4
MOLECULAR GRAPHICS:
VISUALIZATION OF BIOMOLECULES
Computer graphics has changed the way in which chemical structures are presented and perceived. The facile conversion of macromolecular sequences into three-dimensional structures that can be displayed and manipulated on the computer screen have greatly improved the biochemist’s understanding of biomolecular structures. Tools for graphical visualization and manipulation of biomolecular structures are described.
4.1. INTRODUCTION TO COMPUTER GRAPHICS
Molecular graphics (Henkel and Clarke,1985) refers to a technique for the visualization and manipulation of molecules on a graphical display device. The technique provides an exciting opportunity to augment the traditional description of chemical structures by allowing the manipulation and observation in real time and in three dimensions,of both molecular structures and many of their calculated properties. Recent advances in this area allow visualization of even intimate mechanisms of chemical reactions by graphical representation of the distribution and redistribution of electron density in atoms and molecules along the reaction pathway.
All graphics programs must be able to import commands defining representa-tions and translate these into a picture according to the representarepresenta-tions specified.
The graphics programs offer various choices of renderings of the model,with color coding of atoms or groups and with selective labeling. These include the following.
53 An Introduction to Computational Biochemistry. C. Stan Tsai
Copyright¶2002 by Wiley-Liss, Inc.
ISBN: 0-471-40120-X
Line Drawings: Skeletal and Ball-and-Stick Models. Traditionally,draw-ings of small molecules have represented either(a) each atom by a sphere or (b) each bond by a line segment. Bond representations give a clearer picture of the topology or connectivity of a structure. In a simple picture of line drawings,there is a direct correspondence; that is,one line segment equals one bond. There are basically two ways to extract bonds from a given set of atomic coordinates:
1. Screen the atoms by distance. This is the most general approach. For every pair of atoms in the structure,the distance between them is calculated. If the distance is less than the sum of the van der Waals radii of the two atoms,a bond between them is assumed. For proteins or nucleic acids,this approach can be specialized by checking only atoms in the same residue/nucleotide, plus the atoms in the peptide/nucleotide bonds between successive residues/
nucleotides.
2. Create an explicit list of bonded pairs. For protein containing only standard amino acids and common ligands,this can be done once and for all. For each residue type,one can make a list of pairs of atom names,each pair corresponding to a bond. Then in drawing a picture of a protein for each residue,one can search the coordinates of each pair of atoms in the list of bonds and add the appropriate line segment to the drawing. Similar consider-ations apply to nucleic acids. In pdb files,explicit connectivity lists are provided.
A ball-and-stick drawing is a simple skeletal model,in which the representation of the bond is generalized to a cylinder,and a disc is added at the position of each atom. Additional information may thereby be displayed in that different atom types may be distinguished by size and shading,and bonds of different appearance may be drawn. To create the line segments corresponding to a pure skeletal model,one needs only copy the coordinates of each pair of bonded atoms as the line segment end-points. To create ball-and-stick pictures,one must:
1. Draw a circle at the position of each atom with the facility to vary the atomic color and radius.
2. Determine the line segments that represent the bond and attach these segments at the edge of the circle.
Wire models and ball-and-stick models are extremely useful because of the great detail they contain. They are particularly useful in connection with blow-ups of selected protein/nucleic acid molecules.
Shaded-Sphere Pictures. Each atom is shown to represent complete chemi-cal detail of molecules. This category includes three basic types of picture:
1. L ine drawings: Each atom is represented as a disc. The picture is a limit of the ball-and-stick drawings as the radius of each atomic ball is made in proportional to the van der Waals radius.
2. Color raster devices: A raster device can map an array stored in memory on to the screen so that the value of each element of the array controls the appearance of the corresponding point on the screen. It is possible to draw
54 MOLECULAR GRAPHICS: VISUALIZATION OF BIOMOLECULES
Figure 4.1. Cube model for RGB system. The RGB cube model illustrates the definition of colors by the three primary components along the three axes R, G, and B. Each color point is represented by a triple (r, g, b). The three primary colors are red (1, 0, 0), green (0, 1, 0), and blue (0, 0, 1). Other binary-status (0/1 for r, g, b) colors are cyan (0, 1, 1), magenta (1, 0, 1), yellow (1, 1, 0), white (1, 1, 1), and black at origin (0, 0, 0). Different colors are expressed by a combination of r, g, and b values varied between 0 and 1. For example, gray colors correspond to the main diagonal between black and white.
each atom as a shaded sphere,or even to simulate the appearance of the Corey—Pauling—Koltun (CPK) physical models to maintain most of the familiar color scheme (C: black,N : blue,O : red,P : Green,and S: yellow,etc.). In such representation,atoms are usually opaque,so that only the front layer of atoms is visible. However,clipping with an inner plane or rotation can show the packing in the molecular interior.
3. Real-time rotation and clipping: Facilities available on vector graphics devices are very useful in connection with another technique for representing atomic and molecular surfaces. The spatter-painting of the surface of a sphere by a distribution of several hundred dots produces a translucent representation of the surface(dot-surface). It is possible to combine dot-surface representations with skeletal models to show both the topology of the molecule and its space-filling properties (Connolly,1983). Dot-surface pictures used on an interactive graphics device with a color screen have been helpful in solving problems of docking ligands to proteins and exploring the goodness of fit in interfaces.
Basically,any color can be matched by a suitable combination of three primary colors,RGB(red,green,and blue). These three primary colors on a binary status (on/off) provide eight colors (Figure 4.1). Video monitors generate a large number of colors by combining various amount of the three primary components. The observed color of an object depends on the spectrum of the light it emits,transmits, or reflects. Observable colors may be distinguished on the basis of three character-istics:
1. Hue (color): Color in the most common colloquial sense (i.e.,red,green and blue) describes different hues. For monochromic light,different wavelengths
INTRODUCTION TO COMPUTER GRAPHICS 55
Figure 4.2. GenBank format for nucleotide sequence of chicken egg-white lysozyme.
correspond to different hues,but different spectra can give the same perceived hue. A flat spectrum appears achromatic: white,gray,or black.
2. Tone (value): Roughly speaking,the total amount of light per unit area (i.e., multiplying a spectrum by a constant) changes the tone. Members of the series white; gray ; black differ in tone. Empirical scales of tone are not linear in integrated intensity; moreover,changes in tone can alter perceived hue.
3. Saturation (intensity or chroma): The difference between a color and the gray with the same tone exemplifies saturation. A pure or saturated color can be diminished in saturation by adding white light and normalizing the result to the same perceptual tone.
As a result,colors may be thought of as point in a three-dimensional space,the axes of which might be the primary colors (primaries): red,green,and blue (Figure 4.1). Each color is a vector,the components of which are the intensities of the primaries required to match it. For displays generated by three-gun(red,green,and blue) monitors,these are the numbers specified. The literature of computer graphics reveals considerable efforts to achieve truly convincing representations of real objects (Roger,1985; Wyszecki and Stiles,1982).