar techniques also allow ring systems to adopt various conformations, by bond rotation, without breaking the ring, simultaneously permitting the ring to have target positions. The optimizer is unperturbed by under-determined situations, providing a minimum-disturbance result in such cases. All these properties of the optimizer are generated without recourse to any `special cases' by a generalization of the subspace section technique which was used to maintain chain continuity in a `real-space-refinement' program (Diamond, 1971). This is based entirely on the rank of the normal matrix that arises during optimization, which may serve to satisfy a constraint such as chain continuity or ring closure and simultaneously to establish what degrees of freedom remain to be controlled by other criteria. In Bilder this is achieved without establishing eigenvalues or eigenvectors. The method is described in outline in Section 3.3.2.2.1 and in detail by Diamond (1980a,b).

The angular variables used normally comprise all single bonds but may include others, such as the peptide bond with or without a target of 180°. Thus this bond may be completely rigid, elastic, or completely free. Any interbond angles may also be parameterized but at some cost in storage. The normal mode of working is to develop a single chain for the entire length of the molecule, but if cumulative error makes fitting difficult a fresh chain may be started at any stage. Bilder may itself reconnect such chains at a later stage.

Construction and manipulation operates on a few residues at a time within the context of a polymer chain, but any or all of the rest of the molecule, or other molecules, may be displayed simultaneously.

Contouring is done in advance to produce a directoried file of contoured bricks of space, each brick containing up to 20 independently switchable elements which need not all be from the same map. Choice of contour level and displayed volume is thus instantaneous within the choices prepared.

The system is menu driven from a tablet, only file assignments and the like requiring the keyboard, and it offers dynamic parallax as an aid to 3D perception (Diamond et al., 1982). Bloomer et al. (1978), Phillips (1980), and Evans et al. (1981) give examples of its use.