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Chapter 29. Receptor Modeling by Distance Geometry
Chapter 29. Receptor Modeling by Distance Geometry Jeffrey M. Elaney Protos, Inc., Emeryville,CA 94608 J. Scott Dixon SmithKline Eeecham Laboratories, King of Prussia, PA 19406
lntroductlan - Distance geometry is a general molecular model-building method, best known for
determining three-dimensional solution structures of peptides, proteins, and nucleic acids from nuclear overhauser effect (NOE) distance measurements (1,2). Distance geometry has also been applied in a variety of ways to build models of proteins and receptors and to model the interaction of small molecules with receptors. Ghose and Crippen recently published a comprehensive review of distance geometry and its application to receptor modeling, emphasizing their distance geometry quantitative structure-activity relationship (QSAR) approach (3). We will focus on additional distance geometry approaches which have application to receptor modeling and only briefly describe the distance geometry QSAR method.
Distance geometry converts a set of distance bounds (minimum and maximum allowed distances) into a set of coordinates consistent with these bounds (4,5). A molecular structure is described by the set of all pairwise interatomic distance bounds in a distance bounds matrix. This distance bounds matrix describes the complete conformation space of a molecule by entering the maximum possible distance (upper bound) between each atom pair in the upper diagonal and the minimum possible distance (lower bound) in the lower diagonal. All possible conformers therefore must lie between these upper and lower distance bounds. Additional distance bounds constraints, for example from NMR data or a proposed pharmacophore model, may be added to the distance bounds matrix. Distance geometry converts this usually underdetermined distance bounds information into randomly sampled sets of three dimensional coordinates. Protein S t r w Modeling - ONeil and DeGrado used distance geometry to predict the conformation of a calcium-binding loop of calmodulin, as part of their attempt at predicting the entire calmodulin structure based on the homologous sequences and X-ray structures of intestinal calcium-binding protein (ICE) and carp parvalbumin (6). The calmodulin sequence had two insertions in one of the ICB calcium binding loops. Distance geometry was used to generate models for the loop by constraining the ends of the loop to the ICE X-ray coordinates, forcing the side chains of four polar residues and a main chain carbonyl to interact with the calcium cation in a geometry identical to that from the second ICE loop, while maintaining octahedral coordination about the calcium. The remainder of the loop was allowed to remain flexible. Ten unique loop conformers that satisfied the constraints were identified from thirty random trials; these ten structures were energy refined with molecular mechanics. One of the refined conformers had reasonable contacts with the rest of the calmodulin model when reinserted back into the complete protein structure. Have1 and Snow used distance geometry to build complete protein models (not just loop regions) of unknown structures based on the sequence alignments and X-ray structures of homologous proteins (7).Sequence alignments are converted into distance and chiral constraints to maintain equivalent secondary structure, hydrogen bonds, and disulfides. Although the approach still depends critically on correct sequence alignment, the model-building procedure is automated and less biased than conventional approaches, resulting in an ensemble of random models which are consistent with the constraints implied by the sequence alignment. Several test cases demonstrated the feasibility of the approach, but no comparison with other methods was made.
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- Ripka and coworkers (8) designed phospholipase A2 (PLA2) inhibitors based on the high resolution X-ray crystal structure of bovine pancreatic PLA2 (9). Potential binding modes of the substrate phospholipid were first modeled in the active site to suggest conformationally restricted mimics. A model was proposed in which the hydrated ester carbonyl intermediate was hydrogen-bondedto the active site His-48, and a phosphate oxygen was located at one of the water positions in the coordination sphere of the calcium. Distance geometry was used to generate many potential phospholipid binding modes with these constraints. The substrate fits generated by distance geometry suggested a hydrophobic groove in the PLA2 active site which could accept a naphthalene ring. This offered the possibility of building a rigid framework from which additional functionality could be directed to interact with other parts of the site, resulting in the design of a series of acenaphthene inhibitors with good in vitfo activity. Distance geometry was also used to dock the resulting designs into the active site, with no constraints except to maintain reasonable minimum intermolecular distances, to determine additional potential binding modes by randomly sampling the inhibitor designs' conformationswithin the confines of the active site. e Fn- A problem that often occurs in molecular modeling of bioactive compounds is to define the geometry adopted by a pharmacophore. A pharmacophore is a set of atoms or groups which are present in each bioactive molecule and which are required for activity. Often the assumption is made that molecules which have the same biological activity interact at the same receptor by presenting the pharmacophore elements to the receptor in the same way. The question, especially in the absence of a three dimensional structure for the receptor, is whether or not a unique three dimensional geometry can be inferred for the pharmacophore elements by examining several different molecules. In other words, are there conformations for each molecule in which the corresponding pharmacophore elements have the same geometrical arrangement? The important concept is that, while each molecule considered by itself may be quite flexible, the assumption that certain pharmacophore elements have the same geometry between different molecules introduces new constraints that may restrict the allowable conformational space available to each molecule. The computational problem can be stated explicitly in the following way: generate conformations for each molecule such that certain atoms or other structural elements (such as lone pairs or ring centroids) can be overlapped with the corresponding elements in each of the other molecules. This can be expressed quite naturally in a distance matrix. If several independent molecules are placed into a distance matrix representation, the intramoleculardistance bounds for each would be present but all intermoleculardistances would have lower bounds of zero and upper bounds of infinity. Applying the distance geometry algorithm to such a distance matrix would result in conformations for each molecule in random orientations relative to the other molecules. To force certain atoms from each molecule to overlap, the intermolecular upper bounds between those atoms must be lowered to a small value (say 0.3 A) that representsthe tolerance in the overlap. Then the distance geometry algorithm will generate conformations for each molecule such that the pharmacophore elements overlap between molecules. This is the essence of the ensemble distance geometry method (10). For example, the nicotinic agonists shown in Figure 1 were used (along with two others) in an
Figure 1
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ensemble distance geometry calculation in which the corresponding highlighted atoms were used as the pharmacophore (10). The resulting geometry is shown in the lower three dimensional views with the pharmacophore atoms in dark filled circles. Wong and Andrews used manual atom-by-atomsuperimposition, electrostatic potential map superimposition, and a systematic torsion search method to propose a model for the binding of convulsants to the picrotoxinin site of the GABA receptor (11). A total of ten superimposition models were found by these approaches. Ensemble distance geometry also found these ten models, plus one additional model which was not found by the other approaches. There are several possible outcomes for such a calculation. First, there may be no acceptable solution. Second, there may be only one solution in that there is only one possible pharmacophore geometry and each molecule has only one conformation which can present that pharmacophore geometry. Third, there may be only one pharmacophoregeometry but multiple conformationsof at least some of the molecules which are compatible with that geometry. Finally, there may be many solutions both for the pharmacophoregeometry and some or all of the molecules. Systematic torsional search methods have also been used to determine pharmacophore geometries (12,13). The method essentially performs a complete systematic torsion conformational search on one molecule and then uses the resulting sets of distances between pharmacophore elements to prune the search tree for the next molecule, and so on. After all molecules are searched, the remaining sets of distances represent those which can satisfy pharmacophore geometries which are common to all compounds. By recording the torsion angles, the conformations of each compound can be regenerated. There are advantages and disadvantagesto each method. The computational complexity of the ensemble method is a polynomial function of the number of atoms rather than an exponential function of the number of rotatable bonds. Therefore, for systems with many rotatable bonds, the ensemble method will be faster. However, pruning of the search tree as early as possible can improve the speed of the systematic search approach (12). The ensemble method handles ring systems naturally and thus can alter ring conformation in the course of searching for pharmacophore geometries. Torsional searches have difficulty altering ring conformations since changing a single torsion within a ring causes distortions of bond distance and angles in other parts of the ring system. If the chirality of some centers is unknown, the ensemble method can allow the chirality at those centers to randomly vary and choose the chirality which is compatible with the pharmacophore geometry. Systematic torsional searches would need to be done with all possible chiralities of unknown centers to ensure that solutions were not missed.
The main disadvantage of the ensemble method relative to torsional searching methods is that the ensemble method produces random solutions rather than being more deterministic. For a given angle step size, the systematic torsional search assures that all possible solutions have been examined. However, computer time constraints often force one to choose a relatively large angle step size (for example 30") and there is no guarantee that solutions are not missed because they fall between the steps. In addition, in pharmacophore modeling applications, one is usually not interested in enumerating all possible solutions. The useful results are: no answers, in which case the problem has probably not been correctly formulated; one answer, which might be the unique pharmacophore geometry; or more than one answer, in which case the problem is underdetermined and more data are necessary. The ensemble method (and distance geometry in general) also cannot naturally handle problems in which constraints are phrased in terms of lists of acceptable torsion angles (i.e. that an angle can be either trans, gauche +, or gauche -). However, the useful special case of cis or trans (for example, peptide bonds) can be handled by distance geometry using chiral constraints to keep the bonded atoms planar. QSAq - Crippen applied distance geometry to the problem of three-dimensional receptor mapping (3). Ghose and Crippen recently reviewed the approach in detail (3). A very similar approach was also reviewed (14). Their method proposes the geometric requirementsof the
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receptor site based on the experimental data of binding affinities of a series of ligands, which may be conformationally flexible, and hypothesized binding modes (i.e. pharmacophore model) for each ligand. The result is a low-resolution,three-dimensional model of the receptor binding site, which is described as a series of points in space (site points) that interact with specific ligand atoms or groups of atoms (ligand points). Each ligand point is described by atom-centered physicochemical properties (molar refractivity, hydrophobicity, and partial charge) (15,16). A specific interaction 'energy' is assigned to each site point - ligand point interaction by a modified quadratic programming optimization procedure, yielding a quantitative prediction of the binding affinity of each ligand to the site model. Optimization of interaction parameters is performed under the constraint that the interaction energy of the proposed binding mode is more favorable than the interaction energy of all other geometrically possible binding modes. Optimization continues until the proposed binding mode is either proved to be the best or found to be inconsistent, when it is replaced by the most favorable binding mode encountered so far, and optimization is continued. This approach avoids the temptation to bias the fits and avoids preconceptionson how a particular ligand might bind. The three-dimensional geometric model of the binding site involves both energetic and steric features. Since the approach predicts the mode of binding as well as the interaction energies it offers the opportunity to suggest conformationally restricted analogs that might maximize binding to the site. Ghose and Crippen generated a model for the inhibition of E. coli dihydrofolate reductase by 39 compounds from two different structural classes (17). The model contained 19 site pockets of 9 different types and qualitatively agreed with the X-ray crystal structure of the enzyme's active site. Ghose and Crippen recently modified their approach to eliminate much of the subjectivity previously required in choosing conformations and binding modes (18-20). A conformational search is performed for each molecule to identify the lowest energy conformers. A priority score is assigned to each conformer based on the sum of the experimental free energy of binding of the molecule to the receptor site and the calculated energy of the conformer relative to the global energy minimum for the molecule. Starting from the highest priority conformation, the low energy conformersfor the remaining molecules are superimposed on it to give the best overall match based of the atom-centered physicochemical properties. This approach is performed for several different high priority reference conformations, each producing a different possible superimposition model. Each model is then evaluated in the remaining steps to determine the best model. Site points are initially placed at the positions of superimposed atoms and remaining non-coincident atoms. This results in a large number of site points, which is reduced using stepwise reverse regression to eliminate insignificant site points. The optimization step is similar to their original approach. This modified approach appears to be a significant improvement and has been used to model the binding of 28 antiviral nucleosides against an unknown receptor of parainfluenza virus (18), the binding of 29 benzodiazepine receptor ligands to the benzodiazepine receptor (19), and the antileukemic activity of 21 purine-6-substitutednucleosides (20).
. . .
.
- Recently, a new method has been developed which produces a novel receptor site description, called a Voronoi binding site model, using information from the structures and binding affinities of a series of ligands (21,22). The binding site is described by dividing space up into a set of Voronoi polyhedra, which are derived from a set of 'generating points' in a simple way: each polyhedron consists of all points which are closer to one generating point than to any other. Thus, each generating point results in one Voronoi polyhedron. A binding site model is specified by the number and location of a set of generating points. In addition, each Voronoi region is assigned a set of interactionparameters for each type of ligand atom. Thus, a ligand can be placed into the receptor model and an interaction energy calculated by summing the interactions of each atom with the region that contains it. For example, Figure 2 shows a simple receptor model with two regions. Note that there are many equivalent ligand binding modes. The only aspect which is important for interaction energy calculationsis the region into which each ligand falls.
Figure 2
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The object of the Voronoi binding site approach is to find a set of generating points and interaction potentials which reproduce the experimental binding constants within experimental error when each ligand is bound to the receptor site model in the most favorable way. The specific steps in developing a model are: (i) summarize the conformation space of each ligand; (ii) propose a site geometry; (iii) determine all geometrically allowed binding modes of each ligand; (iv) determine the interaction parameters. If step (iv) fails, then the method starts again at step (ii) with a new site geometry. The advantages of the Voronoi method are that it does not require the a priori assumption of a pharmacophore, it accounts in a quantitative way for the observed data, and it does not impose any more detail on the binding site model than is necessary to account for the data. On the other hand, it is necessary for the user to propose the binding site geometry and the overall process is computationally expensive. The method has been successfully applied to two fairly simple test cases (22,23), but at this point it is not yet clear how difficult larger problems will prove to be.
- Relatively few applications of distance geometry have appeared since its original application t o chemical structure problems by Crippen over ten years ago (24). The vast majority of applications and publications have focused o n determining solution structures of small and macromolecules from NMR experiments (1,2). Distance geometry software is now more readily available (25-27), along with a steadily increasing number of applications and publications which demonstrate its unique ability to generate molecular models for complex situations involving drugand receptor docking (8). pharmacophore modeling, protein structure prediction (6,7), conformational analysis (28,29). References 1. 2. 3.
4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.
K. Wuthrich, "NMR of Proteins and Nucleic Acids"; John Wiley and Sons: New York, 1986. K. Wuthrich, Science, m,45 (1989). A.K. Ghose and G.M. Crippen in "Comprehensive Medicinal Chemistry: The Rational Design, Mechanistic Study and Therapeutic Application of Chemical Compounds", Vol. 4. C. Ramsden, Ed.; Pergamon Press, Oxford, 1990; p. 715. G.M. Crippen. 'Distance Geometry and Conformational Calculations"; D. Bawden. Ed.; Research Studies Press (Wiley): New York, 1981. G.M. Crippen and T.F. Havel, 'Distance Geometry and Molecular Conformation"; D. Bawden, Ed.; Research Studies Press (Wiley): New York, 1988. K.T. ONeil W.F. DeGrado. Proc. Natl. Acad. Sci. USA.,-.82.4954 (19851. .. and . * , T.F. Havel and M.E. Snow, J.-Mol.-Eiol., 212,1 (1991). W.C. Ripka. W.J. Sipio and J.M. Blaney, Lectures in Heterocyclic Chemistry. 1x, S95 (1987). B.W. Dijkstra, K.H. Kalk, W.G.J. Hol and J. Drenth, J. Mol. Biol., 142,97 (1981). 29, 899 (1986). R.P. Sheridan. R. Nilakantan. J.S. Dixon and R. Venkataraohavan. J. Med. Chem...~ . . M.G. Wong an'd P.R. Andrews. Eur. J. Med. Chem., 24.325 (1989). R.A. Dammkoehler, S.F. Karasek, E.F.B. Shands and G.R. Marshall, J. Comp.-Aided Mol. Design, 9,3 (1989). 1. Motoc. R.A. Dammkoehler and G.R. Marshall in "Mathematical and Computalional Concepts in Chemistry", N. Trinajstic, Ed.; Ellis Horwood, Ltd., Chichester, 1986; p. 222. G.M.D.-0.d. Kelder, J. Comp.-Aided Mol. Design, 1,257 (1987). A.K. Ghose and G.M. Crippen. J. Comp. Chem., 565 (1986). A.K. Ghose and G.M. Crippen. J. Chem. Inf. Comput. Sci., 22,21 (1987). A.K. Ghose and G.M. Crippen, J. Med. Chem., 28,333 (1985). A.K. Ghose, G.M. Crippen, G.R. Revankar, P.A. McKernan. D.F. Smee and R.K. Robins, J. Med. Chem., 2 , 7 4 6 (1989). 725 (1990). A.K. Ghose and G.M. Crippen, Mol. Pharm., 2, V.N. Viswanadhan, A.K. Ghose. N.B. Hanna, S.S. Matsumoto, T.L. Avery. G.R. Revankar and R.K. Robins, J. Med. Chem..%, 526 (1991). G.M. Crippen, J. Comp. Chem., 8,943 (1987). L.G. Boulu and G.M. Crippan. J. Comp. Chem.. 1p,673 (1989). L.G. Boulu. G.M. Crippen, H.A. Barton, H. Kwon and M.A. Marletta, J. Med. Chem.. Xl, 771 (1990). G.M. Crippen and T.F. Havel, Acta. Cryst., m,282 (1978). T. Havel and K. Wuthrich, Bull. Math. Biol., 673 (1984). J.M. Blaney. G.M. Crippen. A. Dearing and J.S. Dixon, "DGEOM, #590"; Quantum Chemistry Program Exchange, Indiana University: Bloomington, 1990. A. Smellie, "Constrictor"; Oxford Molecular Limited: Oxford, 1990. M. Saunders. K.N. Houk, Y.-D. Wu. W.C. Still, M. Lipton, G. Chang and W.C. Guida, J. Am. Chem. SOC., 112,1419 (1990). C.E. Peishoff, J.S. Dixon and K.D. Kopple, Biopolymers. 45 (1990). ~
z,
a
lntroductlan - Distance geometry is a general molecular model-building method, best known for
determining three-dimensional solution structures of peptides, proteins, and nucleic acids from nuclear overhauser effect (NOE) distance measurements (1,2). Distance geometry has also been applied in a variety of ways to build models of proteins and receptors and to model the interaction of small molecules with receptors. Ghose and Crippen recently published a comprehensive review of distance geometry and its application to receptor modeling, emphasizing their distance geometry quantitative structure-activity relationship (QSAR) approach (3). We will focus on additional distance geometry approaches which have application to receptor modeling and only briefly describe the distance geometry QSAR method.
Distance geometry converts a set of distance bounds (minimum and maximum allowed distances) into a set of coordinates consistent with these bounds (4,5). A molecular structure is described by the set of all pairwise interatomic distance bounds in a distance bounds matrix. This distance bounds matrix describes the complete conformation space of a molecule by entering the maximum possible distance (upper bound) between each atom pair in the upper diagonal and the minimum possible distance (lower bound) in the lower diagonal. All possible conformers therefore must lie between these upper and lower distance bounds. Additional distance bounds constraints, for example from NMR data or a proposed pharmacophore model, may be added to the distance bounds matrix. Distance geometry converts this usually underdetermined distance bounds information into randomly sampled sets of three dimensional coordinates. Protein S t r w Modeling - ONeil and DeGrado used distance geometry to predict the conformation of a calcium-binding loop of calmodulin, as part of their attempt at predicting the entire calmodulin structure based on the homologous sequences and X-ray structures of intestinal calcium-binding protein (ICE) and carp parvalbumin (6). The calmodulin sequence had two insertions in one of the ICB calcium binding loops. Distance geometry was used to generate models for the loop by constraining the ends of the loop to the ICE X-ray coordinates, forcing the side chains of four polar residues and a main chain carbonyl to interact with the calcium cation in a geometry identical to that from the second ICE loop, while maintaining octahedral coordination about the calcium. The remainder of the loop was allowed to remain flexible. Ten unique loop conformers that satisfied the constraints were identified from thirty random trials; these ten structures were energy refined with molecular mechanics. One of the refined conformers had reasonable contacts with the rest of the calmodulin model when reinserted back into the complete protein structure. Have1 and Snow used distance geometry to build complete protein models (not just loop regions) of unknown structures based on the sequence alignments and X-ray structures of homologous proteins (7).Sequence alignments are converted into distance and chiral constraints to maintain equivalent secondary structure, hydrogen bonds, and disulfides. Although the approach still depends critically on correct sequence alignment, the model-building procedure is automated and less biased than conventional approaches, resulting in an ensemble of random models which are consistent with the constraints implied by the sequence alignment. Several test cases demonstrated the feasibility of the approach, but no comparison with other methods was made.
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282
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- Ripka and coworkers (8) designed phospholipase A2 (PLA2) inhibitors based on the high resolution X-ray crystal structure of bovine pancreatic PLA2 (9). Potential binding modes of the substrate phospholipid were first modeled in the active site to suggest conformationally restricted mimics. A model was proposed in which the hydrated ester carbonyl intermediate was hydrogen-bondedto the active site His-48, and a phosphate oxygen was located at one of the water positions in the coordination sphere of the calcium. Distance geometry was used to generate many potential phospholipid binding modes with these constraints. The substrate fits generated by distance geometry suggested a hydrophobic groove in the PLA2 active site which could accept a naphthalene ring. This offered the possibility of building a rigid framework from which additional functionality could be directed to interact with other parts of the site, resulting in the design of a series of acenaphthene inhibitors with good in vitfo activity. Distance geometry was also used to dock the resulting designs into the active site, with no constraints except to maintain reasonable minimum intermolecular distances, to determine additional potential binding modes by randomly sampling the inhibitor designs' conformationswithin the confines of the active site. e Fn- A problem that often occurs in molecular modeling of bioactive compounds is to define the geometry adopted by a pharmacophore. A pharmacophore is a set of atoms or groups which are present in each bioactive molecule and which are required for activity. Often the assumption is made that molecules which have the same biological activity interact at the same receptor by presenting the pharmacophore elements to the receptor in the same way. The question, especially in the absence of a three dimensional structure for the receptor, is whether or not a unique three dimensional geometry can be inferred for the pharmacophore elements by examining several different molecules. In other words, are there conformations for each molecule in which the corresponding pharmacophore elements have the same geometrical arrangement? The important concept is that, while each molecule considered by itself may be quite flexible, the assumption that certain pharmacophore elements have the same geometry between different molecules introduces new constraints that may restrict the allowable conformational space available to each molecule. The computational problem can be stated explicitly in the following way: generate conformations for each molecule such that certain atoms or other structural elements (such as lone pairs or ring centroids) can be overlapped with the corresponding elements in each of the other molecules. This can be expressed quite naturally in a distance matrix. If several independent molecules are placed into a distance matrix representation, the intramoleculardistance bounds for each would be present but all intermoleculardistances would have lower bounds of zero and upper bounds of infinity. Applying the distance geometry algorithm to such a distance matrix would result in conformations for each molecule in random orientations relative to the other molecules. To force certain atoms from each molecule to overlap, the intermolecular upper bounds between those atoms must be lowered to a small value (say 0.3 A) that representsthe tolerance in the overlap. Then the distance geometry algorithm will generate conformations for each molecule such that the pharmacophore elements overlap between molecules. This is the essence of the ensemble distance geometry method (10). For example, the nicotinic agonists shown in Figure 1 were used (along with two others) in an
Figure 1
Chap. 29
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Blaney, Dlxon 283
ensemble distance geometry calculation in which the corresponding highlighted atoms were used as the pharmacophore (10). The resulting geometry is shown in the lower three dimensional views with the pharmacophore atoms in dark filled circles. Wong and Andrews used manual atom-by-atomsuperimposition, electrostatic potential map superimposition, and a systematic torsion search method to propose a model for the binding of convulsants to the picrotoxinin site of the GABA receptor (11). A total of ten superimposition models were found by these approaches. Ensemble distance geometry also found these ten models, plus one additional model which was not found by the other approaches. There are several possible outcomes for such a calculation. First, there may be no acceptable solution. Second, there may be only one solution in that there is only one possible pharmacophore geometry and each molecule has only one conformation which can present that pharmacophore geometry. Third, there may be only one pharmacophoregeometry but multiple conformationsof at least some of the molecules which are compatible with that geometry. Finally, there may be many solutions both for the pharmacophoregeometry and some or all of the molecules. Systematic torsional search methods have also been used to determine pharmacophore geometries (12,13). The method essentially performs a complete systematic torsion conformational search on one molecule and then uses the resulting sets of distances between pharmacophore elements to prune the search tree for the next molecule, and so on. After all molecules are searched, the remaining sets of distances represent those which can satisfy pharmacophore geometries which are common to all compounds. By recording the torsion angles, the conformations of each compound can be regenerated. There are advantages and disadvantagesto each method. The computational complexity of the ensemble method is a polynomial function of the number of atoms rather than an exponential function of the number of rotatable bonds. Therefore, for systems with many rotatable bonds, the ensemble method will be faster. However, pruning of the search tree as early as possible can improve the speed of the systematic search approach (12). The ensemble method handles ring systems naturally and thus can alter ring conformation in the course of searching for pharmacophore geometries. Torsional searches have difficulty altering ring conformations since changing a single torsion within a ring causes distortions of bond distance and angles in other parts of the ring system. If the chirality of some centers is unknown, the ensemble method can allow the chirality at those centers to randomly vary and choose the chirality which is compatible with the pharmacophore geometry. Systematic torsional searches would need to be done with all possible chiralities of unknown centers to ensure that solutions were not missed.
The main disadvantage of the ensemble method relative to torsional searching methods is that the ensemble method produces random solutions rather than being more deterministic. For a given angle step size, the systematic torsional search assures that all possible solutions have been examined. However, computer time constraints often force one to choose a relatively large angle step size (for example 30") and there is no guarantee that solutions are not missed because they fall between the steps. In addition, in pharmacophore modeling applications, one is usually not interested in enumerating all possible solutions. The useful results are: no answers, in which case the problem has probably not been correctly formulated; one answer, which might be the unique pharmacophore geometry; or more than one answer, in which case the problem is underdetermined and more data are necessary. The ensemble method (and distance geometry in general) also cannot naturally handle problems in which constraints are phrased in terms of lists of acceptable torsion angles (i.e. that an angle can be either trans, gauche +, or gauche -). However, the useful special case of cis or trans (for example, peptide bonds) can be handled by distance geometry using chiral constraints to keep the bonded atoms planar. QSAq - Crippen applied distance geometry to the problem of three-dimensional receptor mapping (3). Ghose and Crippen recently reviewed the approach in detail (3). A very similar approach was also reviewed (14). Their method proposes the geometric requirementsof the
Section VI-Topics in Drug Design and Discovery
284
Venuti, Ed.
receptor site based on the experimental data of binding affinities of a series of ligands, which may be conformationally flexible, and hypothesized binding modes (i.e. pharmacophore model) for each ligand. The result is a low-resolution,three-dimensional model of the receptor binding site, which is described as a series of points in space (site points) that interact with specific ligand atoms or groups of atoms (ligand points). Each ligand point is described by atom-centered physicochemical properties (molar refractivity, hydrophobicity, and partial charge) (15,16). A specific interaction 'energy' is assigned to each site point - ligand point interaction by a modified quadratic programming optimization procedure, yielding a quantitative prediction of the binding affinity of each ligand to the site model. Optimization of interaction parameters is performed under the constraint that the interaction energy of the proposed binding mode is more favorable than the interaction energy of all other geometrically possible binding modes. Optimization continues until the proposed binding mode is either proved to be the best or found to be inconsistent, when it is replaced by the most favorable binding mode encountered so far, and optimization is continued. This approach avoids the temptation to bias the fits and avoids preconceptionson how a particular ligand might bind. The three-dimensional geometric model of the binding site involves both energetic and steric features. Since the approach predicts the mode of binding as well as the interaction energies it offers the opportunity to suggest conformationally restricted analogs that might maximize binding to the site. Ghose and Crippen generated a model for the inhibition of E. coli dihydrofolate reductase by 39 compounds from two different structural classes (17). The model contained 19 site pockets of 9 different types and qualitatively agreed with the X-ray crystal structure of the enzyme's active site. Ghose and Crippen recently modified their approach to eliminate much of the subjectivity previously required in choosing conformations and binding modes (18-20). A conformational search is performed for each molecule to identify the lowest energy conformers. A priority score is assigned to each conformer based on the sum of the experimental free energy of binding of the molecule to the receptor site and the calculated energy of the conformer relative to the global energy minimum for the molecule. Starting from the highest priority conformation, the low energy conformersfor the remaining molecules are superimposed on it to give the best overall match based of the atom-centered physicochemical properties. This approach is performed for several different high priority reference conformations, each producing a different possible superimposition model. Each model is then evaluated in the remaining steps to determine the best model. Site points are initially placed at the positions of superimposed atoms and remaining non-coincident atoms. This results in a large number of site points, which is reduced using stepwise reverse regression to eliminate insignificant site points. The optimization step is similar to their original approach. This modified approach appears to be a significant improvement and has been used to model the binding of 28 antiviral nucleosides against an unknown receptor of parainfluenza virus (18), the binding of 29 benzodiazepine receptor ligands to the benzodiazepine receptor (19), and the antileukemic activity of 21 purine-6-substitutednucleosides (20).
. . .
.
- Recently, a new method has been developed which produces a novel receptor site description, called a Voronoi binding site model, using information from the structures and binding affinities of a series of ligands (21,22). The binding site is described by dividing space up into a set of Voronoi polyhedra, which are derived from a set of 'generating points' in a simple way: each polyhedron consists of all points which are closer to one generating point than to any other. Thus, each generating point results in one Voronoi polyhedron. A binding site model is specified by the number and location of a set of generating points. In addition, each Voronoi region is assigned a set of interactionparameters for each type of ligand atom. Thus, a ligand can be placed into the receptor model and an interaction energy calculated by summing the interactions of each atom with the region that contains it. For example, Figure 2 shows a simple receptor model with two regions. Note that there are many equivalent ligand binding modes. The only aspect which is important for interaction energy calculationsis the region into which each ligand falls.
Figure 2
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Receptor Modeling by Distance Geometry
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The object of the Voronoi binding site approach is to find a set of generating points and interaction potentials which reproduce the experimental binding constants within experimental error when each ligand is bound to the receptor site model in the most favorable way. The specific steps in developing a model are: (i) summarize the conformation space of each ligand; (ii) propose a site geometry; (iii) determine all geometrically allowed binding modes of each ligand; (iv) determine the interaction parameters. If step (iv) fails, then the method starts again at step (ii) with a new site geometry. The advantages of the Voronoi method are that it does not require the a priori assumption of a pharmacophore, it accounts in a quantitative way for the observed data, and it does not impose any more detail on the binding site model than is necessary to account for the data. On the other hand, it is necessary for the user to propose the binding site geometry and the overall process is computationally expensive. The method has been successfully applied to two fairly simple test cases (22,23), but at this point it is not yet clear how difficult larger problems will prove to be.
- Relatively few applications of distance geometry have appeared since its original application t o chemical structure problems by Crippen over ten years ago (24). The vast majority of applications and publications have focused o n determining solution structures of small and macromolecules from NMR experiments (1,2). Distance geometry software is now more readily available (25-27), along with a steadily increasing number of applications and publications which demonstrate its unique ability to generate molecular models for complex situations involving drugand receptor docking (8). pharmacophore modeling, protein structure prediction (6,7), conformational analysis (28,29). References 1. 2. 3.
4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29.
K. Wuthrich, "NMR of Proteins and Nucleic Acids"; John Wiley and Sons: New York, 1986. K. Wuthrich, Science, m,45 (1989). A.K. Ghose and G.M. Crippen in "Comprehensive Medicinal Chemistry: The Rational Design, Mechanistic Study and Therapeutic Application of Chemical Compounds", Vol. 4. C. Ramsden, Ed.; Pergamon Press, Oxford, 1990; p. 715. G.M. Crippen. 'Distance Geometry and Conformational Calculations"; D. Bawden. Ed.; Research Studies Press (Wiley): New York, 1981. G.M. Crippen and T.F. Havel, 'Distance Geometry and Molecular Conformation"; D. Bawden, Ed.; Research Studies Press (Wiley): New York, 1988. K.T. ONeil W.F. DeGrado. Proc. Natl. Acad. Sci. USA.,-.82.4954 (19851. .. and . * , T.F. Havel and M.E. Snow, J.-Mol.-Eiol., 212,1 (1991). W.C. Ripka. W.J. Sipio and J.M. Blaney, Lectures in Heterocyclic Chemistry. 1x, S95 (1987). B.W. Dijkstra, K.H. Kalk, W.G.J. Hol and J. Drenth, J. Mol. Biol., 142,97 (1981). 29, 899 (1986). R.P. Sheridan. R. Nilakantan. J.S. Dixon and R. Venkataraohavan. J. Med. Chem...~ . . M.G. Wong an'd P.R. Andrews. Eur. J. Med. Chem., 24.325 (1989). R.A. Dammkoehler, S.F. Karasek, E.F.B. Shands and G.R. Marshall, J. Comp.-Aided Mol. Design, 9,3 (1989). 1. Motoc. R.A. Dammkoehler and G.R. Marshall in "Mathematical and Computalional Concepts in Chemistry", N. Trinajstic, Ed.; Ellis Horwood, Ltd., Chichester, 1986; p. 222. G.M.D.-0.d. Kelder, J. Comp.-Aided Mol. Design, 1,257 (1987). A.K. Ghose and G.M. Crippen. J. Comp. Chem., 565 (1986). A.K. Ghose and G.M. Crippen. J. Chem. Inf. Comput. Sci., 22,21 (1987). A.K. Ghose and G.M. Crippen, J. Med. Chem., 28,333 (1985). A.K. Ghose, G.M. Crippen, G.R. Revankar, P.A. McKernan. D.F. Smee and R.K. Robins, J. Med. Chem., 2 , 7 4 6 (1989). 725 (1990). A.K. Ghose and G.M. Crippen, Mol. Pharm., 2, V.N. Viswanadhan, A.K. Ghose. N.B. Hanna, S.S. Matsumoto, T.L. Avery. G.R. Revankar and R.K. Robins, J. Med. Chem..%, 526 (1991). G.M. Crippen, J. Comp. Chem., 8,943 (1987). L.G. Boulu and G.M. Crippan. J. Comp. Chem.. 1p,673 (1989). L.G. Boulu. G.M. Crippen, H.A. Barton, H. Kwon and M.A. Marletta, J. Med. Chem.. Xl, 771 (1990). G.M. Crippen and T.F. Havel, Acta. Cryst., m,282 (1978). T. Havel and K. Wuthrich, Bull. Math. Biol., 673 (1984). J.M. Blaney. G.M. Crippen. A. Dearing and J.S. Dixon, "DGEOM, #590"; Quantum Chemistry Program Exchange, Indiana University: Bloomington, 1990. A. Smellie, "Constrictor"; Oxford Molecular Limited: Oxford, 1990. M. Saunders. K.N. Houk, Y.-D. Wu. W.C. Still, M. Lipton, G. Chang and W.C. Guida, J. Am. Chem. SOC., 112,1419 (1990). C.E. Peishoff, J.S. Dixon and K.D. Kopple, Biopolymers. 45 (1990). ~
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