**GRASP: Representational Forms**

Atoms can be represented in GRASP as solid (CPK) spheres, or as circles always oriented towards the user. The latter are considerably faster to draw and can be presented in two different ways, namely as circles of with the same radius as is associated with each atom, or as "bond" atoms of constant, reduced size in a traditional "ball-and-stick" representation. In the former case the surface of the circle can either be "sphere-like" or patterned. The former case gives an impression of three dimensionality to the flat circles, the latter is useful for reducing dependence upon color for encoding information.

Bonds have three representational forms, as lines, as "sticks" or as cylinders, in order of increasing draw speed. They are constructed from (externally alterable) distance constraints, and from CONECT records in PDB files.

A spline curve can be constructed from any set of atoms, though the usual set is that of alpha carbons. B-splines are used for smoothness. Linear interpolation is used to extend the splines to the first and last atom within a spline. A user modifiable "break" distance determines chain ends for multiple splines within a single structure. Splines can be represented as line segments, a tube of constant width, a flat ribbon, a thick ribbon, a corded ribbon, wireframe ribbons (in the case of ribbons the tangential direction is determined from the peptide plane if constructed from alpha carbons). There are also secondary structure related representations such as "arrow-headed" ribbons for beta sheets and thin ribbons for random coil.

Surfaces can be constructed as accessible or molecular surfaces. The former is defined as the locus of the center of a probe (of user defined radius) rolled around a molecule, the latter as the contact surface of that probe with the molecule. Construction times are typically of the order of five seconds on an R4000 SGI machine. This is independent of molecular size as the method is grid based where the number of grid points is constant, i.e larger molecules have courser surfaces. This grid size can be adjusted. The method of surface construction from a lattice representation is a form of marching cubes, though the original algorithm predate the description of that method.

Surfaces so formed consist of triangles. Representational forms include solid renderings of the triangles, mesh and point descriptions. In the latter case the point density may be increased beyond that of the triangle vertices alone to include other points sampling each triangular face. The two solid rendering forms differ in that the first uses GL (Graphics Library on SGI machines) lighting calls, the latter does not, rather uses a simple angle of incidence formula to determine shade. The latter has the advantage of speed on some SGI machines.

The peptide plane has its own representation within GRASP as a quadrilateral box whose corners are the two alpha carbons, the oxygen and the nitrogen. The default color scheme for these boxes is the carbon corners are white, the nitrogen corner blue and the oxygen corner red, indicating the electrostatic polarity of this set of atoms (the carbonyl oxygen draws electrons from the peptide bond carbon giving it a negative "partial" charge, and the hydrogen of the amide nitrogen loses electrons giving it a positive partial charge.)

Groups of atoms or sets of surface vertices may be represented by ellipsoids created so as to enclose all such while having minimal volume. Display forms are rendered or mesh form. An example would be to represent the side chain atoms of each residue, as a complement to a backbone representation.

Electrostatic quantities are derived from potential "maps", i.e. cubic grid structures. For instance, GRASP produces isopotential, or threshold, contours from such maps produced by DelPhi or its own internal Poisson-Boltzmann solver (the merits of each will be discussed below). Other representations include vector representations of the field direction and strength from a set of points. Display forms are line and solid "arrow" representations, with length set constant or proportional to field strength. This construct is also used to represent the dipolar moment of a set of atoms. Electric field lines, which trace the path a probe charge would take away from a given set of points, can be calculated and displayed as lines or tubes.

More ephemeral electrostatic map representations are derived from an "intersection" plane set to be parallel to the screen. The potentials are calculate from this map to each point in this plane (65*65 points). The plane can then be color coded to represent these potentials. Alternatively, one can calculate line contours, i.e. a line marking the threshold between regions greater than and less than a certain value, which can also be though of as the the intersection between a isopotential contour of the same value and the plane. Finally, one can evaluate the field directions within the plane via a display form similar to that of "iron filings" for magnetic fields, i.e. at each grid point a small "bar" is aligned in the direction of the field at that point. These display forms are described as "ephemeral" because the plane is fixed with respect to the screen and so as the graphical view is altered the values within the plane are updated, and with them all the forms that depend upon them.

Finally, one can interpolate from the electrostatic map to atom centers and to surface vertices. The potential values are then properties of the atoms and vertices and can be used to select sets of either or to alter display characteristics (i.e. coloring schemes, see below). In the case of surfaces one can also create line contours exactly analogous to those describe for the interpolation plane, i.e. lines upon the surface seperating different potential domains.

A display form that has utility for electrostatics but which is not derivable from maps within GRASP, is that of the interaction, or matrix, strands. These are relations between two sets of atoms, for instance, the electrostatic interaction between two charge residues, or atoms. The representational forms of these pair-wise interactions are lines or cylinders. In the latter case the widths of the cylinders can reflect the strength of the interaction. Other examples of interactions are database derived residue-residue energies, or interproton distances within NMR refinement.

Finally, GRASP contains a set of representations for DNA bases, base pairs, sugars, phosphate backbones and axis. Geometric properties of DNA can be presented via these objects.