means âthe application of ... build (although of course this depends to an extent on ..... (421 D.C. Richardson and J.S. Richardson, TIBS 19 (1994) 135-138.
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Biochemical Education Biochemical Education 26 (1998) 103-110
applications in the biomolecular sciences. Part 1: molecular modelling Clare E. Sansom”, Christopher A. Smithb “Department of Cystallography, Birkheck College. Universi& of London, London WCIE 7HX, UK hDepartment of Biological Sciences, Manchester Metropolitan University, Manchester MI SGD, UK
Abstract This article describes the basic tenets of molecular modelling, a computer-based means of visualizing and investigating the structures and properties of molecules. Its emphasis is on the applications of molecular modelling to the study of biological molecules and its uses in teaching students in the life sciences. 0 1998 IUBMB. Published by Elsevier Science Ltd. All rights reserved
1. Introduction Computers have infiltrated all aspects of educational life, witness the computer-aided learning pages in this journal and, for example, the “Computer Corner” in Trends in Biochemical Sciences. This article on molecular modelling is generally based on our experiences and the material used in teaching and assessing students on the BSc (Hons) in Biological Sciences at the MMU, the BSc (Hons) in Biochemistry and Molecular Biology at the University of Leeds and on the Advanced Certificate in Principles of Protein Structure Using the Internet approved by Birkbeck College of the University of London. Molecular modelling is a computer-based means of representing, visualizing and investigating the threedimensional structures and related properties of molecules. Modern biochemical texts are resplendent with marvellous computer-generated pictures representing biological molecules, while most journals in the biological sciences manage to have a computer graphic on their front covers. Our experiences suggest that many lecturers and students in the biological sciences have little idea of how images of molecules are generated and how their structures and properties may be investigated in s&co (a point recently emphasized by the editor of this journal [l]). Furthermore, these disciplines are relatively poorly supported by texts. None of the large biochemistry books (see for example refs [2-51) explains the basics of bioinformatics or molecular modelling, and those texts that are available are rather detailed requiring some relatively specialized knowledge of chemistry and/or mathematics; and are aimed at the 0307-4412/98/$19.00 + 0.00 0 1998 IUBMB. Published PII: SO307-4412(97)00155-6
by Elsevier
Science
research-level worker (for example refs [6-131). The aim of this article is to provide an easily accessible introduction to the basics of molecular modelling. In a subsequent article we will deal with some relatively restricted aspects of bioinformatics and genome projects. The term bioinformatics means “the application of information technology to the biological sciences”. It is most often used to mean the storage and analysis of one-dimensional biological data, typically sequences (primary structures) of peptides, proteins and nucleic acids. The sheer volume of such data coming out of initiatives, such as the Human Genome Project, is responsible for the growth in importance of bioinformatics in recent years [14-171. Thus, bioinformatics and molecular modelling are complementary and interrelated disciplines.
2. Molecular modelling Using computers it is possible to simulate scientifically meaningful pictures of molecules, to study their physical and chemical properties, for example shape, size and charge; to simulate the dynamic behaviour of atoms and molecules, such as their vibrational, twisting and rotational movements; to explore their interactions with other molecules; to design rationally molecules of biological and clinical interest; and, perhaps most importantly, to greatly improve scientific communication and the teaching of all aspects of biomolecular sciences. It is generally accepted that human brains are designed to receive visual information [18,19], hence Ltd. All rights reserved
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C. E. Sansom, C. A. SmithiBiochemical
molecular modelling has many advantages over the traditional approaches to examining the structures of biomolecules. Real physical models of molecules often lack visual appeal and are unwieldy and fragile, especially when the model is large. In comparison, computer-generated molecules are generally easy to build (although of course this depends to an extent on the molecule in question, the software available and what is known of the structure of the molecule) and are attractive and robust. Molecules can be “built” using an input of atomic coordinates imported from databases, or by using chemical templates stored in the modelling program, or by sketching a two-dimensional image directly using the VDU, or, indeed, a combination of all three. Further, once built, images on a VDU do not have a tendency to “denature” in one’s hands! On the negative side, the programs may run slowly, particularly with older types of personal computers. Molecular modelling may be arbitrarily divided into molecular graphics and computational chemistry [20]. The former is the visualization of chemical structures and molecular properties, although the definition is often extended to include simple manipulations, such as modifying the torsion angles of chemical bonds and basic geometric calculations, for example, estimating inter atomic distances. Computational chemistry involves attempting to calculate numerical properties of molecules, the most common in the molecular/ biochemical sciences being molecular energies. The primary outputs of such calculations are large amounts of numerical data. These are usually analysed using molecular graphics programs, and so the definition between molecular graphics and computational chemistry is becoming increasingly blurred.
3. Molecular
graphics
Molecular graphics offers a number of ways of viewing molecules, which can be exploited to advantage when examining or investigating them. Depth shading and smooth, real-time movement of the structures give realistic three-dimensional images. Models can be moved by rotation or translation. It is also possible to zoom in/out on particular regions of the structure and to clip sections through the model to gain clear views of internal features. They can also be represented in one of a number of forms, e.g. stick, ball and stick, dot surface or space filled, either uniformly or in combinations to highlight specific features. “Realistic” three-dimensional structures and stereo images may be simulated (Fig. 1). Attention can be drawn to individual portions of the model by thickening lines, changing the density or colour of the dots or putting a “ribbon” through the feature of interest (Fig. 1). Molecules may be compared structurally by overlaying the models using a least-square
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analysis of the atomic coordinates; while the rotation of bonds allows the conformational space available to the molecule to be investigated. Molecular graphics may be used to display the vast amounts of numerical data available from computational chemical exercises such as ab in& studies, or simulations such as those involved in molecular mechanics, molecular dynamics and “Boltzmann jumps” (Monte-Carlo simulations) and allow a rapid analysis using appropriate graphical representations. It is an axiom of biology that function follows structure. This is as true of biomolecules as any other biological entity [21,22], hence the great interest in the structures of biological molecules. Biochemists who determine the structures of large biomolecules tend to spend a great deal of time and energy using X-ray crystallography or nuclear magnetic resonance spectroscopy, and consequently techniques such as computational chemistry, which bypass these efforts are clearly very attractive.
4. Computational
chemistry
In theory, quantum mechanical calculations should provide a complete description of the energy of any particular conformation (shape) of a molecule by solving the Schrodinger equation [6-131. This is regarded as fundamental and the approach does not require the input of any experimental data. However, in practice, this so-called ab initio approach is only possible for very small molecules and many biomolecules consist of extremely large numbers of atoms by any definition of the word “large”. It is possible, however, to extend this approach. In the semi-empirical technique, the input of some experimentally derived parameters allows approximate solutions to the Schrodinger equation to be calculated, but the technique is still limited to relatively small molecular structures. In contrast, if a classical mechanical approach is adopted, then simulations of large molecular structures, their dynamics and properties becomes possible [6-131. In general, this type of simulation is possible when a simplified description of the molecular structure is available as a basis for calculations. In computational chemical simulations, the simplified description is a calculated potential energy surface which represents the molecule of interest. This energy is a (complex) function of the atomic coordinates of the molecule. Three major methods for conformational analysis are available to simulate molecular structures: molecular mechanics [6-13, 23-251, molecular dynamics [6-13, 26-281 and Monte-Carlo methods [6-13, 291. Unfortunately, no method is sufficiently well developed to fold a macromolecule into its biologically active structure [30]. Molecular mechanics and dynamic simulations
C. E. Sansom, C. A. Smith/Biochemical
are of use only if a molecule of very similar structure is already known which can act as a starting point for the simulation. If none is available, then a technique like homology modelling (not covered here), will have to be used, assuming the three-dimensional structure of a homolgue is known.
5. Molecular
mechanics
In molecular mechanics (MM) [6-13,23-25,281, the atoms of the molecule are assumed to be incompressible spheres and the (covalent) bonds to consist of elastic
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springs. The energy, E, of such a system (molecule) can then be described by breaking it into a number of constituent parts:
Thus the total or steric energy, E, is considered to be the addition of a series of individual energies, where E, is the energy of the bond(s) on being stretched from their “ideal” values; E,, the energy of bending bond angles away from their ideal values; ET, the energy caused by twisting about a bond; E,,, is the out of plane energy; ENB, the through space or nonbonded energies and E,,,, other energy terms which individuals may wish to
(4
Fig. 1. Shows a variety of ways of representing molecular models. (a) A space fill model of a ferredoxin molecule. The hydrogen atoms have been omitted and the iron-sulphur electron transfer centres are shown in black for clarity. (b) In this representation of the ferredoxin molecule, the polypeptide backbone is shown as a ribbon to highlight its secondary structure and the iron-sulphur centres as sticks emphasizing their regular structure, while the van der Waals’ radii of the individual iron and sulphur atoms are shown as dotted spheres to indicate the overall shapes of the centres. (c) A molecular model of P-trypsin (multishaded) complexed with the pancreatic trypsin inhibitor (prey). Full colour (not available in Biochemical Education) is necessary to appreciate fully these models. All models were constructed using coordinates obtained from the Brookhaven Protein Database.
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include. Each of these terms may be described by one or more relatively simple expressions. Thus the simplest case for bond stretch energy assumes that Hooke’s Law describes the stretching of the bond: Es = &,
