Principles of Protein Structure - G. Schultz 1982

Models, Depiction, and Documentation of Protein Structures
Representation of Complete Structure
Spatial Models

Massive tables containing complete structural data are extremely difficult to comprehend; clearly, they need to be presented in a different, more accessible format. This section outlines all currently used Methods for representing complete protein structures.

Accurate molecular models are bulky yet convenient. The three-dimensional model remains the most practical way to represent molecular Structure. Such a model is indispensable for any experiment relying on the knowledge of a protein's full structure, proving particularly well-suited for identifying substrate and effector binding sites. However, these models are bulky and prohibitively expensive, which accounts for their relatively limited use.

Wire Models

Kendrew–Watson wire models are the most precise. Kendrew–Watson wire models [391], built on a scale of 1 Å = 20 mm with a wire diameter of 2 mm, are widely used for the most accurate three-dimensional representation of Proteins. An example of such a model is shown in Fig. 7.3a. Atomic positions that are not explicitly marked correspond to branch points and wire ends. Valence angles, Bond Lengths, and peptide units in this model are rigid yet adjustable. Dihedral angles can be changed freely, as they are fixed with screws on connecting sleeves. Because only thin wires and screws are used, the models offer excellent visibility.

Typically, Kendrew–Watson models are built directly from electron density maps. For this purpose, the map is plotted to the same scale (1 Å = 20 mm) on translucent plastic sheets. The model is then built "within the map"—meaning the model and the map are superimposed using a semi-reflective mirror under appropriate illumination [392]. This Procedure is illustrated schematically in Fig. 7.4. The transparency of the model allows every part of it to be seen in the mirror, even after the entire molecule has been assembled. At The final stage, atomic coordinates are read from the model using tubes moving along three mutually perpendicular axes.

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Fig. 7.3 (see p. 164).

Fig. 7.3 (see p. 164).

Fig. 7.3. Representation of protein structures.

a — adenylate kinase constructed using a Kendrew–Watson wire model [391] (scale 20 mm — 1 Å); b — Biron wire backbone model of adenylate kinase [393], with three side chains highlighted (scale 5 mm — 1 Å); c — adenylate kinase assembled from Nicholson model components [394] (scale 10 mm — 1 Å); d — space-filling model (CPK components, scale 12.5 mm — 1 Å [395]) of Ribonuclease S (provided by Wyckoff); e — stereoscopic image of the space-filling model (CPK) of the carboxypeptidase Active Site (provided by W. N. Lipscomb); f — stereoscopic image of the space-filling model showing the cytochrome c molecular surface (provided by Feldman and Porter [399]), generated via computer and displayed on a color television screen.

Fig. 7.4. Richards' optical comparator (top view) [392].

A — semi-reflective mirror; B — observer's eye. The model and map are superimposed when viewed in the mirror. C — electron density map plotted on transparent sheets. D — diffused light illuminating the map. E — focused light highlighting the part of the model under construction. F — model under construction. G — rigid framework of the model.

Skeletal wire models are simple to construct. If an approximate idea of the chain folding pattern is needed, a linear wire model with minor bends at the C_α positions can be used. The bending angles of the wire (virtual valence and dihedral angles, Fig. 7.10) are calculated from the C_α positions and transferred to a 3 mm (1/8 inch) diameter wire using a special device [393]. A scale of 1 Å = 5 mm is convenient for such models. Important side chains can be attached after the peptide backbone is built. The model is intuitive and very easy to manufacture. Fig. 7.3b shows such a model of adenylate kinase.

Interlocking Plastic Models

Plastic models provide a clear visualization of chemical properties. Another widely used model is assembled from interlocking plastic components proposed by Nicholson [394]. This model accounts for all atoms: non-hydrogen atoms are represented by spheres 8–10 mm in diameter, and hydrogen atoms by the bonds leading to them (bond diameter 4 mm). The appearance of the model is shown in Fig. 7.3c. At a scale of 1 Å = 10 mm, Nicholson models are significantly more compact than Kendrew–Watson wire models.

The plastic components of these models are color-coded, making the Properties of Individual protein groups much easier to visualize: positively charged groups (ammonium and guanidinium) are blue, negatively charged (carboxyl) and hydroxyl groups are red, sulfur is yellow, and aromatic moieties are purple. Against this backdrop, the white-painted main chain is easily traced. Consequently, Nicholson models are highly convenient for anyone seeking to quickly grasp a molecular structure.

Nicholson models are far less accurate than Kendrew–Watson models. Furthermore, identifying Hydrogen Bonds on them is difficult. Because the spheres and rods are relatively large, the model lacks sufficient "transparency." Therefore, Nicholson models are best constructed from atomic coordinates rather than electron density maps (Fig. 7.4). However, despite these drawbacks, plastic models allow for the quick and easy acquisition of fairly detailed structural information and are also well-suited for educational purposes.

Space-Filling Models

Space-filling models directly convey the molecular surface. Space-filling models are extremely difficult to build for an entire protein molecule. Because building a complete protein model obscures the interior of the molecule, models of this type illustrate only Surface Properties. Accordingly, they are used primarily to identify substrate or effector binding sites, i.e., to elucidate protein–substrate and protein–effector interactions. The appearance of the model is shown in Fig. 7.3d and 7.3e.

Unfortunately, the Components of the most common space-filling models, proposed by Corey, Pauling, and Koltun (CPK) [395], are built to a scale of 1 Å = 12.5 mm, which corresponds to neither the Nicholson nor the Kendrew–Watson model. As a result, these models cannot be used interchangeably, which would undoubtedly be useful in many instances.

Model Maps

Model maps correspond to electron density maps.

Initially, X-Ray Diffraction data are obtained as an electron density map, which is a stack of transparent plates featuring density contours that are subsequently interpreted. Clearly, the molecular structure under investigation can be represented in the same manner. Such an experiment was performed for ribonuclease [395]: all bonds were printed as strips, and the Van der Waals envelopes of the cavities as connecting circles. However, such model maps did not become widespread. Obviously, compared to Other types of models, they are significantly less informative, especially when examining Protein Interactions with other molecules.

Computer Graphics

The projection of a rotating object onto a television screen is perceived as a three-dimensional image. For a long time, computer graphics systems could not compete with solid physical models. The limitations imposed by the two-way screen of a cathode-ray tube were too severe to provide a satisfactory representation of a three-dimensional structure. The situation changed with the advent of "fast" cathode-ray tubes and high-speed electronic devices designed to calculate coordinate changes during rotation [397]. Such a device allows, upon rotating a large set of vectors, to calculate the projection of this set onto a given plane (which defines the image) and simultaneously display it on the screen. At rotation speeds starting from one revolution per ten seconds and higher, the on-screen image closely approximates what we see when viewing an object turning in our hands. Therefore, a rotating object (or set of vectors) on a television screen is perceived in three dimensions.

A set of vectors on a television screen can also convey the Covalent Structure if, for example, the vectors correspond to the wires of a Kendrew–Watson model; a set of vectors can likewise represent an electron density map. PARTS OF THE model and the electron density distribution can be displayed simultaneously, thereby verifying the consistency of the model with the map. Moreover, since these systems are interactive, one can manipulate the model until the best fit with the map is achieved [398]. At the same time, three-dimensional perception is preserved by rotating both the model and the map on the screen.

In the future, computer graphics may well replace solid physical models. In its capabilities, a computer graphics system approaches an optical comparator (Fig. 7.4). However, a graphics system makes it possible to display the electron density map in any desired orientation or at any level, rather than being restricted to fixed directions and levels as in a comparator. Such changes in orientation are crucial when examining electron density distributions.

Volumetric models can also be rendered on a television screen [397, 399]; however, in this case, calculating the internal parts takes so much time that it precludes rotating the model at a speed sufficient to create a three-dimensional illusion. An example of such a display is shown in Fig. 7.3, e.

At present, graphics systems are used only in large research centers that can afford both the equipment and the personnel required to maintain and develop the corresponding software. Nevertheless, the cost of electronic hardware is decreasing so rapidly that the day will likely come when graphics systems replace optical comparators and, perhaps, even molecular models.