DOI: 10.1002/minf.201200015

From Hansch-Fujita Analysis to AFMoC: A Road toStructure-Based QSARChristoph G. W. Gertzen[a] and Holger Gohlke*[a]

Dedicated to the Memory of Corwin Hansch and Toshio Fujita and Their Outstanding Contributions to the Field of QSAR

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Methods Corner

1 Introduction

Correlating the structure of ligands to their activity hasbeen an important goal since the very early days ofmodern chemistry.[1] In a pioneering effort, Hansch andFujita were the first to succeed in establishing quantitativestructure-activity relationships (QSAR) with the 1-s-p-analy-sis.[2] They correlated the biological activity of chemicalcompounds using a Hammett-type relationship[3] with thecompounds’ lipophilicity (expressed as the octanol-waterpartition coefficient) and electronic and steric properties,that is physicochemical properties, by means of a regressionanalysis.[2,4] The method is still used to date due to its vastapplicability.[5] In the same year, Free and Wilson publisheda method for deriving structure-activity relationships thatdoes not model activity contributions with physicochemicalterms but rather attributes incremental activity values tocompounds’ groups and substituents.[6] In many instances,both the Hansch and Free Wilson analyses have been com-bined to a mixed approach, which has turned out to bea powerful tool of classical QSAR.[6a] Moving from the levelof physicochemical properties (1D descriptors) and structur-al formulas (2D descriptors), as in the case of Hansch andFree Wilson analyses, to considering the three-dimensionalstructure of ligands then provided another major break-through that established the field of 3D-QSAR methods.[7]

2 3D-QSAR Methods

2.1 Ligand-Based Methods

3D-QSAR methods can be grouped into structure- andligand-based methods.[8] The first 3D-QSAR method, Com-parative Molecular Field Analysis (CoMFA),[7] introduced byCramer and coworkers, belongs to the latter group. Here,3D structural information of a compound is correlated toactivity data by means of exploiting molecular interactionfields.

To start with, an alignment of 3D structures of a set of li-gands onto the “bioactive conformation” of one of the li-gands is required. In the initial application of CoMFA,[7] thebioactive conformation was obtained by generating a low-energy conformation of one of the more rigid compoundsin the dataset. Alternatively, if a crystal structure of thetarget with a co-crystallized ligand is available, the com-

pounds of interest can be aligned onto this conformation.[9]

Finally, if an apo structure of the target or a homologymodel is available, docking poses of the ligands can begenerated and used for the structural alignment.[9] In thelatter cases, it is reasonable to do an energy minimizationfor each of the aligned ligands in the presence of thetarget structure. That way receptor information is implicitlyincluded in the ligand alignment. This very likely leads toa decrease in the structural overlap of the ligands resultingin models that show a lower correlation between predictedand actual pKi values. Nonetheless, CoMFA models derivedthat way have been shown to have a high predictivepower.[10]

After the structural alignment molecular interaction fieldsbased on van der Waals and Coulomb potentials are gener-ated outside each ligand at fixed intersections of an ortho-rhombic grid; these fields represent the ligand’s steric andelectrostatic properties. Field values are subsequently corre-lated to activity data by means of partial least-squares (PLS)analysis. This takes into account that usually the number offield values exceeds by far the number of activity data. Asa result of the PLS analysis, weights (“coefficients”) are ob-tained for each intersection point and field value that speci-fy to what extent this combination contributes to the activ-ity of a compound. For new compounds, activity data canthen be predicted based on the new compounds’ interac-tion fields and the weights.

Additionally, the derived CoMFA model can be interpret-ed in that so-called Stdev*Coeff fields show where a favora-ble or disfavorable contribution to the activity is to be ex-pected in the presence of sterically demanding or polarsubstituents. This information can be exploited to designnovel ligands in the process of lead optimization. Especiallywhen considered in the binding region of a crystal struc-ture or a homology model, the Stdev*Coeff fields can be in-terpreted in view of the interactions between the targetstructure and the ligands, which simplifies the interpreta-tion of the fields and, hence, the optimization of lead struc-tures.

Abstract : Since the pioneering effort of Hansch and Fujita,quantitative structure-activity relationships (QSAR) haveproved valuable in optimizing lead structures. Enrichingclassical 3D-QSAR analysis, which exploits the three-dimen-sional structure of ligands, with structural information ofthe target has helped to improve the interpretability of thederived models and to increase their predictive power. One

such method is the Adaption of Fields for Molecular Com-parison (AFMoC) approach where protein-specifically adapt-ed knowledge-based pair-potentials are tailored to one par-ticular protein by considering additional structural and en-ergetic information about ligands. Here, we summarize ap-plications of AFMoC, describe recent developments, andprovide an outlook on how to improve the method.

Keywords: Molecular bioinformatics · Structure�activity relationship · Lead optimization · Scoring function · Protein flexibility

[a] C. G. W. Gertzen, H. GohlkeInstitut f�r Pharmazeutische und Medizinische Chemie, Heinrich-Heine-Universit�t D�sseldorf, Universit�tsstr. 1, 40225 D�sseldorffax: + 49-211-8113847*e-mail : Gohlke@hhu.de

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From Hansch-Fujita Analysis to AFMoC: A Road to Structure-Based QSAR

One should note, however, that as the protein environ-ment is not considered during calculation of the fields, theCoMFA analysis examines interactions to all parts of the li-gands, even if the parts are solvent-exposed and so shouldnot contribute to activity. Furthermore, as a drawback ofthe generic (steric, electrostatic) interaction fields used,only suggestions such as “place a more bulky group withmore negative electrostatic potential in this binding pocketsite” can be made, which may be difficult to translate into

actual chemical modifications.[11] To some extent, the latterdisadvantage is reduced in the 3D-QSAR approach Compa-rative Molecular Similarity Index Analysis (CoMSIA).[12] Here,ligands are compared in terms of relative similarities intheir steric, electrostatic, hydrophobic, and H�bond donor/acceptor properties, which provides more detailed informa-tion for interpretation of the QSAR model.

2.2 AFMoC: Protein-Based Tailoring of Knowledge-BasedPotentials

Both of the above disadvantages are overcome in theAFMoC approach,[11] a “reverse” protein-based CoMFAmethod, where protein-specifically adapted knowledge-based pair-potentials are tailored to one particular proteinby considering additional structural and energetic informa-tion about ligands. For this, a regular-spaced grid is placedinto the binding site of a target, and pair-potentials be-tween protein atoms and ligand atom probes are mappedonto the grid intersections resulting in “potential fields”(Figure 1). By multiplying distance-dependent atom-typeproperties of actual ligands docked into the binding sitewith the neighboring grid values, “interaction fields” areproduced from the original “potential fields”. In a PLS analy-sis, these atom-type specific interaction fields are correlatedto the actual binding affinities of the embedded ligands, re-sulting in individual weights for each field value. As inCoMFA, the results of the analysis can be interpreted ingraphical terms by Stdev*Coeff maps, and binding affinitiesof novel ligands are predicted by applying the derived 3D-QSAR equation. As only protein-ligand interactions up toa distance of 6 � are mapped onto neighboring gridpoints, parts of the ligands that are solvent exposed willnot be taken into account in the model derivation, in con-trast to CoMFA and CoMSIA.

Christoph G. W. Gertzen studied phar-macy at the Heinrich-Heine-University,D�sseldorf, and received his diplomafrom Christian-Albrechts-University,Kiel. He is now a PhD student at theInstitute for Pharmaceutical and Me-dicinal Chemistry in D�sseldorf andworks on structure-based liganddesign for GPCRs.

Holger Gohlke is Professor of Pharma-ceutical and Medicinal Chemistry atthe Heinrich-Heine-University, D�ssel-dorf. His research aims at understand-ing and predicting receptor-ligand in-teractions and the modulation of bio-logical processes by pharmacologicallyrelevant molecules. His group devel-ops and applies methods at the inter-face of computational pharmaceuticaland biophysical chemistry and molecu-lar bioinformatics.

Figure 1. Schematic illustration of the generation of interaction fields. By multiplying “potential field” values for ligand atom type “hydroxyloxygen” (left) with values of a Gaussian function centered at the position of a ligand atom (center), pair interactions between a ligandatom and the protein are mapped onto the neighboring grid intersections (right). Figure taken with permission from J. Med. Chem.[11]

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Methods Corner C. G. W. Gertzen, H. Gohlke

AFMoC requires the ligands to be structurally aligned,yet not only with respect to a bioactive conformation butalso inside a binding pocket. The structural alignment ofthe ligands can be achieved by the same means as in theCoMFA analysis. In the case of the AFMoC analysis, eachligand must be energy minimized in the presence of thetarget structure to avoid a compound clashing with thetarget, which would have a strong influence on the analy-sis.

For incorporating the information about the structuralenvironment of the ligands, DrugScore pair-potentials[13]

have been applied so far for calculating the potential fields.These potentials have proven valuable as scoring[13] anddocking functions.[14] They have been derived by convertingstructural database information of experimentally deter-mined protein-ligand complexes, which implicitly includesentropy-driven effects arising from (de-)solvation.[15] Thismay explain as to why convincing results were obtained inAFMoC analyses even if (structural) water molecules werenot included. Furthermore, although these potentials ex-plicitly depend on the distance between two atoms, theyimplicitly contain information about directional features ofan interaction, e.g. the angular dependence of the strengthof a hydrogen bond. This arises from the superimpositionof multiple potentials at one point in space.[16] Finally, asthe pair-potentials are atomtype-specific, so are the result-ing interaction fields. This enables one to propose structur-al modifications during lead optimization in terms of favor-able ligand atom types, in contrast to generic properties asin CoMFA or CoMSIA. We note that by now several variantsof the DrugScore potentials have been derived from struc-tural information on RNA-ligand complexes (DrugScor-eRNA),[17] protein-protein complexes (DrugScorePPI),[18] andnonbonded interactions in small organic molecule crystalpackings (DrugScoreCSD).[19] Each of these potentials can beused in connection with AFMoC depending on the applica-tion area, as could be any other distance-dependent pair-potential such as the Astex Scoring Potential (ASP).[20] Theuse of knowledge-based atom type-specific pair-potentialsdistinguishes AFMoC from a related approach, COMBINE.[21]

Here, first, a ligand-macromolecule interaction energy iscomputed for a set of ligands using molecular mechanicscalculations. Then, by selecting and scaling components ofthe ligand-macromolecule interaction energy that show

good predictive ability, a regression equation is obtained inwhich activity is correlated with the interaction energies ofparts of the ligands and key regions of the macromolecule.Consequentially, COMBINE highlights general interactiontypes that are (dis-)favorable for ligand binding betweenligand parts and subregions of the macromolecule; in con-trast, AFMoC emphasizes atom type-specific contributionsat the location of ligand atoms, clearly denoting regionswhere it is either more favorable or disfavorable to placeligand atoms of a given type with respect to binding affini-ty. We believe that this atom type-specific information iseasier to interpret in the light of ligand design than infor-mation showing generally (dis-)favorable interactions be-tween a ligand and a target structure.[11] These differencesare summarized in Table 1.

So far 3D-QSAR models have been derived by AFMoCanalyses for ligands of the DOXP-reductoisomerase,[22] thecarbonic anhydrase isoenzymes,[23] and factor Xa.[24] In thefirst case, a predictive AFMoC model was obtained despitea small set of ligands and a heterogeneous set of crystalstructures to work with: The crystal structures either haddifferent loop conformations or missing metal ions or co-substrates resulting in different orientations of co-crystal-lized antagonists. Still, fusing parts of the structures to forma complete enzyme representing a near-native state yield-ed the structural information necessary to conduct theAFMoC analysis. Compared to CoMFA and CoMSIA studieson this set of ligands the AFMoC model showed superiorpredictive power.[22] In particular, AFMoC’s ability to gradu-ally transform between generally applicable unadapted in-teraction fields to case-specifically adapted ones proved tobe of major importance. In line with the small training set,using 50 % tailored fields was found to permit the accurateprediction of binding affinities for related ligands withoutlosing the capability to estimate the affinities of structurallydistinct inhibitors.[22]

In the study on carbonic anhydrase, the task was to iden-tify ligand features that determine isoenzyme selectivity of140 ligands. For this, classical 3D-QSAR techniques (CoMFA,CoMSIA), protein-based consensus principal componentanalysis (CPCA), and AFMoC was applied. Encouragingly,the AFMoC approach showed regions for enhancing ligandselectivity that purely ligand-based methods were unableto detect; this was attributed to the fact that AFMoC, in ad-

Table 1. Comparison of QSAR approaches.

Approach 2D/3D Target structure Parameters Interpretation [a]

Hansch-Fujitaanalysis

2D Not considered Lipophilicity, electronic and steric properties Increase lipophilicity

CoMFA 3D Not considered Coulomb and van der Waals interactions Add a bulky, electropositive group at specificposition

COMBINE 3D Considered Bonded & non-bonded force-field energies Increase van der Waals interaction energyinteractions at specific position

AFMoC 3D Considered Atom-type specific pair interactions Add amine group at specific position

[a] Example for an interpretation of the results leading to an improved binding affinity of a ligand.

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From Hansch-Fujita Analysis to AFMoC: A Road to Structure-Based QSAR

dition to ligand information, also exploits information onstructural differences between the isoenzymes.[23]

In the case of factor Xa, a combination of ligand- andstructure-based methods including AFMoC was used forguiding ligand design. While both the ligand- and struc-ture-based methods were used to identify effects that playa dominant role in ligand-receptor interactions, the predic-tive power of only the latter ones was exploited to identifynew synthesis candidates with improved affinities towardsfactor Xa. As a side goal, the potency towards thrombinwas to remain unchanged.[24]

2.3 Recent Developments of AFMoC

Recently, the standard AFMoC approach has been extendedto take into account dynamical behavior and/or structuralinaccuracies of receptor-ligand systems. This resulted in theconsensus AFMoC (AFMoCcon) approach that considers mul-tiple ligand conformations in an ensemble of protein con-formations.[25] The ensemble can either be generated bymolecular dynamics simulations or result from multiple X-ray structures or homology models of the target. This allevi-

ates the need to decide a priori which target structure totake for deriving an AFMoC model. Rather, as shown fora data set of 79 thrombin inhibitors and three structurallydiverse protein models, the AFMoCcon approach led toa QSAR model the internal and external predictivity ofwhich was comparable to the best model derived froma standard AFMoC run.[25] As to the regression technique,AFMoCcon applies partial least-squares regression consider-ing multimode binding (MMB)[26] and a variable influenceon the model(VINFM)-based region selection[27] to an ex-tended descriptor matrix (Figure 2). After an initial PLS anal-ysis considering MMB and a VINFM-based variable selec-tion, a consensus descriptor matrix is generated and sub-jected to another PLS analysis considering MMB. Note thatthere is no principal limitation regarding the number oftarget structure-ligand alignments (TSLA) in this procedure.Furthermore, the approach allows determining the influ-ence of a single TSLA on the overall AFMoCcon model, andthe AFMoCcon model can be interpreted in terms of contourplots that aid in proposing variations of the ligand struc-ture to improve binding.

Figure 2. Variation influence on the model (VINFM)-based variable selection for the generation of a consensus descriptor matrix fromwhich an AFMoCcon model is derived. Figure taken with permission from J. Med. Chem.[19]

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Methods Corner C. G. W. Gertzen, H. Gohlke

A second line of development was followed to allow forthe use of protein-specifically adapted DrugScore potentialfields in docking. This resulted in AFMoCobj,[28] which implic-itly takes into account effects due to protein flexibility andinformation about multiple solvation schemes within a bind-ing pocket. Compared to the application of AFMoC forbinding affinity predictions, a Shannon entropy basedcolumn filtering of the descriptor matrix and the cappingof adapted repulsive potentials within the binding siteturned out to be crucial for the success of this method.When applied to a dataset of 66 HIV-1 protease inhibitors,a significant improvement in the accuracy of binding modeprediction was found.[28] In addition, a significantly higherpredictive power of binding affinities for the AFMoCobj func-tion was observed in this case, compared to if unmodifiedDrugScore potentials were used. Overall, AFMoCobj shouldbe a valuable tool for similarity-driven correct bindingmode identification, which is a prerequisite for accuratebinding affinity prediction and successful virtual screening.

3 Outlook

Although the AFMoC approach has proven successful inseveral validation and application studies, further develop-ments can be envisaged. In particular, considering proteinmobility could be improved. So far, AFMoCcon uses multipleTSLA, which models protein mobility in terms of discretetarget conformations to which ligand conformations areadapted. However, the approach does not allow using indi-vidually adapted protein-ligand complexes, i.e. , thosewhere both the protein and ligand conformations havebeen mutually fit to another. A potential way to overcomethis drawback is to use irregular, deformable 3D potentialfields instead of the regular, static ones currently being ap-plied in CoMFA, CoMSIA, or AFMoC. The underlying idea isto adapt a 3D grid with pre-calculated potential fieldvalues, which were derived from an initial protein confor-mation, to another conformation by moving intersectionpoints in space, but keeping the potential field values con-stant. As before, interaction fields could then be generatedas described above (Figure 1). A representation of an irreg-ular, deformable 3D potential grid has been introduced byus recently in terms of modeling the grid as a homogene-ous linear elastic body that deforms according to displace-ments of the surrounding protein atoms.[29] Such a grid rep-resentation has been successfully applied for protein- andRNA-ligand docking already.[29–30]

Thinking in the opposite direction, information aboutprotein-ligand interactions that come out from an AFMoCanalysis could also be used to improve the quality of ho-mology models of targets. So far, the Modeling BindingSites using Ligand Information Explicitly (MOBILE) ap-proach[31] already uses such information from an alignmentof ligands in a model binding site as restraints in the nextcycle of homology modeling. That is, structural information

about ligands together with generic DrugScore potentialsare applied to adapt the binding pocket region. However,energetic information in terms of experimentally deter-mined binding affinities or activities of the ligands hasbeen neglected so far. This could be overcome by a self-consistent, iterative procedure that combines adaptation ofinteraction fields for an (initial) alignment of ligands in themodel binding site with a subsequent usage of such fieldsin the MOBILE approach.

Thus, even after almost 50 years of Hansch’ groundbreak-ing introduction of the concept of QSAR,[2] and after almost20 years of Hansch thinking to relate polarization effects ofan enzyme binding pocket to the rate of ester hydrolysis[32]

and, hence, to consider the effect of a binding pocket forQSPR, the roads that originate from there are still directedtowards exciting new horizons.

Acknowledgements

This study was supported by the Deutsche Forschungsge-meinschaft (DFG) through the Collaborative Research CenterSFB 974 (“Communication and Systems Relevance duringLiver Damage and Regeneration”, D�sseldorf).

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Received: February 9, 2012Accepted: July 10, 2012

Published online: August 7, 2012

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Methods Corner C. G. W. Gertzen, H. Gohlke