Validation of Poisson-Boltzmann Electrostatic Potential Fields in 3D QSAR

& Combinatorial Science

Validation of Poisson-Boltzmann Electrostatic Potential Fields in 3D QSAR: A CoMFA Study on Multiple Datasets Glen E. Kellogga *, Sharangdhar Phatakb, Anthony Nichollsc and J. Andrew Grantd a b

c d

Department of Medicinal Chemistry & Institute for Structural Biology and Drug Discovery, School of Pharmacy Department of Biomedical Engineering, School of Engineering, Virginia Commonwealth University, Richmond, Virginia, 23298-0540 USA OpenEye Scientific Software, Santa Fe, New Mexico, 87501, USA AstraZeneca Pharmaceuticals, EST(Chem) 26F17, Mereside, Macclesfield, Chesire, SK10 4TG, UK

Full Paper A CoMFA 3D QSAR (Quantitative Structure-Activity Relationships) study was performed on five diverse data sets that have been previously published or are otherwise generally available to assess the value of the ZAP electrostatic potential field (calculated from a solution of the Poisson-Boltzmann Equation) as compared to the Coulombic field as implemented in standard CoMFA. The ZAP field showed an average improvement of 0.114 in q2 (leave-one-out cross-validation) as compared to the Cou-

lombic field, and the steric/ZAP combination field showed an improvement of 0.128 in q2 as compared to the Both (steric and electrostatic) field combination of CoMFA. However, the enhancement is not monolithic ± some of the data sets in this study showed a much larger preference for the ZAP field than others. The ZAP field appears to be more physically realistic than the Coulombic field and should be of significant value in QSAR studies of some data sets.

1 Introduction

etc. effects. The steric fields are calculated with algorithms derived from the Lennard-Jones equation. Usually, the electrostatic fields are calculated as simple Coulombic fields where test atoms with proscribed charge are placed on a three-dimensional grid and the resulting field values are calculated as the Coulombic energy between the test points and the partial charges of atoms in the molecule. This representation of electrostatics, while simple to calculate, has a number of inadequacies and problems. First, Coulombic fields can be discontinuous or undefined, e.g., if a grid point is coincident with or very near an atom. They can also exhibit very abrupt changes in sign. For these reasons the CoMFA protocol invokes an ™inside the molecule∫ cutoff that sets all grid points within the van der Waals volume of each molecule to a uniform value. While obviously artificial, this is not unreasonable because the regions of interest for CoMFA are actually largely outside these molecular volumes. Larger concerns arise from discontinuity issues at or just outside these molecular surfaces due to abrupt sign changes and abrupt dielectric changes. In this report we examine the relative effectiveness of a electrostatic potential field calculated with the ZAP Poisson-Boltzmann Equation solver [11] compared with the usual Coulombic electrostatic field in the CoMFA implementation of 3D QSAR. We have examined five diverse

Since the advent of Three-dimensional Quantitative Structure-Activity Relationships (3D QSAR) initially with CoMFA [1] and HASL [2], and later with an expanding array of technologies such as CoMSIA [3], GOLPE [4], or for a recent review [5], that supplement, enhance or supplant the first generation methods, many drug discovery groups have used 3D QSAR effectively to rationalize and enhance activity of their compounds. This is termed ™ligand-based design∫ because it is generally performed in the absence of structural data on the target protein or enzyme. Most of these methods employ two primary ™fields∫ to represent the molecular properties: steric and electrostatic. Applications of a number of other field types have been previously described [6 ± 10]. The steric component generally represents shape factors, while the electrostatic component is taken to represent the complex mix of electronic, solvation,

* Author to whom correspondence should be addressed: phone: ‡ 1 804 828-6452, fax: ‡ 1 804 827-3664, email: glen. [email protected] Key words: CoMFA, 3D QSAR, electrostatics, Poisson-Boltzmann equation, variable selection

QSAR Comb. Sci. 22 (2003)

DOI: 10.1002/qsar.200330847

¹ 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

959

G. E. Kellogg et al.

& Combinatorial Science CoMFA data sets that are publicly available or that have previously been published: the steroid data set of Cramer et al. [1], the HIV-1 data set of Marshall et al. [12 ± 14], the estrogen data set of Waller et al. [15], the dopamine data set of Martin et al.[16] and the mazindol data set of Kulkarni et al. [17].

2 Computational Methods Molecular Model Preparation. We obtained data sets of the pre-aligned molecular models and associated activities from sources as described in the Results (see Table 1). No changes to molecular structure or alignment were made. However, in some cases it was necessary to add charges with the Gasteiger-H¸ckel algorithm as implemented in Sybyl. Field Calculations and CoMFA runs. The CoMFA regions were first created as described in the Results (see Figure 2). Steric and electrostatic fields (and the ™Both∫ combination) were run using the default settings and controls of the Sybyl/CoMFA module. The ZAP field was created using the default conditions, which included a field cut-off of 30 for grid points inside the van der Waals surface of each molecule. Dielectrics of 80 (outside) and 2 (inside) were used. The cross-validated r2 (q2) data of Tables 2 ± 6 were calculated with the SAMPLS algorithm using leave-oneout sampling. The optimum number of components for each model was selected at break points such that an improvement of greater than around 0.025 in q2 was necessary to justify a further component. Non-cross-validated runs to calculate r2 and field contributions were made at the optimum number of components and included a column filter of 0.5.

tionally. In contrast, continuum or macroscopic methods, such as those that solve the PBE, treat solvents not as discrete molecules but as environmental properties with average values [18 ± 20] and are considerably more accessible. With these methods the electrostatic properties of water can be represented with descriptors for charge, dielectric, and etc. that are distinct from the properties of the atoms in the molecule. Numerical approximations such as the finite difference algorithm are required to solve the PBE for the complex shapes and structures of biological molecules in solution. The numerical solution usually chosen to solve the PBE is to map the molecule onto a three dimensional grid and apply the finite difference approximation. A two-dimensional representation of this is shown in Figure 1. Note that the grid spacing is shown as d, and that the interior of the molecule is assigned a dielectric (emolecule) different from the exterior of the molecule (solvent) which is assigned a dielectric (esolvent). The PBE must be satisfied everywhere in the system, but most importantly at each of the grid points. However, problems in grid-based PBE methods, e.g., DelPhi [19] arise because the physical description of the dielectric is discontinuous. It is low inside the molecule, high outside, and the transition between is infinitely sharp. Not only is this unphysical, it is very hard for grids to represent because the transition is unlikely to fall exactly on a grid point. The ZAP code solves this problem by basing the dielectric description upon atomic-centered Gaussians [11]. This creates a dielectric function that varies from internal to external values smoothly over a range of a few 1/10th of an Angstrom. The Zap solution of the PBE is thus more robust and precise. Because grid-based PBE solvers such as DelPhi

3 Results and Discussion 3.1 ZAP Poisson-Boltzmann Potential Field r¥ [e(r) ¥r¥ f(r)] ‡ 4p1(r) ˆ 0

(1)

ZAP [11] is a new program for solution of the PoissonBoltzmann Equation (also referred to as the PBE) [18 ± 20] (Eq. 1). Here e is the dielectric, f is the potential and 1 is the charge density. The PBE allows the calculation of a variety of electrostatic properties for neutral and charged molecules. To understand the nature of these interactions or supposed interactions it is crucial to characterize the physical and chemical properties of these biological molecules in solution, rather than in vacuum. While the most accurate model for understanding the properties of aqueous solutions would be to explicitly model all molecules in the system, including the solvent molecules, using a molecular mechanics approach, this can be very expensive computa960

Figure 1. Schematic representation of grid-based solution of Poisson-Boltzmann Equation. The dielectric constant for the water solvent is much higher than that inside the molecular volume. The distance between grid points is d.

¹ 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

QSAR Comb. Sci. 22 (2003)

Validation of Poisson-Boltzmann Electrostatic Potential Fields in 3D QSAR

& Combinatorial Science or ZAP natively produce grid map output, they are particularly suited to 3D QSAR. In fact all other results, numerical or otherwise, are derived from this grid. In the basic raw potential map the potential at each grid point is calculated. Note that the potentials inside the molecule are not particularly interesting because they are dominated by the atomic charges. Outside the molecule, however, potentials take on the character of the solvent-screened field. This field is a far more realistic representation of the electrostatic profile that a molecule projects than the simple Coulombic field. PBE methods have almost exclusively been applied to large biomacromolecules, and only rarely in ligand-based drug discovery studies [7]. However, the implementation of ZAP as a Sybyl [21] module and its interface to CoMFA [1], makes possible a relatively simple exercise to use the PBE in generating electrostatic potential fields for large collections of small molecules fairly rapidly, and to import these directly into the Sybyl 3D-QSAR table for analysis with CoMFA. Finally, because the ligand-type molecules used in 3DQSAR are considerably smaller than proteins, the improvement in boundary effects provided by the atom-centered Gaussians of ZAP is relatively more important as a higher proportion of grid points will be on the surface. As noted above, the ZAP grid points within the molecule are not as meaningful as those outside (but they are not discontinuous), so a constant value field cutoff is applied to these points, similar to that used in implementing the standard CoMFA electrostatic field. 3.2 3D QSAR Data Sets and Grid Sampling For this study we chose to reexamine CoMFA data sets that were commonly available and/or had been previously published (see Table 1). We wanted to focus on the value (or lack of value) in using the ZAP electrostatic potential field as opposed to a simple Coulombic electrostatic field. Thus we did not wish to justify model building, alignment rules, etc., as would be required with new CoMFA models. The first data set is the steroid data set of Cramer et al., upon which the CoMFA procedure was first validated [1] and that is available for demonstration purposes within the Sybyl package. The second data set is the dopamine D-2 agonist

data set that was created by Yvonne Martin and is freely available on the QSAR and Modelling Society web page at www.ndsu.nodak.edu/qsar_soc/resource/datasets/martin2.htm. The third is the HIV-1 inhibitor data set that was the basis of a series of articles by Garland Marshall et al. about a decade ago [12 ± 14]. This has been supplemented with several additional compounds [22]. The fourth data set is from a CoMFA study by Waller et al. examining the estrogen receptor binding affinities for a structurally diverse set of chemicals [15]. Finally, the fifth data set is from a recent study by Kulkarni et al. examining mazindol analogs as dopamine transporters [16]. Our requests for several other data sets from recently published CoMFA studies were not answered. Three CoMFA region definitions were used for each field combination (vide infra) on each data set (see Figure 2). The grids were sampled: a) every 1.0 ä starting at a point 5.0 ä below the minimum xyz corner of the molecule union set, proceeding to a point at least 5.0 ä greater than the maximum xyz corner of the set (1A5); b) every 2.0 ä starting at a point 4.0 ä below the minimum xyz corner, proceeding to a point at least 4.0 ä greater than the maximum xyz corner (2A4); and c) every 2.0 ä starting at a point 5.0 ä below the minimum xyz corner, proceeding to a point at least 5.0 ä greater than the maximum xyz corner (2A5). Note that the 2A5 and 2A4 models are independent as they sample completely different points in space, while the 1A5 model can be thought of as a union of 2A4 and 2A5. This approach is similar to one we used previously [23], and gives a fair sampling of both resolution and frame origin. While there have been a number of methods reported by, e.g., Cruciani [4, 24] and Tropsha [25, 26] to optimize region selection, via region focusing, frame translations/rotations, etc., and doubtless higher quality models could be obtained by application of these methods, for consistency our interest here is in using standard CoMFA technology. 3.3 CoMFA Results CoMFA partial least squares (PLS) statistics using leaveone-out cross-validation for the five data sets are set out in Tables 2 ± 6 for the steroid, dopamine D-2, HIV-1, estrogen and mazindol data sets, respectively. As described above

Table 1. Data set summary Data set

Activity measured

Number of Alignment description compounds

Steroid Inhibition of corticosteroid binding globulin Dopamine Dopamine D2 receptor agonism

21 26

HIV-1

Inhibition of HIV-1 protease substrate cleavage

99

Estrogen

Estrogen receptor binding affinity

58

Mazindol

Inhibition of binding [ 3H]WIN35428 to rat dopa- 71 mine transporter

QSAR Comb. Sci. 22 (2003)

Alignment of steroid rings Alignment of hydroxyphenol ring centroid and basic nitrogen Field fit based on HIV-1/ligand complex crystallography Automated molecular steric and electrostatic alignment ( SEAL [27]) Alignment IV (see Ref. 17)

¹ 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Ref. 1 16 13, 22 15 17

961

G. E. Kellogg et al.

& Combinatorial Science

Figure 2. Region selection for three region models. The molecule extents are indicated by the magenta box. 1A5 ± Starting at the lower left corner the black arrows indicate translations of 5.0 ä to the first data point (black crosses). Additional data points are at 1.0 ä increments until  5.0 ä the upper right corner. 2A5 ± Starting at the lower left corner the green arrows indicate translations of 5.0 ä to the first data point (filled green circles). Additional data points are at 2.0 ä increments until  5.0 ä the upper right corner. 2A4 ± Starting at the lower left corner the red arrows indicate translations of 4.0 ä to the first data point (open red squares). Additional data points are at 2.0 ä increments until  4.0 ä the upper right corner.

Table 2. CoMFA field data for steroid data set. Field(s)

ZAP Steric Electrostatic Both ( Steric/Electro.) Steric/Electro. Steric/ZAP

1A5a

2A4b

2A5c

q2 (comp)d

R2e

fractionf

q2 (comp)d

r2e

fractionf

q2 (comp)d

R2e

fractionf

0.765(2) 0.762(2) 0.768(3) 0.736(3) 0.758(3) 0.773(2)

0.932 0.894 0.962 0.948 0.964 0.925

1.000 1.000 1.000 0.366/0.634 0.298/0.702 0.398/0.602

0.800(5) 0.762(2) 0.684(3) 0.738(4) 0.743(2) 0.797(2)

0.981 0.885 0.944 0.958 0.919 0.922

1.000 1.000 1.000 0.397/0.603 0.381/0.619 0.441/0.559

0.705(3) 0.685(3) 0.688(3) 0.659(3) 0.715(3) 0.691(2)

0.935 0.922 0.919 0.939 0.942 0.903

1.000 1.000 1.000 0.328/0.672 0.291/0.709 0.389/0.611

1.0 ä grid spacing; margin  5.0 ä along each Cartesian axis from extents of union molecule set. 2.0 ä grid spacing; margin  4.0 ä along each Cartesian axis from extents of union molecule set. 2.0 ä grid spacing; margin  5.0 ä along each Cartesian axis from extents of union molecule set. d Cross-validated r2 and number of components in optimum model. e Conventional r2 at optimum number of components. f Relative fraction of fields in two-field models. a

b c

three region definitions were used for each data set and field combination. These are indicated using the codes defined above. Several field combinations were used for each data set: ZAP, steric, (standard) electrostatic, ™both∫ ± the automated combination of steric and electrostatic into one CoMFA column in which the ™inside the molecule∫ cutoffs are linked, steric/electrostatic (manual combination) and steric/ZAP. We ran CoMFAwith these two implementations 962

of the steric/electrostatic combination to verify that differences between the steric/ZAP field combination and the steric/electrostatic combination were not arising from the automated dual column of ™both∫, and were not expecting large differences between the two steric/electrostatic implementations. We have noted previously that selecting field combinations is a form of variable selection and that each data set seems to have a distinct ™personality∫ such that

¹ 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

QSAR Comb. Sci. 22 (2003)

Validation of Poisson-Boltzmann Electrostatic Potential Fields in 3D QSAR

& Combinatorial Science Table 3. CoMFA field data for dpamine data set. Field(s)

ZAP Steric Electrostatic Both ( Steric/Electro.) Steric/Electro. Steric/ZAP a±f

1A5a

2A4b

2A5c

q2 (comp)d

R2e

fractionf

q2 (comp)d

r2e

fractionf

q2 (comp)d

R2e

fractionf

0.540(5) 0.540(5) 0.357(3) 0.422(8) 0.416(4) 0.552(5)

0.986 0.954 0.937 0.996 0.965 0.959

1.000 1.000 1.000 0.636/0.364 0.336/0.666 0.384/0.616

0.386(8) 0.602(5) 0.078(1) 0.505(8) 0.348(5) 0.542(7)

0.942 0.930 0.454 0.994 0.971 0.962

1.000 1.000 1.000 0.602/0.398 0.448/0.552 0.483/0.517

0.652(8) 0.432(6) 0.397(3) 0.318(8) 0.388(5) 0.641(8)

0.994 0.954 0.863 0.990 0.971 0.993

1.000 1.000 1.000 0.651/0.349 0.337/0.663 0.384/0.616

See Table 2 footnotes.

Table 4. CoMFA field data for HIV-1 data set. Field(s)

ZAP Steric Electrostatic Both ( Steric/Electro.) Steric/Electro. Steric/ZAP a±f

1A5a

2A4b

2A5c

q2 (comp)d

R2e

fractionf

q2 (comp)d

r2e

fractionf

q2 (comp)d

R2e

fractionf

0.634(5) 0.639(5) 0.515(5) 0.615(8) 0.613(5) 0.642(5)

0.977 0.943 0.890 0.973 0.939 0.969

1.000 1.000 1.000 0.579/0.421 0.391/0.609 0.364/0.636

0.599(4) 0.606(5) 0.455(4) 0.567(8) 0.614(5) 0.658(5)

0.918 0.927 0.800 0.966 0.934 0.959

1.000 1.000 1.000 0.563/0.437 0.407/0.593 0.359/0.641

0.491(2) 0.577(5) 0.360(5) 0.573(6) 0.534(5) 0.534(5)

0.775 0.923 0.841 0.920 0.944 0.944

1.000 1.000 1.000 0.577/0.423 0.407/0.593 0.448/0.552

See Table 2 footnotes.

Table 5. CoMFA field data for estrogen data set. Field(s)

ZAP Steric Electrostatic Both ( Steric/Electro.) Steric/Electro. Steric/ZAP a±f

1A5a

2A4b

2A5c

q2 (comp)d

R2e

fractionf

q2 (comp)d

r2e

fractionf

q2 (comp)d

R2e

fractionf

0.587(3) 0.711(4) 0.487(5) 0.539(8) 0.619(5) 0.659(5)

0.926 0.934 0.961 0.989 0.969 0.975

1.000 1.000 1.000 0.398/0.602 0.322/0.678 0.427/0.573

0.482(2) 0.638(4) 0.362(2) 0.341(2) 0.472(3) 0.567(4)

0.815 0.911 0.722 0.739 0.864 0.947

1.000 1.000 1.000 0.420/0.580 0.370/0.630 0.441/0.559

0.574(3) 0.695(5) 0.258(2) 0.412(2) 0.525(5) 0.665(4)

0.873 0.946 0.687 0.758 0.944 0.937

1.000 1.000 1.000 0.332/0.668 0.435/0.565 0.451/0.549

See Table 2 footnotes.

Table 6. CoMFA field data for mazindol data set. Field(s)

ZAP Steric Electrostatic Both ( Steric/Electro.) Steric/Electro. Steric/ZAP a±f

1A5a

2A4b

2A5c

q2 (comp)d

R2e

fractionf

q2 (comp)d

r2e

fractionf

q2 (comp)d

R2e

fractionf

0.768(5) 0.715(5) 0.672(4) 0.732(4) 0.752(4) 0.758(5)

0.954 0.924 0.881 0.911 0.906 0.944

1.000 1.000 1.000 0.477/0.523 0.417/0.583 0.400/0.600

0.630(3) 0.634(5) 0.611(5) 0.702(4) 0.704(5) 0.718(5)

0.803 0.897 0.883 0.915 0.926 0.926

1.000 1.000 1.000 0.493/0.507 0.401/0.599 0.408/0.592

0.594(4) 0.679(5) 0.654(4) 0.688(4) 0.744(4) 0.733(7)

0.882 0.897 0.869 0.888 0.893 0.967

1.000 1.000 1.000 0.394/0.606 0.367/0.633 0.456/0.544

See Table 2 footnotes.

there is no universally applicable field combination [23]. While this study did not employ a number of other field types we have used in the past, including the Sybyl hydrogen bond field(s), the HINT field [6] and the E-State fields [8], there is still considerable variability in the ™best∫ field or field combination for these data sets. QSAR Comb. Sci. 22 (2003)

The field combination indicating the largest (leave-oneout) cross-validated r2 (q2) for each data set is indicated in Tables 2 ± 6 in bold italic. Eight of the fifteen distinct region/ data set models indicate that a model including the ZAP field has the highest q2. Five of the CoMFA models indicate that the steric field alone is the best model, while only two

¹ 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

963

G. E. Kellogg et al.

& Combinatorial Science models show a preference for the steric/electrostatic combination, and neither of these are the standard CoMFA ™both∫ combination. In fact, contrary to our expectations, the ™both∫ combined steric/electrostatic field column almost invariably (11/15 cases in this study with Dq2 as large as 0.130) has worse performance than using the two fields independently. A possible explanation is that a few information-rich grid points are being differentially excluded from the PLS analysis with the CoMFA algorithm that creates the ™both∫ column. In a direct comparison of the performance of the ZAP field to the electrostatic field, the q2 of ZAP-only models is, on average, 0.128  0.116 higher than electrostatic-only models. For field combinations, the steric/ZAP combination has q2 0.064  0.059 higher than the steric/electrostatic combination and 0.092  0.109 higher than the standard procedure ™both∫ field combination. The influence of the ZAP field is a function of data set: in the steroid data set (Table 2) and mazindol data set (Table 6) the ZAP field is of marginal value, only impacting significantly the 2A4 region models in the former and the 1A5 models in the latter, whereas in the dopamine data set (Table 3) the ZAP field essentially rescued the 3D QSAR models for the 2A5 region. In contrast, the estrogen data set (Table 5) indicates that the binding of these ligands appears to be dominated by steric interactions even though the ZAP field showed considerably more promise than the Coulombic electrostatic field.

4 Conclusions With the collection of data sets examined here the ZAP electrostatic potential field had improved PLS leave-oneout cross-validation statistics over the Coulombic electrostatic field in nearly all cases. This improvement does not in all cases, however, significantly impact the overall CoMFA models as the binding in some data sets is dominated by steric or other effects such that the type of electrostatic field is irrelevant. Where electrostatic effects are important, having a more physically realistic representation of electrostatics, i.e., using the Poisson-Boltzmann equation, appears to be valuable. It is interesting that this (perhaps) somewhat subtle difference between the two implementations of electrostatics can be observed when only a fairly limited number of grid points are actually part of the PLS analysis. This is why grid-based 3D QSAR is so effective.

Acknowledgements We gratefully acknowledge Virginia Commonwealth University and OpenEye Scientific Software for partial support of this research. Sybyl has been made available to VCU through a University Software Grant from Tripos, Inc. We also wish to thank Tudor Oprea (University of New Mexico) for providing the HIV-1 and estrogen data sets and Santosh 964

Kulkarni and Amy Newman (National Institute on Drug Abuse) for providing the mazindol data set.

References [1] R. D. Cramer, D. E. Patterson, J. D. Buntz, J. Am. Chem. Soc. 1988, 110, 5959 ± 5967. [2] A. M. Doweyko, J. Med. Chem. 1988, 31, 1396 ± 1406. [3] G. Klebe, U. Abraham, T. Mietzner, J. Med. Chem. 1994, 37, 4130 ± 4146. [4] M. Baroni, G. Costanino, G. Cruciani, D. Riganelli, R. Valigi, S. Clementi, Quant. Struct-Act. Relation. 1993, 12, 9 ± 20. [5] G. E. Kellogg, S. F. Semus, 3D QSAR in modern drug design, in A. Hillisch, R. Hilgenfeld (Eds.), Modern Methods of Drug Discovery, Birkh‰user Verlag, Switzerland, 2003, pp. 223 ± 241. [6] G. E. Kellogg, S. F. Semus, D. J. Abraham, J. Comput.-Aided Mol. Des. 1991, 5, 545 ± 552. [7] C. L. Waller, G. E. Kellogg, Net. Sci., www.netsci.org/Science/ Compchem/feature10.html. [8] G. E. Kellogg, L. B. Kier, P. Gaillard, L. H. Hall, J. Comput.Aided Mol. Des. 1996, 10, 513 ± 520. [9] R. J. Vaz, M. Edwards, J. Shen, R. Pearlstein, D. Kominos, Int. J. Quantum Chem. 1999, 75, 187 ± 195. [10] M. Bradley, C. L. Waller, J. Chem. Inf. Comput. Sci. 2001, 41, 1301 ± 1307. [11] J. A. Grant, B. T. Pickup, A. Nicholls, J. Comput. Chem. 2001, 22, 608 ± 640. [12] C. L. Waller, T. I. Oprea, A. Giolitti, G. R. Marshall, J. Med. Chem. 1993, 36, 4152 ± 4160. [13] T. I. Oprea, C. L. Waller, G. R. Marshall, J. Med. Chem. 1994, 37, 2206 ± 2215. [14] T. I. Oprea, C. L. Waller, G. R. Marshall, Drug Design Discov. 1994, 12, 29 ± 51. [15] C. L. Waller T. I. Oprea, K. Chae, H. K. Park, K. S. Korach, S. C. Laws, T. E. Wiese, W. R. Kelce, L. E. Gray, Chem. Res. Toxicol. 1996, 9, 1240 ± 1248. [16] Y. C. Martin, C. T. Lin, Three-Dimensional Quantitative Structure-Activity Relationships: D2 Dopamine Agonists as an Example, in C. G. Wermuth (Ed.), The Practice of Medicinal Chemistry, Academic Press, London, 1996, pp. 459 ± 483. [17] S. S. Kulkarni, A. H. Newman, W. J. Houlihan, J. Med. Chem. 2002, 45, 4119 ± 4127. [18] B. Honig, A. Nicholls, Science 1995, 268, 1144 ± 1149. [19] M. K. Gilson, B. Honig, Proteins Str. Funct. Genet. 1988, 4, 7 ± 18. [20] A. Nicholls, B. Honig, J. Comp. Chem. 1991, 12, 435 ± 445. [21] Sybyl and the Sybyl-interfaced ZAP module are available from Tripos, Inc., St. Louis, Missouri, USA, www.tripos.com. [22] T. I. Oprea, personal communication. [23] G. E. Kellogg, Med. Chem. Res. 1997, 17, 417 ± 427. P [24] G. Cruciani, S. Clementi, M. Pastor, Persp. Drug Discov. Des. 1998, 12, 71 ± 86. [25] A. Tropsha, S. J. Cho, Persp. Drug Discov. Des. 1998, 12, 57 ± 69. [26] E. C. Bucholtz, A. Tropsha, Med. Chem. Res. 1999, 9, 675 ± 685. [27] S. K. Kearsley, G. M. Smith, Tetrahedron Comput. Method. 1990, 3, 615 ± 633. Received on September 26, 2003; Accepted on October 20, 2003

¹ 2003 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

QSAR Comb. Sci. 22 (2003)