Chapter 17.2. Molecular graphics and animation

Geometric construction encompasses dots, lines and surfaces described by lists of three-dimensional coordinates and connectivity or by analytic or parametric expressions that can generate such information for rendering. Basically, geometric rendering involves a projection of the 3-D geometry onto a two-dimensional viewing plane using matrix transformations that account for the viewpoint, perspective and clipping within the viewing volume. For dots and lines, the computation may end there; the only depth information in the rendering might be geometric perspective. Additional depth information can be added by `atmospheric perspective' or depth cueing, where the brightness or colour is modulated by the depth values of the points (Fig. 17.2.3.3). Surface representations permit additional three-dimensional cues such as occlusion and shape-from-shading. Occlusion, or `hidden surface removal', and atmospheric perspective depend on maintaining depth information for all of the picture elements (pixels) in screen space. Such `depth-buffer' algorithms provide visibility information for a given viewpoint. Hardware z-buffers facilitate such calculations in the graphics pipeline. Lighting cues, such as shading, are attained by approximating the ambient, diffuse and specular reflectance of the geometry using Lambert's law. Because typical surfaces are composed of polyhedral facets, interpolation schemes are used to produce smooth shaded representations. The most common technique used for molecular graphics is known as Gouraud shading (Gouraud, 1971), which interpolates the shaded colour values assigned at the vertices across the polyhedral face (Fig. 17.2.3.4). Phong shading (Phong, 1975), a more accurate but costly technique, interpolates the values of the normals of the facets to produce a more realistic rendering. Shading templates for specific geometries, such as spheres, can give very smooth results without having to resort to large polyhedral descriptions for each sphere. In the past, this approach was implemented in the graphics hardware design, resulting in very fast sphere rendering for molecular applications. With the advent of consumer-level 3-D graphics these specialized features have become increasingly rare. Shadows may also provide useful three-dimensional cues in viewing molecular objects, but may also be confusing when they provide too much visual contrast or clutter. Ray tracing is a general technique for producing a complete reflectance and shadow rendering of a three-dimensional scene. It can, however, be very costly in computational time, since every light ray in the final image must be iteratively traced back to its source. Faster approximations for shadow rendering have been implemented that work well for molecular scenes (Gwilliam & Max 1989; Lauher, 1990).

Figure 17.2.3.3| top | pdf | Simple bonding diagram of a DNA structure (PDB code: 140D) (Mujeeb et al., 1993). On the left all lines are of equal intensity. On the right the lines are depth-cued to show which parts of the structure are closer to the viewer.

Figure 17.2.3.4| top | pdf | CPK representation of the same DNA structure as in Fig. 17.2.3.3. The model on the left uses highly tessellated spheres for the atoms, while the one on the right uses a coarser tessellation. The Gouraud shading model produces some lighting artifacts, such as the star-shaped highlights, which are most apparent on the right-hand figure. This is due to colour interpolation between the facet vertices.

A number of useful surface representations have been developed that describe the interaction of a molecule with the surrounding solvent. Perhaps the most widely used are the solvent-accessible surface (Lee & Richards, 1971) and the molecular surface (Richards, 1977; Connolly, 1983; Sanner et al., 1996), sometimes referred to as the Connolly or solvent-excluded surface (Fig. 17.2.3.5). For large molecules, such as proteins, which have many atoms buried from solvent, these surfaces have proven to be important in studying molecular interactions. They not only help to visualize the complementarity of interacting molecules, but they are also important in quantifying the entropic changes associated with solvent effects upon binding.

Figure 17.2.3.5| top | pdf | Solvent-excluded surface of the DNA structure using a water probe radius of 1.5 Å. The figure on the left shows a depth-cued dot surface, while the figure on the right shows a Gouraud-shaded triangulated surface.

Surface representations have opened up the possibilities of displaying a large variety of computed or experimental molecular properties by mappings onto the surface using colour coding. Electrostatic potential, hydrophobicity, sequence conservation, surface shape and any other characteristic of the molecule that can be projected onto the surface can be colour coded and displayed. Typically, this is accomplished by colouring the vertices of the surface mesh using a colour mapping or scale and interpolating the colour across the polygonal faces of the mesh. Since colour values are interpolated between vertices, this can produce unwanted colour artifacts if there are abrupt spatial changes in the properties displayed, or if the colour interpolation does not correspond to the property mapping (Fig. 17.2.3.6).

Figure 17.2.3.6| top | pdf | Hydrophobicity mapped onto a molecular surface. A spherical-harmonic approximation of the actin monomer solvent-excluded surface is shown. (a) Vertex colouring of a medium-mesh tessellated surface. The hydrophobicity colour scale is shown above. Notice that the colours blend between vertices, producing colour artifacts in relationship to the property scale. (b) The same medium-mesh representation as in (a) but using a property-based (one-dimensional) texture map, applying the same colour scale. Notice that the boundaries between the colours are distinct, even when they intersect vertices. Here the property value is interpolated. (c) A coarser mesh showing the same texture-mapping technique used in (b). Since the properties are only sampled at the vertices of the mesh, the finer details of the mapping are lost at this coarse triangulation. (d) A two-dimensional texture map created as a `Mercator-like' projection in spherical coordinates (θ, φ) from the same hydrophobicity scale used in (a)–(c). (e) The 2-D texture map shown in (d) mapped onto the medium-mesh actin surface. Notice that the linear nature of the interpolation seen in (b) using the same mesh is no longer present. (f) The same 2-D texture map applied to the coarse-mesh surface of actin. Notice that, unlike in (c), the detail of the texture map is preserved independent of the mesh.

Another method for projecting information on a surface is texture mapping, an approach that is analogous to applying an image `decal' onto the surface. In this approach, instead of assigning colours to the surface vertices, indices are assigned which serve as coordinates into the image to be mapped. Thus, a great amount of detail may be displayed on a surface mesh that has relatively few polygons describing the geometry. Texture mapping has been used extensively in highly interactive graphics, such as flight simulators and video games, since transformation of the geometry tends to be the computational bottleneck. Since texture mapping requires an indexing scheme that relates an image to a set of geometric vertices on the molecular surface, one needs a rational way of producing such a map. For one-dimensional texture maps, this is relatively easily accomplished by assigning the texture index of each vertex to an appropriate property scale (Teschner et al., 1994) (Fig. 17.2.3.6). This approach, however, is still tied to the level of triangulation. The more general two-dimensional or location-based surface texture mapping requires a global scheme for assigning texture indices. While the original molecular surface geometry does not lend itself directly to this type of texture mapping, recent analytical approximations to these surfaces, such as spherical-harmonics-based molecular surfaces (Duncan & Olson, 1993), provide simple hierarchical meshing schemes that can be easily texture mapped by using a `Mercator'-like projection between the image and the molecular surface (Duncan & Olson, 1995) (Fig. 17.2.3.6).

Molecular properties are not confined to bonds and surfaces. These, in fact, are geometric constructs or abstractions of the time-dependent volumetric characteristics of molecules. In crystallography, electron density is the primary volumetric property to be visualized. Other derived or computed volumetric properties have become important to visualize as well, especially for macromolecules and their complexes. Electrostatic potential and field gradients help establish a molecule's effect at a distance, and a variety of volumetric atomic affinity potentials or grids (Goodford, 1985) can provide a picture of the types of molecular interactions that are energetically favoured.

Traditionally, electron density and other volumetric properties have been displayed as isocontour or isosurface representations, in which lines or surfaces of constant value are rendered in planes or in 3-D space to reveal characteristics of the volumetric property. Early computer-graphic pen plots of planar Fourier projections of electron density were usually sufficient to reveal atomic structure. As the molecules of study became larger and more complex, stacks of two-dimensional slices, creating three-dimensional isocontours, became necessary. The first computer representations of such 3-D isovalue surfaces were composed of three orthogonal 2-D plots – giving the impression of a `basket weave'. These plots depicted surface isocontours of the three-dimensional density, but had several problems from a computational and representational point of view. Since there were preferred directions of the contours (along the x, y and z axes), particular views were difficult to interpret. Additionally, the three orthogonal contours did not define a well formed triangulated geometric surface, so modern surface rendering techniques could not be applied directly. Moreover, the computation and recomputation of isosurfaces was relatively inefficient. An algorithm to compute directly the three-dimensional isosurface, called `marching cubes', was devised by Lorenson & Kline (1987) (Fig. 17.2.3.7). This algorithm speeded up the contouring process and enabled shaded surface representation of these surfaces. More recently, the re-computation of isosurfaces has been speeded up through the pre-computation of seed points that span all values of the volume. Using these seed points to flood-fill an isosurface of a given value reduces the contouring computation from a three-dimensional to a two-dimensional calculation. This enables the interactive modification of contour levels for even very large volumes (Bajaj et al., 1996)

Figure 17.2.3.7| top | pdf | Crystallographic electron-density isosurfaces, showing details of a protein iron–sulfur cluster. The surfaces are coloured by the gradient of the electron density, highlighting the iron and sulfur densities. Image by Michael Pique, The Scripps Research Institute.

While isocontours and isosurfaces have been the dominant modes of volumetric representation in molecular graphics, there has been a trend in scientific visualization to use alternative techniques, termed `direct volume rendering'. These methods bypass the construction of contours or surfaces to represent values within the volume, and instead use the scalar (or sometimes vector) values within the volume to produce an image directly. A general technique to accomplish this type of volumetric rendering is termed ray casting. If one considers a function that maps the scalar values of a volume into optical properties such as colour and opacity, one can simulate the passage of light rays through the volume, projecting the resulting rays onto the image plane. Given an appropriate transfer function or look-up table, the image represents the distribution of all of the values within the volume, circumventing the need to select only certain values as required for isocontouring. Such techniques have been used extensively in medical tomography (Höhne et al., 1989) and electron microscopy (Kremer et al., 1996; Hessler et al., 1996). Their use has also been explored in the rendering of volumetric properties of molecules (Goodsell et al., 1989). The images that are obtained by direct volume rendering tend to appear cloud-like, with soft edges. While this may be a `true' representation of the molecular characteristics, it is sometimes difficult to interpret visually. Techniques for imparting shading cues into these renderings by using gradient information in the volume has made this type of rendering more interpretable (Drebein et al., 1988). Another potential drawback to these methods is the cost of the computations. Since these methods require computing the effect of every element of the volume, the amount of computation scales as the cube of the linear dimension. There have been several clever software and hardware approaches to overcoming this problem. One novel hardware approach is to use three-dimensional texture mapping. By stacking texture-mapped planes to represent the colour and opacity of the volume, and using the hardware depth-buffer capabilities to compose the final image in the viewing plane, one can manipulate and render reasonable-size volumes (128³) at highly interactive rates. For molecular visualization, one would like to be able to represent both geometric and volumetric characteristics in the same rendering to visualize, for instance, model and data (Fig. 17.2.3.8). The three-dimensional texture-mapping approach enables this easily, since the planes upon which the volume data are mapped are in fact geometric. Other direct-volume rendering codes provide this capability as well.

Figure 17.2.3.8| top | pdf | A difference-electron-density map of a minor-groove drug binding in DNA. This image combines volumetric rendering of the electron density with a geometric model of the DNA molecule. Data courtesy of R. E. Dickerson, UCLA. Image by David Goodsell, The Scripps Research Institute.

While molecular-structure research deals directly with objects in three dimensions, it is at times advantageous to abstract this three-dimensional information into diagrams that show relationships that are not readily apparent by examination of a set of geometric models or volumes themselves. This type of representation is broadly termed `information visualization'. In the arena of molecular structure, probably the best known and most widely used diagram of this type is the Ramachandran plot (Ramachandran & Sasisekharan, 1968), which maps the positions of each of a protein's amino-acid residues into the backbone torsion-angle space of φ and ψ. Such a diagram readily pinpoints the parts of the protein backbone that have unusual (and sometimes erroneous) configurations. It also nicely shows the clustering of residues into the standard secondary structural motifs and their variations. There have been several enhancements of the Ramachandran plot over the years, some of which superimpose computed energy contours or colour-code residues by characteristics such as sequence order.

Another visualization approach that has become very useful is the distance matrix plot, and its derivative, the difference distance matrix (Phillips, 1970). By constructing a matrix of distances between each amino-acid α-carbon and contouring or colouring the resulting values, one can readily see the patterns of α-helices and β-sheets within the structure. An advantage of this type of visualization is that it is coordinate-frame independent. Thus two structures can be compared for features without first superposing their coordinates in the same frame. This approach also works well when comparing two different structures of the same molecule, where there may be some movement between the two. By computing the distance matrix for each structure, and then computing the difference between the two distance matrices, the resulting difference distance matrix will indicate those parts of the structure that stay in the same relative relationships and those that may move relative to each other (Fig. 17.2.3.9).

Figure 17.2.3.9| top | pdf | A difference distance matrix plot of the α1–β2 interface of haemoglobin in the T to R transformation. The x axis represents the α1 subunit and the y axis the β2 subunit. Red points indicate residues that are closer following the transformation and blue points indicate residues that move farther apart. Plot by Raj Srinivasan, Johns Hopkins University.

Animating trajectories of molecular structures and changes in volumetric properties over time is one way to look for trends and patterns in molecular dynamics and other time-course simulations. However, other modes of information visualization can assist analysis and communication of results, sometimes more effectively. Plotting an array of small images showing the time course of key properties can reveal patterns that may be difficult to see in a trajectory. For instance, using the program MolMol (Koradi et al., 1996), the time course of the seven nucleic-acid backbone torsion angles during a dynamics simulation of an RNA polynucleotide can be plotted on a circular graph (starting from the centre and progressing outward) to uncover patterns of change and correlation between a large number of variables over time.

In addition to the enormous amount of information generated by computational simulations of molecular dynamics, dockings and other multi-structure, multi-modal techniques, the floodgates of molecular information have opened, gushing data from genomics and high-throughput structure determination. Thus, the need for novel visualization methods has become even more acute. Circle maps defining genomic structure at various levels of detail and annotation have become a common graphical form for organizing and communicating the positional and functional aspects of genome structure. Aligned nucleic acid or amino-acid sequences coded by conservation, chemical property, or any number of other functional relationships have become the lingua franca of gene hunters and gatherers. As the protein structure database continues its exponential growth, the opportunities for defining and refining structural family relationships abound. Developing methods for effectively visualizing the relationships that arise from all-by-all computational comparisons of the entire database is an important current challenge in molecular graphics.

In print media, shaded colour images can present a number of difficulties. In addition to the issue of cost, colour shifting, reproducibility and loss of detail in the half-toning process may lead to less than the desired result. Simple line art is an effective way to bypass many of these complications. Since the advent of printing in the middle ages, artists and scientists have explored the problems of creating illustrations within the limitations of the printing process. Over time, artists have built a vocabulary of outlines, hatched shading and varied textures to simplify and clearly portray an object. While the creation of such illustrations was time consuming and required considerable artistic talent, they effectively portrayed the observational science of the day. The advent of computers and computer graphics removed any requirement for skilled hand draftsmanship in the production of molecular representations, but did not solve all of the problems of good illustration. As mentioned above, prior to the widespread use of interactive computer graphics, molecular structures were often published as outline drawings of ball-and-stick models using programs such as ORTEP or PLUTO (Motherwell & Clegg, 1978). More recently, programs such as MOLSCRIPT (Kraulis, 1991) have re-established the popularity of line-art illustration in the molecular realm. A good ORTEP drawing usually took a great deal of preparation time in order to get the best representation and viewpoint to display the structure effectively. As the visual repertoire of molecular structure has expanded to a wide variety of shapes including ribbons, tubes and solvent-based surfaces, the challenge of automating the general illustration process has grown. A number of techniques have been developed in the computer-graphics community to generate images in the style of technical or artistic illustrations (Fig. 17.2.4.1). These approaches use lighting, depth information and geometry to produce black-and-white drawings with shapes defined by silhouette lines and cross-hatched shading, and details shown by a variety of textures. MOLSCRIPT has used some of these techniques for ribbon and ball-and-stick renderings. More general applications of these approaches to molecular illustration have also been described by Goodsell & Olson (1992).

Figure 17.2.4.1| top | pdf | Line-art molecular illustration. The figure on the left depicts the α-carbon backbone and molecular surface of the α subunit of haemoglobin (PDB code: 2hhb). Outlines define the shapes of the surfaces and tubes, and contour lines enhance their three-dimensionality. Hatch lines, normally used for shadows, are used here to darken the inside of the molecular surface. The figure on the right shows the interior of a human red blood cell (300 Å3), showing all molecules except water. The picture is drawn with outlines defining each molecule. Shadows and depth cuing are used to enhance the three-dimensional character of the image. Contour lines are not used. From Goodsell & Olson (1992).

A significant advantage of digital black-and-white illustration is the efficiency of representation. Since each picture element takes only a single bit of information (black or white), and since there are typically large areas that are of constant value, these images can be compressed, stored, transmitted and printed very efficiently. Thus, with the advent of electronic web publication, such illustrations represent an attractive alternative to full colour. These same characteristics represent significant advantages for the digital transmission and use of animated sequences as well.

Computer-graphic molecular animations began to appear in the late 1960s. Recording directly off their vectorscope, Levinthal and colleagues in Project Mac produced a record of an interactive molecular modelling session in 1967. In the early 1970s, a number of molecular animations were produced to convey new scientific results. Wilson at UC San Diego showed vibrational modes of small molecules in a film produced frame-by-frame on a vectorscope. Parr & Polyani painstakingly filmed pen plotter drawings of space-filling diatomic molecules to animate a bimolecular chemical reaction. Sussman & Seeman produced a black-and-white vector animation of the dinucleotide UpA structure in 1972 by recording directly off a vectorscope. Seeman, Rosenberg & Meyserth produced a more ambitious molecular animation in 1973 entitled Deep Groove, which depicted the structure of double helical segment ApU CpC and its implications for more extended DNA geometry. This film was shot in colour, using a monochrome vectorscope and multiple exposures through a colour filter wheel. Around this time, Knowlton, Cherry & Gilmer at Bell Labs used early frame-buffer devices to display and animate patterns of crystal growth based upon aggregation of spheres. In the mid-1970s, Porter & Feldman had developed a scan-line based CPK representation for raster displays and had animated molecular structures, and Langridge and co-workers had taken up recording off the black-and-white vector displays then available. By the end of the 1970s, Max had produced high-quality animations of DNA using a high-resolution Dicomed film writer (Max, 1983) and Olson had used an early colour vector display from Evans and Sutherland to produce an eight-minute animation depicting the structure of tomato bushy stunt virus (Olson, 1981). By the early 1980s, animation projects became more ambitious. Olson produced large-screen OmniMax DNA and virus animation segments for Disney's EPCOT center in 1983. Max produced a red–blue stereo OmniMax film for Fujitsu entitled We Are Born of Stars, which included a continuous scene depicting the hierarchical packaging of DNA from atoms to chromosomes, based on the best current model of the time.

Computer-graphics animation has presented both great potential and significant challenges to the molecular scientist wishing to communicate the results of structural research. Animation can not only enhance the depiction of three-dimensional structure through motion stereopsis, it can show relationships through time, and demonstrate mechanism and change. The use of pans, zooms, cuts and other film techniques can effectively lead the viewer through a complex scene and focus attention on specific structures or processes. The vocabulary of film, video and animation is familiar to all, but can be a difficult language to master. While short animations showing simple rotations or transitions between molecular states, or dynamics trajectories, are now routinely made for video or web viewing, extended animations showing molecular structure and function in depth are still relatively rare. The time, tools and expertise that are required are not generally available to structural researchers.

While the use of physical models of molecules has largely been replaced by computer graphics, new computer-driven rapid-prototyping technologies which originated in the manufacturing sector have begun to be utilized in the display of molecular structure. A number of `three-dimensional printing' methods have been developed to build up a physical model directly from a computational surface representation of an object (Burns, 1954). One of the earliest methods, stereolithography, uses a resin which is polymerized when exposed to laser light of a given wavelength. The laser is passed through a vat of the liquid resin and is lowered, layer-by-layer as it plots out the shape of the object (Fig. 17.2.4.2). Other approaches build up layers of paper or plastic through lamination or deposition. These methods have been used by a number of scientists to produce various representations of molecular structure (Bailey et al., 1998). The ability to hold an accurate representation of a molecular surface in one's hand and feel its shape can give great insight, not only to people with visual impairments, but to anyone. Moreover, when one is dealing with processes such as docking and assembly, these physical models can add a haptic and manipulative appreciation of the nature of the problem. While at this point colour has not been implemented in these technologies, there remains the promise that such automated production of molecular models will enhance the communication and appreciation of molecular structure.

Figure 17.2.4.2| top | pdf | A stereolithographic model of betalactamase inhibitory protein (BLIP). The model depicts the shape of the molecule as represented by a spherical-harmonic approximation of the solvent-excluded surface. Inside the surface is a hollow tube which follows the α-carbon trace of the protein backbone. The model was designed by Michael Pique and Arthur Olson, and fabricated on a 3D systems SLA 1000 by Beryl Hodgson.