Computational Models for Predicting the Binding Affinities of Ligands

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Chem. Res. Toxicol. 2003, 16, 1652-1660

Computational Models for Predicting the Binding Affinities of Ligands for the Wild-Type Androgen Receptor and a Mutated Variant Associated with Human Prostate Cancer Ni Ai,† Robert K. DeLisle,‡ Seong Jae Yu,†,§ and William J. Welsh*,† Department of Pharmacology, University of Medicine & Dentistry of New Jersey, Robert Wood Johnson Medical School, 675 Hoes Lane, Piscataway, New Jersey 08854, and Pharmacopeia, Inc., Box 5350, Princeton, New Jersey 08543 Received August 7, 2003

In the present study, values of the binding energy (BE) were calculated for the rat androgen receptor on a data set of 25 steroidal and nonsteroidal compounds for which published values of the observed binding affinity (Ki) are available. A correlation between BE and pKi was evident (r2 ) 0.50) for the entire data set and became more pronounced when the steroids and nonsteroids were plotted separately (r2 = 0.76). Including BE as an additional descriptor to supplement the default steric-electrostatic descriptors in comparative molecular field analysis dramatically improved the predictive ability of the resulting three-dimensional quantitative structure-activity relationship models. We also demonstrate that the observed loss in ligand specificity between the wild-type (wt) AR and the T877A mutant AR associated with androgenindependent prostate cancer is reflected in decreased BE values (i.e., higher binding affinity) for the antiandrogen pharmaceutical hydroxyflutamide and for several nonandrogenic endogenous steroids, most notably cortisol, corticosterone, 17β-estradiol, progesterone, and 17Rhydroxyprogesterone.

Introduction The androgen receptor (AR), a member of the steroid hormone receptor superfamily, is responsible for signal transduction of 5R-dihydrotestosterone (5R-DHT or simply DHT (1, 2)). DHT, classically considered the “male” sex hormone, is required for embryonic development of male characteristics as well as secondary sex characteristics arising at the onset of puberty. In the adult male, DHT is essential during spermatogenesis and appears to play a significant role in bone health. In both sexes, testosterone (the precursor to DHT) is an intermediate in the synthesis of estrogen and, thus, linked both directly and indirectly to normal bone formation as well as the myriad of effects attributed to this classical “female” sex hormone. Mutations in the AR have been identified that interfere with DHT binding as well as other steps within the normal signal transduction pathway, including association with accessory proteins and DNA binding. These mutations have been ascribed to various degrees of androgen insensitivity syndrome (AIS). Conversely, some common AR mutants isolated from prostatic cancer cells have been linked with activity acquisition events (3). In particular, the lymph node carcinoma of the prostate (LNCaP) cell line, which contains an AR mutant that alters threonine 877 to an alanine (T877A), has been * To whom correspondence should be addressed. E-mail: welshwj@ umdnj.edu. † Robert Wood Johnson Medical School. ‡ Pharmacopeia, Inc.. § Present Address: FMC Corporation, Agricultural Product Group, Box 8, Princeton, NJ 08543.

implicated in attenuation of ligand specificity (4). This single mutation appears to convert nonandrogenic ligands such as progesterone and cortisol into viable agonists, thereby stimulating growth of androgen sensitive prostate cancer cell types. The ligand promiscuity of this altered receptor also dramatically reduces the clinical effectiveness of the antiandrogen hydroxyflutamide (HOF), the active metabolite of flutamide that is widely used for the therapeutic treatment of prostate cancer. This socalled “androgen escape” generally occurs in cases of late-stage prostate cancer in which the prostatic cancer cells no longer require androgen stimulation for growth (5-7). Considering the multiple roles played by the AR in both normo- and pathophysiological systems, it is not surprising that concerns have arisen regarding the potential deleterious effects of environmental pollutants collectively known as endocrine disrupting compounds (EDCs) (8-10). In a recent study by Tamura et al. (11), the ability of organophosphate pesticide compounds to interact with the wild-type (wt) AR was investigated in order to identify the structural determinants of this interaction. This work further establishes that AR is a target for environmental antiandrogens and, coupled with reported evidence of the antiandrogenic activity of vinclozolin and p,p′-1,1-dichloro-2,2-bis(p-chlorophenyl)ethylene (DDE) (12, 13), emphasizes the need for evaluation of existing and potential environmental contaminants. However, large-scale in vitro assessment of suspected EDCs remains a labor intensive and time-consuming operation. A more efficient and economical alternative would be to employ in silico molecular modeling approaches for the

10.1021/tx034168k CCC: $25.00 © 2003 American Chemical Society Published on Web 11/20/2003

Predicted Binding Affinity of Androgen Receptor Ligands

Chem. Res. Toxicol., Vol. 16, No. 12, 2003 1653

purpose of predicting end points and prioritizing chemicals for subsequent in vitro and in vivo screening. The ability to calculate specific AR-ligand interactions and binding affinities for both the wt and the T877A mutant AR is now possible by virtue of the recently published X-ray crystal structures of their ligand binding domains (LBDs) complexed with DHT (14). Quantitative structureactivity relationship (QSAR) models, which can rapidly predict the biological activity and/or toxicity of chemicals even in cases where the particular receptor’s threedimensional (3D) structure is absent, have been constructed and employed successfully for the AR (15), the estrogen receptors R and β (16-20), and for several other members of nuclear receptor family (21). Furthermore, these same models also serve as a knowledge base for the discovery of new chemical entities as potential therapeutic and diagnostic agents. In this paper, we show that the calculated binding energy (BE) correlates well with experimentally derived binding affinities (expressed as pKi) for a diverse set of androgenic and nonandrogenic compounds. Moreover, inclusion of these BE values to supplement the standard steric-electrostatic descriptors generated by comparative molecular field analysis (CoMFA) yielded a 3D QSAR model that is far superior in predictive ability as compared with CoMFA alone. We also show that changes in the calculated BE values reflect observations from numerous studies of increased responsiveness of the T877A AR mutant relative to the wt AR for the antiandrogen therapeutic agent HOF and for many nonandrogenic steroids including the female hormones estrogen and progesterone (for recent reviews, see refs 22-24).

operating system. The molecular structure of DHT, extracted from the crystal structure of the wt rAR-DHT complex (I137), was used as the template to build the steroidal compounds of the data set. Molecular structures for the remaining compounds were constructed from the Sybyl 6.7 fragment database. Each compound was energy minimized to the putative global low energy conformation in the following manner. Using the standard Tripos molecular force field with a dielectric constant of ) 4.0, molecules were first geometry optimized to the nearest local minimum energy conformation until an energy difference of 0.001 kcal/mol between successive iterations was achieved. All rotatable (i.e., single) bonds were then systematically searched in 10° increments, and after the torsion angles were set to the lowest energy conformer among those scanned, the molecule was geometry optimized a final time. These optimized structures served as the base point for further energy calculations and receptor docking studies. Preparation of Protein-Ligand Complexes. The crystal structure of the rAR LBD complexed with DHT was energy minimized using the CVFF force field accessed through the Discover module of InsightII. To minimize the risk of physically unrealistic movements and/or entrapment in local energy minima, the DHT-rAR complex was energy minimized for subsequent docking calculations gradually in three successive steps: (i) only the hydrogen atoms, (ii) all side chains, and (iii) full relaxation of the receptor’s ligand contact residues while holding other residues fixed. The ligand contact residues in the rAR LBD were defined as those 24 residues within a 5.0 Å radius of the bound DHT. The DHT molecule was held fixed until the final step, at which time it was allowed full freedom of movement. Each energy minimization procedure was performed using steepest descent optimization for 5000 iterations or until the maximum derivative was less than 0.1 kcal/(mol Å), followed by conjugate gradient optimization for 3000 iterations or until the maximum derivative was less than 0.001 kcal/ (mol Å). BE Calculations. Each ligand was manually docked into the wt or mutant rAR crystal structure using the pose of the cocrystallized DHT molecule as a guide to orient the molecule. This same alignment rule was employed later in the CoMFA study (vide infra). The resulting ligand-receptor complexes were then energy minimized as described above. Values of the ligand-receptor BE were calculated as the potential energy of the ligand-receptor complex (Ecomplex) minus the sum of the potential energy of the ligand (Eligand) and the potential energy of the receptor (Ereceptor), each in isolation:

Experimental Procedures Data Sets for Analysis. Experimental values of the AR binding affinity for the data set of 25 ligands (Figure 1) were obtained from Waller et al. (15), who used a competitive rat AR (rAR) binding affinity assay with [3H]R1881. Binding affinities were reported as pKi, the negative log of the inhibition constant Ki. This data set comprises four structurally diverse chemical families with 11 steroids and 14 nonsteroids. The steroids under study included 17β-estradiol (estrogen), progesterone, cortisol, and corticosterone since numerous studies have reported promiscuous stimulation of AR-mediated transcriptional activation by these nonandrogenic endogenous hormones in LNCaP cell lines and in specimens containing the T877A mutant AR (3, 4, 6, 7, 25, 26). Notable among the nonsteroidal compounds are the pharmaceuticals HOF and diethylstilbestrol (DES), the environmental antiandrogens DDE, vinclozolin, and two polychlorinated biphenyls (PCBs). Three compounds (viz., kepone, procymidone, and P1) were omitted from the Waller data set due to the absence of appropriate force field parameters in the commercial molecular mechanics program employed in the present study. To evaluate the external predictive ability of the resulting 3D QSAR models, we divided the data set into five nonredundant combinations of 20 compounds for training and five compounds for testing (external validation). AR Receptor Structures. Structural data for the LBD of the rAR complexed with DHT were obtained from the Research Collaboratory for Structural Bioinformatics-Protein Data Bank (RCSB-PDB). The accession numbers are 1I37 for the wt rAR and 1I38 for the corresponding T877A mutant structure (14). Molecular Modeling. All molecular modeling operations were performed using Sybyl 6.7 (Tripos, Inc., St. Louis, MO) and Insight II (Accelrys, Inc., San Diego, CA), running on a Silicon Graphics (SGI) O2 workstation under the IRIX 6.5

BE ) Ecomplex - (Eligand + Ereceptor)

(1)

CoMFA. Because of their similar multiple ring structures, the steroidal compounds were directly aligned to DHT by minimizing the root mean square deviation for the steroidal backbone atoms. For the nonsteroidal compounds, the sixmembered ring was aligned to the A-ring of DHT. The process of CoMFA modeling has been described in detail previously (16, 18). Briefly, following alignment, the molecules were placed in a 3D cubic lattice with 2 Å spacing. Steric (van der Waals) and electrostatic (Coulombic) field descriptors were calculated for each molecule at each mesh point using a sp3-hybridized carbon atom with a +1.0 charge as a probe. The steric and electrostatic field energies were truncated to (30 kcal/mol. The statistical method of partial least squares (PLS) regression (27) was used to correlate the biological activity of the 20 training set compounds with the CoMFA-generated steric and electrostatic fields. A large number of steric-electrostatic descriptors were reduced to a few principal components (PCs), and the optimum number of PCs was determined by the leave-one-out (LOO) cross-validation procedure (28). The LOO procedure excludes each compound once from the training set, after which its activity is predicted by the model constructed from the remaining compounds. Using the reported optimal number of PCs, the PLS analysis was repeated without LOO cross-validation to

1654 Chem. Res. Toxicol., Vol. 16, No. 12, 2003

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Figure 1. Molecular structures of compounds under study. generate a final 3D QSAR model. A second 3D QSAR model was built in which the BE associated with each compound was included as an additional descriptor to supplement the standard CoMFA steric-electrostatic descriptors.

Results Correlation between BE and pKi. Plots of BE vs pKi for the data set of 25 AR ligands revealed a moderate linear correlation (r2 ) 0.50). The correlation coefficient improved substantially when the 11 steroids (r2 ) 0.81) and 14 nonsteroids (r2 ) 0.77) were plotted separately. These results suggest that while a correlation between BE and pKi is clearly evident regardless of whether these two groups are considered together or separately, the steroids and nonsteroids can be differentiated into distinct subpopulations with respect to their binding affinity

for the AR. Separation of the structural classes appears to deconvolute the global model into independent, local models that exhibit improved statistical measures of performance. Enhancement of CoMFA Models by Inclusion of BE. Five separate CoMFA models were constructed from the original data set of 25 compounds. Each 3D QSAR model comprised a training set of 20 compounds and a test set of five arbitrarily chosen compounds such that each compound appeared in the test set only once. This effectively yields a leave-five-out approach to model validation (29), similar to the standard LOO validation performed within CoMFA as described above. This 5-fold validation approach was implemented to ensure that the 3D QSAR models were robust, stable, and independent of the compounds chosen for the training set.



Table 1. Predicted pKi Values Computed by CoMFA without and with Inclusion of BE as a Supplementary Descriptor

a

compounds

experimental pKi

predicted pKi (CoMFA)

residuala

predicted pKi (CoMFA + BE)

residuala

DHT testosterone ∆4-androstenedione 5R-androstane-3R,17β-diol corticosterone estradiol pregnenolone progesterone 17R-hydroxyprogesterone mibolerone methyltrienolone diethylstibestrol (DES) p,p′-DDT o,p′-DDT p,p′-DDE methoxychlor HOF vinclozolin linuron HPTE M1 M2 hydroxylinuron PCB153 hydroxyPCB153

8.30 7.82 6.60 6.70 3.30 6.96 3.30 3.60 3.60 9.00 9.00 5.34 4.74 4.52 5.52 3.30 5.52 3.30 4.00 5.52 4.37 5.80 3.46 3.30 4.21

7.75 7.52 6.32 6.86 5.47 6.76 3.44 4.01 5.77 7.61 8.24 7.30 5.42 4.37 4.80 4.99 4.22 4.50 4.98 4.22 4.87 4.60 5.11 4.75 3.33

0.55 0.30 0.28 -0.16 -1.17 0.20 -0.14 -0.41 -2.17 1.39 0.76 -1.96 -0.68 0.15 -1.28 -1.69 1.30 -1.20 -0.98 1.30 -0.50 1.20 -1.65 -1.45 0.88

7.72 7.61 6.42 6.64 3.97 7.31 3.25 3.78 4.07 7.94 8.91 6.40 4.15 4.35 5.24 3.27 5.52 4.50 4.14 5.52 4.30 5.59 2.74 3.43 4.13

0.58 0.21 0.18 0.16 -0.67 -0.35 0.05 -0.18 -0.47 1.06 0.09 -1.06 0.59 0.17 0.28 0.03 -0.82 -1.20 -0.14 -0.82 0.07 0.21 0.72 -0.13 0.08

The residual was calculated as the difference between corresponding experimental and CoMFA-predicted pKi values.

The five CoMFA models yielded an impressive r2 ) 0.97 and rcv2 ) 0.78 on average. These values are typical of such models that are regarded as self-consistent and internally predictive. However, evaluation of the external predictive ability of the models using the test sets suggested otherwise. Comparison of the CoMFA-predicted and experimentally observed pKi values for each compound when it belonged to the test set revealed residual values ranging from 0.15 to over 2.0 log units (Table 1) and a standard error of prediction of 1.09 log units. These results are consistent with those presented in the study by Waller et al. (15). Inclusion of BE as an additional descriptor to the standard CoMFA field descriptors, however, yielded a dramatic improvement in the external predictive ability of the models as reflected by lower overall residual values (Table 1). Specifically, the standard error of prediction diminished to 0.49 log units and the maximum residual value among the compounds was only slightly above 1.0 log unit. Moreover, the number of structures with residual values >1.0 log units was reduced from 11 (without BE) to 3 (with BE). This marked improvement becomes more apparent by comparing plots of the CoMFA-predicted vs experimentally observed pKi values for the test set compounds from both analyses (Figure 3). Visual inspection reveals that the residuals of the points are considerably larger in magnitude from CoMFA alone (panel A) than from CoMFA with inclusion of BE (panel B). Quantitatively, the correlation coefficient from the leave-five-out crossvalidation improved substantially from 0.65 for CoMFA alone to 0.93 for CoMFA with the inclusion of BE. Clearly, inclusion of BE to supplement the standard CoMFA steric-electrostatic fields led to 3D QSAR models with vastly improved internal consistency and predictive ability. Analysis of contributions of the separate components (i.e., steric field energies, electrostatic field energies, and BE) gave further evidence of the impact of BE in improving the 3D QSAR models. Specifically, the separate contributions were 39% from the steric fields, 45% from the electrostatic fields, and 16% from BE.

Calculated Ligand-Receptor Binding Energies Are Sensitive to AR Point Mutations. Numerous AR mutations have been identified and associated with pathological disease states such as AIS and prostate cancer (25). Among these, the T877A mutant has been frequently associated with hormone refractory prostate cancer (6). In vitro studies have demonstrated that this mutant is activated by nonandrogenic steroids such as 17β-estradiol, cortisol, and progesterone arising from the enhanced binding affinity of steroids for this mutant as compared with wt AR (26). To investigate whether this increased binding affinity is reflected in the calculated BE, each compound in the data set was docked within the crystal structure of the mutant rAR followed by energy minimization as performed with the wt rAR. The calculated values of BE are listed in Table 2 for all 25 compounds in the data set, where the natural steroids, synthetic steroids, and nonsteroids are separated into three groups. Cortisol, which was not part of the original data set studied by Waller et al. (15), was also included here by virtue of the reported enhanced responsiveness of the T877A mutant, and hence the growth of LNCaP cells, to this adrenal hormone (4-7, 26). Among the 12 steroids listed in Table 2, our calculations predict an appreciable (>2.5 kcal/mol) increase in binding affinity for the mutant AR over the wt AR in every case. In terms of differences in the Gibbs free energy of binding (∆(∆G)binding), the value 2.5 kcal/mol would correspond to nearly a 100-fold increase in Ki at physiological temperature (from ∆(∆G)binding ) -RTln[(Ki)T877A/(Ki)wt). This trend is generally consistent with the preponderance of evidence from in vitro and in vivo studies cited above. Testosterone and DHT are predicted to exhibit increased binding affinity for the mutant receptor by about the same amount (2.5-2.8 kcal/mol). This preference was even greater for the DHT precursors ∆4-androstenedione and 5R-androstane-3R,17β-diol (3.84.5 kcal/mol) and for the synthetic steroids mibolerone and methyltrienolone (3.7-3.8 kcal/mol). Among the steroids considered in the present study, methyltrienolo-


Figure 2. Experimental pKi vs calculated values of the BE: (A) steroidal compounds; (B) nonsteroidal compounds.

ne is predicted to exhibit the highest binding affinity (most negative BE) for both the wt AR (-47.6 kcal/mol) and the mutant AR (-51.4 kcal/mol). In terms of clinical significance, perhaps the most noteworthy finding is the sharp increase in preference for the mutant AR over the wt AR calculated for corticosterone (7.6 kcal/mol), 17β-estradiol (6.5 kcal/mol), progesterone (7.3 kcal/mol), and 17R-hydroxyprogesterone (6.5 kcal/mol). These four nonandrogenic endogenous hormones exhibit low affinity for the wt AR but have been shown to activate the mutant receptor at concentrations normally found in blood (26, 30, 31). Cortisol, another steroid hormone shown to stimulate growth of LNCaP cells, also exhibited increased binding affinity although to a lesser degree (3.4 kcal/mol) than corticosterone, 17β-estradiol, and progesterone. The enhanced binding affinity, as found by the present calculations of cortisol, corticosterone, 17β-estradiol, progesterone, and 17R-hydroxyprogesterone (-42.3, -44.8, -47.6, -44.4, and -45.9 kcal/mol, respectively) vs DHT (-46.1 kcal/mol) for the mutant receptor might help explain their ability to effectively compete with DHT whereas they are relatively low affinity ligands (-38.9, -37.2, -41.1, and -37.1 kcal/

Ai et al.

Figure 3. Plot of experimental vs predicted pKi for all compounds in the data set: (A) CoMFA alone; (B) CoMFA models with inclusion of BE values.

mol, respectively) vs DHT (-43.6 kcal/mol) for the wt AR. Unlike the steroids, the nonsteroids were not uniform in terms of their relative preferences for the wt and mutant AR (Table 2). Interestingly, the pharmaceuticals HOF and DES showed opposite tendencies. HOF was predicted to bind more tightly to the mutant AR than to the wt AR by 3.2 kcal/mol. This result is consistent with experimental binding and functional assays revealing that the T877A mutation alters the AR so that HOF, which is a strong antagonist of wt AR, becomes a strong agonist (6, 7). DES, the powerful estrogen agonist that has been recommended for the treatment of patients with androgen-independent prostate cancer (32), is predicted to exhibit high affinity for the wt AR (-50.1 kcal/mol), which is much reducedsbut still highsfor the mutant AR (-44.2 kcal/mol). Patients with prostate cancer are more frequently using complementary and alternative therapies, particularly in cases where more conventional options have been exhausted. The herbal formulation known commonly as PC-SPES has been demonstrated to exhibit beneficial effects, although the product is apparently no longer

Predicted Binding Affinity of Androgen Receptor Ligands Table 2. Calculated Values of BE (in kcal/mol) for Selected Biologically Relevant Ligands for the wt and T877A Mutant AR compounds

BE (wt AR)

BE (T877A)

∆(BE)a

-46.14 -47.20 -47.98 -44.79 -42.28 -44.83 -47.60 -41.35 -44.44 -45.93

-2.50 -2.78 -3.81 -4.51 -3.36 -7.62 -6.54 -6.29 -7.31 -6.55

-46.87 -51.37

-3.81 -3.73

-54.47 -44.17 -47.97 -48.40

-3.24 5.88 -5.93 -4.87

-38.55 -34.99 -43.65 -27.76 -41.33 -34.19 -34.74 -36.56 -40.64 -43.75 -28.54 -35.84

2.29 1.09 0.60 -1.23 0.85 -4.49 -4.94 0.89 -6.01 -1.02 -0.13 1.22

natural steroids DHT -43.64 testosterone -44.42 ∆4-androstenedione -44.17 5R-androstane-3R,17β-diol -40.28 cortisol -38.92 corticosterone -37.21 17β-estradiol -41.06 pregnenolone -35.06 progesterone -37.13 17R-hydroxyprogesterone -39.38 mibolerone methyltrienolone

synthetic steroids -43.06 -47.64

nonsteroidal compounds pharmaceuticals HOF -51.23 DES -50.05 (S)-β-hydroxy-DHP -42.04 (R)-β-hydroxy-DHP -43.53 environmental chemicals p,p′-DDT -40.84 o,p′-DDT -36.08 p,p′-DDE -44.25 methoxychlor -26.53 HPTE -42.18 linuron -29.70 hydroxylinuron -29.80 vinclozolin -37.45 M1 -34.63 M2 -42.73 PCB153 -28.41 hydroxyPCB153 -37.06

a ∆(BE) corresponds to the difference in the ligand’s BE between the T877A mutant and the wt rAR. A negative value indicates an increase in binding affinity for the mutant receptor. Negative values of ∆(BE) g 2.5 kcal/mol in magnitude are highlighted in boldface for emphasis. Values of BE e 2.5 kcal/mol higher in energy than the corresponding value of BE for DHT associated with the same receptor are also highlighted in boldface for emphasis.

commercially available in the U.S. While its specific mode of action remains unclear and may involve multiple targets, evidence suggests that downregulation of the AR is one possibility (for a recent review, see ref 33). PCSPES contains licorice root, whose components include several compounds that visual inspection might suggest high binding affinity for ER and AR (34). We selected 1-(2,4-dihydroxyphenyl)-3-hydroxy-3-(4′-hydroxyphenyl)1-propanone (β-hydroxy-DHP) from among these isolated components and calculated its binding affinity as both R and S stereoisomeric forms to wt and mutant AR (Table 2). The differences in predicted binding affinity between the two stereoisomers were negligible, so their average values can be considered. The present calculations predict that the binding affinity of β-hydroxy-DHP for both the wt and the mutant AR (-42.8 and -48.2 kcal/mol, respectively) is comparable to DHT (-43.6 and -46.1 kcal/mol, respectively). Moreover, its binding affinity is greater for the mutant AR than wt AR by approximately 5.4 kcal/mol. These results suggest that β-hydroxy-DHP can compete with DHT (and testosterone) in terms of binding affinity for AR, although its possible role as an AR agonist or antagonist cannot be determined on the basis of binding affinity alone. Among the compounds listed in Table 2 as environmental chemicals, only linuron, hydroxylinuron, and M1


are predicted to exhibit appreciable (>2.5 kcal/mol) increases in binding affinity for the mutant AR vs the wt AR. Even with these increases, linuron and hydroxylinuron appear to still possess low affinity (∼ -35 kcal/ mol) vs DHT (-46.1 kcal/mol) for the mutant AR. M1 and M2, the two principal metabolites and thus close structural analogues of the fungicide vinclozolin (Figure 1), behave very differently. Although vinclozolin is predicted to exhibit low binding affinity for both receptors (-37.5 and -36.6 kcal/mol, respectively), M1 shows preferentially high affinity for the mutant as compared with wt AR (-40.6 and -34.6 kcal/mol, respectively) while M2 shows high affinity for both receptors (-42.7 and -43.8 kcal/mol, respectively). It is worth noting that M1 and, even more so, M2 bear a close resemblance in structure to HOF. These predictions are generally consistent with experimental findings that M1 and M2 are antiandrogenic whereas vinclozolin is a poor AR inhibitor (see ref 13 and references therein). Moreover, they suggest that the binding affinity of M1 and M2 is as high or higher for the mutant AR as compared with the wt AR. Visual inspection of p,p′-DDT, o,p′-DDT, p,p′-DDE, methoxychlor, and HPTE (Figure 1) presents another series of structurally analogous compounds. HPTE and p,p′-DDE are, respectively, the major hormonally active metabolites of methoxychlor and p,p′-DDT. Although none of these five compounds are predicted to exhibit differential binding affinities between the wt and the mutant AR (Table 2), a consistent trend emerges in predicted binding affinities: p,p′-DDE > HPTE > p,p′DDT . o,p′-DDT . methoxychlor. This general order is consistent with observations that p,p′-DDE and HPTE exhibit strong androgenic effects whereas methoxychlor itself is only weakly androgenic (12, 13, 35). While the actual effect of the T877A mutation on the binding affinity of the steroidal and nonsteroidal compounds in this data set is unknown due to an absence of specific experimental binding data, the present findings suggest notable differences in this respect between the wt and the mutant AR. These results for the mutant AR, in conjunction with the strong correlation found between the calculated and the experimentally observed binding affinities (i.e., BE vs pKi) for the wt AR, demonstrate the utility of computational approaches as a sensitive yet rapid tool in toxicology for the in silico screening of AR ligands and in drug discovery for the structure-based design of selective androgen-receptor modulators (3638).

Discussion In a previous study (39), we found a strong correlation between calculated values of the ligand-receptor BE and observed values of the relative binding affinities (RBA) for the estrogen receptors R and β. This strong correlation provided support for the validity of a homology model constructed for estrogen receptor β. In the current study, we have demonstrated again a strong correlation between BE and experimentally determined pKi values for a structurally diverse set of steroidal and nonsteroidal ligands binding to the rAR. An interesting finding is that the correlation improved when the steroids and nonsteroids were evaluated independently (r2 = 0.77-0.81) rather than together (r2 ) 0.50). This marked improvement suggests that steroids and nonsteroids may adopt different binding modes within the AR ligand binding


pocket. The AR has evolved to bind natural steroids, in particular androgens, which share a characteristic fusedring core structure that imposes structural and conformational rigidity. Hence, the steroids considered in the present study would be expected to adopt very similar orientations within the AR binding pocket. Likewise, the various enthalpic and entropic contributions to the binding free energy are expected to be fairly uniform across this series of compounds. In contrast, the synthetic nonsteroids (Figure 1) are structurally distinct from the steroids. They still share many common features (e.g., substituted benzene ring); yet, in general, they are structurally more diverse, conformationally more flexible, and smaller in volume than the steroids. Unlike the steroids, the nonsteroids are likely capable of sampling a greater variety of conformations and orientations within the AR binding pocket. Nevertheless, a strong correlation (r2 = 0.77) was obtained for the nonsteroids between the observed pKi and the calculated BE values obtained from energy minimization without resorting to computationally more exhaustive measures such as conformational averaging and inclusion of entropic and solvation effects. Another, and perhaps more likely, explanation for the improved correlation between pKi and BE when the steroids and nonsteroids were plotted separately may stem from differences in the range of biological activities covered by each group of compounds (Table 1). Specifically, the range is much more narrow for the nonsteroids (pKi, 3.30-5.80) as compared with the steroids (pKi, 3.30-9.00) owing to their general trend of lower biological activities. These two activity patterns represent different distributions; consequently, it is reasonable to expect that the steroids and nonsteroids would fit separate regression equations better than a single equation. CoMFA has been used widely to develop 3D QSAR models that are ultimately used for the purpose of predicting the binding affinity of untested chemicals. To this end, we have developed high quality CoMFA models (r2 ) 0.97, q2 ) 0.78) that meet the accepted criteria for self-consistency (r2 g 0.9) and internal predictive ability (q2 g 0.5) and that are comparable to those obtained by Waller et al. (15). To evaluate the external predictive ability of the models, the data set of 25 compounds was divided into five combinations of 20 training set compounds and five test set compounds. Combining the predictions for each test set, the models yielded less than satisfactory results: predictive r2 ) 0.65 and standard prediction error >1.0 log unit. However, inclusion of BE with the standard CoMFA steric-electrostatic field descriptors produced a dramatic improvement: predictive r2 ) 0.93 and standard prediction error ) 0.49 log units. As demonstrated in previous studies by this laboratory (39-41), the present study reveals that calculated ligandreceptor binding energies prove useful for the prediction of ligand-receptor binding affinity and for the enhancement of CoMFA models. The dramatic improvement in the predictive ability of CoMFA models by inclusion of BE as an additional descriptor supports the use of this approach in many applications ranging from drug discovery (39-41) to computational toxicology (16, 18, 39). For example, our laboratory has developed and applied QSAR/3D QSAR models for the identification and prediction of potential environmentally hazardous chemicals known as EDCs (16-20, 42-44). These predictive models allow for rapid prioritization of the ∼80 000 commodity

Ai et al.

chemicals prior to labor intensive and time-consuming in vitro and in vivo testing of their endocrine disrupting properties in humans and wildlife. Calculated values of BE were employed to compare the RBA of several biologically relevant steroids and nonsteroids for both the wt and the T877A mutant rAR (Table 2). The prevalence of this mutant AR in prostate cancer has been well-established (5, 6, 45), and our BE values reveal a uniform trend of increased binding affinity (more negative BE value) for the mutant AR consistent with a loss in ligand specificity. Other workers have shown that the T887A mutant AR is activated by cortisol, corticosterone, progesterone, 17β-estradiol, and possibly other steroids, and even by nonsteroidal antiandrogens such as HOF thereby promoting prostate cancer cell growth (5, 6, 26, 30, 46). The propensity of the T877A mutant to inappropriately respond to nonandrogenic ligands remains a serious problem during therapeutic treatment of prostate cancer (14, 47). The sensitivity of calculated BE values to this single mutation in the AR lends support to the potential value of this computational approach as a fast and efficient means for predicting the binding affinity of ligands under normoand pathophysiological conditions. At the same time, it is recognized by the authors that the in vivo androgenic effects of compounds such as those considered in the present study are influenced not only by binding affinity to receptors but also by many other factors such as absorption, binding to serum proteins, metabolism, and agonist vs antagonist effects.

Acknowledgment. W.J.W. acknowledges the financial support for this research from the U.S. Environmental Protection Agency’s Science to Achieve Results (STAR) program. Although the research described in this article has been funded in part by the U.S. Environmental Protection Agency’s STAR program through Grant GAD R826133, it has not been subjected to any EPA review and, therefore, does not necessarily reflect the views of the Agency, and no official endorsement should be inferred.

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Computational Models for Predicting the Binding Affinities of Ligands

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