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Torsion Angle

Figure 2.20 • Diagram showing the energy maxima and minima as two substituted carbons connected by a single bond are rotated 360 degrees relative to each other.

different ways, depending on the properties one decides to highlight. Dorzolamide is a good example of a drug that involved computer-aided drug design (CADD) methods in its development.22 Figure 2.21 shows a standard representation of dorzolamide from a molecular modeling software package. The atoms can be color coded in various ways according to the different properties that one might want to highlight. As noted previously, however, it is important to know the size and shape of the molecule. Various representations are possible. A convenient visualization technique is to have the atoms and bonds displayed simultaneously with the van der Waals surface represented by an even distribution of dots. These dot surfaces are convenient, in that the atomic connectivity is shown along with the appropriate size and shape of the molecular surface. As computer graphics technology has improved, it has become possible to represent the surface as a translucent volume, shown in Figure 2.22, in which the

Figure 2.21 • A computer-generated representation of dorzolamide. The structure has been energy minimized using Spartan '08.
Figure 2.22 • The ball-and-stick minimized model is displayed with superimposed translucent van der Waals surface showing both atomic connectivity of the molecular structure and its 3D shape and size.

molecular structure appears to be embedded in a clear gelatin material.

Finally, computer graphics images of drug-receptor interactions, whether taken from x-ray crystal data or in silico generated, provide insight into the binding interactions, as shown in Figure 2.23. A full display of all the atomic centers in a protein structure gives too much detail. Most commonly, as shown in Figure 2.23, a ribbon structure traces the backbone of the protein main chain.23 The Richardson approach is another commonly used display to highlight secondary structural features, in which cylinders denote a-helices, arrows denote ^-sheets, and tubes are used for coils and turns.24

Because drug molecules make contact with solvents and receptor sites through surface contacts, it is paramount to have accurate methods to represent molecular surfaces correctly. Algorithms have been developed for such purposes, and they continue to be improved. The most straightforward way to represent a molecular shape is by the so-called van der Waals surface (Fig. 2.22), in which each constituent atom contributes its exposed surface to the overall molecular surface. Each atom is assigned a volume corresponding to its van der Waals radius, and only the union of atomic spheres contributes. These van der Waals surfaces have

Figure 2.23 • A computer-generated representation of a thienothipyran-2-sulfonamide bound to the active site of carbonic anhydrase. Note that the ribbon has been traced through the protein backbone. Proteins are commonly displayed this way.

small crevices and pockets that cannot make contact with solvent molecules. Another surface, known as the solvent accessible or Connolly surface, can be generated.25 The algorithm takes the van der Waals surface and rolls a sphere, having the volume of a water molecule with a radius of 1.4 A, across it. Wherever the sphere makes contact with the original surface, a new surface is created. This expanded surface is a more realistic representation of what water molecules contact. Another similar solvent-accessible surface is known as the Lee and Richards surface.26 This surface is constructed in an analogous way, with a sphere rolled over the van der Waals surface, but the boundary is taken as a line connecting the center of mass of the sphere from point to point. Also, it is possible to calculate the solvent excluded surface. The polar and nonpolar surface areas can be used as QSAR descriptors, and many computer models for solvation use solvent-accessible surface areas (SASA). Commonly, the electrostatic density may be displayed on the surface of a molecular structure, providing an easily recognized color coded grid that may be used to infer the complementary binding functional groups of the putative receptor.

A goal of docking programs is to screen large dataset to locate compounds that appear to have the atomic structure and conformation to dock readily at the receptor. Although there are several software programs available, their ability to differentiate between known ligands and decoys has not reached a level that this approach to searching databases has become standard. In other words, the programs will selected valid ligands and show them docking accordingly with the receptor, but they also docked the decoys and also usually do a poor job of predicting ligand binding affinity.27,28 So challenging is this problem that a database of docking decoys has been created.29

Three-Dimensional Quantitative Structure-Activity Relationships

With molecular modeling becoming more common, the QSAR paradigm that traditionally used physicochemical descriptors on a two-dimensional molecule can be adapted to 3D space. Essentially, the method requires knowledge of the 3D shape of the molecule. Accurate modeling of the molecule is crucial. A reference (possibly the prototype molecule) or shape is selected against which all other molecules are compared. The original method called for overlapping the test molecules with the reference molecule and minimizing the differences in overlap. Then, distances were calculated between arbitrary locations on the molecule. These distances were used as variables in QSAR regression equations. Although overlapping rigid ring systems such as tetracy-clines, steroids, and penicillins are relatively easy, flexible molecules can prove challenging. Examine the following hypothetical molecule. Depending on the size of the various R groups and the type of atom represented by X, a family of compounds represented by this molecule could have various conformations. Even when the conformations might be known with reasonable certainty, the reference points crucial for activity must be identified. Is the overlap involving the tetrahedral carbon important for activity? Or should the five-membered ring provide the reference points? And which way should it be rotated? Assuming that Rb is an important part of the pharmacophore, should the five-membered ring be rotated so that Rb is pointed down or up? These are not trivial questions, and successful 3D-QSAR studies have depended on just how the investigator positions the molecules relative to each other. There are several instances in which apparently very similar structures have been shown to bind to a given receptor in different orientations.

There are various algorithms for measuring the degree of conformational and shape similarities, including molecular shape analysis (MSA),30 distance geometry,31 and molecular similarity matrices.32,33 Many of the algorithms use graph theory, in which the bonds that connect the atoms of a molecule can be thought of as paths between specific points on the molecule. Molecular connectivity is a commonly used application of graph theory.34-36

Besides comparing how well a family of molecules overlaps with a reference molecule, there are sophisticated software packages that determine the physicochemical parameters located at specific distances from the surface of the molecule. An example of this approach is comparative molecular field analysis (CoMFA).37,38 The hypothetical molecule is placed in a grid (Fig. 2.24) and its surface sampled at a specified distance. The parameter types include steric, Lennard-Jones potentials and other quantum chemical parameters, electrostatic and steric parameters, and partition coefficients. The result is thousands of independent variables. Standard regression analysis requires that the dimensionality be reduced and rigorous tests of validity be used. Partial least squares (PLS) has been the most common statistical method used. Elegant as the CoMFA algorithm is for explaining ligand-receptor interactions for a set of molecules, the method alone does not readily point the

CoMFA grid.

CoMFA grid.

Molecule situated in a investigator toward the next molecule that should be synthesized. To get around the problem of strict alignment of one particular conformation with another, there are methods that sample several possible conformations of a set of possible ligands. This is called 4D-QSAR.39

The CoMFA methodology is used in similarity analyses comparing molecular conformers' ability to bind to a receptor. This is called comparative molecular similarity indices analysis or CoMSIA.40 It is similar to CoMFA in that the molecules are aligned in a grid, but differs in the type of indices or descriptors with Gaussian functions producing descriptors that describe binding to the receptor being the most useful.

Database Searching and Mining

As pointed out previously, receptors can be isolated and cloned. This means that it is possible to determine their structures. Most are proteins and that means having to determine their amino acid sequence. This can be done either by degrading the protein or by obtaining the nucleotide sequence of the structural gene coding for the receptor and using the triplet genetic code to determine the amino acid sequence. The parts of the receptor that bind the drug (lig-and) can be determined by site-directed mutagenesis. This alters the nucleotide sequence at specific points on the gene and, therefore, changes specific amino acids. Also, keep in mind that many enzymes become receptors when the goal is to alter their activity. Examples of the latter include acetylcholinesterase, monoamine oxidase, HIV protease, rennin, ACE, and tetrahydrofolate reductase.

The starting point is a database of chemical structures. They may belong to large pharmaceutical or agrochemical firms that literally have synthesized the compounds in the database and have them sitting on the shelf. Alternatively, the database may be constructed so that several different chemical classes and substituent patterns are represented. (See discussion of isosterism in the next section.) The first step is to convert the traditional or historical two-dimensional molecules into 3D structures whose intramolecular distances are known. Keeping in mind the problems of finding the "correct" conformation for flexible molecule, false hits and misses might result from the search. Next, the dimensions of the active site must be determined. Ideally, the receptor has been crystallized, and from the coordinates, the intramolecular distances between what are assumed to be key locations are obtained. If the receptor cannot be crystallized, there are methods for estimating the 3D shape based on searching crystallographic databases and matching amino acid sequences of proteins whose tertiary structure has been determined.

Fortunately, the crystal structures of literally thousands of proteins have been determined, and their structures have been stored in the Brookhaven Protein Databank. It is now known that proteins with similar functions have similar amino acid sequences in various regions of the protein. These sequences tend to show the same shapes in terms of a-helix, parallel and antiparallel ^-pleated forms, turns in the chain, etc. Using this information plus molecular mechanics parameters, the shape of the protein and the dimensions of the active site can be estimated. Figure 2.25 contains the significant components of a hypothetical active site. Notice that four amino acid residues at positions

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