IntroductionMolecular graphicsAnimationStructure representationRepresentation of structuresDisplaying structures

Visualizing the unseeable world of molecules is the fundamental goal of crystallographic structure determination. Thus there is a natural synergy between the science of unravelling molecular structure and the technology of representing it. Graphics have always had a significant role in the analysis of diffraction data, the synthesis of molecular models and the communication of the information and knowledge gained in these scientific pursuits. At least since the time of René Häuy in the 18th century, crystallographers have attempted to use graphics and physical models to understand and explain the underlying nature of the solid state (Fig. 17.2.1.1). Over the years, crystallography has pushed the development of new technologies to aid in structure solution, and crystallographers have been early adaptors of new technologies. No technology has had more impact on crystallography than electronic computing. Nowhere is that impact more apparent than in what we have been able to study and how we have been able to visualize our structural results. With the pervasiveness of three-dimensional computer graphics in many aspects of everyday life, it is easy to forget the role that X-ray crystallography has played in its genesis and the role that graphics technology continues to play in the advancement of molecular structure analysis.

The human genome project and other efforts in biology and medicine have produced heightened emphasis on molecular depictions of increasing complexity. Visualization of such systems through computer-graphics technology is a key component in our understanding of these data and the models that we use to explain them. In fact, modelling and visualization techniques provide a bridge between experimental data at different scales, enabling placement of detailed atomic models of molecules from crystallography into lower-resolution data on large assemblies from electron microscopy or scanning probe imaging.

Background – the evolution of molecular graphics hardware and software

The complexity of molecular structure and the fact that these sub-microscopic objects of study are not directly visible have necessitated the use of physical or pictorial representations to aid in interpretation, manipulation and understanding. Illustrations and models made of wood, plastic or metal served these purposes from the development of the original theories of molecular structure through to the first nucleic acid and protein structures solved in the 1950s. Over the following years, computer graphics has evolved into a significant and ubiquitous technology, helping to sustain the explosive growth of macromolecular structure research. Today, computer graphics pervade the activities of much molecule-based research, from quantum chemistry to molecular biology.

Computer-based molecular graphics can be traced back to 1948 and the X-RACX-RAC project of R. PepinskyPepinsky, R. at Pennsylvania State University (Pepinsky, 1952). Pepinsky developed an analogue computer to carry out the Fourier transformation of X-ray structure factors to produce electron-density maps. Integrated within X-RAC was an oscilloscope that could display the contours of the electron density (Fig. 17.2.2.1). These displays were, to my knowledge, the first computer-generated images of molecular structure. Crystallographers from around the world came to Pennsylvania State University to use X-RAC and to marvel at the speed and automation possible in the solution of molecular structures. While the digital revolution quickly overtook the analogue approach, X-RAC clearly set the precedent for molecular scientists as early implementors and adaptors of computational and graphics technology.

In the 1960s, two seminal projects laid the foundation for modern molecular graphics. Early in the decade, Johnson's ORTEP ORTEP (Johnson, 1970) program became widely available, allowing crystallographers to produce illustrations of three-dimensional (3-D) molecular structures on a pen plotter. These black-and-white line drawings of ball-and-stick models were used both for working drawings during structure analysis and for creating illustrations for publication. A few years later, experiments lead by Levinthal under Project MACProject MAC (Levinthal, 1966) at MIT pioneered the interactive display and transformation of 3-D molecular structures on a computer screen. By the end of the decade, the groundwork for molecular graphics was set: ORTEP convincingly demonstrated to a large number of scientists that the computer could be used as an alternative to the human hand to produce accurate drawings and stereoscopic pairs for the analysis and communication of the results of structural research. Project MAC showed that the computer could be used as an interactive environment in which to model and simulate on the molecular scale. These two projects helped define the two broad functions of molecular graphics: publication graphics, for which clarity of presentation is the essential goal, and working graphics, for which rapid feedback and high interactivity are the key elements.

In the 1970s, 3-D interactive computer-graphics systems became commercially available. Hardware offerings from companies such as Evans and Sutherland, Vector General, and Adage prompted a number of laboratories to develop interactive molecular-modelling software. Several of these early systems were devoted to the task of building an atomic model of a protein into the crystallographically derived electron-density map. Programs such as BILDER BILDER (Diamond, 1982), MMSX MMSX (Barry & McAlister, 1982), FRODO FRODO (Jones, 1978) and GRIP GRIP (Wright, 1982) began to replace metal Kendrew models and the cumbersome `Richards Box'Richards box optical comparitors. This application, more than any other, sold these expensive ($100 000) monochrome line-drawing graphics devices to the molecular-research community. Moreover, during that time, biomolecular structure determination was a major civilian consumer of 3-D interactive graphics devices.

Technical, commercial and scientific advances in the 1980s prompted enormous growth in the use of molecular graphics. As late as 1983, a worldwide list of laboratories using high performance graphics computers for molecular work could be maintained – the number was below 100 (Olson, 1983). By the end of the decade, that number grew into the thousands, and utilization spread beyond any ability to track it. At the beginning of the decade the expensive vector-graphics terminals were the only way to achieve interactive 3-D display. Ten years later, the colour raster display had taken over the interactive computer-graphics market, driving prices down and broadening display capabilities from lines and dots to include shaded surface representation. Early in the 1980s, several academic software packages, such as GRAMPS/GRANNY GRAMPS/GRANNY (O'Donnell & Olson, 1981; Connolly & Olson, 1985), MIDAS MIDAS (Ferrin et al., 1988) and HYDRA HYDRA (Hubbard, 1986), went beyond electron-density fitting to provide general graphics functionality for examining molecular structure and properties. Over the decade, the remarkable evolution of computer hardware – the advent of microprocessors, very large scale integration (VLSI) devices, personal computers and scientific workstations – increased the accessibility of molecular graphics. By the mid-1980s, the demand was such that several commercial companies had been established to market molecular graphics and modelling software. By the end of the decade, structural scientists in academic and industrial research settings had a wide variety of use-tested hardware and software platforms with which to perform molecular modelling.

The 1990s witnessed remarkable advances in the technology and sociology of computing as well as in the science of molecular structure and design. Moore's lawMoore's law of the microcosm, which estimates that `the effectiveness of microprocessors doubles every 18 months', continued to track growth accurately. Thus the performance-to-cost ratio of late 1990s computers was a millionfold higher than those of the mid-1960s. A 1997 200 Nintendo-64 game machine was faster and had more memory and far superior graphics than the Control Data 6600 supercomputer and peripherals of the 1960s, and, with its optional ($70) disk, bettered almost every technical specification of a 1980 VAX 11/780. Gelder's lawGelder's law of the telecosm posited in 1993 that `bandwidth will treble every year for at least the next 25 years'. This, coupled with Metcalf's lawMetcalf's law, that `the total value of a network to its users grows as the square of the total number of users' implies that the `teleputer', or non-localized computing, is becoming the computational environment of the future.

While software development continues to lag behind hardware growth, the emergence of the World Wide Web and the concepts of network-based computing have catalysed a rethinking of the nature of software, its development, distribution and inter-operability. The concepts of cyberspace and `virtual reality'Virtual reality have been implanted into the minds and expectations of the general public, promoting a renaissance in user-interface exploration and development. It is transforming the computer from a window through which to look into a portal through which to step. Suddenly, the other senses – sound, touch, taste and smell – can become part of the computational experience.

Representation and visualization of molecular data and modelsMolecular graphicsStructure representationRepresentation of structuresDisplaying structures

In the early days of molecular computer graphics, the major goal was to represent the spatial structures of molecules, principally the locations of the atom centres and the covalent connectivity between them. Using X-ray diffraction analysis, one would first plot the electron density as line contours projected onto a plane and locate the atom centres from multiple projections. The molecule would then be represented by a simple bond diagram. As experimental and computational methods advanced, other representations were used to convey additional information about the structure. Johnson's ORTEP program plotted the thermal ellipsoids of each of the atoms, visualizing the magnitude and direction of their thermal vibrations as derived from the anisotropic temperature factors (Fig. 17.2.3.1). As colour raster displays became available, space-filling CPK representationsMolecular graphicsCPK modelsStructure representationCPK modelsRepresentation of structuresCPK modelsDisplaying structuresCPK modelsCPK models were used to visualize molecular shape and volume while using an atom-based colour scheme to show atomic composition and distribution (Porter, 1979) (see Fig. 17.2.3.4). The complexity of protein molecules prompted the introduction of simplified representations that replaced the all-atom visualization with tubes or ribbons (Branden et al., 1975; Carson, 1991) (Fig. 17.2.3.2) that represented the fold of the protein chain. This simplification allowed the comparison of protein folds, and led to the beautiful classification of protein motifs by Richardson (1981).

As more structural information has become available, and as computational hardware technology has advanced, the ability to visualize a variety of molecular properties has become possible. Meanwhile, issues of interactivity, intelligibility and interpretability have become increasingly important as the systems under study have become more complex. There are three general approaches to visualizing the structures, properties and relationships of molecular systems: geometric construction, direct volumetric rendering and generic information visualization. Today almost all macromolecular modelling and visualization work is done using geometric representations of bonds, ribbons and surfaces, which are annotated by colour to represent atom type, chain characteristics, or electrostatic potential. For these purposes, there are several `turn-key' programs that facilitate display and interaction. Programs such as RASMOL RasMol (Sayle & Milner-White, 1995), GRASP GRASP (Nichols et al., 1995) and MOLSCRIPT MolScript (Kraulis, 1991) are widely used by the molecular-structure community. Some of the fundamentals of representation used in these types of programs, as well as more exploratory techniques, are described below.

While the world is continuous, our measurements of it tend to be finite and sampled. Thus data are usually represented as discrete values on a line, plane, volume or hypervolume. On the other hand, in order to capture the nature of the world, our models tend to be represented as continuous functions. Geometric construction is useful for rendering continuous models, while other techniques, such as volume rendering, lend themselves to the visualization of discrete data.

17.2.3.1. Geometric representationMolecular graphicsgeometric representationStructure representationgeometricRepresentation of structuresgeometricDisplaying structuresgeometric representation

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Geometric representationMolecular graphicsgeometric representationStructure representationgeometricRepresentation of structuresgeometricDisplaying structuresgeometric representation

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 representationsSurfaces, representation ofRepresentation of surfaces 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-buffersz-buffer 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 shadingGouraud shadingRepresentation of surfacesGouraud shadingSurfaces, representation ofGouraud shading (Gouraud, 1971), which interpolates the shaded colour values assigned at the vertices across the polyhedral face (Fig. 17.2.3.4). Phong shadingPhong shadingRepresentation of surfacesPhong shadingSurfaces, representation ofPhong 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 tracingRay tracingMolecular graphicsray tracingStructure representationray tracingRepresentation of structuresray tracingDisplaying structuresray 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).

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 surfaceSolvent-accessible surfaceSurfacessolvent-accessible surface (Lee & Richards, 1971) and the molecular surfaceMolecular surfaceSurfacesmolecular surface (Richards, 1977; Connolly, 1983; Sanner et al., 1996), sometimes referred to as the ConnollyConnolly surfaceSurfacesConnolly surface or solvent-excluded surfaceSolvent-excluding surfaceSurfacessolvent-excluding 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.

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 codingRepresentation of surfacescolour codingSurfaces, representation ofcolour 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).

Another method for projecting information on a surface is texture mappingRepresentation of surfacestexture mappingSurfaces, representation oftexture mappingTexture 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).

17.2.3.2. Volumetric representationMolecular graphicsvolumetric representationStructure representationvolumetricRepresentation of structuresvolumetricDisplaying structuresvolumetric representation

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Volumetric representationMolecular graphicsvolumetric representationStructure representationvolumetricRepresentation of structuresvolumetricDisplaying structuresvolumetric representation

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 representationsIsosurface representationsStructure representationisosurfacesRepresentation of structuresisosurfacesDisplaying structuresisosurfaces, 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'Marching-cube algorithm, 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)

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'Molecular graphicsdirect volume renderingStructure representationdirect volume renderingRepresentation of structuresdirect volume renderingDisplaying structuresdirect 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.

17.2.3.3. Information visualizationRepresentation of informationDisplaying informationVisualization of information

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Information visualizationRepresentation of informationDisplaying informationVisualization of information

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 plotRamachandran 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 plotDistance matrix plot, and its derivative, the difference distance matrixDifference distance matrix plot (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).

AnimatingAnimationof molecular-dynamics trajectoriesMolecular dynamicsanimation of trajectories 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.

Presentation graphics

Much of molecular graphics can be classified as working or `throw-away' graphics. Typically this involves the interactive creation of graphical representations on screen or paper that are used in the course of research to build, modify and analyse molecular structures, their motions and interactions. Such graphics need only be intelligible to the researchers involved. On the other hand, a presentation or publication graphic must be able to stand on its own to convey information to a broader audience. Thus it requires additional thought and work in its creation. It is unfortunate that many scientists simply capture the working graphics on their computer screens for use in publications or other forms of communication. Both interpretability and intelligibility may suffer badly if a number of issues are not considered in the production of a presentation graphic: What is the medium of publication? What is the main point of the graphic? Who are the target audience? How will reproduction or the viewing environment affect the impact of the graphic? Even seemingly simple issues such as when and how to use colour can in reality be a complex mixture of aesthetics, psychology, technology and economics. While an in-depth discussion of these issues is beyond the scope of this chapter, it is worthwhile to look at two categories of publication graphics, illustration and animation, in this context.

Looking ahead

Moore's law has already delivered on the promise of three-dimensional graphics capability for the desktop and laptop. The internet and World Wide Web have made molecular structure data and display software available to the masses. Have molecular graphics reached a stage of maturity beyond which only small incremental changes will be made?

The Human Genome Initiative and high-throughput structure determination are beginning to change the scope of the questions asked of molecular modelling. Prediction of function, interactions, and large-scale assembly and mechanism will become the dominant domain of molecular graphics and modelling. These tasks will challenge the capabilities of the hardware, software and, particularly, the user interface. New modes of interacting with data and models are coming from the computer-graphics community. Molecular docking and protein manipulation using force-feedback devicesForce-feedback devices have been demonstrated at the University of North Carolina (Brooks et al., 1990). The same team has developed a `nanomanipulatorNanomanipulator' which couples a scanning atomic force microscope with stereoscopic display and force-feedback manipulation to control and sense the positioning and interactions of the probe within the molecular landscape (Taylor et al., 1993). The challenge of bridging across the scales of size and complexity of the molecular world may lead us into the realm of virtual reality. Data from X-ray crystallography are being combined with data from large molecular complexes, characterized by electron microscopy. These data, in turn, can be integrated with those from optical confocal microscopy and other imaging techniques. With structures of molecules, assemblies and distributions, as well as data on molecular inventories, we can start to piece together integrated pictures of cellular environments, but with full atomic modelling at the base (Fig. 17.2.5.1). Thus, while climbing around inside a protein molecule might not add much in the way of perceptual advantage, navigating through the molecular environment of a cell may prove to be instructive as well as inspirational.

Model of a crystal structure proposed by René Häuy in Traite elementaire de Physique, Vol. 1 [Paris: De L'Imprimerie de Delance et Lesueur, 1803]. This model, proposed in 1784, was the first to connect the external facets of a crystal with an underlying regular arrangement of building blocks.

Model of a crystal structure proposed by René Häuy

Figure 17.2.2.1 | top | pdf | One bay of X-RAC showing coefficient panels and the display oscilloscope. Inset: photo from the oscilloscope, showing a region of the phthalocyanine Fourier map. Reproduced from Pepinsky (1952).

One bay of X-RAC showing coefficient panels and the display oscilloscope. Inset: photo from the oscilloscope, showing a region of the phthalocyanine Fourier map. Reproduced from Pepinsky (1952).

One bay of X-RAC showing coefficient panels and the display oscilloscope

Figure 17.2.3.1 | top | pdf | ORTEP plot of phenylhydroxynorbornanone showing atomic thermal ellipsoids (from Thermal ellipsoid analysis: the fossil footprints of restless atoms, by Carroll K. Johnson and Michael N. Burnett, Buerger Award Lecture at the ACA meeting in St. Louis, July 20–26, 1997).

ORTEP plot of phenylhydroxynorbornanone showing atomic thermal ellipsoids (from Thermal ellipsoid analysis: the fossil footprints of restless atoms, by Carroll K. Johnson and Michael N. Burnett, Buerger Award Lecture at the ACA meeting in St. Louis, July 20–26, 1997).

ORTEP plot of phenylhydroxynorbornanone showing atomic thermal ellipsoids

Figure 17.2.3.2 | top | pdf | Ribbon diagram of actin monomer (PDB code: 1atn) (Kabsch et al., 1990).

Ribbon diagram of actin monomer (PDB code: 1atn) (Kabsch et al., 1990).

Ribbon diagram of actin monomer (PDB code: 1atn) (Kabsch et al

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.

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.

Simple bonding diagram of a DNA structure (PDB code: 140D) (Mujeeb et al

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.

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.

CPK representation of the same DNA structure as in Fig. 17.2.3.3

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.

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.

Solvent-excluded surface of the DNA structure using a water probe radius of 1.5 Å

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.

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.

Hydrophobicity mapped onto a molecular surface

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.

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.

Crystallographic electron-density isosurfaces, showing details of a protein iron–sulfur cluster

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.

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.

A difference-electron-density map of a minor-groove drug binding in DNA

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.

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.

A difference distance matrix plot of the α₁–β₂ interface of haemoglobin in the T to R transformation

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).

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).

Line-art molecular illustration

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.

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.

A stereolithographic model of betalactamase inhibitory protein (BLIP)

Figure 17.2.5.1 | top | pdf | This image represents a volume of blood plasma 750 Å on a side. Within the three-dimensional model, antibodies (Y- and T-shaped molecules in light blue and pink) are binding to a virus (the large green spherical assembly on the right), labelling it for destruction. It shows all macromolecules present in the blood plasma at a magnification of about 10 000 000 times. This model is composed of over 450 individual protein domains, ranging in size from the 60 protomers making up the poliovirus to a single tiny insulin molecule (in magenta). The model was constructed using atomic level descriptions for each molecule, for a total of roughly 1.5 million atoms. Detailed surfaces were computed for each type of protein using MSMS by Michel Sanner and then smoothed to a lower resolution using the HARMONY spherical-harmonic surfaces developed by Bruce Duncan. The model geometry contains over 1.5 million triangles.

This image represents a volume of blood plasma 750 Å on a side. Within the three-dimensional model, antibodies (Y- and T-shaped molecules in light blue and pink) are binding to a virus (the large green spherical assembly on the right), labelling it for destruction. It shows all macromolecules present in the blood plasma at a magnification of about 10 000 000 times. This model is composed of over 450 individual protein domains, ranging in size from the 60 protomers making up the poliovirus to a single tiny insulin molecule (in magenta). The model was constructed using atomic level descriptions for each molecule, for a total of roughly 1.5 million atoms. Detailed surfaces were computed for each type of protein using MSMS by Michel Sanner and then smoothed to a lower resolution using the HARMONY spherical-harmonic surfaces developed by Bruce Duncan. The model geometry contains over 1.5 million triangles.

This image represents a volume of blood plasma 750 Å on a side