COSMOsim: Bioisosteric Similarity Based on COSMO-RS sigma Profiles

COSMOsim: Bioisosteric Similarity Based on COSMO-RSσ Profiles

Michael Thormann,† Andreas Klamt,*,‡ Martin Hornig,‡ and Michael Almstetter†

Origenis GmbH, Gmunder Str. 37A, 81379 Mu¨nchen, Germany, and COSMOlogic GmbH and Co. KG,Burscheider Str. 515, 51381 Leverkusen, Germany

Received October 20, 2005

A novel approach for the quantification of drug similarity is proposed, which makes use of the surfacepolarities, that is, conductor surface polarization charge densitiesσ, as defined in the quantum chemicallybased conductor-like screening model for realistic solvation(COSMO-RS). The histogram of these surfacepolarities, the so-calledσ profiles, have been proven to be the key for the calculation of all kinds of partitionand adsorption coefficients and, therefore, of relevant absorption, distribution, metabolism, and excretionparameters such as solubility, pKa, log BB, and many others. They also carry a large part of the informationrequired for the estimation of desolvation and binding processes responsible for receptor binding and enzymeinhibition of drug molecules. Thus, a large degree of similarity with respect to theσ profiles appears to bea necessary condition for drugs of similar physiological action. Driven by this insight, we propose aσ-profile-based drug similarity measure COSMOsim for the detection of new bioisosteric drug candidates. In severalexamples, we demonstrate its statistical and pharmaceutical plausibility, its practicability for real drug researchprojects, and its unique independence from the chemical structure, which enables scaffold hopping in anatural way.

INTRODUCTION

Bioisosteric transformation is one of the most frequentlyused approaches to the design and optimization of com-pounds with biopharmacological importance. Both scaffoldhopping and group interchange converge seamlessly in thisapproach. Current computational approaches to bioisosterictransformation are, so far, a posteriori classifiers that deductrules, which are then applied in a project-dependent manner.We describe the development and application of an a priorimethod for the prediction of bioisosters. We assume thatbioisosters must have similar physicochemical properties thatrule their interactions with different environments such assolvents, membranes, and ultimately protein receptors. Theseinteractions define their biological effects and biopharma-cological properties. We built our method, therefore, uponthe conductor-like screening model for realistic solvation(COSMO-RS), a general and fast methodology for the apriori prediction of thermophysical data. Cheap unimolecularquantum chemical calculations combined with exact statisti-cal thermodynamics provide the information necessary forthe evaluation of molecular interactions. Thus, we canrepresent molecules detached from their chemical structuresas electronic surfaces. For the rapid comparison of COSMOsurfaces, they are projected into 1Dσ profiles. Suitablesimilarity metrics are then developed based on theσ profiles.Empirical data of many thousand bioisosteric transformationsare used to validate the method and to further optimize thefree parameters of the similarity metrics. Finally, the methodis applied to bioisosteric transformations of functional groupsand for virtual high-throughput screening (vHTS).

A number of biological targets of pharmaceutical interestare currently beyond the scope of experimental 3D structure

determination. Examples of such targets are membrane-standing proteins such as ion channels and G-protein coupledreceptors. The design of potent modulators for such targetsis, though, not a hopeless task. The ligand-based design ofcompounds makes use of the structural information of well-characterized compounds that is used at different levels ofabstraction for subsequent intermolecular similarity calcula-tions.1-3 Ideally, the selection of target ligands should followthe concepts of ligand efficiency.4-6 Two scenarios of ligand-based design strategies can be envisaged. First, ligands withimproved potency or improved biophysical properties ulti-mately related to their adsorption, distribution, metabolism,excretion, and toxicity (ADMET) profiles are searched withinthe class of ligands described by the scaffold. Second,alternative structural classes are explored for backup orpatent-busting purposes, a concept termed scaffold hopping.Both approaches are intimately related to the concept ofbioisosterism, that is, the introduction of structural changesinto a given active compound leading to a derivative thatbroadly maintains the bioactivity at the given receptor inquestion following the well-known active analogue principle.

The search for novel and better bioisosters has been thechallenge for medicinal chemistry over the past decades. Onthe one hand, a lot of experience has been gained via trialand error. A survey of successful bioisosteric transformationsis accessible in form of the Bioster database.7 This is a well-suited data set for method development in the bioisosterismfield.8,9 A posteriori analyses of successful bioisosterictransformations led to the common classical and nonclassicalcategorizations of bioisosters.10,11 On the other hand, somea priori concepts tried to rationalize bioisosterism on the basisof physical concepts such as Grimm’s hydride displacementlaw.12,13 Newer nonclassical definitions focus on certainaspects of the compound structures such as molecular shape,topology, pharmacophoric patterns, and electronic isosters.14

However, none of the currently available bioisosteric ap-proaches is built on a solid physicochemical basis.

* Corresponding author phone:+49-2171-731680; fax:+49-2171-731689; e-mail: [email protected].

† Origenis GmbH.‡ COSMOlogic GmbH and Co. KG.

1040 J. Chem. Inf. Model.2006,46, 1040-1053

10.1021/ci050464m CCC: $33.50 © 2006 American Chemical SocietyPublished on Web 03/01/2006

Ultimately, a suitable method must provide an intermo-lecular similarity measure that ranks proven bioisosteric pairsof compounds high while ranking random pairs low. It canthen be used for picking tentative bioisosters for a targetligand from compound databases. Furthermore, intermolecu-lar similarity is used as an objective function for the designand optimization of target-focused compound libraries.

MATERIALS AND METHODS

COSMO-RS. While almost all computational chemistrymethods used in drug design are based either on the force-field concept or on decomposition concepts such as groupcontributions or fingerprints, a rather orthogonal and fun-damental approach has been developed over the past 15years, which is based on quantum chemistry combined withdielectric continuum solvation and statistical thermodynam-ics. Having been developed in an industrial computationalchemistry lab, COSMO-RS15-17 was originally consideredfor the quantification of environmental and technical partitionbehavior, before it was recognized as being a very generallyapplicable and most predictive model for fluid phasethermodynamics in the chemical engineering community. Inlight of its applicability in wide ranges of chemistry, itsapplicability to biophysical properties became apparent, andit has been proven in several papers on solubility, physi-ological partition properties such as log BB or intestinalabsorption, and pKa during the past years,18-21 and itsextension toward the problem of ligand receptor bindingappears attractive and is presently being exploited. Whiledetailed descriptions of the COSMO-RS theory have beengiven elsewhere, the basic concept of the methods is outlinedas follows.

In the first step, all chemical compounds of a liquid (orpseudo-liquid) ensemble are considered as embedded andswimming in an infinite, perfect conductor. This state of thecompounds can be very well treated by quantum chemicalcalculations combined with dielectric continuum solvationmodels, the most efficient and natural choice for the latterbeing the conductor-like screening model, COSMO.22 Forquantum chemistry, density functional theory (DFT) has beenproven to provide a good compromise of computationalefficiency and reliability, because the much faster semiem-pirical methods suffer from severe deficiencies in solvationelectrostatics, especially if hypervalent elements such assulfur or phosphorus come into play. By such a combinationof methods, the self-consistent state of a molecule withinsuch a virtual conductor, that is, its energy, its geometry,and electron distribution, and the surface polarization charges

of the conductor on the molecular surface can be calculatedat almost the same costs as those in the gas phase.23

This state of molecules in a conductor has proven to be avery useful reference for the understanding of molecularbehavior in the liquid. It is much better suited than thetraditional reference state of an isolated molecule in avacuum. The conductor surface polarization charge density,σ, is a very good local measure of molecular surface polarity,carrying more information than the often considered elec-trostatic potential. Examples of COSMO surfaces color codedby σ are given for water, caffeine, and theophylline in Figure1. The regions of strongly negative molecular polarity aredisplayed in red. It is important to recognize that the negativemolecular regions carry a positive polarization chargedensity,σ, becauseσ is just compensating the molecularelectrostatic field and has, thus, the opposite sign. Thestrongly positive molecular regions carrying negativeσ arecolored blue, while the neutral parts of the molecules withσ close to zero appear green.

A big conceptual advantage of the conductor referencestate is the fact that the molecules together with theirpolarization charges now are electrostatically perfectly non-interacting, because no electric field can escape through thesolute-conductor interface. As long as we leave at least athin film of conductor between the molecules, we can buildany geometrical configuration of the molecules withoutchanging the energy of the system. By allowing for small,volume conserving, and energetically irrelevant deformationsof the surfaces, we can finally build densely packed,liquidlike systems of the molecules, as schematically shownin Figure 2, but still assuming an infinitely thin film ofconductor separating and screening the molecules from eachother. If we suppose that the small deformations requiredfor the close packing do not significantly influence the energyand the polarization charge densities, our ensemble now stillhas the same energy as that in the dilute state in theconductor, but each surface segmentµ with polarizationσµ

of a molecule has a nearest neighbor segmentν with σν;that is, we only have direct face-to-face segment pairs.

Because in nature there is no conductor between themolecules, in the next step, the thin film of conductorbetween the surface segments has to be removed. As shownin the COSMO-RS papers in more detail, we can do thissegment pair by segment pair. In this way, we can considerthe energy difference going along with the removal ofthe conductor between a segment pair (µ,n) as a local sur-face interaction of the neighboring molecules, and wecan quantify its electrostatic and hydrogen bond contribu-

Figure 1. COSMO surfaces color coded by the polarization charge densityσ for water, caffeine, and theophylline.

COSMOSIM J. Chem. Inf. Model., Vol. 46, No. 3, 20061041

tions per unit surface area as

and

whereσ andσ′ are the polarization charge densities of theinteracting surfaces. While the electrostatic misfit part canbe quite accurately derived from theoretical arguments, thehydrogen bond energy term must be considered as anempirical but physically plausible expression. Given the veryfew parameters in these formulas, the interaction energy ofa fixed configuration of our ensemble of molecules relativeto its conductor reference state can, thus, be calculated asan integral of all local pairwise surface interactions.

For a liquid system, we have to calculate the thermody-namic averages of the relevant configurations of our en-semble. Normally, this requires the generation of largenumbers of such ensembles, as done in Monte Carlo ormolecular dynamics simulations. But, because of the localpairwise surface interactions description, the thermodynamicscan be reduced to an ensemble of independently interactingsurface segments. For this purpose, we just need the surfacepolarization charge density distributionpX(σ), the so-calledσ profile, of each compound X, which tells us how muchsurface of polarityσ is available on the surface of compoundX. Because theseσ profiles are of central importance forour new similarity approach, a collection ofσ profiles isshown in Figure 3. Theseσ profiles turned out to be veryuseful fingerprints of molecules. Next, we denote thenormalizedσ profile of a solvent S bypS(σ). For a puresolvent,pS(σ) is just the normalizedσ profile of the solutemolecule, and for a mixture, it is trivially generated fromthe mole fraction weightedσ profiles of the components.On the basis ofpS(σ), the statistical thermodynamics of theinteracting surface pairs can be solved efficiently and exactlyfrom the integral equation

whereµS(σ) is the chemical potential of an additional surfacesegment in the ensemble S andaeff is the size of an effectivecontact segment. The functionµS(σ), called theσ potentialfrom here on, has to be derived recursively from eq 3 becauseof its appearance on both sides of the equation. Theσpotential describes how much a solvent S likes additionalsurface area of polarityσ. As explained in more detailelsewhere, theseσ potentials express a wide range ofimportant aspects of the interaction capabilities of the solvent,including electrostatics, hydrogen bonding, and hydrophobic-ity. Finally, the chemical potential of a compound X insolvent S is calculated from theσ profile of the solute andthe σ potential of the solvent as

where µS,combX is a usually small correction for the size

effects of the solute and solvent and, thus, a combinatorialcontribution, depending on volumes and surface areas of thesolute and solvent. Hence, the important part of the chemicalpotential of a solute X in a solvent S is expressed as a surfaceintegral of the solventσ potential over the surface of thesolute X, becausepX(σ) dσ is just the amount of surface areaof polarity σ on the surface of X.

In this way, COSMO-RS gives access to the chemicalpotentials of almost arbitrary compounds in almost arbitraryliquid phases using theσ profile of the solute as the onlyinformation. While chemically well-defined phases such aswater, octanol, alkanes, and so forth and the correspondingpartition coefficients are directly accessible by COSMO-RStheory, partitioning between a physiological phase such asbetween the blood and brain and other ADME propertiescan be derived from theσ profiles with a slightly moreempirical extension, theσ-moment approach. Finally, it hasbeen shown that even drug solubility can be calculated fromthe σ profiles, using the chemical potentialµX

X of the drugin its virtual liquid state as the most important input.

Because solubility and ADME properties can be well-described from theσ profile alone, we can expect that twocompounds with similarσ profiles should have similarADME characteristics. But, we must be aware that thebinding of a drug to a receptor involves constraints relatedto the 3D relations of the various polar, hydrogen bonding,and hydrophobic interaction sites. This information is notincluded in theσ profile any more. Nevertheless, it is at least

Figure 2. Schematic visualization of COSMO-RS contacts andinteractions in the molecular cavity.

Figure 3. Solventσ profiles. These profiles show the amount ofmolecular surface in a given interval of polarization charge densityσ.

µSX ) ∫ µS(σ) pX(σ) dσ + µS,comb

X (4)

emisfit(σ,σ′) = R′2

(σ + σ′)2 (1)

ehb(σ,σ′) = chb(T) min[0,σσ′ + σhb2] (2)

µS(σ) )

-kT ln{∫ pS(σ′) exp[- aeff eint(σ,σ′) - µS(σ′)kT ] dσ′} (3)

1042 J. Chem. Inf. Model., Vol. 46, No. 3, 2006 THORMANN ET AL.

a necessary though not sufficient requirement for stronglybinding ligands of a receptor that they have roughly the sameamount of surface area available for the various interactionmodes. Thus, it is at least plausible that a drug candidatewith a σ profile similar to that of a known strongly bindingligand has a good chance to be strongly binding as well.Summarizing the above considerations, we consider it as aplausible assumption that the similarity ofσ profiles shouldbe a powerful measure for the assessment of drug similarity.

Application of COSMO-RS to Protein-Ligand Inter-actions.COSMO-RS provides access to chemical potentials(Gibbs free energies) of almost arbitrary compounds inalmost arbitrary phases. This grants direct access to importantchemophysical and biophysical properties such as phasepartition (e.g.,n-octanol water partition as expressed in logP) and thermodynamic solubility in different solvents (e.g.,intrinsic aqueous molar solubility logS). COSMO-RSprovides, furthermore, a sound basis for the computation ofchemical potentials in mixed phases on the basis of statisticalthermodynamics (COSMOtherm). This allows the treatmentof more complex compartment partitions including extra-cellular matrix/cellular membranes, intestinal lumen/blood,and blood/brain.

Noncovalent reversible protein-ligand interactions canwell be described by the thermodynamic cycle given inFigure 4 for ligand A binding to receptor P, forming theligand-receptor complex AP.24 The complex formation isdetermined by the binding free energy,∆Gbinding, underthermodynamic equilibrium conditions.

The binding free energy,∆Gbinding, and complex dissociationconstantKD can be interconverted following

whereR is the gas constant andT is the temperature.The rigorous statistical thermodynamic treatment of the

ligand, receptor, and ligand-receptor complex as homoge-neous pseudo-liquid phases represents the only approxima-tion. Obviously, at the atomic level, protein-ligand inter-actions can be hampered by steric hindrance due to theanisostropic character of the protein, although electroniccomplementarity in the COSMO concept is given and wouldconsistently lead to energetically favorable interaction.

Data Sets.A virtual screening database of>3.5 millionunique compounds was compiled from various in-house,medchem, and vendor databases. COSMOfrag25 was usedto calculate approximateσ profiles for all of the compounds.This database is dynamically maintained and updated withnew screening compounds. The search for bioisosters of

groups and entire molecules was performed with thisdatabase.

The Bioster database7 contains data on successful bio-isosteric transformations for various receptors and chemicalclasses. This data set was previously used for the evaluationof methods to distinguish between bioisosteric pairs andrandom pairs of molecules.8,9 These molecular pairs wereextracted from the database, and approximateσ profiles werecalculated using COSMOfrag. Obvious prodrugs, ambiguouspairs, and molecules for which noσ profiles could becalculated, like ions, were removed from the set. A list ofrandom pairs was prepared from the same set of moleculesby scrambling the right column of the pair table. The finalsets contained 6041 bioisosteric pairs and 5823 random pairs.All similarity and energy calculations were run on these twosets.

Biophysical Concept of Bioisosteric Transformations.Medicinal chemistry uses bioisosteric transformation as a toolfor the replacement of certain functional groups withalternatives that display higher potency, better specificity,improved safety, and other pharmacological properties or forthe design of novel bioactive compounds via scaffoldhopping for backup and patent-busting purposes such astherapeutic copies of commercialized drugs.26 Commonconcepts deduce rules from data sets that describe previouslysuccessful bioisosteric transformations, and these rules arethen applied to prioritize the synthesis and characterizationof analogues.27 Our approach attempts to provide a biophysi-cal basis for bioisosteric transformations and will allow, assuch, the a priori prediction of bioisosters.

In the ligand-based drug design approach, the receptor isassumed to be constant while the ligand is the variable. Thebioisosteric transformation of ligand A to ligand B, bothbinding to receptor P, can be formulated as a thermodynamiccycle (see Figure 5). For ligand-based drug design purposes,A can be regarded as the target ligand while B is the resultof the bioisosteric transformation applied. This approachallows the calculation of the energetic cost of the bioisosterictransformation∆∆GAP,BP,binding.

All terms of this thermodynamic cycle are directlyaccessible via COSMO-RS and COSMOtherm under theprinciple assumption of interacting pseudo-liquid molecules.The protein desolvation term∆∆GP,aq cancels out. Forcompounds A and B with identicalσ profiles, the mixed-phase desolvation term∆∆GAP,BP,aqbecomes zero, as doesthe protein-ligand interaction term∆∆GAP,BP,cosmo.

The success of a bioisosteric transformation can, thus, bequantified prior to synthesis by computing∆∆GAP,BP,binding.For practical purposes, successful bioisosteric transformationsshould not exceed 1-3 kcal/mol (about 2 log orders ofmagnitude in the binding constantKD). The final goal is togain access to the estimated energetic cost of a bioisosterictransformation to be used to rank different transformationsin virtual screening.

COSMOthermdefines the energetics of molecular interac-tions on the basis of pairwiseσ interactions; thus, theunimolecularσ profiles of the ligands in question ultimatelydefine the energetic contributions. Consistently, the more

Figure 4. Thermodynamic cycle for the equilibrium binding freeenergy∆Gbinding of ligand A binding to receptor P, forming thenoncovalent complex AP.

∆Gbinding ) ∆Gcosmo- ∆GA,aq - ∆GP,aq+ ∆GAP,aq (5)

∆Gbinding ) -RT ln KD (6)

∆∆GAP,BP,binding) ∆∆GAP,BP,cosmo- ∆∆GA,B,aq -∆∆GP,aq+ ∆∆GAP,BP,aq (7)


similar the σ profiles of A and B become, the more theligand-dependent contributing terms cancel out. The nextsection focuses on different intermolecular similarity methodsbased onσ profiles.

Similarity Coefficients. COSMOtherm represents theσprofiles using 61 real values for the relevantσ range fromσ) -3 to +3 e/nm2. We initially started from this 61-binrepresentation, which represents a one-dimensional structure-free holographic electronic profile. We termσ-profile-basedsimilarity methods COSMOsim.

A large set of coefficients is available1,28 to calculateintermolecular distances on the basis of binary, integral, orfloating point vectors containing chemical information. Oneof the widely used coefficients is the Tanimoto coefficient,which has been found to be useful for distance measures ofbinary and integral vectors encoding molecular descriptors.To compareσ profiles, we started with examining thesuitability of the Tanimoto coefficient. Usually, the binaryvariant of the Tanimoto coefficient is used. However,extension to non-negative floating point values is straight-forward:

The Tanimoto coefficientTc is the intermolecular similarity,and l is the number of bins,NA,i and NB,i are the surfaceareas corresponding to bini in molecules A and B,respectively.

Equation 8 reveals that the usability of the Tanimotocoefficient suffers when many bins are nonzero and few binsdiffer largely. In such cases, very high similarities arecomputed that neglect substantial differences. To illustratethese consequences, a congeneric set ofn-alcohols (n-propanol throughn-hexadecanol) was prepared; the corre-spondingσ profiles were computed for all of the compoundsin the set (Figure 6), andTc was calculated usingn-propanolas the target ligand. Despite the very different molecular sizesof n-propanol andn-hexadecanol, high, physically implau-sible Tc values result (Figure 7).

A straightforward solution to this problem appeared to bethe utilization of the relative molecular sizes. The molecularsize is here defined as the molecular surface area (COSMOsurface) that equals the sum over all bins of theσ profile.We call the novel similarity measure the Tanimoto primecoefficient,Tc′.

WhereTc is the Tanimoto coefficient andSA andSB are theCOSMO surface areas of compounds A and B, respectively.

The bin-based Tanimoto similarity ofσ profiles suffersfrom a few theoretical weaknesses. First, its values quitestrongly depend on the fineness of the discretization of theσ range, while a theoretically robust similarity definitionshould be almost independent of the discretization level.Second, because only the ratio of deviation and sum of thetwo σ values of a bin enters the definition of bin similarity,bins with small values of the similarity may have the sameinfluence on the Tanimoto similarity coefficient as bins withlarge values, while under physical aspects, bins with smallvalues should be less important. Finally, the bin-basedsimilarity definition totally disregards the physical neighbor-hood relation ofσ bins. If one compound has a high intensityin bin i while the other has a high intensity in bini + 1, theTanimoto coefficient considers this as dissimilarity, whilesuch slightly shifted peaks would still cause rather similarphysicochemical behavior.

Figure 5. Thermodynamic cycle for the bioisosteric transformation of target ligand A to ligand B, both targeting receptor P.

Figure 6. σ profiles of a congeneric series ofn-alcohols.

Figure 7. σ-profile-based similarities of a congeneric series ofn-alcohols compared ton-propanol using different COSMOsimcoefficients.

Tc )

∑i)1

l

1 -|NA,i - NB,i|NA,i + NB,i

l(8)

T′c ) Tc

min (SA,SB)

max (SA,SB)(9)


On the basis of these considerations, we defined anothersimilarity measure that we callσ-match similarity (SMS).The basic idea behind it is the matching of the most similarsurface area pairs, starting with the most polar segmentspresent in either of the twoσ profiles and proceeding to theleast polar ones. In the first step, the most polar piece of thesurface available in the twoσ profiles is matched with thesame area of the most polar surface segment of the samepolarity sign of the other compound. Now, the minimum areaasegof the two matched surface segments is subtracted frombothσ profiles and a contribution dSMS, as given in eq 10,is added to the raw similarity measure SMS0.

whereσ andσ′ are the twoσ values matched in this step.To better understand this expression, it is useful to considerit first with the two parametersb andc set to zero. In thiscase, the formula apparently gives a contribution identicalto the matched area, if the two matchedσ values are identical.Otherwise, the contribution to the raw similarity index isreduced by a Gaussian function. Hence, the similaritystrongly decreases with an increasing mismatch of the twoσ values. The parametera is a measure for theσ-mismatchtolerance. By repeating the described procedure until nosurface area is left in one of theσ profiles, we finally get araw similarity coefficient SMS0. At the end of the procedure,we will have a residual surface areaares left in the bigger ofthe two compounds. The maximum value of SMS0 can bethe value of the smaller of the two components. This canonly be achieved if the twoσ profiles are identical. Usingthe two parametersb andc, we can introduce two differentways to increase the sensitivity of theσ-similarity measurein the polarσ regions, which might be useful consideringthe fact that especially the hydrogen bond interactionscontribute very strongly in the polar regions thus makingthem more important for drug similarity than the less polarregions. A positive value ofb decreases theσ tolerance inthe polar regions, while a positive value ofc increases theweight of the surface area of polar segments compared withthat of the less polar segments.

If we calculate the maximum achievable values of the rawsimilarity of the two compounds, that is, their raw self-similarities, and denote them by SMS1 and SMS2, respec-tively, then we can define our final expression for theσ-match similarity coefficient SMS by

whered is a parameter responsible for the treatment of theresidual surface areaares. For d ) 0, ares is considered asmaximally dissimilar; ford ) 1, it is treated as maximallysimilar.

The presented definition of theσ-match similarity fulfillsall of the requirements of a similarity metric; that is, it isunity if applied to identical compounds, asymptotically takesa value of 0 for very dissimilar compounds, and is com-mutative with respect to the compounds. Furthermore, it israther independent of the bin discretization of theσ range,reasonably weights its contributions according to the surfaceareas, and introduces a mismatch tolerance with respect toσ. Reasonable values for the four parametersa, b, c, anddof the SMS definition will be presented in the next section.

SMS Parameter Optimization.A genetic algorithm (GA)was used in order to optimize the four free variablesa, b, c,andd in the SMS similarity calculation using empirical dataof the Bioster database. The target function for the GAoptimization was the maximization of the separation ofrandom versus bioisosteric pairs. Therefore, the correspond-ing similarity values were split into 51 bins covering theSMS similarity range from 0 to 1. The overlapping gray zone,g, was defined as follows, and the GA was used to maximize1 - g.

A total of 200 generations of GA optimization with 20 uniqueindividual parameter sets per generation were performedstarting with random values fora (1.0 e a e 5.0),b (0 e be 0.01), andc (0 e c e 0.01). For each individual parameterset, the intermolecular similarity values were recalculatedfor the bioisoster and random data sets, and the individualgvalues were calculated thereupon. The individual solutionswere than sorted byg, and the next generation of individualparameter sets was created by applying crossover andmutation to the binary genomic representations of the better-than-average solutions.

In the first approach,d was held fixed to 0, while in asecond independent run,d was also optimized within 0e de 1. To check for the possible effects of the four parameters,the GA was rerun but this time maximizingg, thus leadingto the worst model possible. The resulting parameters alongwith the parameter-free metricsTc andTc′ are shown in Table1. The optimized parameter sets lead to practically indistin-guishable separation values. To limit the number of free para-meters, the three-parameter model withd set to zero is usedthroughout the paper for the COSMOsimSMS calculations.

Energetic Cost of Bioisosteric Transformation.A bio-isosteric transformation of A to B can hardly be performed

Table 1. Overview of SMS Parameters and Statistics of Separation of Bioisosteric and Random Molecular Pairs

model aa bb cc dd gebioisosters avgSMS( std dev

random avgSMS( std dev

worst 1.096 0.009 430 0.001 310 0.993 0.745 0.570( 0.155 0.471( 0.142best 3 parameters 2.533 0.000 350 0.009 960 fixed 0 0.424 0.697( 0.191 0.382( 0.207best 4 parameters 2.561 0.000 124 0.009 990 0.130 0.424 0.713( 0.180 0.416( 0.197Tc 0.406 0.726( 0.126 0.528( 0.112Tc′ 0.395 0.636( 0.165 0.369( 0.145

a σ tolerance.b σ tolerance of polar surface.c Weighting of polar surface.d Size tolerance.e Gray zone overlap.

g ) ∑i)0

50

min(nbioisoster,i

mbioisoster

,nrandom,i

mrandom) (12)

dSMS(aseg,σ,σ′) )

aseg[1 + c4(σ + σ')2] exp{(σ - σ′)2[1 + b

4(σ + σ′)2]

a2 } (10)

SMS)SMS0 + dares

xSMS1 + SMS2

(11)


in practice without affecting the electronic nature of thecompound. Such changes will have a more or less drasticeffect on the various energetic contributions to the relativebinding free energies (eq 5). For practical purposes, abioisosteric transformation can be regarded as successful ifB does not lose more than around 1-2 log orders ofmagnitude in binding affinity. Such a factor of 10-100 inKD corresponds to a change in binding free energy by 1.3-2.7 kcal/mol at room temperature.

It is conceptually straightforward to suppose that thechange in binding free energies upon bioisosteric transforma-tion becomessmall as the intermolecular similarity ap-proaches unity. The underlying distance metric, however,can have a substantial influence on the meaning ofsmall.To give a qualitative estimation on the energetic cost ofbioisosteric transformation,∆∆GAP,BP,binding, in differentsimilarity metrics concepts, one would ideally compute allof the terms of the thermodynamic cycle given in Figure 5.This is currently not possible with reasonable efforts.

To get a rough estimation of the energetic cost, thedesolvation term∆∆GA,B,aq can be rapidly computed withreasonable accuracy (∼0.5 kcal/mol), as reported previ-ously.19 The difference in free energy of ligand desolvationprovides an estimate for the energetic cost of the bioisosterictransformation for one of the three terms of eq 8.∆Gaq wascalculated for every molecule in the bioisoster and randomdata sets using COSMOtherm.29 Subsequently,∆∆GA,B,aqwascalculated for all pairs.

For a qualitative assessment of the energetic cost, theintermolecular similarity values were plotted against∆∆GA,B,aq.Funnel-shaped curves are obtained for each similarity coef-ficient (see Figures 8-10), which shows that the solvationfree energy differences do becomesmall as the intermolec-ular similarity approaches unity. As expected, the funnelshape depends on the metrics. To get a statistically meaning-ful quantitative estimation of the energetic cost of the bioiso-steric transformation, the molecular pairs were binned accord-ing to their intermolecular similarities. For each of the 21bins, the mean averages and standard deviations of∆∆GA,B,aq

were calculated. The results are presented in Figure 11.On the basis of the quantitative energetic assessment,

reasonable similarity thresholds were derived for the various

distance metrics at the 1, 1.5, and 2 kcal/mol levels.Additionally, the number of bioisosteric and random pairsretrieved at these levels were extracted from the similaritycalculations.

Figure 8. Free energy of solvation changes upon bioisosterictransformation of compound A into B for bioisosteric and randompairs using the COSMOsim Tanimoto coefficient.

Figure 9. Free energy of solvation changes upon bioisosterictransformation of compound A into B for bioisosteric and randompairs using the COSMOsim Tanimoto prime coefficient.

Figure 10. Free energy of solvation changes upon bioisosterictransformation of compound A into B for bioisosteric and randompairs using the COSMOsim SMS coefficient.

Figure 11. Standard deviation of free energy of solvation changesupon bioisosteric transformation of compound A into B forbioisosteric and random pairs using various COSMOsim coef-ficients.


Proper and Improper Bioisosters.Commonly, bioisos-ters are seen as pairs of compounds that show comparableactivity on the target in question. The energetic cost of thecorresponding bioisosteric transformation is low for allbioisosters. We have shown that, for compounds withvery similar σ profiles, that is, COSMOsim approachingunity, the energetic cost of the bioisosteric transformation,∆∆GAP,BP,binding, becomes small as a result of the differentenergetic contribution terms, according to eq 7, becomingsmall. The reverse is, however, not necessarily given: notall fairly equipotent ligands need to have similarσ profiles.Consistently, the COSMOsimvalues of such ligand pairs arelow. The reason can be found in the different energetic contri-bution terms to∆∆GAP,BP,bindingthat sum up to zero, althoughthe single terms do considerably differ from zero and haveopposite signs. This distinct energetic behavior gives rise tothe definition of two principle classes of bioisosters:

Proper Bioisosters.All contributions to the energetic costof the bioisosteric transformation, according to eq 7, aresmall. They have overall similar physicochemical properties,and their similarity is principally receptor-independent. Ahypothetical example is given below:

Improper Bioisosters.The energetic cost of the bioisosterictransformation is small, but the discrete contributions are not

small. They have different biophysical properties, and theirsimilarity is receptor-dependent. A hypothetical example isgiven below:

The application of COSMOsim methods in vHTS will,therefore, yield proper bioisosters. They can fail at the targetreceptor for steric mismatch or repulsion reasons, which are,though, beyond pseudo-liquid treatment. We are, therefore,currently extending COSMOsimtoward the third dimension,and the first results were recently published.30

Separation of Bioisosteric from Random MolecularPairs. The general applicability of COSMOsim was evalu-ated aiming at the numeric separation of the two sets ofmolecular pairs, bioisosteric and random. The differentcoefficientsTc, Tc′, and SMS with optimized parameters wereapplied to each molecular pair. Subsequently, the resultingintermolecular similarities were evaluated in the normalizedand cumulative histograms (Figures 12-14).

Group Exchange Transformations with COSMOsim.Group exchange applications are useful for the selection ofstarting materials to be employed in the next generation ofcompounds maintaining the scaffold (and therefore minimiz-ing the chance of steric repulsion and maximizing thesuitability of the pseudo-liquid treatment). We have selected

Figure 12. Separation of known bioisosters from random pairs resulting from the application of the COSMOsimTanimoto coefficient tothe BioSter data set (left: normalized distribution; right, cumulative normalized distribution).

Figure 13. Separation of known bioisosters from random pairs resulting from the application of the COSMOsimTanimoto prime coefficientto the BioSter data set (left, normalized distribution; right, cumulative normalized distribution).

∆∆GAP,BP,binding) 0 kcal) 0 + 0 + 0 + 0 kcal

∆∆GAP,BP,binding) 0 kcal) 5 - 8 + 15 - 12 kcal


four small molecules that are found incorporated in a plethoraof natural compounds and xenobiotics and for which manybioisosteric conformations are known, that is, cyclohexane,naphthalene, thiazole, and propionic acid. Theσ profiles ofthese compounds were calculated, and theσ-profile database

was screened for the most similar molecules according tothe COSMOsimSMS coefficient. To make a comparison towell-established 2D fingerprint similarity techniques possible,we calculated the Tanimoto coefficient on the basis of 1024-bit Daylight keys,31 often just (wrongly) called Tanimoto

Figure 14. Separation of known bioisosters from random pairs resulting from the application of the COSMOsim SMS coefficient to theBioSter data set (left, normalized distribution; right, cumulative normalized distribution).

Figure 15. Bioisosters resulting from vHTS using cyclohexane as the target. COSMOsimSMS coefficients are given below the structures(left) along with the corresponding Daylight key Tanimoto coefficient (right).


similarity, for the top-ranking compounds. The results aregiven in Figures 15-18.

Whole Molecule Transformations with COSMOsim. Avirtual screening application of COSMOsimwas performed.The target ligand, chlorpromazine, is a member of thetricyclic antidepressants class. The most similar compoundsof the σ-profile database, in terms of SMS, are given inFigure 19 along with the corresponding Daylight fingerprintTc values.

RESULTS AND DISCUSSION

COSMO-RS and COSMOtherm provide the basis for arigorous treatment of the energetic contributions of protein-ligand interactions. The only necessary assumption is thatthe ligand, receptor, and noncovalent ligand-receptor com-plex behave as pseudo-liquids or isotropic phases. Thisimplies that there is no steric repulsion between the ligandand receptor upon complex formation, which is certainlyvalid for many potent, highly efficient ligands.4 Stericmismatch and repulsion and their energetic consequences are,thus, beyond the scope of COSMOsim.

We have focused our work on ligand-based design,following the concept of bioisosteric transformations, thatis, hypothetical reactions linking compounds A and B.Bioisosteric transformations target the same receptor and can,thus, be formulated as the thermodynamic cycle given inFigure 5. This thermodynamic cycle provides the basis forthe calculation of the energetic cost,∆∆GAP,BP,binding, of thebioisosteric transformation on the basis of structure-free 1Dσ profiles and can be regarded as the biophysical backgroundof COSMOsim.

For practical applications, this energetic cost has to be low,on the order of a few kilocalories per mole, to not lose toomuch binding affinity. For a large number of successfulbioisosteric transformations and random molecular pairs, wecould show that bioisosters do indeed have more similarσprofiles than random molecular pairs (see Table 2). Thesimple Tanimoto similarity coefficient was apparently im-proved by the introduction of the relative molecular sizes,as outlined in the alcohol example (see Figure 6). Thenumber of bioisosteric pairs retrieved at the same energeticcost (see Table 1) was, though, slightly lower for the

Figure 16. Bioisosters resulting from vHTS using naphthalene as the target. COSMOsimSMS coefficients are given below the structures(left) along with the corresponding Daylight key Tanimoto coefficient (right).


Tanimoto prime coefficient. The neighborhood of bins inthe σ profile and the resulting biophysical impact arecompletely neglected by both Tanimoto-based coefficients.Therefore, we developed the SMS metric that accounts forthe biophysical relevance of neighboring bins, the distinctimportance of polar versus apolar regions, and differencesin molecular size.

The four free parameters of the SMS were optimized toachieve maximum separation of the bioisosters from randompairs. A closer investigation of the parameter sets obtainedfrom the GA optimization as given in Table 1 reveals thefollowing trend: improved metrics are obtained with abalancedσ tolerance (abest3) 2.533 andabest4) 2.561), whileits neglect leads to a bad separation (aworst ) 1.096); a harshdecrease of theσ tolerance in the polar region leads to badseparation (bworst ) 0.009 430), while a slight decrease yieldsa good separation (bbest3) 0.000 350 andbbest4) 0.000 124);the similarity of polar regions must be weighted higher thanthat of apolar regions (cbest3 ) 0.009 960 andcbest4 )0.009 990) otherwise the separation suffers (cworst ) 0.001 310);

and molecular size should not change for a bioisosterictransformation otherwise the separation suffers (dworst )0.993).

These findings are in accordance with previous findingsconcerning the size of bioisosteric groups10 and the generalimportance of polar groups for binding6 and solvation. Themost striking difference in SMS as opposed to the Tanimotocoefficients is, however, the introduction of theσ-toleranceparametera that does, indeed, lead to a great improvementof the method. The application of the various coefficients tothe bioisoster and random pair molecule sets show that allCOSMOsim coefficients can be used for the prediction ofbioisosters. However, the SMS metric is to be preferred overthe Tanimoto-coefficient-based measures because it is builtupon a sound biophysical concept. Moreover, SMS retrieves,about twice as often, bioisosters at the same energetic costfor the bioisosteric transformation, as expressed in the meansquare change in solvation∆∆GA,B,solv (see Table 1).

COSMOsim is extremely fast (29 689, 28 078, and 9869compounds per second on a single 3 GHz Pentium 4 CPU

Figure 17. Bioisosters resulting from vHTS using thiazole as the target. COSMOsimSMS coefficients are given below the structures (left)along with the corresponding Daylight key Tanimoto coefficient (right).


for Tc, Tc′, and SMS) and is, therefore, well-suited for thevirtual HTS of billions of compounds. We recommendperforming explicit calculations at the DFT BP-SVP-COSMO-SP level using a bioactive conformation of the target ligandin order to improve the quality of the targetσ profile.Moreover, explicit calculations can be run overnight on thetop-ranking compounds because the corresponding DFT-basedσ profiles provide a basis for the calculation ofbiophysically relevant properties such as pKa, log P, log S,and so forth with higher accuracy.19,20,32

The assessment of the group transformation applicationsreveals clearly that COSMOsimperceives molecular similar-ity in a way that medicinal chemists do. The results givenin Figures 15 and 16 underline the apolar aliphatic andaromatic characters and sizes of cyclohexane and naphthalenebioisosters, respectively. These simple bioisosteric transfor-mations are, though, not at all perceived by the Daylightkey (substructure) based similarities. Similar results areexpected for Unity or MDL keys, but one has to keep inmind that these methods were mainly developed as hash keysand bioisosterism is beyond their scope, although they arewidely used for this purpose.33 The two polar group examplesreveal further advantages of the structure-free comparisonCOSMOsim. Well-known bioisosters of thiazole (see Figure

17) such as oxazole and pyridine appear in the top-rankinglist as expected, while the structure-based approach wouldmiss them in every virtual screening. It is important to stressthat the same structure-based approach would likely fail torank larger compounds containing thiazole and pyridine asfunctional groups as well. The propionic acid example (seeFigure 18) paints a good picture of how electronics andmolecular size are reflected in COSMOsim. Obviously, quitea few hits are carboxylic acids of similar size, that is, trivialstructure derivatives and as such well-perceived by theDaylight key method. COSMOsim, however, retrieves ad-ditional well-known bioisosters such as carbamic and hy-droxamic acids; enoles; phosphinic, boronic, and sulfenicacids; and acidic heterocycles such as tetrazoles and oxa-diazolones. To our knowledge, COSMOsim is the onlymethod that retrieves the latter nonclassical bioisosters apriori.

The bioisosteric transformation of chlorpromazine shouldexemplify the suitability of COSMOsimto the discovery anddesign of therapeutic copies. Chlorpromazine is one of theoldest tricyclic antidepressants, found more than 50 yearsago by chance.34 Apart from its antidopaminergic activity,it antagonizes, furthermore, histamine, 5-hydroxytryptamine,acetylcholin, and cannabinoid receptors. Since its discovery,

Figure 18. Bioisosters resulting from vHTS using propionic as the target. COSMOsim SMS coefficients are given below the structures(left) along with the corresponding Daylight key Tanimoto coefficient (right).


a plethora of bioisosters have been discovered and designedthat focus on some central nervous system activity or another.The top-ranking compounds in Figure 19 clearly show thatmany of the strategies employed in medicinal chemistry areperceived by COSMOsim, that is, small variations aroundthe same scaffold, ring substitutions, side-chain-length varia-tions, and various approaches to rigidify the molecules.26

Again, the structure-based screening would have omittedmost of the chlorpromazine analogues found by COSMOsim.This example shows impressively that bioisosteric transfor-mations introducing only small electronic changes can yielda huge variety of distinct proper bioisosters.

The energetic cost of a bioisosteric transformation can bemeasured experimentally in a biological assay after chemical

synthesis. In virtual screening, target-focused solutions areranked according to the corresponding fitness values, forexample, COSMOsim values. It is important to know whatthe energetic cost of a bioisosteric transformation can be andhow this cost depends on the intermolecular COSMOsimsimilarity. Unfortunately, the Bioster database does notcontain any information on binding or inhibition constantsthat could serve to calculate the energetic cost of thecorresponding bioisosteric transformations. It can be as-sumed, however, that bioisosteric pairs do not differ by morethan 2 log orders of magnitude in their inhibition, whichcorresponds roughly to 2.7 kcal/mol. This value is on theorder of magnitude of the solvation energy changes atrelevant similarity levels, according to Table 1. We can,

Figure 19. Bioisosters resulting from vHTS using chlorpromazine as the target. COSMOsimSMS coefficients are given below the structures(left) along with the corresponding Daylight key Tanimoto coefficient (right).

Table 2. Solvation Free Energy Cost-Based Threshold Similaritiestsim and Number of Bioisosters and Random Pairs Found To Be MoreSimilar thantsim

std dev(∆∆GA,B,solv)

<1.0 kcal/mol <1.5 kcal/mol <2.0 kcal/molCOSMOsimcoefficient tsim bioisosters random tsim bioisosters random tsim bioisosters random

SMS 0.883 846 0 0.789 2380 120 0.715 3379 357Tc′ 0.891 191 0 0.789 1152 6 0.689 2522 72Tc 0.906 356 0 0.823 1477 2 0.755 2740 83


therefore, conclude that the energetic changes in solvationof the protein-ligand complexes∆∆GAP,BP,aqand the protein-ligand binding∆∆GAP,BP,cosmoare of the same magnitude.Consistently, bioisosteric transformations with high COS-MOsim values will likely lead to proper bioisosters if noadditional steric repulsion is introduced. Also, the energeticcost drops as the proper bioisosteric pair becomes moresimilar.

It should be underlined that other physicochemical mo-lecular properties (log P, log S, etc.) follow the samethermodynamic cycle for a bioisosteric transformation shownin Figure 5 by substituting the protein receptor P with anotherpure or mixed isotropic or anisotropic phase of interest(water, octanol, blood, brain, etc.). Successful bioisosterictransformations will, therefore, yield compounds with overallsimilar properties with the exception of their chemicalstructure.

For isotropic phases, steric repulsion does not exist.Anisotropic phases such as proteins can, however, displaythe steric mismatch and repulsion issues, and consistently, aproper bioisosteric transformation will eventually not workfor a given receptor (while it might well work for anotherreceptor). The biological assay remains to provide theultimate proof. COSMOsimwas successfully employed in avariety of projects for group transformations and target-focused library design where it already delivered a varietyof potent inhibitor families for different targets.

REFERENCES AND NOTES

(1) Bender, A.; Glenn, R. C. Molecular Similarity: a Key Technique inMolecular Informatics.Org. Biomol. Chem.2004, 2, 3204-3218.

(2) Jain, A. N. Ligand-Based Structural Hypotheses for Virtual Screening.J. Med. Chem.2004, 47, 947-961.

(3) Agrafiotis, D. K.; Myslik, J. C.; Salemme, F. R. Advances in DiversityProfiling and Combinatorial Series Design.Mol. DiVersity 1999, 4,1-22.

(4) Kuntz, I. D.; Chen, K.; Sharp, K. A.; Kollman, P. A. The MaximalAffinity of Ligands. PNAS1999, 96, 9997-10002.

(5) Hopkins, A. L.; Groom, C. R.; Alex, A. Ligand Efficiency: a UsefulMetric for Lead Selection.Drug DiscoVery Today2004, 9, 431-433.

(6) Andrews, P. R.; Craik, D. J.; Martin, J. L. Functional GroupContributions to Drug-Receptor Interactions.J. Med. Chem.1984, 27,1648-1657.

(7) BIOSTER Database, Synopsys Scientific Systems. http://www.syn-opsys.co.uk (accessed mmm yyyy).

(8) Schuffenhauer, A.; Gillet, V. J.; Willet, P. Similarity Searching ofThree-Dimensional Chemical Structures: Analysis of the BIOSTERDatabase Using Two-Dimensional Fingerprints and Molecular FieldDescriptor.J. Chem. Inf. Comput. Sci.2000, 40, 295-307.

(9) Vidal, D.; Thormann, M.; Pons, M. LINGO, an Efficient HolographicText Based Method To Calculate Biophysical Properties and Inter-molecular Similarities.J. Chem. Inf. Model.2005, 45, 386-393.

(10) Patani, G. A.; LaVoie, E. J. Bioisosterism: A Rational Approach inDrug Design.Chem. ReV. 1996, 96, 3147-3176.

(11) Burger, A. Isosterism and Bioisosterism in Drug Design.Prog. DrugRes.1991, 37, 287-371.

(12) Grimm, H. G. Structure and Size of the Nonmetallic Hydrides.Z.Electrochem.1925, 31, 474-480.

(13) Grimm, H. G. On the Systematic Arrangement of Chemical Com-pounds from the Perspective of Research on Atomic Composition andon Some Challenges in Experimental Chemistry.Naturwissenschaften1929, 17.

(14) Kier, L. B.; Hall, L. H. Bioisosterism: Quantitation of Structure andProperty Effects.Chem. BiodiVersity 2004, 1, 138-151.

(15) Klamt, A. COSMO-RS: From Quantum Chemistry to Fluid PhaseThermodynamics and Drug Design; Elsevier: Amsterdam, 2005.

(16) Klamt, A. Conductor-Like Screening Model for Real Solvents: A NewApproach to the Quantitative Calculation of Solvation Phenomena.J.Phys. Chem.1995, 99, 2224-2235.

(17) Klamt, A.; Jonas, V.; Buerger, T.; Lohrenz, J. C. W. Refinement andParametrization of COSMO-RS.J. Phys. Chem. A1998, 102, 5074-5085.

(18) Klamt, A.; Eckert, F.; Hornig, M. COSMO-RS: A Novel View toPhysiological Solvation and Partition Questions.J. Comput.-Aided Mol.Des.2001, 15, 355-365.

(19) Klamt, A.; Eckert, F.; Hornig, M.; Beck, M. E.; Burger, T. Predictionof Aqueous Solubility of Drugs and Pesticides with COSMO-RS.J.Comput. Chem.2002, 23, 275-281.

(20) Klamt, A.; Eckert, F.; Diedenhofen, M.; Beck, M. E. First PrinciplesCalculations of Aqueous pKa Values for Organic and Inorganic AcidsUsing COSMO-RS Reveal an Inconsistency in the Slope of the pKaScale.J. Phys. Chem. A2003, 107, 9380-9386.

(21) Klamt, A.; Diedenhofen, M.; Jones, R.; Connolly, P. C. The use ofsurface charges from DFT calculations to predict intestinal absorption.J. Chem. Inf. Model.2005, 45, 1337-1342.

(22) Klamt, A.; Schueuermann, G. COSMO: A New Approach to DielectricScreening in Solvents with Explicit Expressions for the ScreeningEnergy and Its Gradient.J. Chem. Soc., Perkin Trans. 21993, 799-805.

(23) Scha¨fer, A.; Klamt, A.; Sattel, D.; Lohrenz, J. C. W.; Eckert, F.COSMO Implementation in TURBOMOLE: Extension of an EfficientQuantum Chemical Code Towards Liquid Systems.Phys. Chem.Chem. Phys.2000, 2, 2187-2193.

(24) Gohlke, H.; Klebe, G. Approaches to the Description and Predictionof the Binding Affinity of Small-Molecule Ligands to MacromolecularReceptors.Angew. Chem., Int. Ed.2002, 41, 2644-2676.

(25) Hornig, M.; Klamt, A. COSMOfrag: A Novel Tool for HighThroughput ADME Property Prediction and Similarity ScreeningBased on Quantum Chemistry.J. Chem. Inf. Model.2005, 45, 1169-1177.

(26) Wermuth, C. G.Practice of Medicinal Chemistry, 2nd ed.; AcademicPress Ltd.: New York, 2003.

(27) Sheridan, R. P. The Most Common Chemical Replacements in Drug-Like Compounds.J. Chem. Inf. Comput. Sci.2002, 42, 103-108.

(28) Salim, N.; Holliday, J.; Willett, P. Combination of Fingerprint-BasedSimilarity Coefficients Using Data Fusion.J. Chem. Inf. Comput. Sci.2003, 43, 435-442.

(29) Eckert, F.; Klamt, A.COSMOtherm, version C2.1, revision 01.04;COSMOlogic KG: Leverkusen, Germany, 2004.

(30) Bender, A.; Klamt, A.; Wichmann, K.; Thormann, M.; Glen, R. C.Molecular Similarity Using COSMO Screening Charges (COSMO/3PP).Lect. Notes Comput. Sci.2005, 3695, 175-185.

(31) Daylight; Daylight Chemical Information Systems: Santa Fe, NM.http://www.daylight.com (accessed Jan 2005).

(32) Klamt, A.; Eckert, F. COSMO-RS: A Novel and Efficient Methodfor the a priori Prediction of Thermophysical Data of Liquids.FluidPhase Equilib.2000, 172, 43-72.

(33) Martin, Y. C.; Traphagen, L. M. Do Structurally Similar MoleculesHave Similar Biological Activity?J. Med. Chem.2002, 45, 4350-4358.

(34) Shen, W. W. A History of Antipsychotic Drug Development.Compr.Psychiatry1999, 40, 407-414.

CI050464M


COSMOsim: Bioisosteric Similarity Based on COSMO-RS sigma Profiles

Documents

Transcript of COSMOsim: Bioisosteric Similarity Based on COSMO-RS sigma Profiles