Knowledge-based Scoring Function to Predict Protein-Ligand ...€¦ · LUDI (Bohm, 1992) and FlexX...

Article No. jmbi.1999.3371 available online at http://www.idealibrary.com on J. Mol. Biol. (2000) 295, 337±356

Knowledge-based Scoring Function to PredictProtein-Ligand Interactions

Holger Gohlke, Manfred Hendlich and Gerhard Klebe*

Department of PharmaceuticalChemistry, Philipps-Universityof Marburg, Marbacher Weg 6D-35032 Marburg, Germany

E-mail address of the [email protected]

Abbreviations used: SAS, solventFEP, free energy perturbation; TI, thintegration; rmsd, root-mean-square

0022-2836/00/020337±20 $35.00/0

The development and validation of a new knowledge-based scoring func-tion (DrugScore) to describe the binding geometry of ligands in proteinsis presented. It discriminates ef®ciently between well-docked ligand bind-ing modes (root-mean-square deviation <2.0 AÊ with respect to a crystallo-graphically determined reference complex) and those largely deviatingfrom the native structure, e.g. generated by computer docking programs.Structural information is extracted from crystallographically determinedprotein-ligand complexes using ReLiBase and converted into distance-dependent pair-preferences and solvent-accessible surface (SAS) depen-dent singlet preferences for protein and ligand atoms. De®nition of anappropriate reference state and accounting for inaccuracies inherentlypresent in experimental data is required to achieve good predictivepower. The sum of the pair preferences and the singlet preferences is cal-culated based on the 3D structure of protein-ligand binding modes gener-ated by docking tools. For two test sets of 91 and 68 protein-ligandcomplexes, taken from the Protein Data Bank (PDB), the calculated scorerecognizes poses generated by FlexX deviating <2 AÊ from the crystalstructure on rank 1 in three quarters of all possible cases. Compared toFlexX, this is a substantial improvement. For ligand geometries generatedby DOCK, DrugScore is superior to the ``chemical scoring'' implementedinto this tool, while comparable results are obtained using the ``energyscoring'' in DOCK. None of the presently known scoring functionsachieves comparable power to extract binding modes in agreement withexperiment. It is fast to compute, regards implicitly solvation and entropycontributions and produces correctly the geometry of directional inter-actions. Small deviations in the 3D structure are tolerated and, since onlycontacts to non-hydrogen atoms are regarded, it is independent fromassumptions of protonation states.

# 2000 Academic Press

Keywords: scoring function; knowledge-based; protein-ligand interactions;docking; virtual screening
*Corresponding author
Introduction

The process of ®nding novel leads for a new tar-get is the most important and undoubtedly one ofthe most crucial steps in a drug development pro-gram. Today two complementary strategies are fol-lowed: experimental high-throughput screening todiscover possible leads from large compoundlibraries, and computational methods exploitingstructural information of the protein binding site

ing author:

-accessible surface;ermodynamicdeviation.

aiming at the construction of a ligand de novo ortheir discovery by virtual screening of large data-bases (Kubinyi, 1998; Muller, 1995; Van Drie &Lajiness, 1998; Walters et al., 1998). The latterapproaches try to predict, e.g. via docking, theactual binding mode of a ligand at the binding site(Kuntz et al., 1994; Lengauer & Rarey, 1996). Theycan only be applied in the present context if theyare (1) fast enough to scan over several hundred tothousand compounds, (2) if they suggest reliablegeometries in agreement with experimental knowl-edge, (3) if the generated multiple solutions (poses)are ranked correctly, i.e. those most closely resem-bling the experimental structures are scored best,and (4), as an extension, if the Gibbs free energy ofbinding is predicted reliably. Usually the perform-

# 2000 Academic Press

338 Prediction of Protein-Ligand Interactions

ance of such methods is determined by assessingwhether the binding geometry of protein-ligandcomplexes resolved by X-ray crystallography orNMR is reproduced{. This latter validation cri-terion imposes some preconditions onto themethods being developed. Due to the limited resol-ution of the structure determination techniquesapplied, no precise data on protonation states ofligand functional groups and the binding site resi-dues are given. The development of methods incomputer-aided drug design has to cope withthese inherent inaccuracies and shortcomings.

Meanwhile several of the published docking pro-cedures are fast enough to serve the outlined pur-pose (Jones et al., 1997; Kuntz et al., 1982; Rareyet al., 1996). The recently performed CASP2 compe-tition (Dixon, 1997) revealed that among the mul-tiple solutions generated by different approaches,in nearly all cases several solutions were foundapproximating the native pose. Though found inmost cases, the pose being most close to the exper-imentally given situation is often not ranked as theenergetically most favorable one. This indicatesthat a near-native geometry cannot be recognizedwithin a set of poses largely deviating from thecrystal structure. Since this step is of utmostimportance for the relevance of any computer-assisted lead ®nding process, we embarked intothe development of a new scoring function. Thepurpose of the work presented here is to correctlyidentify those computer-generated poses whichmost closely resemble the native structure, sincethis is the crucial step prior to any estimation ofthe binding energy.

Usually binding af®nity is quanti®ed by thebinding constant Ki assuming thermodynamicequilibrium conditions for the protein-ligand com-plex formation. Gibbs free energy of binding �G0

is then related to the binding constant by:

�G0 � ÿRT ln Ki �1�At best, �G0 is determined by statistical thermo-dynamics resulting in a master equation that con-siders all contributing effects (Beveridge &DiCapua, 1989; Kollman, 1993). Although beingtheoretically the most convincing approach, elabor-ate methods such as free energy perturbation (FEP)or thermodynamic integration (TI) are computa-tionally too demanding for the applicationdescribed above. Even so an explicit treatment ofthe solvent environment is included, the resultsobtained by FEP or TI can still suffer from insuf®-cient sampling over contributing conformationalstates of the system or inaccuracies in the force-®eld used (Kollman, 1996). Various levels ofapproximations have been considered, particularlythe treatment of electrostatics, e.g. of the solvent,by continuum methods or the estimation of con®g-

{ In the following the binding geometry found in theexperimentally determined structure will be callednative pose.

urational entropy (Honig & Nicholls, 1995;Warshel & Aqvist, 1991). Generally, with increas-ing level of approximation, the methods try to par-tition binding af®nity into several additive terms(Dill, 1997).

The partitioning into individual terms ordescriptors is a widely accepted assumption for thedevelopment of empirical regression-based scoringfunctions. Usually a number of empirically derivedcontributions is ®tted to a data set of experimentalobservations (Bohm, 1994, 1998; Jain, 1996; Murrayet al., 1998; Rose, 1997). In some of theseapproaches, e.g. SCORE by (Bohm, 1994), the con-sidered terms are selected following physical con-cepts and aimed at a fundamental understandingof the binding process. Approaches such as VALI-DATE (Head et al., 1996) are based on the ideas ofQSAR and use ef®ciently the information derivedfrom protein-ligand complexes by combining aheuristic correlation analysis with various molecu-lar 3D descriptors. These approaches achieve a pre-cision of about 1 to 1.5 orders of magnitude whenpredicting Ki (Bohm, 1994; Head et al., 1996). How-ever, any regression analysis suffers severely fromthe fact that the obtained conclusions can only beas precise and generally valid as the data used cov-ers all contributing and discriminating effects inprotein-ligand complexes.

The concept introduced by SCORE has beenimplemented into the commonly used design toolsLUDI (Bohm, 1992) and FlexX (Rarey et al., 1996).A detailed analysis of binding modes generated byFlexX for a test set of 200 examples suggests that inabout 80 % of the cases a binding geometry closeto the native pose is generated among the multiplesolutions. Yet, in half of the cases, it is ranked lessfavorable than other obviously arti®cial solutions(B. Kramer, M. Rarey & T. Lengauer, unpublishedresults). Quite similar ®ndings have been reportedfor the two popular docking tools DOCK andGOLD. As a ®rst consequence, Stahl & Bohm(1998) developed several penalty ®lters to success-fully discard computer-generated artifacts from thelist of favorable ligand poses. However, such post-processing ®lters will only be as complete as thedata set that is used for their development containsall possibly in¯uencing effects.

We decided to follow an alternative way todevelop a scoring function based on empiricalknowledge. Following the ideas of a so-called``inverse Boltzmann'' distribution (vide infra), it isassumed that only those binding modes are favor-able that ®t to the maxima of distributions ofoccurrence frequencies among interatomic contactsbetween particular atom pairs in experimentallydetermined structures. A scoring function based onthis concept is supposed to rank best all ligandposes that are geometrically very similar to thenative pose. During its development we decidednot to assign proper protonation states to the con-sidered atom types, assuming that the derived stat-istical preferences implicitly re¯ect these in¯uencesalong with any favorable long-range interaction

Prediction of Protein-Ligand Interactions 339

patterns between functional groups. Any bindingfeature not in agreement with the most frequentlyobserved contact preferences will likely be pena-lized due to its minor occurrence.

Knowledge-based potentials have been appliedsuccessfully to rank different solutions of the pro-tein-folding problem (Jernigan & Bahar, 1996;Torda, 1997; Vajda et al., 1997). Up to now, thisapproach has only been applied to four case stu-dies for the ranking of different protein-ligandcomplexes. None of these, however, engaged inidentifying near-native poses of one ligand withrespect to one protein. Wallqvist and co-workers(Wallqvist & Covell, 1996; Wallqvist et al., 1995)classi®ed the surfaces of buried ligand atomsfound in 38 complexes and developed a model topredict the Gibbs free energy of binding based onthese observed atom-atom preferences. Analyzingten HIV protease inhibitor complexes, theyapproximated the free energy of binding to anaccuracy of �1.5 kcal/mol.

Using a data set of 30 HIV-1, HIV-2, and SIVproteases, Verkhivker et al. (1995) compiled a dis-tance-dependent knowledge-based pair-potentialwhich was then combined with the hydrophobicity(Sharp et al., 1991) and conformational entropyscales (Pickett & Sternberg, 1993) that originallyhad been developed to explain protein folding andstability. Applied to different HIV-1 protease com-plexes, differences in the binding af®nity could beestimated.

DeWitte & Shaknovich (1996) used a sample of126 structures from the PDB (Bernstein et al., 1977)to develop a set of ``interatomic interaction freeenergies'' for a variety of atom types. In combi-nation with a Metropolis Monte Carlo moleculargrowth algorithm, ligands were gradually con-structed in the binding site and energeticallyscored.

Muegge & Martin (1999) explored structuralinformation of known protein-ligand complexesfrom the PDB and derived distance-dependentHelmholtz free interaction energies of protein-ligand atom pairs. Tested on 77 protein-ligandcomplexes, the calculated score displayed a stan-dard deviation from the observed binding af®nitiesof 1.8 log Ki units. The scoring function was furtherevaluated by docking weak-binding ligands to theFK506-binding protein (Muegge et al., 1999).

Here, we describe in detail the development of anew scoring function tailored to discriminate mul-tiple ligand poses. It is based on the vast structuralknowledge stored in the entire PDB and retrievedusing ReLiBase (Hendlich, 1998). Knowledge-basedprobabilities, well adjusted to describe speci®cshort-range distances between ligand and proteinfunctional groups are combined with terms consid-ering solvent-accessible surface portions of bothpartners that become buried upon binding. For the®rst time, knowledge-based probabilities are usedto discriminate and predict ligand-binding modes.The new function has been applied to data sets of91 and 68 complexes of known crystal structure.

Multiple solutions, generated for these examplesby FlexX, have been re-ranked to obtain a signi®-cantly improved scoring with respect to their devi-ation from the native pose. To test the performanceof our new DrugScore approach in the context ofother docking programs, a subset of 100 protein-ligand complexes was extracted from both datasets and used to generate ligand geometries withDOCK (Ewing & Kuntz, 1997; Makino & Kuntz,1997). Both, the ``energy'' and ``chemical scoring''together with our scoring function were applied torank the resulting binding modes.

Theory

In the following, we shortly summarize thetheoretical background of the selected approach.

The non-covalent binding of ligand Laq. to pro-tein Raq. to form a complex RLaq. typically occursin aqueous environment. The transfer from thesolute state with complete separation of both reac-tants to the complexed state involves either enthal-pic and entropic effects (Bohm & Klebe, 1996) thatcontribute to the Gibbs free energy of binding. Inturn, it is related to the complex formationequilibrium:

�G0 � �H0 ÿ T�S0 � ÿRT ln Ki �2�Accordingly, for an appropriate description of thebinding properties of a RLaq. complex, the con-sideration of effects resulting from the deliberationof solvent molecules from the binding site or thereorganization of the surrounding solvent must betaken into account (Blokzijl & Engberts, 1993). Atreatment only in terms of enthalpic contributionswill be insuf®cient and must, in general, lead tofalse predictions (Bohm & Klebe, 1996).

At ®rst sight, it seems hardly possible to modelentropic effects by solely considering atom pair,triplet, or higher-order interactions. Nevertheless,an implicit description of the complex solute-sol-vent interactions and solvent entropic effects alongwith the involved enthalpic contributions resultingfrom interatomic forces (e.g. electrostatic or vander Waals) is re¯ected by the formalism used toderive potentials of mean force from databaseknowledge (Sippl, 1995; Jernigan & Bahar, 1996).

As recently pointed out by Koppensteiner &Sippl (1998), there is a dissatisfying confusion inliterature using terms such as ``potential of meanforce'' and ``knowledge-based potentials'' whenrelating database-derived quantities to the Boltz-mann equation. The term ``potential of meanforce'' has its physically sound basis in the theoryof liquids derived from statistical mechanics (Ben-Naim, 1987). There, a n-particle correlation func-tion g�n��~r1; . . . ; ~rn� can be translated into a potentialof mean force via:

W�n��~r1; . . . ; ~rn� � ÿRT ln g�n��~r1; . . . ; ~rn�: �3�Taking a two-body case with spherical symmetry,


the correlation function g�2��~r1; ~r2� corresponds tothe radial pair distribution function g(2)(r12), withr12 equal to j~r1 ÿ ~r2j. In principle, the latter functioncan be derived straight-forwardly from crystal databy simply sampling the frequencies of both atomsin a distance interval between r12 and r12 � dr.Although not obvious for physical reasons, theBoltzmann law has been applied successfully totranslate such a quantity into a potential of meanforce (Burgi & Dunitz, 1988).

Strictly speaking, the Boltzmann law is onlyapplicable to an ensemble of equal particles beingin thermodynamic equilibrium. In contrast, a data-base of protein structures consists of many differ-ent particles not necessarily residing in the sameglobal energy minimum. In addition, it is notknown if each member of this heterogeneous setresides in its own global energy minimum. Fur-thermore, it is by no means trivial to assign a ®xedabsolute temperature to a sample retrieved from adatabase of crystal structures (Finkelstein et al.,1995).

In contrast to the folding problem, in the presentstudy, we do not evaluate the properties of pro-teins in total but we are interested in the propertiesof a ``fragment-of-interest'' (e.g. an atom-atom paircontact) embedded into the molecular environmentof various protein structures. Any statistical evalu-ation is focussed on this ``fragment-of-interest''. Itis assumed that this fragment is exposed in a stat-istically representative way to all relevant states.

The physical ground appears even less solid if,instead of energies or potentials, the logarithm ofoccurrence frequencies is enumerated (Godzik,1996):

quantity � ÿ lngobserved

gexpected�4�

Despite these assumptions and short-comings, westill believe our heuristic knowledge-basedapproach is appropriate for the problem to besolved. We note that the ``quantity'' above shouldbe termed a ``knowledge-based quantity'' or a``statistical preference'' (Koppensteiner & Sippl,1998) instead of a ``potential'', and we want theexpression ``potential'' to be understood in thissense in the following. As with any empiricalapproach, the selected evaluation procedure canonly be justi®ed by the results obtained and itspredictive power to reproduce or estimate exper-imental data.

Distance-dependent pair-potentials

In the context of protein-fold predictions it hasbeen shown that coarse-grained (i.e. low resol-ution) energy models (Bowie et al., 1991; Hendlichet al., 1990; Jones et al., 1992; Kocher et al., 1994;Miyazawa & Jernigan, 1996) can effectively dis-criminate experimentally observed (i.e. crystalstructures) and near-native folds from decoy con-formations. In addition, the incorporation of arti®-

cial distance-dependencies into Miyazawa-Jernigancontact potentials (Park & Levitt, 1996) as well asthe use of smaller interaction radii for the develop-ment of such potentials (Bahar & Jernigan, 1997),corresponding to increased resolution, unravelsmore details contained within the data.

To correctly distinguish (near) native ligandposes from computer-generated artifacts, e.g.obtained by docking, an approach on an atomiclevel is followed by compiling distance-dependentpair-potentials between ligand and protein atomsof type i and j. In our approach, we have followedthe formalism developed by Sippl (1990, 1993):

�Wi;j�r� �Wi;j�r� ÿW�r� � ÿ lngi;j�r�g�r� �5�

g�r� �P

i

Pj gi;j�r�

i�j�6�

where gi,j(r) is the normalized radial pair distri-bution function for atoms of types i and j, separ-ated by a distance in the interval of r and r � dr;g(r) is the normalized mean radial pair distributionfunction for a distance between any two atoms inthe range of r and r � dr. It corresponds to thereference state and incorporates all non-speci®cinformation common to all atom pairs present inan environment typical for proteins. Takentogether, the net statistical preferences �Wi,j areobtained by comparing the mean statistical prefer-ences of the subsystems i, j (Wi,j) to the referencesystem (W).

In addition, both radial distribution functionsare normalized with respect to the volume 4pr2drof the spherical shell associated with the intera-tomic distance r to achieve a faster convergencetoward zero at large distances (Bahar & Jernigan,1997).

The ®xing of an upper radius limit rmax for inter-actions between atoms i and j (Godzik et al., 1995)determines the overall shape of the resulting poten-tials. Sampling over short distances up to this limitwill emphasize the speci®c interactions formed bya ligand functional group to the neighboring bind-ing-site residues. An extension of this samplingregion to much larger distances incorporates thein¯uences of an averaged solvent contribution thatis mainly entropy driven (DeWitte & Shaknovich,1996). Recently, Muegge & Martin (1999) devel-oped potentials for large distances of up to 12 AÊ .Since we want to focus on the geometrical dis-crimination of various ligand binding modes, werestrict our sampling to 6 AÊ , thereby guaranteeingthat highly speci®c interactions will dominate. Therationale for this limit arises from the fact that a6 AÊ contact is short enough not to involve a watermolecule as mutual mediator of a ligand-to-proteininteraction.

To avoid the sampling over large distances, analternative approach to incorporate solvent effectsis required. As discussed in the context of protein-


fold prediction, solvent effects can be consideredby two-body potentials to a different extent(Godzik et al., 1995; Skolnick et al., 1997). As wasnoted ®rst by Sippl (1993) and later by Miyazawa& Jernigan (1999), solvent-mediated effects areunderestimated when solely applying pair poten-tials. Nevertheless, the recent study of Muegge &Martin has obviously demonstrated the oppositeby ®nding correlations between the sum of atompair potentials and binding free energies of pro-tein-ligand complexes. The authors explain thisbehavior by the consideration of a large cutoff fortheir atom pair interactions. It thus converts thedegree of ligand penetration into the protein in animplicit recognition of solvation effects.

Non-polar surface-dependent singlet-potential

A combination of the short-distances samplingtogether with the ®ndings from protein-fold pre-diction motivated us to derive a knowledge-basedone-body potential scaled to the size of the sol-vent-accessible surface (SAS) of the protein and theligand that becomes buried upon complexformation:

�Wi�SAS; SAS0� � Wi�SAS� ÿWi�SAS0�

� ÿ lngi�SAS�gi�SAS0� �7�

In this equation, gi is the normalized distributionfunction of the surface area of an atom i in the bur-ied state (SAS) (considering ligand and proteinindividually) in comparison to the solvated state(SAS0). It is calculated by an approximate cube-algorithm (see Methods). In this assumption anypolar portion of the SAS that becomes buried inthe complex in a polar environment is consideredto remain ``solvent-accessible'' (Koehl & Delarue,1994). The latter strategy is based on the rationalethat changes in the Gibbs free energy can only beexpected if polar molecular portions are transferredfrom a polar solvent to a non-polar proteinenvironment. In contrast, polar portions carriedover from the polar solvent to a polar binding siteenvironment can be neglected.

In contrast to the atom pair potential mentionedabove (equation (6)), gi(SAS0) is not an averageddistribution function over all atom types but refersto the atom of type i only. Thus, �Wi re¯ects thecontribution arising from differences in the sol-vent-accessible surface between the protein-boundand fully solvated state.

As a ®rst approximation, the ligand confor-mations as found by X-ray crystallography ordocking procedures are assumed to be identical tothose adopted in the solvent. In this rough model,conformational changes, e.g. due to a ``hydro-phobic collapse'' of the ligand (Testa et al., 1996),are not considered.

Calculation of the total score to rankligand poses

Individual atom-pair potentials sampled for pro-tein-ligand complexes are intercorrelated anddepend on speci®c features arising from the directmolecular environment embedding a particularcontact. However, in our approach we assume thata reasonable description of the total preference �Wfor a particular binding geometry can be approxi-mated by summing all individual contributions(i.e. of ki ligand atoms of type i and lj proteinatoms of type j):

�W � gX

ki

Xlj

�Wi;j�r� � �1ÿ g�

��X

ki

�Wi�SAS; SAS0�

�X

lj

�Wj�SAS; SAS0��

�8�

g is an adjustable parameter, optimized empiricallyto be 0.5.

The scorings thus obtained will only be com-pared among different poses of the same ligand inone given protein. Additional contributions to thebinding energy such as conformational, rotational,and translational entropy are not required, sincethey cancel out in a relative comparison of differ-ent poses. In accordance to our goal to rank mul-tiple binding modes suggested by a docking run,this relative estimate is therefore satisfactory. Inter-estingly enough Muegge & Martin (1999) showedin their approach that a pure consideration ofknowledge-based potentials is suf®cient to deriveabsolute binding constants. This suggests that theabove-mentioned entropy-related ordering par-ameters are implicitly accounted for in thisapproach, or (unlikely) that they hardly matter inthe ligand-binding process.

Our approach does not incorporate any energycontribution arising from intramolecular inter-actions (van der Waals and torsion potentials).Since popular docking tools such as FlexX, DOCK,and GOLD generate only favorable ligand confor-mations, we believe that these terms can only be ofminor importance in comparison to the solute statecontributions. This assumption is supported by arecent study by Bostrom et al. (1998). The authorsdemonstrate that energies resulting from confor-mational transitions between a bound andunbound state usually amount to less than 3 kcal/mol. Contributions resulting from the inherent¯exibility of the protein are supposed to have neg-ligible impact on the calculated scoring, in particu-lar since the protein is assumed rigid duringdocking runs.


Methods

Protein-ligand complexes for derivationof potentials

Both, short-range pair and SAS-potentials arederived using for data extraction the ReLiBase sys-tem (Hendlich, 1998), which contains 6026 PDBprotein structures holding all ligands with bondand atom-types notation according to the SYBYLtype convention.

For our purpose, we evaluated crystallographi-cally determined complexes only with resolutionbetter than 2.5 AÊ . Complexes with covalentlybound ligands or ligands with less than six ormore than 50 non-hydrogen atoms were excluded.The latter restriction is used to regard ligands onlywith a size of typical drug molecules. Due to the®rst pass effect in the liver, a rather strict upperlimit of about 600 Daltons can be applied for atypical organic molecule. Examples with frequentlyoccurring prosthetic groups such as haemoglobin,¯avin-adenine-dinucleotide or nicotinamide-ade-nine-dinucleotide were not considered as explicitligands but as part of the protein.

Furthermore, we excluded all complexes thatwere subsequently used in the validation of thepredictive power of the potentials in order to avoidany redundancy or training effects due to over®t-ting. To check for further redundancy bias, wecompiled additional data sets by considering onlyproteins with a mutual sequence homology of lessthan 30 % compared to the protein used to test thepredictive capability of the approach. Though, thiswas not found to introduce a signi®cant changeeither in terms of the depths or the position of theminima. To account for the volume occupied bythe ligand, a correction term similar to the one pro-posed by Muegge & Martin (1999) was investi-gated. However, on ®nding that it did not effectthe overall shape of the potentials signi®cantly, itwas omitted in further calculations.

Potentials were derived for the following atomtypes: C.3 (carbon sp3), C.2 (carbon sp2), C.ar (car-bon in aromatic rings), C.cat (carbon in amidiniumand guanidinium groups), N.3 (nitrogen sp3), N.ar(nitrogen in aromatic rings), N.am (nitrogen inamid bonds), N.pl3 (nitrogen in amidiniumand guanidinium groups), O.3 (oxygen sp3),O.2 (oxygen sp2), O.co2 (oxygen in carboxylategroups), S.3 (sulfur sp3), P.3 (phosphorus sp3),F (¯uorine), Cl (chlorine), Br (bromine), Met (Ca,Zn, Ni, Fe).

Due to their low occurrence frequency or non-unique assignment criteria, the following atomtypes were grouped together: S.2 (sulfur sp2) andS.3, N.4 (positively charged nitrogen ) and N.3.

Compilation of distance-dependent pair-potentials

A normalized distance-dependent radial pairdistribution function for atom pairs with types i

and j is given by:

gi;j�r� �Ni;j�r�=4pr2Pr�Ni;j�r�=4pr2� �9�

Scaling to 4pr2 accounts for the volume of thespherical shell of the radius r and the thickness dr.

The number Ni,j(r) of atom pairs i,j at a distancebetween r and r � dr is obtained by counting theoccurrences:

Ni;j�r� �X

i

Xj

d�j~ri ÿ ~rjj; r� �10�

where the double summation runs over all atomtypes i and j present in the database, respectively.The delta function d equals 1, if r4j~ri ÿ ~rjj4r� dr,otherwise 0.

Using gi,j(r) (equation (9)), the mean radial pairdistribution function g(r) and the distance depen-dent pair-potentials Wi,j(r) and W(r) (equations (5)and (6)) and ®nally the net potential �Wi,j(r)(equation (8)) are computed (see Theory).

The size of the bins dr was chosen in a way thata suf®ciently high resolution is guaranteed and anadequate amount of data are sampled within eachbin. Thus, statistically signi®cant results can beobtained. A bin size dr of 0.1 AÊ was found toreveal satisfactory results.

The minimal distance boundary rmin was set to1 AÊ , especially since metal-to-oxygen/nitrogencontacts occur at short distances around 1.8 AÊ ; themaximal distance bound rmax was set to 6 AÊ . Anyspecial treatment of ``short contact distances'' (withno occurrences) to re¯ect repulsive terms are notrequired, since these will not be present in either acrystal structure or a computer-docked complex.Both techniques inherently avoid short atom-to-atom contacts due to the consideration of van derWaals repulsion terms.

To account for uncertainties inherently presentin experimental data (for a resolution of 2.5 AÊ ,inaccuracies of atom positions may be as large as0.4 AÊ (Kossiakoff et al., 1992)), a smoothing func-tion is applied to the distribution data. It effec-tively distributes a single hit over more than onebin according to a triangular weighting scheme.This scheme causes one hit to be assigned to allneighboring bins within a 0.2 AÊ distance from thecentral bin, with a weight linearly falling off fromone to zero within this range.

Compilation of solvent-accessiblesurface-dependent singlet-potentials

The solvent-accessible surface-dependent singlet-potentials are calculated separately for ligand andprotein atoms from the normalized distributionfunctions (equation (11)):

gi�SAS� � Ni�SAS�PSAS Ni�SAS� �11�


and:

gi�SAS0� � Ni�SAS0�PSAS0

Ni�SAS0� �12�

gi(SAS) is the probability to ®nd an atom of type iwith an exposed solvent-accessible surface SAS ina complexed state, while gi(SAS0) is the probabilityto ®nd the same atom with the same solvent-acces-sible surface in a state totally separated from thecomplex. The normalization (denominator)accounts for the total number of occurrences inboth cases.

The solvent-accessible surface is calculated by afast and approximate cube-algorithm adapted fromBohm (1994). A cubic grid with a spacing of 1 AÊ isconstructed around a ligand and embedded intothe active site of the protein. All cubes with centerswithin a distance of less than rvdW � 1.4 AÊ of aligand or a protein atom are de®ned as occupied inthe ®rst step. Subsequently, those cubes being sim-ultaneously located in the neighborhood of at leastone O or N atom in the protein and in the ligandare excluded. In the next step, for those of theunoccupied cubes that fall next to occupied ones,the closest atom is determined and these cubes arelabeled to be ``surface portion'' of the neighboringatom. Summing up all cubes assigned to atoms®nally yields a value which is approximately pro-portional to the considered surface portion (Bohm,1994).

Van der Waals radii are used according to theTripos force ®eld (Clark et al., 1989), those of Oand N atoms are reduced by 0.2 AÊ (Li & Nussinov,1998) to account for a potential involvement inhydrogen bonding.

{ 1abe 1abf 1atl 1azm 1bbp 1cbx 1cde 1cil 1com 1cps1ctr 1did 1die 1dr1 1dwc 1dwd 1ela 1epb 1frp 1ghb1hfc 1hgj 1hsl 1hyt 1icn 1imb 1ivc 1ivd 1ive 1ivf 1lah1lcp 1lic 1lna 1lst 1mld 1mrg 1mrk 1nis 1nsc 1pbd 1phf1poc 1pph 1ppl 1pso 1rbp 1rds 1rnt 1rob 1slt 1snc 1srj1tlp 1tng 1tnh 1tni 1tpp 1ukz 1wap 1xid 1xie 2ada 2ak32cgr 2cht 2cmd 2cpp 2gbp 2mth 2pk4 2sim 2tmn 2xis2ypi 3aa 3cpa 3hvt 4fbp 4hmg 4phv 4tim 4tln 4ts1 5abp5p2p 6abp 6rnt 6tmn 7tim 8atc

{ 121p 1aaq 1acm 1aco 1aec 1aha 1ake 1apt 1avd1bma 1byb 1cbs 1cdg 1coy 1dbb 1eap 1eed 1elb 1elc1eld 1ele 1etr 1fen 1fkg 1glp 1glq 1hdc 1hef 1hvr 1ida1igj 1ivb 1ldm 1lmo 1lpm 1mbi 1mdr 1mmq 1nco 1phd1phg 1ppc 1ppi 1ppk 1ppm 1rne 1tnk 1tnl 1tph 1trk2ctc 2er6 3cla 3gch 3ptb 4dfr 4fxn 4hvp 4phv 4tmn 5cts5tim 5tmn 6cpa 6tim 7cpa 8gch 9hvp

} 1abe 1abf 1acj 1ack 1ase 1azm 1blh 1cbx 1cde 1cil1cps 1ctr 1dbm 1did 1die 1dr1 1dwd 1ela 1frp 1ghb1hfc 1hgi 1hgj 1hsl 1hti 1hyt 1icn 1imb 1ivc 1ivd 1ive1ivf 1lah 1lcp 1lic 1lna 1lst 1mld 1mrg 1mrk 1mup 1nis1nsc 1pbd 1phf 1poc 1pph 1ppl 1pso 1rds 1rnt 1rob1snc 1srj 1tdb 1thy 1tlp 1tng 1tnh 1tni 1tpp 1ukz 1ulb1wap 1xid 1xie 2ada 2ak3 2cgr 2cht 2cmd 2cpp 2gbp2lgs 2mcp 2mth 2pk4 2r04 2r07 2sim 2tin 2xis 2yhx 2ypi3aah 3cpa 4cts 4est 4fab 4fbp 4phv 4tim 4tln 5abp 5p2p6abp 6rnt 6tmn 7tim 8atc

The surface attributed to the solvated state is cal-culated similarly without considering any particu-lar counterpart (ligand/protein). The conformationin solution is assumed to be identical to the oneadopted in the crystal structure or the docked com-plex.

Test data to evaluate ranking performance

We have tested the performance of the derivedpotentials by assessing for two different data setstheir capability to rank best those ligand poses thatclosely approximate the native one. The ®rst dataset{ is a subset of 91 protein-ligand complexesextracted from the 200 examples that have beenused in the validation of the FlexX docking pro-gram (Rarey et al., 1996). These 91 complexes covera broad range of ligand diversity, e.g. consideringthe number of rotatable bonds (ranging from 0 to27), the number of hydrogen-bond donors andacceptors (ranging from 1 to 17) or the number ofnon-polar atoms (from 2 to 39). In half of the cases,FlexX ®nds solutions with an rmsd value of lessthan 2 AÊ to the crystal structure on the ®rst rank,while for the other portion FlexX fails to selectthese ``well-docked'' cases as best solutions. Theligand poses are generated using standard input®les for FlexX (B. Kramer et al., unpublishedresults) with default parameter settings.

The second set{ consists of 68 protein-ligandcomplexes matching the same criteria as thoseapplied to the ®rst set. Again ligand poses are gen-erated using FlexX. However, for only 30 examplesFlexX ®nds a solution deviating by less than 2.0 AÊ

from the X-ray reference. Out of these 30 cases, for28 (93%) a computed solution <2.0 AÊ is found byFlexX on rank 1. In our study, this second set wasused for a cross-validation of our scoring functionin conjunction with FlexX, since it was notinvolved in the parameter adjustment duringdevelopment of the function.

To test DrugScore in context with DOCK, 100protein-ligand complexes} are extracted from bothdata sets to generate input ®les following the pro-cedure described by Ewing (1997). Flexible dockingwith dihedral and rigid body minimization isapplied using default parameter settings except forthe ``peripheral seeds'' parameter which is set to50. All generated solutions using ``uniformsampling'' are ranked and stored by either apply-ing the ``energy'' or ``chemical score''. Since thetwo scorings are used during structure generation,the resulting solutions in either cases are distinct.In the ®rst case, DOCK generates in 61% of allcases a solution that deviates by less than 2.0 AÊ

from the crystal structure and recognizes in 54%out of these cases a geometry <2.0 AÊ on the ®rstrank. Applying the ``chemical score'', in 43% of allcases a solution with less than 2.0 AÊ deviationfrom experiment is generated; in 46% out of thesecases such a ligand geometry is ranked best. Thus,in the present case and different from recently pub-lished work of Knegtel et al. (1999) who applied

Figure 1. Pair distribution functions of polar/chargedinteractions as computed by equation (9). The ®rstatom-type label refers to the ligand atoms, the second toprotein atoms. The reference state (mean distributionfunction over all pairs) as calculated by equation (6) isdepicted by solid squares.

Figure 2. Pair distribution functions of nonpolar andaromatic interactions as computed by equation (9).Atom-type characterization and reference state aredisplayed as given in Figure 1.


DOCK to the ¯exible docking of 32 thrombininhibitors, the ``energy score'' reveals better resultscompared to the ``chemical score''.

Results

Ligand-protein atom pair correlation functionsand statistical preferences

Pair correlation functions for ligand-proteinatom pairs were derived by counting the occur-rence frequencies of distinct pairs at discrete dis-tances using equation (10). The pair correlationfunctions for polar/charged interactions are pre-sented in Figure 1, those of non-polar interactionsin Figure 2. Statistical preferences were computedby equation (5). Utilizing 17 different atom typesyields 289 possible pair combinations depicted inFigures 3 and 4, respectively. In all cases, the ®rstatom-type index i is attributed to a ligand atom,the second j to a protein or cofactor atom. In thefollowing we will focus on some illustrativeexamples.

Frequency of occurrences of pair interactions

Based on 1376 protein structures considered theminimum number of hits integrated over a dis-tance range from 1 to 6 AÊ for the examples pre-sented here amounts to 8028 in the case of theO.co2-N.pl3 pair; the highest count was found forthe C.3-C.3 pair to be 120,533. Thus, in the case ofO.co2-N.pl3, on average more than 160 hits are col-lected within one bin of width 0.1 AÊ . Although thisaverage number gives only a rough estimate onthe statistical signi®cance of this distribution, wenote that for the distance range below 2.4 AÊ thenumber of counts is markedly lower. It thus yields

less signi®cance in this area. Of all pair distri-butions, 173 (60 % of 289) contain less than 500hits, i.e. less than ten hits per bin on average. For156 (i.e. 54 % of all) of these, one of the atom typesof either the ligand or the protein belongs to S.3,P.3, C.cat, metal, F, Cl, or Br.

The rare occurrence of S.3, F, Cl, and Br in the X-ray structures used to compile the statistical prefer-ences is also re¯ected in the test data set. However,we anticipate that as long as interactions involvingS.3/F/Cl/Br-X contacts do not dominate the ener-getics of ligand binding, a reliable scoring can stillbe estimated based on the contributions resultingfrom the remaining more frequently populatedatom pairs.

Atoms of type P.3 are usually connected to oxy-gen, carbon and nitrogen atoms, resulting in phos-phate, phosphonate or phosphinate derivatives.Being not exposed to the molecular surface, themajor contributions of these functional groups aredetermined by the preferences arising from thehighly populated distributions of the neighboringoxygen and nitrogen atoms. As a ®rst approxi-mation, the same holds for C.cat coding for the car-bon atom in amidinium and guanidinium groups.These atoms are at least in the molecular planeshielded by the surrounding nitrogen atoms.

Reference state of pair interactions

The reference state is calculated as arithmeticmean over all normalized pair correlation functionsof atom types ij. It is represented by ®lled squaresin Figures 1 and 2. De®ned in this way, it may beregarded as a mean interaction preference between``averaged atom-types'', thus mainly representingnon-speci®c contributions from dense packingeffects.

The nature of certain features expressed in thedistributions or the subsequently derived statistical

Figure 3. Statistical preferences for polar/charged pairinteractions as a function of the distance R, calculatedaccording to equation (5).

Figure 4. Statistical preferences for nonpolar/aromaticpair interactions as a function of the distance R, calcu-lated according to equation (5).


preferences are dif®cult to partition into types ofinteraction that operate between isolated pairs ofatoms, since the compiled pair-correlation func-tions are averages of the ensemble, comprisingintercorrelated many-body interactions occurringin a dense packing and arising from several physi-cal effects (electrostatic, steric, solvent, etc.).

Our reference state is derived from a largesample of protein-ligand complexes, accordinglysome structuring of this distribution is observed.Local ¯uctuations in the distribution supposedlyarise at low distances (�2 AÊ ) from metal contacts,around 2.7 AÊ from polar and charge-assisted inter-actions. The elevated probability around 4 AÊ ispresumably caused by aromatic contacts andstructuring at larger distances may be attributed tocontacts resulting from pattern formation in thesecond coordination sphere.

Individual distributions and statistical preferencesof pair interactions

To distinguish ligand binding modes approxi-mating the native structure from inappropriateones generated by docking tools, it is importantthat the type-speci®c distributions differ substan-tially from each other.

Based on a visual inspection of the computedpreferences we decided to refrain from averaging i-j and j-i atom-type contacts (®rst letter correspondsto ligand atom, second one to protein atom). If ourdata originated from isolated atoms or a hom-ogenous non-structured molecular distribution,symmetrical conditions would be expected. How-ever, for the data selected the applied mean-®eldapproach reveals clear differences due to a distinctmolecular embedding of the considered atom-types in ligand and protein environments.

The derived distributions can be divided intotwo main classes: the ®rst contains interactionsbetween polar and charged atoms and exhibits

pronounced maxima at distances between 2.5 and3.0 AÊ . They correspond to hydrogen bonds andsalt bridges (Figure 1). The second class comprisesnon-polar interactions and displays broader distri-butions. The latter reveal higher probabilities com-pared to the reference state at distances >3.5 AÊ

(Figure 2).The distributions within one group show differ-

ences to which a physical meaning can be attribu-ted. Going from O.3-O.3 to O.3-O.co2 and O.co2-N.pl3, the distribution maxima corresponding tothe shell of next neighbors fall into a decreasingdistance range, thus exhibiting higher probabilityat lower distances. Contacts between the above-mentioned atom types can be assigned to a``normal'' hydrogen bond, a polar charge-assistedinteraction and a salt-bridge (Davis & Teague,1999). Expressed in terms of statistical preferences(equation (5)), an ideal O.3-O.3 interaction is2.5 times less probable than a similar O.3-O.co2interaction.

Surprisingly, at a ®rst glance, O.3-O.co2 andO.co2-N.pl3 interactions are equally probable con-tradicting to the assumption that salt bridges withboth partners bearing opposite charges contributemore to the stability of a protein-ligand complexthan a single charge-assisted H-bond (Hossain &Schneider, 1999). According to our de®nition,N.pl3 atom types only occur in amidinium andguanidinium groups. In consequence, a carboxylategroup and an amidinium/guanidinium group inideal bidentate H-bonding geometry show twoO.co2-N.pl3 interactions instead of one ideallyoriented O.3-O.co2 interaction. Thus, the contri-bution of a bidentate salt-bridge, considering onlyinteractions at the contact distance, amounts toabout twice that of the polar-charged interaction.

For non-polar contacts (Figures 2 and 4), theC.ar-C.ar interaction shows a slightly more struc-tured distribution compared to the C.3-C.3 inter-action and the maximum of the former resides at a

Figure 6. Statistical preferences for ligand atoms oftype C.3 and O.co2 as calculated from the distributionfunctions for solvent accessibility of both atom types forcomplexed and separated state from the protein accord-ing to equation (7). The number of cubes (#cubes) is anapproximate measure for the solvent accessibility; zerocubes refer to complete burial.


shorter distance of 3.7 AÊ . Accordingly, the C.ar-C.ar contact exhibits an elevated preference com-pared to the all-atom distribution at this distance,in agreement with the well-known aromatic-aro-matic interactions (Burley & Petsko, 1985). In con-trast, C.3-C.3 interactions do not show anypreference of the atom pair distribution over theentire distance range of 1 to 6 AÊ sampled here.This is clearly in agreement with the well-knownfact that the latter type of interaction hardly exhi-bits any directional preferences.

In comparing the depth of the preference mini-ma, one has to consider that at short distances(<3 AÊ ), on average, only one direct partner will beinvolved. With increasing distance additional next-neighbors get into contact and the coordinationnumber roughly scales with the square of the dis-tances. Estimating the total contribution of onespeci®c contact to the stability of a ligand-proteincomplex, both the individual strength and itsoccurrence frequency have to be considered.

The derived statistical preferences display differ-ences when compared to pure van der Waals inter-actions operating between isolated atom pairs intwo aspects. The occurrence of multiple minima atlarger distances results from particular packingpatterns present in a protein-type environment andre¯ects organization in high-order coordinationshells. In addition, our preferences fall off belowdistances of 2 AÊ and display minima at 1 AÊ . This isbound to occur, since for good reasons, no exper-imental observations are recorded at such shortdistances. We believe there is no need for a speci®ccorrection term to cope with this non-de®ned dis-tance range, since the computed binding modesfrom FlexX or other docking programs will notcontain geometries with mutually penetrating pro-tein and ligand atoms.

The compiled preferences for a given atom pairi, j are calculated only as a function of the distancebetween the atoms, any directional preference pat-terns are implicitly contained and re¯ected; e.g. let

Figure 5. Intrinsic geometrical constraints re¯ected bythe atom pair preferences of O.2-O.3 and C.2-O.3. Giventhe minima of the statistical pair preferences (O.2-O.3:2.55 AÊ ; C.2-O.3: 3.45 AÊ ) and the bond length (C.2-O.2:1.22 AÊ ), the C.2-O.2-O.3 angle is calculated to be 128 �.

us consider a hydrogen-bond between a carbonylgroup and an O.3-type oxygen (Figure 5). Theminimum of an O.2-O.3 interaction (not shownhere) is located at 2.55 AÊ , the C.2-O.3 interactionhas a minimum at 3.45 AÊ . Assuming a C.2-O.2bond length of 1.22 AÊ , a mean spatial C.2-O.2-O.3angle of 128 � is calculated. Taking the preferreddistances O.2-O.3 and C.2-O.3 together, these con-ditions clearly constrain the frequently observedhydrogen-bonding geometry of a carbonyl groupwith an alcohol-type oxygen atom. The same orien-tational preference is observed for representativefragments stored in ISOSTAR (Bruno et al., 1997).Additional contact preferences formed by theneighboring atoms will further de®ne the spatialarrangement of a speci®c directional interaction.

SAS-dependent preferences for solvent-exposure of ligand and protein atoms

To incorporate solvent effects we derived a SAS-dependent singlet preference either for ligand andprotein atoms. As de®ned by equation (7), this pre-ference is calculated as the logarithm of the prob-ability for a ligand or protein atom of type i toexpose parts of its SAS in the complexed state com-pared to a state where both partners are comple-tely separated from each other (see Methods). Wenote that by de®ning the reference state in thisway, the derived preferences are independent fromeach other and not a result of a mean-®eldapproach.

Figure 6 shows the statistical preferences for aC.3-type or O.co2-type ligand atom to be exposedin the protein-bound state compared to theunbound state. Here the ``number of cubes'' isapproximately proportional to the SAS area.

Except for very small surface portions remainingsolvent-exposed at the binding site, complete bur-


ial of C.3 atoms in protein-ligand complexes isstrongly favorable for complex formation which isexpressed by a deep minimum near zero cubes.

A completely different although quite reasonablebehavior is observed for O.co2-type atoms: in theisolated state, carboxylate oxygen atoms stronglyprefer to be solvent-exposed. In complexed state,the distribution is the result of a compromisebetween several effects. On the one hand, burial ofO.co2 atoms diminishes the SAS (shift to a smallernumbers of cubes). On the other hand, surface por-tions contacting polar protein atoms are not con-sidered as being buried. Hence, ``partial'' burial forO.co2 results as best compromise for the com-plexed state. Expressed in terms of preferences, a``partial'' burial stabilizes complex formation incontrast to a complete burial; additionally a com-plete solvent exposure is also slightly unfavorable.

``Scoring the scoring function''

Usually the root-mean-square deviation of aligand pose, generated by a docking tool, is deter-mined with respect to the corresponding crystalstructure. This is a generally accepted qualitymeasure for the obtained docking result. Wede®ne, based on this measure, those ligand poses

Figure 7. Correlations of scores, normalized to values betstructure for the protein-ligand complexes 1bbp, 1lst, 1rbp,carbon) ligand atoms amounts from 52 % for 2ada to 95 %2ada) to 6 (1bbp) and the number of solutions generated bymetries correspond to low scores on the ordinate.

as ``well-docked'' that do not deviate more than2.0 AÊ from the crystal structure. Visual inspectionof a number of test cases showed that within thislimit the generated solutions usually resemble thenative binding mode.

To assess the discriminatory power of a scoringfunction, i.e. its capability to distinguish betweenwell-docked and clearly different solutions, weselected the criterion that one of the ``well-docked''solutions has to end up on the best scoring rank.Since this condition is more stringent than justdemanding one of the ``well-docked'' solutions tobe among, i.e. the ten best rankings, our criterionmeets the requirement for virtual screening oflarge databases.

As an even more stringent criterion, we candemand that the experimentally given solution isranked better than any other computer-generatedligand binding pose (including the ``well-docked''ones). However, we have to remember that eventhese ``ideal'' reference solutions are affected byexperimental de®ciencies. Taking this limited accu-racy into account, we also consider our scoringfunction to operate satisfactorily if solutions,deviating not further than 2.0 AÊ from theexperimentally given structure (``well-docked''

ween 0 and 100, versus the rmsd value from the crystaland 2ada are depicted. The percentage of non-polar (i.e.for 1rbp, the number of rotatable bonds from 1 (1rbp,FlexX from 99 (1rbp) to 289 (1lst). Favorable ligand geo-

Figure 8. Accumulated number of complexes as afunction of the rmsd value from the crystal structurefound for ligand poses on rank 1 scored by FlexX (*)and DrugScore (~), respectively. The number of com-plexes with the best geometry found on any rank byFlexX is depicted as ®lled squares.


solutions), are ranked better than the crystalstructure.

Correlation of the calculated scores versusrmsd of the crystal structure

Total preferences were calculated according toequation (8) for the different solutions obtained bydocking experiments. They were plotted versus thermsd value from the crystal structure. This pro-cedure involves the projection of the total prefer-ence score, multifactorily composed from manyindividual contributions, onto the single geometri-cal rmsd descriptor. It is dif®cult to estimate whatkind of correlation will be present; however, onecan expect that the crystal structure and approxi-mate ligand poses should be ranked better thanstrongly deviating solutions. Furthermore, thelower envelope of the resulting scatter plot mayexhibit multiple local minima (due to the rough-ness of the potential hypersurface).

We have to recall that similar rmsd values donot necessarily represent similar ligand poses,especially for large values. Accordingly, poses fall-ing into the same range of larger rmsd values canobtain quite different scorings. In contrast, similarligand binding modes should reveal similar scoresif the underlying function is suf®ciently ``soft'' totolerate some geometric deviations.

In Figure 7 the correlations of calculated scoresfor ligand geometries generated by FlexX versusthe rmsd value from the crystal structure for fourprotein-ligand complexes are displayed; the indi-vidual scores were normalized to values between 0and 100. Favorable solutions correspond to lowscores. The examples shown were selected to rep-resent quite distinct cases (e.g. spread of non-polarsurface contribution, number of rotatable bonds,number of generated FlexX solutions).

In all cases, the crystal structure (rmsd � 0) isrepresented by the best score. For 1bbp, 1lst and2ada, the native geometry is well separated fromany computed solution. Docked geometries beingclearly apart from the native structure are satisfac-torily separated from the approximating poses.These latter solutions tend to obtain a better scor-ing with decreasing rmsd.

In conclusion, for all four cases the scoring func-tion, de®ned by equation (8), successfully recog-nizes the experimental and ``well-docked'' posesamong a set of up to 289 distinct ligand poses(Figure 7).

Validation of the approach on large test sets ofprotein-ligand complexes

The successful reproduction of some test casesindicates the scope of the method; however, to rig-orously validate our method we evaluated largesets of protein-ligand complexes.

Two test sets are taken from a sample used tovalidate FlexX (B. Kramer et al., unpublishedresults). In the ®rst case, comprising 91 protein-

ligand complexes, FlexX has already recognized agenerated solution with rmsd <2.0 AÊ on the ®rstrank in 54 % of the cases. For the remaining 46 %,FlexX also generates a geometry with rmsd <2.0 AÊ ;however, theses poses are attributed to a worserank.

The second test set contains 68 additional com-plexes. Out of these, for 28 cases a computedsolution with rmsd <2.0 AÊ is found by FlexX onrank 1. For 38 remaining cases, FlexX did not gen-erate a pose with rmsd <2.0 AÊ using default set-tings. This second set was not involved in thedevelopment of the scoring function, i.e. parameteradjustment was solely performed on the basis ofdata from the ®rst set. We used this set for a cross-validation of our scoring function in conjunctionwith FlexX.

Out of both data sets, 100 protein-ligand com-plexes were selected to evaluate the performanceof DrugScore with respect to docking solutionsgenerated by DOCK. Applying the DOCK speci®c``energy scoring'' (or ``chemical scoring''), a gener-ated solution with rmsd <2.0 AÊ is recognized onthe ®rst rank in 54 % (46 %) of the cases by DOCK.

We want to stress that all complexes used forvalidating our approach (including those shown inFigure 7) have been excluded from the databaseused to compute the probability distributions andto derive the statistical preferences.

Recognition of ``well-docked'' solutions

Figure 8 summarizes the accumulated number ofcomplexes plotted versus the rmsd value withrespect to the crystal structure of the best rankedligand pose either determined by FlexX or the scor-ing function described here (DrugScore).

Table 1. Results for scoring multiple docking solutions of 91 protein-ligand complexes generated by FlexX andDrugScore

% of complexes with solutions exhibiting rmsd of the crystal structure

<1.0 AÊ <1.5 AÊ <2.0 AÊ 52.0 AÊ

All ranksa 65 76 84 161st rankb FlexX 20 37 54 46

DrugScore 39 66 73 27Improvementc 95 78 35 ÿ41

a All solutions of each docking experiment for the 91 complexes are considered. This number expresses the portion of allcomplexes for which at least one solution with the given rmsd value was computed by FlexX.

b Only the ligand geometry scored to be on the ®rst rank by either FlexX or DrugScore is considered. The numbers are related tothe ones in the ®rst line.

c The improvement is calculated by (%DrugScore ÿ %FlexX)/%FlexX.


In addition, for all examples the solution gener-ated by FlexX that obtains the smallest rmsd value,disregarding its actual scoring rank, is also plotted.These values give an idea how well an ideal scor-ing function could perform. It also indicates byhow much the generated poses with the bestmatching geometry deviate from the X-ray refer-ence. Note that all cumulated values are sortedindependently. Thus, the ordinate displays a coun-ter for the complexes and not an identi®cationnumber.

As is obvious from the diagram, the new scoringfunction performs signi®cantly better than the oneimplemented in FlexX. Table 1 gives the percentageof test cases found on rank 1 with rmsd values of<1.0 AÊ , <1.5 AÊ , <2.0 AÊ and 52.0 AÊ compared tothe best approximating geometry found on anyrank. With respect to the recognition of posesdeviating by <2 AÊ on rank 1, FlexX succeeds in54 % of the cases whereas DrugScore detects 73 %.

The difference in rmsd value, exhibited by thesolutions ranked best according to FlexX or Drug-Score, respectively, are shown in Figure 9. Whereasin ten cases, DrugScore selects a solution deviatingmore strongly in geometry (by more than 1 AÊ ) onthe ®rst rank compared to FlexX, in 28 cases a poseis selected being more than 1 AÊ closer to the X-ray

Figure 9. The differences between rmsd values exhib-ited by solutions found on rank 1 by FlexX and Drug-Score are displayed, respectively, for each protein-ligandcomplex. The broken line shows the mean value of alldifferences of ÿ0.7 AÊ .

reference. Averaged over all 91 complexes, themean improvement in reducing the rmsd value forrank 1 is 0.7 AÊ .

For the second test set (68 complexes), out of the30 cases satisfactorily docked by FlexX (below 2 AÊ

rmsd), the scoring in FlexX and DrugScore obtainnearly identical success rates (93 % and 92 %,respectively).

In Figure 10, the accumulated number of com-plexes is plotted versus the rmsd value from thecrystal structure of the best ranked ligand poseeither selected by the ``chemical scoring'' in DOCKor by DrugScore. Furthermore, the generated sol-utions with the smallest rmsd values are accumu-lated disregarding their actual scoring rank.

Table 2 gives the percentage of test cases foundon rank 1 with rmsd values of <1.0 AÊ , <1.5 AÊ ,<2.0 AÊ and 52.0 AÊ compared to the best approxi-mating geometry found on any rank. With respectto the recognition of ``well-docked'' solutions(<2 AÊ ) on rank 1, the ``chemical scoring'' in DOCKsucceeds in 46 % of the cases whereas DrugScoredetects 70 %. When using the ``energy scoring''during structure generation (data not shown here),the scoring of DOCK and DrugScore yields similarsuccess rates (54 % and 51 %, respectively).

Recognition of the crystal structures

As mentioned above, assuming the crystallogra-phically determined structures to be ``optimal'' sol-utions, they should obtain the best scoringcompared to any computer-generated ligand pose.As shown in Figure 11, this is actually the case for54 % of the examples of the ®rst test set for FlexX(91 complexes). If we alleviate, as described above,the criterion to complexes falling into a window of2 AÊ deviation, in even 71 % of the cases the crystalstructure or a ``well-docked'' geometry will beranked by DrugScore as favorable.

What are the reasons that some cases do not per-form well? Visual inspection of some of the unsuc-cessful examples provides some explanations. Inthe case of 1icn (resolution: 1.74 AÊ ; Figure 12), thecrystal structure is scored on rank 35. The ligandoleate is oriented with its carboxylate grouptowards the interior of the protein, thereby expos-

Figure 10. Accumulated number of complexes as afunction of the rmsd from the crystal structure foundfor ligand poses on rank 1 scored by DOCK (``chemicalscoring'') (*) and DrugScore (~), respectively. Thenumber of complexes with the best geometry found onany rank by FlexX is depicted as solid squares.

Figure 11. The rank of the crystal structure calculatedby DrugScore among all decoy geometries generated byFlexX for each of the 91 protein-ligand complexes of the®rst test set is shown.


ing the non-polar end of the hydrocarbon chaintowards the solvent. The carboxylate group is notinvolved in any directional interaction to any pro-tein functional group within a distance of 3.5 AÊ ;only a water molecule occurs in its next neighbor-hood (3.3 AÊ ). Instead, a ligand pose with reversedorientation of the molecule (rmsd � 11.3 AÊ ) isranked best. In this mode, two hydrogen bonds toa protein amide group are formed and the non-polar terminus is buried inside the pocket, result-ing in a much better score. Interestingly, in thecrystal structure the carboxylate group is disor-dered and three alternative positions are given inthe PDB. Additionally, a weak but continuous, J-shaped electron density is reported beyond thelocation of the terminal methyl of oleate in thewild-type holo protein (Eads et al., 1993), whichhas an arginine at the bottom of the binding pock-et. In contrast, this amino acid has been replacedby a glutamine in the mutated protein used for1icn. It thus can not form a salt bridge with the car-boxylate of the fatty acid. With some care, these®ndings could also allow for an interpretation of

Table 2. Results for scoring multiple docking solutions(applying ``chemical scoring'') and DrugScore

% of complexe

<1.0 AÊ

All ranksa 171st rankb DOCK 18

DrugScore 41Improvementc 128

a All solutions of each docking experiment for the 100 complecomplexes for which at least one solution with the given rmsd value

b Only the ligand geometry scored to be on the ®rst rank by eithethe ones in the ®rst line.

c The improvement is calculated by (%DrugScore ÿ %DOCK)/%D

the reported electron density with a reversed orien-tation of the ligand. Then, the disordered part ofthe electron density would correspond to thehydrocarbon tail and this inverted orientationmatches with our predictions. In the complex 2pk4(resolution: 2.25 AÊ ; Figure 13), o-amino-hexanoicacid is placed into a shallow groove close to theprotein surface. While a solution with rmsd 1.3 AÊ

is ranked best, the crystal structure (rank 129) itselfshows an interaction between the amino group ofthe ligand and a protein carboxylate group of2.1 AÊ . This remarkably short distance is scored asrepulsive by the corresponding atom pair prefer-ence.

Applying the scoring function to the second testset for FlexX, 65 % of all crystal structures arefound on rank 1. In 90 % of the 68 cases, onlydocked solutions with rmsd <2 AÊ reveal a higherrank than those of the native structure, i.e. thesecases ful®ll the alleviated conditions (results notshown here).

For the set of complexes generated by DOCKusing the ``chemical scoring'' (``energy scoring''),DrugScore ®nds in 76 % (57 %) of all cases the crys-tal structure on rank 1. Using the alleviated con-dition, in 83 % (62 %) of all cases the crystal

of 100 protein-ligand complexes generated by DOCK

s with solutions exhibiting rmsd of the crystal structure

<1.5 AÊ <2.0 AÊ 52.0 AÊ

31 43 5733 46 5448 70 3045 52 ÿ44

xes are considered. This number expresses the portion of allwas computed by DOCK.

r DOCK or DrugScore is considered. The numbers are related to

OCK.

Figure 12. A section of the binding pocket of 1icn is displayed together with the X-ray structure of the ligand(color-coded by atom type) found on rank 35 by DrugScore and the geometry with rmsd � 11.3 AÊ ranked best (redcolored). The entrance to the pocket orients toward the right, bottom and top parts are clipped for clarity. The car-boxylate group of the crystal structure has no adequate interaction partner except a water molecule (not shown here)at 3.3 AÊ distance. In contrary, the better ranked, however geometrically deviating pose does not only form twohydrogen bonds to an amide-NH (distances 2.8/2.9 AÊ , depicted as dotted lines), but also buries its non-polar termi-nus towards the interior of the protein. See the text for explanations.


structure or a ``well-docked'' solution is rankedbest (data not shown here).

Investigation of factors that might influence therecognition rate of solutions approximating theexperimentally given structures

Considering two knowledge-based quantitiesthat re¯ect either pair distributions of atom-atomcontacts or solvent-accessible surface portionsraises the question, how much redundancy isexpressed by both terms? In Figure 14, we sum-marize the performance of both types of statisticalpreferences separately applied to the ®rst test setused for FlexX in order to detect the ``well-docked''solutions. Again the accumulated number of com-plexes is plotted versus the rmsd value observedfor the solution on rank 1. While the score basedon atom-atom preferences alone clearly performsbetter than the FlexX score (showed as ®lled cir-cles), the SAS-dependent score shows only a slightimprovement at low rmsd. Interestingly, the latterscore does not contain any information on thenature of a molecular counterpart of either theligand or of the binding site residue. It only takesinto account whether polar or non-polar molecularportions are found in a polar or non-polar environ-ment, respectively. Moreover, there is no implicitconsideration of detailed atom pair interactions noris there any information about the geometry of theinteractions.

Although the statistics using the total prefer-ences, calculated as a sum of the atom-pair andSAS preferences, only show a slight improvementcompared to the consideration of atom-pair prefer-

ences alone, in 5 % of all 91 cases a correct recog-nition of a ``well-docked'' solution on rank 1would have failed without the SAS-dependentscore. An illustrative example exhibits the protein-ligand complex 1ela (Figure 15). The ligand codedby atom types represents the crystal structure, themolecule shown in blue corresponds to the bestsolution found by only considering the atom-pairpreferences (rmsd � 11.9 AÊ ) and the one in redresults from using both preference scores(rmsd � 2.5 AÊ ). For the incorrect, strongly deviat-ing mode (blue) a deep hydrophobic pocket, com-posed by methyl groups of Thr221, Thr236 andVal224, remains accessible to the solvent. Further-more, a hydrophobic CF3 group of the ligand alsoexposes its surface to the solvent. Both features canonly be treated correctly if the approach includingthe SAS-dependent score is applied.

To obtain some insight whether the developedapproach depends on the detailed composition ofthe ligands, we plotted the rmsd values of the bestsolutions versus the percentage of non-polar atoms,the percentage of hydrogen bond donor and accep-tor atoms (all related to the total number of heavyatoms), the absolute number of rotatable bonds orthe resolution of the experimental structure deter-minations. No signi®cant correlation could befound for either of these features, apart from apossibly very slight dependence on the number ofrotatable bonds. It is likely that the latter pointstoward the complexity of the problem. The largerthe number of rotatable bonds, the more dif®cultthe prediction of a reasonable binding confor-mation will be. Accordingly, it is not surprising

Figure 13. A section of the bind-ing pocket of 2pk4 is showntogether with the conformation ofthe ligand as found by X-ray crys-tallography (ranked as no. 129 byDrugScore, color-coded by atomtype). The geometry of the bestscored docking solution deviatingby 1.3 AÊ from the crystal structureis depicted in red. In the crystal,the ligand forms a hydrogen bondbetween the terminal amino groupand a carboxylate group of the pro-tein that measures to only 2.1 AÊ

length (shown as a dotted line).


that a more rigid ligand usually obtains a smallerrmsd value.

Discussion and Conclusion

In this study, distance-dependent pair prefer-ences and SAS-dependent singlet preferences arederived from crystallographically determined pro-tein-ligand complexes. A scoring function incorpor-ating both terms has been shown to be verypromising{. It discriminates satisfactorily betweenwell-docked (rmsd <2.0 AÊ ) ligand binding modesand those largely deviating from the native struc-ture generated by the docking tools FlexX andDOCK. This has been shown for test sets compris-ing 91 and 68 complexes (FlexX) and a mixed sub-set of 100 complexes (DOCK). A substantialimprovement is achieved compared to the originalscoring in FlexX as well as the ``chemical scoring''in DOCK. In comparison with the ``energy scor-ing'' in DOCK, similar results are obtained.

Apart from computationally demandingmethods based on ®rst principles such as FEP orTI, knowledge-based as well as regression-basedapproaches are primarily applied to predict pro-tein-ligand interactions. While for the latterregression-based approaches the partitioning of thetotal ligand-to-protein binding features into severaladditive terms increases our understanding of the

{ The new scoring function is still underdevelopment. It is planned to incorporate this functioninto ReLiBase (http://www2.ebi.ac.uk:8081/home.html),a database for the handling of protein-ligand complexes,and to make it available in the framework of this dataanalysis tool.

contributions to the binding process arising fromdifferent physical origin, it is dif®cult to assesswhether this set of considered terms is complete.In addition, only anticipated effects can be con-sidered during the regression analysis and it is byno means clear how strongly these terms are inter-correlated. As a consequence, including even moresophisticated terms to existing state-of-the-artregression-based scoring functions only revealedminor improvements (Bohm, 1998; Stahl & Bohm,1998). Furthermore, the predictive power of theserelationships towards protein-ligand complexes,distinct from all examples used in the training set,is dif®cult to estimate. Although PLS-derivedrelations (Head et al., 1996) are in agreement with

Figure 14. The performance of both statisticallyderived preference schemes applied to the ®rst test setof 91 protein-ligand complexes to recognize ``well-docked'' solutions in comparison to the original FlexXscoring.

Figure 15. The binding pocket ofelastase (PDB code: 1ela) is dis-played. The crystal structure of theligand is color-coded by atom type,the best ranked solution(rmsd � 11.9 AÊ ) applying only thedistance-dependent pair preferencescheme is colored in blue, the sol-ution (rmsd � 2.5 AÊ ) found on rank1 applying the pair and the SAS-dependent singlet preferences iscolored in red. The deep sub-pocket on the right is composed ofthe side-chain of Val224 and twomethyl groups of Thr221 andThr236.


those derived by multiple linear regression, thecontribution of each individual term in these for-mer equations is dif®cult to understand due to thefact that implicitly ``new'' orthogonal descriptorsare calculated as linear combinations in terms ofthe original ones.

Knowledge-based approaches are assumed to bemore general, since they implicitly incorporateeven those effects that are yet not fully understood.The conversion of structural database informationof experimentally determined geometries into stat-istical preferences regards cooperative effects aswell as mainly entropy-driven effects arising fromthe solvation. They are expected to be taken intoaccount as a result of the mean-®eld character ofthe approach. Moreover, less frequently populatedstates are considered with lower statistical prefer-ences, thus implicitly penalizing computer-gener-ated artifacts.

Since no explicit training set is used in contrastto the derivation of regression-based scoring func-tions, our scoring function should be generallyapplicable. This was demonstrated for exemplarycases where all proteins with a homology >30 % tothe test case protein were excluded from the data-base used to derive the preferences. Nevertheless,several parameters had to be adjusted in the con-text of our approach to reveal optimal results: e.g.the interatomic distance cut-off, the bin size fordata sampling and the scaling of the pair prefer-ences to the singlet preferences.

As mentioned already, the choice of the refer-ence state is crucial and could lead to the underes-timation of several contributions (Godzik et al.,1995). To account for solvent effects, not suf®-ciently considered by pair preferences collected upto 6 AÊ (Bahar & Jernigan, 1997), we introduced aSAS-dependent singlet potential.

Only non-hydrogen atom types are used withinour scoring function. On the one hand, most com-

plexes in PDB either lack or only contain force-®eld generated polar hydrogen atoms. Accord-ingly, most of these atoms would have to bemodel-built prior to the derivation of the prefer-ences. On the other hand, in particular hydrogen-atom positions strongly depend on the in¯uencesof their molecular environment. The local electro-static ®eld in a protein can change upon ligandbinding and might result in substantial pKa shiftsof ionizable groups. In consequence, de®ning pro-tonation states a priori, e.g. during a docking exper-iment, is by no means straightforward. Althoughat a ®rst glance, the neglect of H-atom positionsappears to imply the loss of information aboutdirectionality of polar interactions, the simul-taneous consideration of many-fold pair-prefer-ences in a compact molecular environmentrecovers these features (Figure 5).

Using the data in the Cambridge structural data-base (CSD; Allen et al., 1991) instead of the PDB toderive statistical preferences of intermolecularinteractions could cope with these shortcomings.Furthermore, additional data and an enhancedscope of atom types could be studied. However,protein-ligand complexes are usually crystallizedfrom water, whereas the overwhelming part oforganic small molecules are crystallized fromorganic solvents. As a consequence, for a quantitat-ive correlation as anticipated here the in¯uence ofthe hydrophobic effect is expected to be smaller inthe data derived from the CSD compared to thePDB. This in¯uence was ®rst recognized byVerdonk et al. (1999) during the development ofSuperStar. Furthermore, since the CSD data are ofhigher accuracy compared to those in the PDB, thederived statistical preferences are expected to exhi-bit less scatter.

The recent studies of Verkhivker et al. (1995) andMuegge & Martin (1999) use the same formalismto derive potentials; however, they follow a quite


different objective: the application of a knowledge-based scoring function to predict �G values ofexperimentally determined protein-ligand com-plexes. Our goal is to render prominent the ligandgeometry most closely resembling the native struc-ture. The rationale behind this intention is theobservation, that scoring functions such asSCORE2 (Bohm, 1998) are already reliable enoughto correctly predict �G within 1.3 log units ifapplied to native-like geometries. Virtual screeningtools presently generate a whole set of arti®calligand binding modes that have to be detected assuch. Moreover, both studies follow a differentprocedure to derive the potentials or preferences.While Verkhivker and co-workers compile ligand-protein interactions up to 6-7 AÊ from a small dataset of 30 HIV and SIV proteases and relate thesepair-interaction potentials to other explicit entropicand solvation terms, Muegge & Martin derivepotentials of mean force from 697 complexes storedin the PDB using a cut-off at 12 AÊ together with acorrection term regarding the volume occupied bythe ligand in order to incorporate solvent effectsinto their pair potentials.

Several improvements and enhancements can beimagined. So far our scoring function is applied topost-process solutions from FlexX and DOCK. It isencouraging that DrugScore performs comparablywell, independent of the methods applied to gener-ate ligand poses. This suggests its general applica-bility. Nevertheless, it is not totally obviouswhether solely using our approach would revealcomparable results or whether only the combi-nation of two subsequently applied scoring func-tions (Bohm's SCORE in FlexX or ``chemicalscoring''/``energy scoring'' in DOCK and our scor-ing function) achieves the reported success rate.We are currently implementing DrugScore intoFlexX to study these effects. Furthermore, geo-metrical complementation of the binding sites dueto crystal contacts are not yet taken into accountduring the derivation and the application of ourapproach. Even if only a minor in¯uence on theshape of the preferences as well as the predictivepower is expected, this assumption has to be inves-tigated. The same holds for water molecules oftenbeing a mediator for ligand-protein interactions.Cofactors are considered as part of the proteinduring the compilation of atom/atom preferences,yet they are neglected during ligand scoring. Forthe latter two situations, a correlation with theactually evaluated binding mode is obvious. Theseeffects have to be taken into account.

Note Added in Proof

During revision of this paper, Mitchell et al.(1999b) published the development of an atomiclevel potential of mean force using high-resolutionX-ray structures from the PDB. In total 820 possibleatom-atom pairs are evaluated. The performance toidentify low-energy binding modes from decoy

conformations is tested for one case, the heparinbinding to bFGF (PDB code: 1bfc) (Mitchell et al.,1999a). While the crystal structure was ranked low-est, the best scored geometry generated by FTdockdeviates largely from the experimental one.

Acknowledgments

This work was performed as part of the RELIMO-Pro-ject (grant number 0311619) funded by the German Fed-eral Ministry for Education, Science, Research, andTechnology (BMBF). We also acknowledge the help of A.Kulke and H. Velec (University of Marburg) in preparingthe DOCK input ®les. Parts of the work were presentedat the 12th European QSAR Symposium, Copenhagen/Denmark, September 1998, and the International Work-shop on Virtual Screening, Rauischholzhausen/Germany, March 1999.

References

Allen, F. H., Davies, J. E., Galloy, J. J., Johnson, O.,Kennard, O., Macrae, C. F., Mitchell, E. M.,Mitchell, G. F., Smith, J. M. & Watson, D. G. (1991).The development of version-3 and version-4 of theCambridge Structural Database system. J. Chem. Inf.Comput. Sci. 31, 187-204.

Bahar, I. & Jernigan, R. L. (1997). Inter-residue potentialsin globular proteins and the dominance of highlyspeci®c hydrophilic interactions at close separation.J. Mol. Biol. 266, (1), 195-214.

Ben-Naim, A. (1987). Solvation Thermodynamics, PlenumPress, New York.

Bernstein, F. C., Koetzle, T. F., Williams, G. J., Meyer,E. E., Jr, Brice, M. D., Rodgers, J. R., Kennard, O.,Shimanouchi, T. & Tasumi, M. (1977). The ProteinData Bank: a computer-based archival ®le formacromolecular structures. J. Mol. Biol. 112, (3), 535-542.

Beveridge, D. L. & DiCapua, F. M. (1989). Free energy-via molecular simulation: applications to chemicaland biomolecular systems. Annu. Rev. Biophys. Bio-phys. Chem. 18, 431-492.

Blokzijl, W. & Engberts, J. B. F. N. (1993). Hydrophobeeffekte-ansichten und tatsachen. Angew. Chem. 105,1610-1648.

Bohm, H. J. (1992). The computer program LUDI: a newmethod for the de novo design of enzyme inhibi-tors. J. Comput. Aided Mol. Des. 6, (1), 61-78.

Bohm, H. J. (1994). The development of a simple empiri-cal scoring function to estimate the binding constantfor a protein-ligand complex of known three-dimen-sional structure. J. Comput. Aided Mol. Des. 8, (3),243-256.

Bohm, H. J. (1998). Prediction of binding constants ofprotein ligands: a fast method for the prioritizationof hits obtained from de novo design or 3D data-base search programs. J. Comput. Aided Mol. Des. 12,(4), 309-323.

Bohm, H.-J. & Klebe, G. (1996). What can we learn frommolecular recognition in protein-ligand complexesfor the design of new drugs? Angew. Chem. Int. Ed.Engl. 35, (22), 2566-2587.


Bostrom, J., Norrby, P. O. & Liljefors, T. (1998). Confor-mational energy penalties of protein-bound ligands.J. Comput. Aided Mol. Des. 12, (4), 383-396.

Bowie, J. U., Luthy, R. & Eisenberg, D. (1991). A methodto identify protein sequences that fold into a knownthree-dimensional structure. Science, 253, (5016),164-170.

Bruno, I. J., Cole, J. C., Lommerse, J. P., Rowland, R. S.,Taylor, R. & Verdonk, M. L. (1997). IsoStar: alibrary of information about nonbonded inter-actions. J. Comput. Aided Mol. Des. 11, (6), 525-537.

Burgi, H. B. & Dunitz, J. D. (1988). Can statistical anal-ysis of structural parameters from different crystalenvironments lead to quantitative energy relation-ships. Acta Crystallog. sect. B, 44, 445-448.

Burley, S. K. & Petsko, G. A. (1985). Aromatic-aromaticinteraction: a mechanism of protein structure stabil-ization. Science, 229, (4708), 23-28.

Clark, M., Cramer, R. D., III & Van Opdenbosch, N.(1989). Validation of the general purpose Tripos 5.2force ®eld. J. Comp. Chem. 10, 982-1012.

Davis, A. M. & Teague, S. J. (1999). Hydrogen bonding,hydrophobic interactions, and failure of the rigidreceptor hypothesis. Angew. Chem. Int. Ed. Engl. 38,(6), 736-749.

DeWitte, R. S. & Shaknovich, E. I. (1996). SMoG: de novodesign method based on simple, fast, and accuratefree energy estimates. 1. Methodology and support-ing evidence. J. Am. Chem. Soc. 118, 11733-11744.

Dill, K. A. (1997). Additivity principles in biochemistry.J. Biol. Chem. 272, (2), 701-704.

Dixon, J. S. (1997). Evaluation of the CASP2 dockingsection. Proteins: Struct. Funct. Genet. Suppl. 1, 198-204.

Eads, J., Sacchettini, J. C., Kromminga, A. & Gordon, J. I.(1993). Escherichia coli-derived rat intestinal fattyacid binding protein with bound myristate at 1.5 AÊ

resolution and I-FABPArg106! Gln with boundoleate at 1.74 AÊ resolution. J. Biol. Chem. 268, (35),26375-26385.

Ewing, T. (1997). Editor of DOCK Version 4.0 Manual,Regents of the University of California, San Fran-cisco, CA.

Ewing, T. J. A. & Kuntz, I. D. (1997). Critical evaluationof search algorithms for automated molecular dock-ing and database screening. J. Comput. Chem. 18, (9),1175-1189.

Finkelstein, A. V., Gutin, A. M. & Badretdinov, A. Y.(1995). Perfect temperature for protein structure pre-diction and folding. Proteins: Struct. Funct. Genet.23, (2), 151-162.

Godzik, A. (1996). Knowledge-based potentials for pro-tein folding: what can we learn from known proteinstructures? Structure, 4, (4), 363-366.

Godzik, A., Kolinski, A. & Skolnick, J. (1995). Are pro-teins ideal mixtures of amino acids? Analysis ofenergy parameter sets. Protein Sci. 4, (10), 2107-2117.

Head, R. D., Smythe, M. L., Oprea, T. I., Waller, C. L.,Green, S. M. & Marshall, G. R. (1996). VALIDATE:a new method for the receptor-based prediction ofbinding af®nities of novel ligands. J. Am. Chem. Soc.118, 3959-3969.

Hendlich, M. (1998). Databases for protein-ligand com-plexes. Acta Crystallog. sect. D, 54, 1178-1182.

Hendlich, M., Lackner, P., Weitckus, S., Floeckner, H.,Froschauer, R., Gottsbacher, K., Casari, G. & Sippl,M. J. (1990). Identi®cation of native protein foldsamongst a large number of incorrect models. The

calculation of low energy conformations frompotentials of mean force. J. Mol. Biol. 216, (1), 167-180.

Honig, B. & Nicholls, A. (1995). Classical electrostaticsin biology and chemistry. Science, 268, (5214), 1144-1149.

Hossain, M. A. & Schneider, H.-J. (1999). Flexibility,association constant, and salt effects in organic ionpairs: how single bonds affect molecular recog-nition. Chem. Eur. J. 5, (4), 1284-1290.

Jain, A. N. (1996). Scoring noncovalent protein-ligandinteractions: a continuous differentiable functiontuned to compute binding af®nities. J. Comput.Aided. Mol. Des. 10, (5), 427-440.

Jernigan, R. L. & Bahar, I. (1996). Structure-derivedpotentials and protein simulations. Curr. Opin.Struct. Biol. 6, (2), 195-209.

Jones, D. T., Taylor, W. R. & Thornton, J. M. (1992). Anew approach to protein fold recognition. Nature,358, (6381), 86-89.

Jones, G., Willett, P., Glen, R. C., Leach, A. R. & Taylor,R. (1997). Development and validation of a geneticalgorithm for ¯exible docking. J. Mol. Biol. 267, (3),727-748.

Knegtel, R. M., Bayada, D. M., Engh, R. A., von derSaal, W., van Geerestein, V. J. & Grootenhuis, P. D.(1999). Comparison of two implementations of theincremental construction algorithm in ¯exible dock-ing of thrombin inhibitors. J. Comput. Aided Mol.Des. 13, (2), 167-183.

Kocher, J. P., Rooman, M. J. & Wodak, S. J. (1994). Fac-tors in¯uencing the ability of knowledge-basedpotentials to identify native sequence-structurematches. J. Mol. Biol. 235, (5), 1598-1613.

Koehl, P. & Delarue, M. (1994). Polar and nonpolaratomic environments in the protein core: impli-cations for folding and binding. Proteins: Struct.Funct. Genet. 20, (3), 264-278.

Kollman, P. (1993). Free energy calculations: applicationsto chemical and biochemical phenomena. Chem.Rev. 93, 2395-2417.

Kollman, P. A. (1996). Advances and continuing chal-lenges in achieving reaistic and predictive simu-lations of the properties of organic and biologicalmolecules. Acc. Chem. Res. 29, (10), 461-469.

Koppensteiner, W. A. & Sippl, M. J. (1998). Knowledge-based potentials-back to the roots. Biochemistry(Moscow), 63, (3), 247-252.

Kossiakoff, A. A., Randal, M., Guenot, J. & Eigenbrot, C.(1992). Variability of conformations at crystal con-tacts in BPTI represent true low-energy structures:correspondence among lattice packing and molecu-lar dynamics structures. Proteins: Struct. Funct.Genet. 14, (1), 65-74.

Kubinyi, H. (1998). Structure-based design of enzymeinhibitors and receptor ligands. Curr. Opin. DrugDiscov. Devel. 1, (1), 4-15.

Kuntz, I. D., Blaney, J. M., Oatley, S. J., Langridge, R. &Ferrin, T. E. (1982). A geometric approach to macro-molecule-ligand interactions. J. Mol. Biol. 161, 269-288.

Kuntz, I. D., Meng, E. C. & Shoichet, B. K. (1994). Struc-ture-based molecular design. Acc. Chem. Res. 27, (5),117-123.

Lengauer, T. & Rarey, M. (1996). Computationalmethods for biomolecular docking. Curr. Opin.Struct. Biol. 6, (3), 402-406.

Li, A.-J. & Nussinov, R. (1998). A set of van der Waalsand Coulombic radii of protein atoms for molecular


and solvent-accessible surface calculation, packingevaluation, and docking. Proteins: Struct. Funct.Genet. 32, 111-127.

Makino, S. & Kuntz, I. D. (1997). Automated ¯exibleligand docking method and its application for data-base search. J. Comput. Chem. 18, (14), 1812-1825.

Mitchell, J. B. O., Laskowski, R. A., Alex, A., Forster,M. J. & Thornton, J. M. (1999a). BLEEP-potential ofmean force describing protein-ligand interactions:II. Calculation of binding energies and comparisonwith experimental data. J. Comput. Chem. 20, (11),1177-1185.

Mitchell, J. B. O., Laskowski, R. A., Alex, A. &Thornton, J. M. (1999b). BLEEP-potential of meanforce describing protein-ligand interactions: I. Gen-erating potential. J. Comput. Chem. 20, (11), 1165-1176.

Miyazawa, S. & Jernigan, R. L. (1996). Residue-residuepotentials with a favorable contact pair term and anunfavorable high packing density term, for simu-lation and threading. J. Mol. Biol. 256, (3), 623-644.

Miyazawa, S. & Jernigan, R. L. (1999). Self-consistentestimation of inter-residue protein contact energiesbased on an equilibrium mixture approximation ofresidues. Proteins: Struct. Funct. Genet. 34, (1), 49-68.

Muegge, I. & Martin, Y. C. (1999). A general and fastscoring function for protein-ligand interactions: asimpli®ed potential approach. J. Med. Chem. 42, (5),791-804.

Muegge, I., Martin, Y. C., Hajduk, P. J. & Fesik, S. W.(1999). Evaluation of PMF scoring in docking weakligands to the FK506 binding protein. J. Med. Chem.42, (14), 2498-2503.

Muller, K. (1995). De novo design. In Perspectives inDrug Discovery and Design (Anderson, P. S.,Kenyon, G. L. & Marshall, G. R., eds), vol. 3,ESCOM, Leiden.

Murray, C. W., Auton, T. R. & Eldridge, M. D. (1998).Empirical scoring functions. II. The testing of anempirical scoring function for the prediction ofligand-receptor binding af®nities and the use ofBayesian regression to improve the quality of themodel. J. Comput. Aided Mol. Des. 12, (5), 503-519.

Park, B. & Levitt, M. (1996). Energy functions that dis-criminate X-ray and near native folds from well-constructed decoys. J. Mol. Biol. 258, (2), 367-392.

Pickett, S. D. & Sternberg, M. J. (1993). Empirical scaleof side-chain conformational entropy in proteinfolding. J. Mol. Biol. 231, (3), 825-839.

Rarey, M., Kramer, B., Lengauer, T. & Klebe, G. (1996).A fast ¯exible docking method using an incremen-tal construction algorithm. J. Mol. Biol. 261, (3), 470-489.

Rose, P. W. (1997). Scoring Methods in Ligand Design, 2ndUCSF Course in Computer-Aided MolecularDesign, San Francisco.

Sharp, K. A., Nicholls, A., Friedman, R. & Honig, B.(1991). Extracting hydrophobic free energies from

experimental data: relationship to protein foldingand theoretical models. Biochemistry, 30, (40), 9686-9697.

Sippl, M. J. (1990). Calculation of conformational ensem-bles from potentials of mean force. An approach tothe knowledge-based prediction of local structuresin globular proteins. J. Mol. Biol. 213, (4), 859-883.

Sippl, M. J. (1993). Boltzmann's principle, knowledge-based mean ®elds and protein folding. An approachto the computational determination of protein struc-tures. J. Comput. Aided Mol. Des. 7, (4), 473-501.

Sippl, M. J. (1995). Knowledge-based potentials for pro-teins. Curr. Opin. Struct. Biol. 5, (2), 229-235.

Skolnick, J., Jaroszewski, L., Kolinski, A. & Godzik, A.(1997). Derivation and testing of pair potentials forprotein folding. When is the quasichemical approxi-mation correct? Protein Sci. 6, (3), 676-688.

Stahl, M. & Bohm, H.-J. (1998). Development of ®lterfunctions for protein-ligand docking-fast, fully auto-mated docking of ¯exible ligands to protein bindingsites. J. Mol. Graph. Model. 16, (3), 121-132.

Testa, B., Carrupt, P. A., Gaillard, P., Billois, F. &Weber, P. (1996). Lipophilicity in molecular model-ing. Pharm. Res. 13, (3), 335-343.

Torda, A. E. (1997). Perspectives in protein-fold recog-nition. Curr. Opin. Struct. Biol. 7, (2), 200-205.

Vajda, S., Sippl, M. & Novotny, J. (1997). Empiricalpotentials and functions for protein folding andbinding. Curr. Opin. Struct. Biol. 7, (2), 222-228.

Van Drie, J. H. & Lajiness, M. S. (1998). Approaches tovirtual library design. Drug Discov. Today, 3, (6),274-283.

Verdonk, M. L., Cole, J. C. & Taylor, R. (1999). Super-Star: a knowledge-based approach for identifyinginteraction sites in proteins. J. Mol. Biol. 289, (4),1093-1108.

Verkhivker, G., Appelt, K., Freer, S. T. & Villafranca, J. E.(1995). Empirical free energy calculations of ligand-protein crystallographic complexes. I. Knowledge-based ligand-protein interaction potentials appliedto the prediction of human immunode®ciency virus1 protease binding af®nity. Protein Eng. 8, (7), 677-691.

Wallqvist, A. & Covell, D. G. (1996). Docking enzyme-inhibitor complexes using a preference-based free-energy surface. Proteins: Struct. Funct. Genet. 25, (4),403-419.

Wallqvist, A., Jernigan, R. L. & Covell, D. G. (1995). Apreference-based free-energy parameterization ofenzyme-inhibitor binding. Applications to HIV-1-protease inhibitor design. Protein Sci. 4, (9), 1881-1903.

Walters, W. P., Stahl, M. T. & Murcko, M. A. (1998). Vir-tual screening - an overview. Drug Discov. Today, 3,(4), 160-178.

Warshel, A. & Aqvist, J. (1991). Electrostatic energy andmacromolecular function. Annu. Rev. Biophys. Bio-phys. Chem. 20, 267-298.

Edited by R. Huber

(Received 2 August 1999; received in revised form 8 November 1999; accepted 8 November 1999)

Knowledge-based Scoring Function to Predict Protein-Ligand ...€¦ · LUDI (Bohm, 1992) and FlexX...

Documents

Transcript of Knowledge-based Scoring Function to Predict Protein-Ligand ...€¦ · LUDI (Bohm, 1992) and FlexX...