Young - Computational chemistry
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Once a number of lead compounds have been found, computational and laboratory techniques are very successful in re®ning the molecular structures to yield greater drug activity and fewer side e¨ects. This is done both in the laboratory and computationally by examining the molecular structures to determine which aspects are responsible for both the drug activity and the side e¨ects. These are the QSAR techniques described in Chapter 30. Recently, 3D QSAR has become very popular for this type of application. These techniques have been very successful in the re®nement of lead compounds.
A more logical approach would be to model the binding site for a target molecule and then ®nd molecules that will dock in this site. Unfortunately, the binding site may not be known. It is fairly easy to determine the sequences of proteins and nucleotides. However, it is much more di½cult to obtain structural information by X-ray crystallography. Because of this disparity, there has been an immense amount of work on solving the protein folding problem, which is to determine the three dimensional structure of a protein from its sequence. Although computing the relative energies of conformations is one of the greatest successes of computational chemistry techniques, the incredibly huge number of possible conformers of a protein make this a daunting task. Two ingenious methods for simplifying this problem are distance geometry and homology modeling. Distance geometry is a means for imposing constraints on the problem, which are obtained from two-dimensional NMR studies. Homology modeling is used to ®nd the known structure with the most similar sequence, then using that geometry for those sections of the unknown. These techniques are discussed in more detail in Chapter 21. Once a binding site is known, a molecule to bind in that site can be determined with the techniques described in the next section.
38.2SITE-SPECIFIC INTERACTIONS
If it is known that a drug must bind to a particular spot on a particular protein or nucleotide, then a drug can be tailor-made to bind at that site. This is often modeled computationally using any of several di¨erent techniques. Traditionally, the primary way of determining what compounds would be tested computationally was provided by the researcher's understanding of molecular interactions. A second method is the brute force testing of large numbers of compounds from a database of available structures.
More recently, a set of techniques, called rational drug design or De Novo techniques, have been used. These techniques attempt to reproduce the researcher's understanding of how to choose likely compounds. Such an understanding is built into a software package that is capable of modeling a very large number of compounds in an automated way. Many di¨erent algorithms have been used for this type of testing, many of which were adapted from arti- ®cial intelligence applications. No clear standard has yet emerged in this area so it is not possible to say which is the best technique.
298 38 BIOMOLECULES
38.3GENERAL INTERACTIONS
Interestingly, QSAR is as useful for predicting general interactions as it is for the optimization of activity for very speci®c interactions. In this case, QSAR rather than 3D QSAR is most e¨ective. It has been used for predicting environmental toxicity, biodegradation, and other processes. This serves as a good screening technique to determine which compounds should be examined closer. These methods are never completely reliable and should not be considered a substitute for standard testing techniques. They are best used for categorizing compounds as having a high or low likelihood of acceptability.
It is possible to obtain the sequence of a DNA strand, but that does not give an understanding of the attribute of the organism described by a particular piece of genetic code. Homology modeling can be used to shed light on this type of information, as well as for determining structure. Homology modeling is the systematic comparison of DNA sequences to determine regions of similarities and di¨erences. This can yield information as broad as the di¨erences between reptiles and mammals or information as narrow as the di¨erences between individuals.
38.4RECOMMENDATIONS
The modeling of biomolecules is a very broad and sophisticated ®eld. The description given in this chapter is only meant to provide the connections between the topics in this book and this ®eld. Before embarking on a computational biochemical study, it is recommended that the researcher investigate the literature pertaining to this ®eld more closely. The references provided below should provide a good starting point for such a survey.
BIBLIOGRAPHY
Books presenting relevant computational techniques are
A.K. RappeÂ, C. J. Casewit, Molecular Mechanics across Chemistry University Science Books, Sausalito (1997).
A.R. Leach, Molecular Modelling Principles and Applications Longman, Essex (1996).
H.-D. Holtje, G. Folkers, T. Bierer, W. Sippl, D. Rognan, Molecular ModelingÐBasic Principles and Applications John Wiley & Sons, New York (1996).
G.H. Grant, W. G. Richards, Computational Chemistry Oxford, Oxford (1995).
Books speci®cally addressing biomolecules are
Practical Application of Computer-Aided Drug Design P. S. Charifson, Ed., Marcel Dekker, New York (1997).
BIBLIOGRAPHY 299
Guidebook on Molecular Modeling in Drug Design N. C. Cohen, Ed., Academic, San Diego (1996).
H.Van de Waterbeemd, Advanced Computer-Asissted Techiques in Drug Discovery John Wiley & Sons, New York (1995).
G. L. Patrick, An Introduction to Medicinal Chemistry Oxford, Oxford (1995).
Computer-Aided Molecular Design Applications in Agrochemicals, Materials and Pharmaceuticals C. H. Reynolds, M. K. Holloway, H. K. Cox, Eds., American Chemical Society, Washington (1995).
Molecular Modelling and Drug Design J. G. Vintner, M. Gardner, Eds., CRC, Boca Raton (1994).
A.Warshel, Computer Modeling of Chemical Reactions in Enzymes and Solutions John Wiley & Sons, New York (1991).
Computer-Aided Drug Design Methods and Applications T. J. Perun, C. L. Propst, Eds., Dekker, New York (1989).
J.A. McCammon, S. C. Harvey, Dynamics of Proteins and Nucleic Acids Cambridge, Cambridge (1987).
General review articles are
D.B. Boyd, Encycl. Comput. Chem. 1, 795 (1998).
G. W. A. Milne, Encycl. Comput. Chem. 3, 2046 (1998).
L. M. Balbes, S. W. Mascarella and D. B. Boyd, Rev. Comput. Chem. 5, 337 (1994).
P. Kollman, Chem. Rev. 93, 2395 (1993).
B. Pullman, Adv. Quantum Chem. 10, 251 (1977).
L. Balbes, Guide to Rational (Computer-aided) Drug Design is online at http:// www.ccl.net/cca/documents/drug.design.shtml
There are many links to online information on Soaring Bear's web page at
http://ellington.pharm.arizona.edu/%7Ebear/
Applications of arti®cial intelligence are reviewed in
D. P. Dolata, Encycl. Comput. Chem. 1, 44 (1998).
Predicting biodegredation is reviewed in
G. Klopman, M. Tu, Encycl. Comput. Chem. 1, 128 (1998).
Carcinogenicity is reviewed in
L. v. SzentpaÂly, R. Ghosh, Theoretical Organic Chemistry 447 C. PaÂrkaÂnyi, Ed., Elsevier, Amsterdam (1998).
Chemometrics are reviewed in
K.Varmuza, Encycl. Comput. Chem. 1, 347 (1998).
Conformation searching of biomolecules is reviewed in
M. VaÂsquez, G. NeÂmethy, H. A. Scheraga, Chem. Rev. 94, 2183 (1994).
300 38 BIOMOLECULES
Information about De Novo techniques is in
Rational Drug Design A. Parrill, M. R. Reddy, Eds., Oxford, Oxford (1999). A. P. Johnson, S. M. Green, Encycl. Comput. Chem. 1, 650 (1998).
H. J. BoÈhm, S. Fischer, Encycl. Comput. Chem. 1, 657 (1998).
D. E. Clark, C. W. Murray, J. Li, Rev. Comput. Chem. 11, 67 (1997). S. Borman, Chem. and Eng. News 70, 18 (1992).
Distance geometry techniques are reviewed in
T. F. Havel, Encycl. Comput. Chem. 1, 723 (1998).
M. P. Williamson, J. P. Walto, Chem. Soc. Rev. 21, 227 (1992).
Modeling DNA is reviewed in
J. Sponer, P. Hobza, Encycl. Comput. Chem. 1, 777 (1998).
R.Lavery, Encycl. Comput. Chem. 3, 1913 (1998).
S.Lemieux, S. Oldziej, F. Major, Encycl. Comput. Chem. 3, 1930 (1998).
D. L. Beveridge, Encycl. Comput. Chem. 3, 1620 (1998).
P. Au½nger, E. Westhof, Encycl. Comput. Chem. 3, 1628 (1998).
G.Ravishanker, P. Au½nger, P. R. Langley, B. Jayaram, M. A. Young, Rev. Comput. Chem. 11, 317 (1997).
Docking techniques are reviewed in
C. M. Oshiro, I. D. Kuntz, R. M. A. Knegtel, Encycl. Comput. Chem. 3, 1606 (1998). M. Vieth, J. D. Hirst, A. Kolinski, C. L. Brooks, III, J. Comput. Chem. 19, 1612 (1998). M. Vieth, J. D. Hirst, B. N. Dominy, H. Daigler, C. L. Brooks, III, J. Comput. Chem.
19, 1623 (1998).
Electron transfer is reviewed in
T. Hayashi, H. Ogoshi, Chem. Soc. Rev. 26, 355 (1997).
Ligand design is reviewed in
M. A. Murcko, Rev. Comput. Chem. 11, 1 (1997).
Modeling membranes is reviewed in
S. Yoneda, T. Yoneda, H. Umeyamn, Encycl. Comput. Chem. 1, 135 (1998). H. J. c. Berendsen, D. P. Tieleman, Encycl. Comput. Chem. 3, 1638 (1998). A. Pullman, Chem. Rev. 91, 793 (1991).
J. Houk, R. H. Guy, Chem. Rev. 88, 455 (1988).
Modeling micelles is reviewed in
P. L. Luisi, Adv. Chem. Phys. 92, 425 (1996).
Molecular dynamics of biomolecules is reviewed in
T. P. Lybrand, Rev. Comput. Chem. 1, 295 (1990).
BIBLIOGRAPHY 301
Neural network reviews are
J. A. Burns, G. M. Whitesides, Chem. Rev. 93, 2583 (1993).
Oligosaccharide modeling is reviewed in
R. J. Woods, Rev. Comput. Chem. 9, 129 (1996).
Pesticide modeling is reviewed in
E.L. Plumber, Rev. Comput. Chem. 1, 119 (1990).
Protein & peptide reviews are
J.Skolnick, A. Kolinski, Encycl. Comput. Chem. 3, 2200 (1998). B. Rost, Encycl. Comput. Chem. 3, 2243 (1998).
L. Pedersen, T. Darden, Encycl. Comput. Chem. 3, 1650 (1998). K. E. Laidig, V. Daggett, Encycl. Comput. Chem. 3, 2211 (1998). C. L. Brooks, III, D. A. Case, Chem. Rev. 93, 2487 (1993).
G. E. Marlow, J. S. Perkyns, B. M. Pettitt, Chem. Rev. 93, 2503 (1993).
Ê
J. Aqvist, A. Warshel, Chem. Rev. 93, 2523 (1993).
H.Scheraga, Rev. Comput. Chem. 3, 73 (1992).
J. M. Troyer, F. E. Cohen, Rev. Comput. Chem. 2, 57 (1991).
M. Karplus, Modelling of Molecular Structures and Properties J.-L. Rivail, Ed., 427, Elsevier, Amsterdam (1990).
J. Skolnick, A. Kolinski, Ann. Rev. Phys. Chem. 40, 207 (1989).
Adv. Chem. Phys. C. L. Brooks, III, M. Karplus, B. M. Pettitt, Eds., vol. 71 (1988).
J.A. McCammon, M. Karplus, Ann. Rev. Phys. Chem. 31, 29 (1980).
QSAR reviews are
H.Kubinyi, Encycl. Comput. Chem. 4, 2309 (1998). S. P. Gupta, Chem. Rev. 94, 1507 (1994).
H. H. Ja¨eÂ, Chem. Rev. 53, 191 (1953).
An introduction to structure-based techniques is
I. D. Kuntz, E. C. Meng, B. K. Shoichet, Acct. Chem. Res. 27, 117 (1994).
Toxicity prediction is reviewed in
D. F. Lewis, Rev. Comput. Chem. 3, 173 (1992).
Computational Chemistry: A Practical Guide for Applying Techniques to Real-World Problems. David C. Young Copyright ( 2001 John Wiley & Sons, Inc.
ISBNs: 0-471-33368-9 (Hardback); 0-471-22065-5 (Electronic)
39 Simulating Liquids
This chapter focuses on the simulation of bulk liquids. This is a di¨erent task from modeling solvation e¨ects, which are discussed in Chapter 24. Solvation e¨ects are changes in the properties of the solute due to the presence of a solvent. They are de®ned for an individual molecule or pair of molecules. This chapter discusses the modeling of bulk liquids, which implies properties that are not de®ned for an individual molecule, such as viscosity.
39.1LEVEL OF THEORY
The simplest case of ¯uid modeling is the technique known as computational ¯uid dynamics. These calculations model the ¯uid as a continuum that has various properties of viscosity, Reynolds number, and so on. The ¯ow of that ¯uid is then modeled by using numerical techniques, such as a ®nite element calculation, to determine the properties of the system as predicted by the Navier± Stokes equation. These techniques are generally the realm of the engineering community and will not be discussed further here.
Nearly all liquid simulations have been done using molecular mechanics force ®elds to describe the interactions between molecules. A few rare simulations have been completed with orbital-based methods. It is expected that it will still be a long time before orbital-based simulations represent a majority of the studies done due to the incredibly large amount of computational resources necessary for these methods.
Monte Carlo simulations are an e½cient way of predicting liquid structure, including the preferred orientation of liquid molecules near a surface. This is an e½cient method because it is not necessary to compute energy derivatives, thus reducing the time required for each iteration. The statistical nature of these simulations ensures that both enthalpic and entropic e¨ects are included.
Molecular dynamics calculations are more time-consuming than Monte Carlo calculations. This is because energy derivatives must be computed and used to solve the equations of motion. Molecular dynamics simulations are capable of yielding all the same properties as are obtained from Monte Carlo calculations. The advantage of molecular dynamics is that it is capable of modeling time-dependent properties, which can not be computed with Monte Carlo simulations. This is how di¨usion coe½cients must be computed. It is also possible to use shearing boundaries in order to obtain a viscosity. Molec-
302
39.2 PERIODIC BOUNDARY CONDITION SIMULATIONS 303
ular dynamics and Monte Carlo methods are discussed in more detail in Chapter 7.
A very important aspect of both these methods is the means to obtain radial distribution functions. Radial distribution functions are the best description of liquid structure at the molecular level. This is because they re¯ect the statistical nature of liquids. Radial distribution functions also provide the interface between these simulations and statistical mechanics.
Another way of predicting liquid properties is using QSPR, as discussed in Chapter 30. QSPR can be used to ®nd a mathematical relationship between the structure of the individual molecules and the behavior of the bulk liquid. This is an empirical technique, which limits the conceptual understanding obtainable. However, it is capable of predicting some properties that are very hard to model otherwise. For example, QSPR has been very successful at predicting the boiling points of liquids.
39.2PERIODIC BOUNDARY CONDITION SIMULATIONS
A liquid is simulated by having a number of molecules (perhaps 1000) within a speci®c volume. This volume might be a cube, parallelepiped, or hexagonal cylinder. Even with 1000 molecules, a signi®cant fraction would be against the wall of the box. In order to avoid such severe edge e¨ects, periodic boundary conditions are used to make it appear as though the ¯uid is in®nite. Actually, the molecules at the edge of the next box are a copy of the molecules at the opposite edge of the box, as shown in Figure 39.1.
The use of periodic boundary conditions allows the simulation of a bulk ¯uid, but creates the potential for another type of error. If the longest-range nonbonded forces included in the calculation interact with the same atom in two images of the system, then a long-range symmetry has been unnaturally incorporated into the system. This will result in an additional symmetry in the results, such as a radial distribution function, which is an artifact of the simulation. In order to avoid this problem, the long-range forces are computed only up to a cuto¨ distance that must be less than half of the box's side length. This is called the minimum image convention. It ensures that the system appears to be nonperiodic to any given atom. It also limits the amount of CPU time that will be required for each iteration.
Calculating nonbonded interactions only to a certain distance imparts an error in the calculation. If the cuto¨ radius is fairly large, this error will be very minimal due to the small amount of interaction at long distances. This is why many bulk-liquid simulations incorporate 1000 molecules or more. As the cut- o¨ radius is decreased, the associated error increases. In some simulations, a long-range correction is included in order to compensate for this error.
A radial distribution function can be determined by setting up a histogram for various distances and then looking at all pairs of molecules to construct the diagram. Di¨usion coe½cients can be obtained by measuring the net distances
304 39 SIMULATING LIQUIDS
FIGURE 39.1 Periodic boundary conditions in two dimensions. The molecules that appear to be around the center box are actually copies of the center box.
moved by the solute molecules. Some statistical processes that could be the modeled in a similar way given a more sophisticated setup are chromatographic retention times, crystal growth, and adsorption of molecules on a surface.
These calculations can incorporate various types of constraints. It is most common to run simulations with a ®xed number of atoms and a ®xed volume. In this case, the temperature can be computed from the average kinetic energy of the atoms. It is also possible to adjust the volume to maintain a constant pressure or to scale the velocities to maintain a constant temperature.
If a su½ciently large number of iterations have been performed, the ensemble average of any given property should not change signi®cantly with additional iterations. However, there will be ¯uctuations in any given property computable as a root-mean-square deviation from the ensemble average. These ¯uctuations can be related to thermodynamic derivatives. For example, ¯uctuations in energy can be used to compute a heat capacity for the ¯uid. Alter-
BIBLIOGRAPHY 305
natively, a heat capacity can be determined from its derivative formula after running simulations at two temperatures.
It is also possible to simulate nonequilibrium systems. For example, a bulk liquid can be simulated with periodic boundary conditions that have shifting boundaries. This results in simulating a ¯owing liquid with laminar ¯ow. This makes it possible to compute properties not measurable in a static ¯uid, such as the viscosity. Nonequilibrium simulations give rise to additional technical dif- ®culties. Readers of this book are advised to leave nonequilibrium simulations to researchers specializing in this type of work.
39.3RECOMMENDATIONS
Setting up liquid simulations is more complex than molecular calculations. This is because the issues mentioned in this chapter must be addressed. At least the ®rst time, researchers should plan on devoting a signi®cant amount of work to a liquid simulation project.
BIBLIOGRAPHY
Books dedicated to simulating liquids are
D. M. Hirst, A Computational Approach to Chemistry Blackwell Scienti®c, Oxford (1990).
M. P. Allen, D. J. Tildesley, Computer Simulation of Liquids Oxford, Oxford (1987). C. G. Gray, K. E. Gubbins, Theory of Molecular Fluids Oxford, Oxford (1984).
J. A. Barker, Lattice Theories of the Liquid State Pergamon, New York (1963).
General review articles are
B. Smit, Encycl. Comput. Chem. 3, 1742 (1998).
W. L. Jorgensen, Encycl. Comput. Chem. 4, 2826 (1998).
K. Nakaniski, Chem. Soc. Rev. 22, 177 (1993).
B. J. Alder, E. L. Pollock, Ann. Rev. Phys. Chem. 32, 311 (1981).
Simulating aqueous interfaces is reviewed in
A. Pohorille, Encycl. Comput. Chem. 1, 30 (1998).
Brownian dynamics simulations are reviewed in
J. D. Madura, J. M. Briggs, R. C. Wade, R. R. Gabdoulline, Encycl. Comput. Chem. 1, 141 (1998).
Computing dielectric constants is reviewd in
P. Madden, D. Kivelson, Adv. Chem. Phys. 56, 467 (1984).
306 39 SIMULATING LIQUIDS
Simulation of nonequilibrium processes is reviewed in
P. T. Cummings, A. Baranyai, Encycl. Comput. Chem. 1, 390 (1998).
Describing the structure of liquids is reviewed in
M. S. Wertheim, Ann. Rev. Phys. Chem. 30, 471 (1979). D. Chandler, Ann. Rev. Phys. Chem. 29, 441 (1978).
Simulation of supercritical ¯uids is reviewed in
S. C. Tucker, Encycl. Comput. Chem. 4, 2826 (1998).
A. A. Chialvo, P. T. Cummings, Encycl. Comput. Chem. 4, 2839 (1998).
Computing transport properties is reviewed in
J. H. Dymond, Chem. Soc. Rev. 14, 317 (1985).
Computing viscosity is reviewed in
S. G. Brush, Chem. Rev. 62, 513 (1962).