Bioinformatics Advance Access originally published online on September 5, 2007
Bioinformatics 2007 23(20):2678-2685; doi:10.1093/bioinformatics/btm431
Structure-based calculation of drug efficiency indices
1Institute of Chemical Physics, University of Tartu, 2 Jakobi Street, 51014 Tartu, Estonia and 2Department of Organic Chemistry, Faculty of Pharmacy, Semmelweis University, Budapest, Hungary
*To whom correspondence should be addressed.
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ABSTRACT |
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 TOP ABSTRACT 1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Motivation: The efficiency indices (EI's) have been derived from the experimental binding affinities of drug candidates to macromolecules. These ‘two-in-one’ measures include information on both pharmacodynamics and pharmacokinetics of the candidate molecules. The time-consuming experimental measurement of binding affinities of extensive molecule libraries may become a bottle-neck of large scale generation and application of EI's.
Results: To overcome this limitation, structure-based calculation of new EI's is introduced using the modified free energy function of the popular program package AutoDock. The results are validated on experimental binding data of biochemical systems such as potent inhibitors bound to ß-secretase, a key enzyme of Alzheimer's disease and various drug–protein complexes. Application of new EI's is tested. Thermodynamics of EI's and their role in virtual high - throughput screening of drugs and in the development of docking programs are discussed.
Contact: csabahete{at}yahoo.com
Supplementary information: Accompanies this manuscript on the publisher's web site.
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1 INTRODUCTION |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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The mechanism of drug action generally involves a long chain of interactions with the molecules of the human body. There are numerous experimental and in silico drug design tools describing the terminal link of these chains, i.e. the estimation of equilibrium binding affinities (BA) of drug candidates (ligands) to the targeted macromolecules. Although BA is undoubtedly a key property, other pharmacokinetic and non-equilibrium links in the chain such as absorption, distribution and excretion of the candidate molecules also affect drug-likeness (Swinney, 2004, 2006).
Accordingly, most of the current in silico molecular design strategies (Lipinski and Hopkins, 2004) include modeling steps for the equilibrium binding and also for the pharmacokinetics of drugs. Atomic level techniques have been introduced for structural calculation of binding in ligand–target complexes. Computational molecular docking (Fig. 1) is the most advanced among these techniques (Brooijmans and Kuntz, 2003). The BA values of the ligands can be calculated directly from docked ligand–protein complex structures with free energy (scoring) functions. Another important step is the optimization of pharmacokinetics and drug-likeness of ligand databases using empirical rules of selection (Lipinski et al., 1997). These rules define limit values of simple, size-dependent molecular descriptors, e.g. the molecular weight (MW) which can be used for filtering of compound databases.
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)AlaAlaGluPhe (red) is included in this figure. Further references on the role of ß-secretase can be found in works of Hetényi et al. (Recently, new measures, the efficiency indices (EI) were introduced (Abad-Zapatero and Metz, 2005; Hopkins et al., 2004) linking the above mentioned different steps of drug design. EI's have promptly gained applications connecting structural diversity and biological activity of drugs (Schuffenhauer et al., 2006) and in optimization of synthetic receptors (Chen et al., 2006). The introduction of EI's was inspired by earlier studies (Kuntz et al., 1999) showing the usefulness of normalization of BA with the number of heavy atoms (NHAT) for drug design purposes.
In EI's, the normalized quantities [Equation (1)] are represented by commonly used measures of BA such as the experimental free energy of binding (
GE), the negative logarithms of experimental dissociation constant (pKd), inhibition constant (pKi) or inhibitor concentration at 50% inhibition (pIC50). The above mentioned simple descriptors, i.e. MW (Abad-Zapatero and Metz, 2005) or NHAT (Hopkins et al., 2004) are typical examples of the size-dependent normalizing factors (SNF).
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| (1) |
GC) values from scoring (Hetényi et al., 2006) of docked ligand–protein structures instead of GE may become successful alternative for obtaining EI's. Remarkably, computational docking has an advantage of producing atomic level protein–ligand complex structures within reasonable time. The calculation of GC (scoring) is either performed along with the docking calculations or independently in post-docking mode (Fig. 1). In both cases it requires negligible time and, therefore, allows reduction of time-consuming and expensive biochemical measurements of BA's. Picking up the speed of in silico docking and scoring, the calculation of EI's can become an essential part of high-throughput, structure-based virtual compound screening and drug design. The aim of the present study is to introduce and investigate rapid calculation of various EI's on the basis of a set of biologically relevant structural and thermodynamic experimental data. |
2 METHODS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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2.1 Binding data and structure-based free energy calculation of protein–ligand systems
GE and GC values of 53 protein–ligand complexes were adopted from a previous study (Hetényi et al., 2006) and listed in Supplementary Material. Proteins having large, peptidic ligands (MW > 350) and physiological importance such as the ß-secretase enzyme of Alzheimer's disease (Fig. 1), HIV-1 protease, streptavidin and immunoglobulins were prioritized for the study. The atomic coordinates of 41 of the complexes, were obtained from the Protein Databank (PDB, Berman et al., 2000). The 12 ß-secretase- inhibitor systems (om12, om13, om14, om15, om16, om17, om18, om19, om22, om23, om24 and om99-1) with no PDB structures available were modeled by modification of the 1fkn structure. Details on the systems, modeling and minimization of the complexes can be found in the previous paper (Hetényi et al., 2006). Although the peptidic ligands of these systems may become excellent lead compounds, they cannot be considered as drugs (Rishton, 2003). Thus, a set of an additional 20 drug–protein complexes (Table 1) having both PDB structures and GE values was collected and used in the external validation and application tests of the new EI's introduced in this study. The sources and the procedure of collection of these data are described in details in the Supplementary Material. Altogether the 53 + 20 ligands represent a wide range of compounds including larger, lead-like non-drugs and actual drugs.
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The
GC's were calculated using the minimized protein–ligand complexes, according to the modified AutoDock 3.0 (AD3, Morris et al., 1998) and AutoDock4 (AD4, Huey et al., 2007) scoring functions [Equation (2)].
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| (2) |
The f coefficients were determined empirically from a multi-linear regression (MLR) to a set of 30 protein–ligand complexes (AutoDock calibration set) with known binding constants (Morris et al., 1998). The indices i and j correspond to ligand and protein atoms, respectively. The Coulombic term includes the partial charges (q) and a distance-dependent dielectric function (
) (Morris et al., 1996). A, B, C and D are the Lennard–Jones parameters in the dispersion/repulsion 12-6 and H-bonding 12-10 formulas and r denotes the distance between the atomic pairs. 
(t) is a directional weight depending on angle t at the H-bonds. S and V denote the solvation parameter and fragmental volume, respectively, in the solvation function of Stouten et al. (1993). In the scoring function of AutoDock 3.0, only the C atoms of the ligand molecules are involved in the solvation model. The exponential term is an envelope function with a constant-value of 
= 3.5 Å. For simplicity, the sum of Coulombic and Lennard–Jones (enthalpic) terms is marked as HC and the last, desolvation term is marked as Gs,C. Remarkably, the AutoDock4 scoring function has different parametrization of the GC(AD4) part, especially for the desolvation term. Details on the new AD4 scoring function can be found in the original paper of Huey et al. (2007). In the present study, all systems were re-scored using the epdb command of AutoDock4. Besides the GC(AD4), i.e. the intermolecular enthalpic + desolvation terms, the full AD4 binding free energy [Gfull(AD4)] was also calculated and checked for applicability in EI calculations.
2.2 Regression analyses
The LR's were statistically analyzed and the SNF values were obtained using the program package CODESSA (ver. 2.0) (Karelson et al., 1996; Katritzky et al., 1995). Results of the regression analyses, i.e. mean square errors and t-values of the regression coefficients, the F-values, and the squares of the correlation coefficients (r2) of the regressions are tabulated in section Results. The principal moments of inertia were calculated for the binding conformations of ligand molecules using the Analyze program of the TINKER software package (Ren and Ponder, 2003). Numerical values used in the calculations and the correlations of SNF's are tabulated in Supplementary Material.
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3 RESULTS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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3.1 Definition of new EI's
The list and definitions of the SNF's [Equation (1)] corresponding to new, and formerly published (Abad-Zapatero and Metz, 2005; Hopkins et al., 2004) EI's can be found in Table 2. Some of these SNF's are commonly applied as two-dimensional (2D) descriptors in quantitative structure-activity relationship (QSAR) equations (Devillers and Balaban, 1999) and show relatively large degree of correlation with each other (Supplementary Material). The more complicated SNF's contain information also on molecular complexity involving internal (topological) distances and branching of the ligands resulting in their more unique profile and, in some cases, moderate correlations with each other. Whereas 2D descriptors are derived solely from the Lewis formula, i.e. the empirical connectivity list or molecular graph of the ligands, calculation of
GC requires the knowledge of spatial atomic positions in the protein–ligand complex. In a recent study (Hetényi et al., 2006), it was found that GE's of even large, flexible peptides (Fig. 1) can be predicted with a modified scoring function (GC) of the docking program package AutoDock 3.0 (Morris et al., 1998). As GC shows a significant correlation with the GE values (Hetényi et al., 2006) it was selected to represent BA in the structure-based, calculated EI values throughout the present investigations [BA = GC in Equation (1)].
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3.2 Correlation of experimental and calculated EI's
To test the reliability and predictive value of calculated EI's, simple linear regression (LR) analyses were performed with EI's obtained from the measured
GE values [Equation (3)].
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| (3) |
, and ß represent the regression coefficient and the intercept, respectively. The k's are the residuals at each data point. The total number of data points (N), i.e. the number of protein–ligand systems adopted from the previous study (Hetényi et al., 2006) was 50. A systematic series of LR's were developed for EI's based on the SNF's of Table 2 and GC's calculated with the scoring schemes of AutoDock3.0 and AutoDock4, respectively. The results and statistical parameters of the LR's are summarized in Table 3 and in the Supplementary Material.
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All LR's are statistically significant, and show higher r2 values than the correlation (r2 = 0.706) obtained between
GE and GC (Hetényi et al., 2006). Importantly, the high r2 values in Table 3 are not trivial consequences of this correlation in the previous work, as the SNF values are different for the 50 different ligand molecules [Equation (3)].
An advantage of 2D descriptors such as the Wiener index (W) involved in the best correlation (Fig. 2; Table 3) is that they can be unambiguously and rapidly calculated from the internal connectivity information coded in the molecular graph (Table 2). For example, W involves a simple summation of shortest topological distances in a molecule. Comparably good correlations could be achieved at all other SNF's including Balaban index (J) which is also defined by internal topological distances (Table 2) and was found to be useful as a QSAR descriptor in prediction of the entropic parts of GE (Hetényi et al., 2006). In addition, even the three outlier protein–ligand systems (1hhj, om22, om24) of the previous study (Hetényi et al., 2006) could be involved in the models [N = 53 in Equation (3)]. In case of W the level of correlation (r2 = 0.962) did not decrease when the three former outliers were included.
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3.3 Cross-validation of the correlations
There were different methods applied for cross-validation of the correlations presented in Table 3. The cross-validated correlation coefficients (
) of the leave-one-out (LOO) and leave-50%-out (L50%O) methods (Table 3) shows that exclusion of one or more data points from the models does not decrease the level of correlation dramatically. A set of 20 drug–protein complexes (Table 1) was used as an external validation set (EXT). Most of the corresponding r2 values are above 0.5 showing that the models can predict the EI values for smaller, drug ligands not included in the training set (50 systems). Notably, GC(AD4) produced higher 
values for the external validation than GC(AD3), probably due to the more advanced solvation terms and the larger compound database included in its parametrization. The Gfull(AD4) function did not result better EI-correlations (data not shown) than GC(AD4), and, therefore GC(AD4) was selected for the final evaluations (Table 3).
The results of the cross-validated correlations in Table 3 allow us to conclude that structure-based calculation of EI's works for both the ‘traditional’ (Abad-Zapatero and Metz, 2005; Hopkins et al., 2004) and the newly introduced 2D SNF's (W, 
's, J, etc.). The formulas in Equation (3) and Table 2 and the validated models can be coded and applied as EI-calculators during the in silico drug design process (Fig. 1). Direct implementation of EI-calculator algorithms in docking/scoring program packages such as AutoDock is also possible.
- To check the applicability of two new EI's with the best correlations (Table 3), the distributions of GE and EI values were compared for the sets including the 50 peptidic compounds (non-drugs) and the 20 drugs, respectively. It was found (Fig. 3 and Supplementary Material) that overlapping distributions of GE's (Fig. 3A) of drugs and non-drugs are separated for the EI's (Fig. 3B). There are one or two orders of magnitude difference (Table 4) in the median/average values of EI's for both W and IAIBIC and there are considerably large gaps between the minimum values of drugs and non-drugs, as well. These results emphasize the applicability of the new EI's in separation of drugs from non-drugs.
- The introduction of EI's in a virtual screening process improves the selectivity of screening. As a test case, the binding pocket of progesterone receptor was used as a target in the docking of 1760 compounds including an abridged version of the NCI Diversity Set (NCI/NIH; Lindstrom et al., 2003) and the native drug ligand norethindrone (1sqn, Table 1). GC's were collected and W- and IAIBIC-based EI's were calculated. Details on the methods of these procedures are described in the Supplementary Material. It was found, that the use of GC's alone ranked norethindrone to the best 10% of the 1760 compounds. Re-ranking of the best 10% according to W- and IAIBIC-based EI's resulted norethindrone in the second and sixth best position (< top 0.5%) on the list of the 1760 compounds, respectively. This test showed that in a second ranking step these new EI's can improve the quality of selection of a real drug.
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4 DISCUSSION |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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4.1 The background of the thermodynamics of EI's
The binding free energy (
G) can be written as the sum of experimental enthalpic (H) and entropic (S) binding contributions [Equation (4)], where T is the thermodynamic temperature.
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| (4) |
S can be further split into translational (St), rotational (Sr) and vibrational (Sv) entropy changes [Equation (5)] at the ligand molecule. In some articles (Noskov and Lim, 2001), further contributions are also considered such as solvation/desolvation free energy (Gs) of the ligand and/or the protein molecules, etc. As the SNF's depend solely on the ligands, involvement of protein effects is not necessary in the forthcoming discussion.
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| (5) |
The use of statistical thermodynamics expressions (Carlsson and Åqvist, 2005, Murray and Verdonk, 2002) for estimation of components St, Sr (Table 5) and Sv of molecular entropy is quite common. Sv depends on the frequencies of normal modes of the ligand molecule, which cannot be connected with the simple SNF's of this study. Gs includes both enthalpic and entropic contributions (Zou et al., 1999) and partly depends on the molecular size and shape of the ligand via the solvent accessible surface area. Accordingly [Equation (5)], the division of GE [left side of Equation (3)] with SNF's results in normalized HE's and SE's.
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On the right side of Equation (3) there is
GC Equation (6), including three terms [Equation (2), Methods section], which can be assigned (Brooijmans and Kuntz, 2003, Calderone and Williams, 2001) to the enthalpic (HC) contributions of binding. The fourth term of GC (Gs,C) is an estimate of Gs which represents only a minor portion of GC [Equation (6)].
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| (6) |
GC [Equations (3) and (6)] contains mostly normalized HC (and negligible Gs,C). Most importantly, there are no terms estimating St, Sr and Sv on the right side.
If assuming that experimental entropy (SE), i.e. St and Sr becomes zero after ligand binding, then St and Sr will include size-dependent factors, such as MW or the product of principal moments of inertia (IAIBIC), respectively (Table 5). However, it was correctly discussed (Carlsson and Åqvist, 2005), that the assumption of zero final entropy is rather hypothetical as the ligand does fluctuate around its binding position. Whereas the formulas of Table 5 can hardly be applied for calculation of binding entropy of ligands in their present forms, they obviously show the dependence of molecular entropy on MW and IAIBIC of ligands. Thus, normalization of SE [left side of Equation (3)] with SNF's such as MW or IAIBIC can be expected to decrease the ligand-dependency of the SE terms resulting in a constant part of the normalized SE.
The constant part of SNF-normalized SE does not affect the level of correlation and the remaining SNF-normalized enthalpic terms in Equation (3) correlate well with each other (Table 3).
4.2 New 3D SNF's
To test the prediction of the previous section, i.e. the usefulness of IAIBIC as a 3D SNF, it was employed in Equation (3). The statistical parameters of the corresponding LR (Table 3, Supplementary Material) show an excellent correlation (r2 = 0.966) verifying the expectation. Remarkably, both the 3D IAIBIC and the 2D W involve the calculation of real or topological internal lengths of the ligand molecules, and, therefore their connection is trivial. Their correlation for the 50 ligands is r2 = 0.864. Interestingly, the 2D W performed as well (Table 3) as the obviously more elaborate 3D IAIBIC in case of the 50 systems. It was also found, that IAIBIC works even for smaller subsets of the 50 investigated systems resulting in, e.g. an r2 of 0.973 for the 10 modeled ß-secretase complexes alone (AD3 scoring).
Other internal distance-based 3D SNF's such as the gravitation index (GI), a descriptor successful in prediction of boiling points (Katritzky et al., 1996) also provided good LR results in calculation of EI's (Table 3).
4.3 Methodological aspects of the results
Scoring functions of docking programs are generally based on correlations of GE with GC. However, during the development of scoring functions, separate fit of experimental HE and SE to the corresponding enthalpic and entropic terms (Brooijmans and Kuntz, 2003) of the scoring functions would be an ideal way (Murphy, 1999) to decrease errors coming from overlapping and/or coupled terms. However, most of the experimental thermodynamic BA data available are GE values or pK's from which GE's can be calculated (Wang et al., 2004). The amount of enthalpic data is limited as experimental binding enthalpy (HE) can be obtained only by additional measurements with special techniques, e.g. isothermal titration calorimetry (Campoy and Freire, 2005). The LR's of the previous sections showed, that the SNF-normalization of GE provides excellent correlation with the normalized HC without additional measurements of HE, due to the high enthalpic content of both sides of Equation (3) (see previous sections for details).
It can also be recognized [Equation (3)], that the reciprocals of the SNF's are actual weights in the weighted least squares fit of the calculated enthalpic terms to the experimental GE's. By using these weights during development of scoring functions, the degree of correlation and the accuracy of computational docking-scoring methods can be increased.
4.4 Practical applications
The EI's are simple indicators developed to aid rational drug design and hit-to-lead approaches (Keser
and Makara, 2006). In the present study, new EI's involving 2D and 3D SNF's were introduced. It was shown, that precise, structure-based calculation of EI's is a real alternative of time-consuming measurements and that the new EI's can be used in separation of drugs from non-drugs. The calculation of EI's of a large set of available drugs will allow the determination of reference EI-limits for selection of drug-like candidates in the future. The building of an EI database for the precise determination of EI-limits has already been started in our laboratory. As the proposed EI-calculators are fast and cost-effective, they will help to reduce the number of experimental measurements and can easily be combined with available methods in high-throughput computational docking and scoring (Fig. 1).
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ACKNOWLEDGEMENTS |
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TOPABSTRACT1 INTRODUCTION2 METHODS3 RESULTS4 DISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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The authors are thankful to Foundation Innove (www.innove.ee) project No. 1.0101-0310 for the financial support. The referees of the manuscript are acknowledged for their constructive suggestions.
Conflict of Interest: none declared.
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FOOTNOTES |
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Associate Editor: Anna Tramontano
Received on March 17, 2007; revised on August 6, 2007; accepted on August 18, 2007
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