building molecular charge distributions from fragments: application to hiv-1 protease inhibitors

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Building Molecular Charge Distributionsfrom Fragments: Application to HIV-1Protease Inhibitors

L. YOUNG,1U I. A. TOPOL,1 A. A. RASHIN,2 and S. K. BURT1

1Structural Biochemistry Program, Frederick Biomedical Supercomputing Center, SAIC Frederick,NCI-FCRDC, Frederick, MD 21702; and 2BioChemComp Inc., Teaneck, NJ

Received 6 February 1996; accepted 25 June 1996

ABSTRACT

Interaction energies are a function of the molecular charge distribution. Inprevious work, we found that the set of atomic partial charges giving the bestagreement with experimental vacuum dipole moments were from densityfunctional theory calculations using an extended basis set. Extension of suchcomputations to larger molecules requires an atomic partial charge calculationbeyond present computational resources. A solution to this problem is thecalculation of atomic partial charges for segments of the molecule andreassociation of such fragments to yield partial charges for the entire molecule.Various partitions and reassociation methods for five molecules relevant toHIV-1 protease inhibitors are examined. A useful method of reassociation isintroduced in which atomic partial charges for a large molecule are computedby fitting to the combined electrostatic potential calculated from the fragmentpartial charges. As expected, the best sites for partitions are shown to be carbon—carbon rather than carbon—nitrogen bonds. Q 1997 by John Wiley & Sons,Inc.

Introduction

major challenge in the field of drug designA is the calculation of free energies of binding.Since most drugs and inhibitors are not covalentlybound to their targets, a good model of the electro-static interaction is important. Atomic partialcharges may be used to model this interaction;

UAuthor to whom all correspondence should be addressed.

however, calculation of these charges must be per-formed such that they represent the molecularcharge distribution as accurately as possible.

Semiempirical methods may be used to calcu-late these charges; however, in the case of certainsmall molecules, the molecular dipole momentsfrom such computations do not agree well withexperiment.1 Calculations of molecular dipole mo-

Ž .ments using density functional theory DFT andan extended basis set with diffuse functionsŽ 2 .DZVPD have shown exceptional agreement with

( )Journal of Computational Chemistry, Vol. 18, No. 4, 522]532 1997Q 1997 by John Wiley & Sons CCC 0192-8651 / 97 / 040522-11

MOLECULAR CHARGE DISTRIBUTIONS

experiment.3, 4 In addition, calculation of hydrationenthalpies for 50 small molecules using partialcharges fit to the DFTrDZVPD electrostatic poten-tial agreed with experimental enthalpies of hydra-tion to within 1.5 kcalrmol, on average.4

Extending the quantum-mechanical partialcharge calculation to larger molecules such as

Ž . ŽHIV-1 protease HIV PR inhibitors as large as 60.nonhydrogen atoms , while maintaining the large

basis set, is beyond present computational re-sources. The usual solution to this problem dividesthe molecule into fragments of a size suitable forcalculation and then reassociates these fragments,yielding partial charges for the large molecule. Inthe following sections, problems surrounding thefragmentation and reassociation of molecules forpartial charge calculations are investigated usingcompounds relevant to HIV PR inhibitors. Weintroduce a novel method for reassociation basedon the electrostatic potential. Finally, such partialcharges for an inhibitor of HIV PR are used in acalculation of an inhibitor]enzyme interactionenergy.

Fragment Problem

The use of a large basis set to calculate atomicŽpartial charges for large molecules 50]60 nonhy-

.drogen atoms is at present computationallyintractable. However, such a calculation may beperformed for fragments and the fragments reasso-ciated to yield the large molecule atomic charges.If atomic charges could be calculated for themolecule as a whole, the values would reflectintramolecular polarization effects. When the par-tial charges are calculated from combining frag-ments, some of this polarization effect is lost. Thus,the proper modeling of polarization is the issue.This issue may be addressed both by examinationof different bond type partitioning and by thestudy of different fragment reassociation methods.

When partitioning the molecule into fragments,the best schemes may be those that cut bonds withthe least polar character such as those formedbetween tetrahedral carbon atoms. For moleculesin which such bond types are lacking, other frag-mentation sites must be examined. Once a frag-ment is produced, a terminal chemical group must

Ž .be added to saturate the cut bond Fig. 1 . Tocurtail large alterations of the fragment dipolemoment, a near neutral terminal group, such as ahydrogen atom or methyl group, is used.

FIGURE 1. }H and }CH terminal groups are shown3( )saturating the cut bond dashed line of one of the

fragments generated from a larger molecule. Methods ofreassociation of the fragments must eliminate theseterminal groups.

For reassembly of the fragments, two methodsŽ . 5are tested here. 1 The neutralization method

simply sums the partial charges of the terminalgroups into the atoms to which they are bonded.For example, the partial charge of the terminal Hatom or terminal methyl group is summed into

Ž .that of the adjoining nitrogen in Figure 1. 2 TheŽ .CEP combined electrostatic potential fit method

combines the fragment electrostatic potentials cal-culated from the fragment partial charges, includ-ing those of terminal hydrogen atoms. These val-ues are calculated at the surface points of thewhole molecule. The atom-centered partial chargesfor the reassembled molecule are calculated byfitting to this combined electrostatic potential. Inthe process, the partial charges of the terminalhydrogen atoms are eliminated and their effect isrepresented in the values of the new set of atom-centered charges.

In summary, the CEP fit method attempts tomodel the polar character of the fragmented bondusing the extra hydrogens as part of the chargedistribution located along the bond, in much thesame way that bond-centered charges are some-times used to better reproduce electric multipoledata. The charges fit to the combined electrostaticpotential are, however, only the atom-centeredcharges. In this way, the CEP fit eliminates thepartial charges on the bond, representing theireffect in the atomic-centered partial charges of thewhole molecule. Although fitting the electrostaticpotential to derive atomic partial charges is com-mon,1, 6, 7 using combined fragment electrostaticpotentials to eliminate terminal hydrogens andthus yield charges for the reassociated moleculehas not, to our knowledge, been reported.

A second version of the CEP fit method wasalso tested. Instead of combining the fragment

JOURNAL OF COMPUTATIONAL CHEMISTRY 523

YOUNG ET AL.

electrostatic potentials by calculating them fromthe fragment partial charges, the fragment DFTelectrostatic potentials may be calculated at themolecular surface of the whole molecule, allowinga simple sum of the DFT fragment electrostaticpotential values at each whole molecule surfacepoint to produce the CEP for the reassociatedmolecule. This version has the advantage of elimi-nating the need for fragment partial charges.

Finally, two other methods are discussed. Over-lap partitioning involves a different method offragmentation. The fragments are cut such thatthey have several atoms in common. Upon reasso-ciation these atoms overlap. Thus, in the averageoverlap method of reassociation, the overlappingatom partial charges are simply averaged.8

The other method is the use of neutral blockinggroups.9 This method allows any type and size ofterminal group. Upon calculating fragmentcharges, this group is constrained to be neutral,allowing reassociation of the fragments by simplydropping the terminal groups.

Calculations

Fragment atomic partial charges were calcu-lated using the electrostatic potential fit option1, 6

in Gaussian 92rDFT single point calculations.10

This software was also used to calculate the frag-ment DFT electrostatic potential on the molecularsurface of the whole molecule. The density func-tional calculations were performed using Becke’sthree-parameter exchange functional11 with thePerdew correlation functional12 using a DZVPDbasis set.2, 13 To compare the recombined moleculecharge distribution with the whole molecule chargedistribution, values of the electrostatic potentialŽ . 1EP from both were calculated at surface points.

Ž .Root mean square RMS differences in the EPvalues were used to evaluate the methods of reas-sociation of the fragments. This evaluation waschosen over a direct comparison of atomic charges,because the value of the interaction energy de-pends on the EP, and the set of atomic partialcharges that can produce a given EP is not unique.Although the best results were expected for bondscut between tetrahedral carbons, other types ofbond partitions were also evaluated by EP RMSdifferences. In addition to the EP evaluation, addi-tional properties were calculated, namely, dipolemoments, free energies of hydration, and interac-tion energies.

Dipole moments were calculated from theatomic partial charges. Free energies of hydrationof the test systems were calculated using theboundary element method.4 The evaluation of theinteraction energies of the enzyme]inhibitor com-plexes were performed using CHARMm 2214, 15

and AMBER 4.0,16 with the corresponding all-atomforce fields. Hydrogen atoms were added to theenzyme and minimized in energy to a gradient

˚tolerance of 0.1 kcalrmol ? A. The nonhydrogenatoms were fixed.

Results and Discussion

Evaluation of various partitions and reassocia-tions requires a comparison of the whole and reas-sociated molecules. For this reason, the moleculeschosen must be large enough for fragmentationbut small enough for a DFTrDZVPD electrostaticpotential calculation. In some cases, more than one

Žcombination of partitions is tested hereafter, acombination of partitions for a molecule will be

.referred to as the fragmentation scheme . The typesof bonds partitioned or cut are mostly differenttypes of carbon—carbon and carbon—nitrogenbonds. The types of atoms at the partitions are

Ž . Ž .tetrahedral carbons CT , carbonyl carbons C ,Ž .aromatic ring carbons CR , proline alpha carbons

Ž . Ž .CP , and amide nitrogens N . Thus, a fragmenta-tion scheme with two partitions, each containingtetrahedral carbons, would be represented by thenotation CT—u CT, CT—u CT, where the slash rep-resents the cut bond.

Ž .We chose to study five model systems A-E asshown in Figure 2. The partitioning schemes stud-ied are represented by dashed lines in Figure 2.These molecules are portions of HIV PR inhibitorsand their geometries were taken from the en-zyme]inhibitor crystallographic data.17 ] 19

EP RMS COMPARISONS

The results from the EP RMS difference calcula-tion between whole and reassociated moleculesare given in Table I. In general, the smallest EPRMS differences are for the CEP fit method withpartitions between carbon atoms. The italicized EPRMS difference values in Table I denote the small-est differences for each molecule. These range from0.9 to 1.4 kcalrmol.20 More specifically, the small-est difference in EP RMS for each molecule using

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( )FIGURE 2. Five molecules A ]E , which are pieces of HIV-1 protease inhibitors, are used to study the fragmentproblem. The dashed lines represent the partitions used to generate the fragments. The combination of partitions for amolecule is referred to as the fragmentation scheme. In most cases, more than one scheme is studied.

the —H neutralization method is 1.4 kcalrmol, onaverage. Using the —CH neutralization method,21

3

it is 2.0 kcalrmol, on average, and the CEP fitmethod yields 1.3 kcalrmol, on average. The elec-trostatic potential was also calculated from theatomic partial charges of fragments with methylterminal groups; however, the results of the fit ofatomic partial charges to this combined electro-static potential from —CH terminal fragments3

were mixed and not as consistent as those usingthe —H terminal group.

f w hol e and f r eassoc are the electrostatic potentialdue to partial charges from the whole moleculecalculation and the fragment joined calculation,respectively. Differences in these values at a singlepoint usually range from 0 to 6 kcalrmol in abso-lute value for the best schemes of each test

Ž .molecule italicized values in Table I , with the


YOUNG ET AL.

TABLE I.Comparison of Electrostatic Potentials of Reassociated Molecules with Those of Whole Molecules forNeutralization and CEP Fit Methods.

Reassociation EP RMS diffa ( )Fragmentation scheme method kcal / mol

b( ) ( ) ( )A Test molecule A di AC-SS diol N = 2046CT }u CT, CT }u CT }H, neutralization 1.219CT }u CT, CT }u CT CEP fit 0.914CT }u CT, CT }u CT }CH , neutralization 1.8533

CT }u N, CT }u N }H, neutralization 4.771CT }u N, CT }u N CEP fit 2.691CT }u N, CT }u N }CH , neutralization 3.6363

( ) ( [[ ( ) ] ] ) ( )B Test molecule B N = N-methyl-N- 2-pyridinylmethyl amino carbonyl -Val-methylamide N = 1641CT }u N, CT }u N }H, neutralization 2.660CT }u N, CT }u N CEP fit 1.725CT }u N, CT }u N }CH , neutralization 3.5773

CT }u N, CT }u C }H, neutralization 1.607CT }u N, CT }u C CEP fit 1.296CT }u N, CT }u C }CH , neutralization 2.4263

CT }u CR, CT }u C }H, neutralization 1.776CT }u CR, CT }u C CEP fit 1.451CT }u CR, CT }u C }CH , neutralization 1.6883

( ) ( ( ) ( ) ) ( )C Test molecule C N- 5-isoquinolyloxyacetyl -methylthioalanine- 2-phenyl ethyl amide N = 1973CT }u C, CT }u C }H, neutralization 1.435CT }u C, CT }u C CEP fit 1.665CT }u C, CT }u C }CH , neutralization 2.3853

( ) ( ) ( )D Test molecule D N-propionate-methylthioalanine-allophenylnorstatine-thioproline-tert-butylamide N = 2413CT }u C, CT }u CT, C }u CP }H, neutralization 2.961CT }u C, CT }u CT, C }u CP CEP fit 1.870

CT }u C, CT }u C }H, neutralization 1.839CT }u C, CT }u C CEP fit 1.289

CT }u C, C }u CP }H, neutralization 1.793CT }u C, C }u CP CEP fit 1.495( ) ( ) ( )E Test molecule E Ace ]Ser ]Leu ]Asn ]Nme N = 1975CT }u C, CT }u C }H, neutralization 1.184CT }u C, CT }u C CEP fit 1.155

C }u N, C }u N }H, neutralization 2.500C }u N, C }u N CEP fit 3.538

aFragmentation schemes are shown in Figure 2.2b N w hole r e assoc whole( )'EP RMS diff = Ý f y f / N , where, for N grid points, f is the electrostatic potential at the i th grid pointi= 1 i i i

due to the partial charges calculated for the unfragmented molecule, and f r e assoc is the electrostatic potential at the i th grid pointidue to the partial charges calculated for the reassembled molecule.

largest deviations appearing near the region offragmentation. Such deviations appear for only afew points out of a total of more than 1000.

Finally, we note that the partial charges of thewhole molecule are obtained by fitting the EPcalculated from the electron density. The quality ofthis fit is also given by an EP RMS difference. Forthe set of test molecules in Figure 2, these valuesrange from 1.0 to 1.3 kcalrmol.

DIPOLE MOMENT AND HYDRATIONENERGY COMPARISONS

In addition to comparing the electrostatic poten-tials of the reassociated and whole molecules,dipole moments and hydration energies were alsocalculated. Table II shows dipole moments andfree energies of hydration for the molecules and

Ž .fragmentation schemes already introduced Fig. 2

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TABLE II.Comparison of Properties of Reassociated Molecules With Those of the Whole Molecule.

ª ªwhole reassoc reassoc whole reassocreassoc b c m ? m DG DG y DGm Dm angleReassoc. solv solv solvwhole 2( ) ( ) ( ) ( ) ( ) ( )Fragmentation method Debye Debye degrees m kcal / mol kcal / mol

( ) ( )A Test molecule A di AC-SS diolwhole wholeDG = y25.29 kcal / mol, m = 5.5 Debyesolv

CT }u CT, CT }u CT }H, neut. 6.1 y0.6 1.9 1.1 y26.05 0.76CT }u CT, CT }u CT CEP fit 5.9 y0.4 1.2 1.1 y25.54 0.25CT }u CT, CT }u CT }CH , neut. 6.3 y0.8 3.4 1.1 y27.01 1.723

CT }u N, CT }u N }H, neut. 6.5 y1.0 4.0 1.2 y33.19 7.90CT }u N, CT }u N CEP fit 7.0 y1.5 4.6 1.3 y29.00 3.71CT }u N, CT }u N }CH , neut. 6.5 y1.0 4.9 1.2 y30.06 4.773

( ) ( [[ ( ) ] ] )B Test molecule B N- N-methyl-N- 2-pyridinylmethyl amino carbonyl -Val-methylamidewhole wholeDG = y12.23 kcal / mol, m = 2.2 Debyesolv

CT }u N, CT }u N }H, neut. 2.3 y0.1 39.7 0.8 y13.55 1.32CT }u N, CT }u N CEP fit 2.0 0.2 23.6 0.8 y12.04 y0.19CT }u N, CT }u N }CH , neut. 2.2 0.0 43.5 0.7 y13.22 0.993

CT }u N, CT }u C }H, neut. 1.9 0.3 11.4 0.9 y12.45 0.22CT }u N, CT }u C CEP fit 2.3 y0.1 2.5 1.1 y11.81 y0.42CT }u N, CT }u C }CH , neut. 2.1 0.1 28.7 0.8 y12.60 0.373

CT }u CR, CT }u C }H, neut. 2.3 y0.1 10.0 1.0 y11.84 y0.39CT }u CR, CT }u C CEP fit 2.9 y0.7 5.5 1.3 y11.56 y0.67CT }u CR, CT }u C }CH , neut. 2.1 0.1 7.3 1.0 y11.77 y0.463

( ) ( ( ) ( ) )C Test molecule C N- 5-isoquinolyloxyacetyl -methylthioalanine- 2-phenyl ethyl amidewhole wholeDG = y16.74 kcal / mol, m = 5.0 Debyesolv

CT }u C, CT }u C }H, neut. 5.5 y0.5 8.6 1.1 y17.03 0.29CT }u C, CT }u C CEP fit 5.3 y0.3 12.5 1.0 y17.03 0.29CT }u C, CT }u C }CH , neut. 5.6 y0.6 13.3 1.1 y18.63 1.893

( ) ( )D Test molecule D N-propionate-methylthioalanine-allophenylnorstatine-thioproline-tert-butylamidewhole wholeDG = y28.82 kcal / mol, m = 3.1 Debyesolv

CT }u C, CT }u CT,C }u CP }H, neut. 4.3 y1.2 19.8 1.3 y32.69 3.87

CT }u C, CT }u CT,C }u CP CEP fit 3.5 y0.4 4.3 1.1 y30.95 2.13

CT }u C, CT }u C }H, neut. 3.7 y0.6 13.4 1.2 y29.73 0.91CT }u C, CT }u C CEP fit 2.9 0.2 10.7 0.9 y29.04 0.22

CT }u C, C }u CP }H, neut. 3.7 y0.6 11.3 1.2 y31.46 2.64CT }u C, C }u CP CEP fit 3.3 y0.2 7.8 1.1 y31.16 2.34

( ) ( )E Test molecule E Ace ]Ser ]Leu ]Asn ]Nmewhole wholeDG = y35.11 kcal / mol, m = 9.8 Debyesolv

CT }u C, CT }u C }H, neut. 10.0 y0.2 2.5 1.0 y35.52 0.41CT }u C, CT }u C CEP fit 10.3 y0.5 1.9 1.1 y35.45 0.34

C }u N, C }u N }H, neut. 8.9 0.9 7.6 0.9 y32.42 y2.69C }u N, C }u N CEP fit 8.4 1.4 11.3 0.8 y30.57 y4.54

aFragmentation schemes are shown in Figure 2.bDm = mwhole y mr e assoc.

c © ©w hole r e asso cThe angle is between m and m .


YOUNG ET AL.

using the CEP fit, —H neutralization, and —CH3neutralization methods of reassociation. Becauseproperties such as free energies of hydration aresensitive not only to the magnitude of the dipolemoment, but also to its direction,4 a normalizedvector inner product between the dipole moment

ªw hol evector of the whole molecule m and that of theªr eassocreassociated molecule m is used to evaluate

the reassociated molecule charge distribution:ª ªw hol e r eassoc w ho l e 2Ž .m ? m r m . In this way, if the twovectors are perfectly aligned and of the same mag-nitude, the value of the expression is one. Table IIshows that the dipole moments of the reassociatedmolecules are comparable to those of the whole

© ©w hol e r eassoc w ho l e 2Ž .molecules, as m ? m r m deviatesfrom 1.0 by a maximum of "0.3. For a singlemolecule and fragmentation scheme, Table IIshows that this expression is often the same ordeviates very little for different methods. Thus thedipole moment vector is not a sensitive measurefor distinguishing between various reassociationmethods for a particular fragmentation scheme.On the other hand, the free energy of hydrationcomparisons are more sensitive and follow veryclosely the rankings found using the EP RMS com-parisons.

Table II shows that the use of the CEP fit methodfor partitions between carbon atoms yields freeenergies of hydration for the reassociated moleculewhich are closest to those of the whole molecule.These numbers range in absolute value from 0.2kcalrmol to 0.3 kcalrmol and are shown in italicsin Table II. The smallest absolute value of thedifferences in hydration energies of the reassoci-ated and whole molecules for each of the five testmolecules using the —H neutralization methodare 0.5 kcalrmol, on average. For the —CH neu-3tralization method, they are 1.3 kcalrmol, on aver-age,21 and for the CEP fit method, 0.3 kcalrmol, onaverage. The reassociated charge distributions re-produce the whole molecules hydration energiesbetter than the whole molecule surface point EPvalues.

INTERACTION ENERGY COMPARISONS

Interaction energies are a direct function of themolecular charge distribution. This property israrely readily available in the evaluation of atomicpartial charges. Since the test molecules in thisstudy are constitutive segments of inhibitors ofHIV PR, we have a unique opportunity to checkthe effect of fragmentation schemes and reassocia-

tion methods on the interaction energy of the testmolecule with HIV PR. The last column of TableIII shows the differences between interaction ener-gies calculated with the whole molecule chargedistribution and those calculated with the reassoci-ated molecule charge distribution. The smallestabsolute value of these differences for eachmolecule is 0.8 kcalrmol, on average, for —Hneutralization, 1.7 kcalrmol,21 on average, for—CH neutralization, and 0.7 kcalrmol, on aver-3age, for the CEP fit method. For three of the fivemolecules, —H neutralization gives the smallestdifferences, whereas, the CEP fit method is compa-rable, albeit slightly better, on average.

( )CEP FIT METHOD VERSION 2

Version 2 of the CEP fit method was tested formolecule A using scheme CT—u CT, CT—u CT andmolecule B using scheme CT—u N, CT—u N. In thisversion, the fragment EP values are calculated onthe whole molecule surface using DFTrDZVPD,and no fragment partial charges are required. Thefragment EP values are simply summed and thewhole molecule partial charges fit to this CEP. TheEP RMS difference was improved by 0.15 kcalrmolfor molecule A and 0.19 kcalrmol for molecule B.Because these changes are not significant, this ver-sion of the CEP fit method was not repeated forthe other molecules and schemes. The improve-ment reflects the small error in the fragment par-tial charge distribution.

OVERLAP PARTITIONING

The overlap partitioning scheme was tested formolecules A and E. These molecules were chosenbecause they yield the best results for EP RMScomparisons. Two overlapping schemes weretested for molecule A as shown in Figure 3A andB. In one case, the overlap is the diol group only;in the other case, the overlap is extended andincludes both the diol group and the Phe sidechains. The EP RMS difference for the diol overlapis 1.5 kcalrmol, which is not an improvement overthe other methods. For the diol and Phe side chainsoverlap, the EP RMS difference is 2.5 kcalrmol.The error introduced by cutting the CT—N bondis lessened in this case by the use of overlapping

Ž .fragments, but the CEP fit method Table IA , withfragmentation scheme CT—u CT, CT—u CT and anEP RMS of 0.9 kcalrmol, still gives better resultsthan either of these overlapping fragment calcula-

ªw hol etions. The calculated dipole moment ratio, m ?

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TABLE III.Comparison of HIV PR } Reassociated Molecule Interaction Energies With Those of the Whole Molecules forNeutralization and EP Fit Methods.

Interactionc dReassociation energy Difference

b ( ) ( )Fragmentation scheme method kcal / mol kcal / mol

a( ) ( )A Test molecule A di AC-SS diol , interaction energy = y109.3 kcal / mol

CT }u CT, CT }u CT }H, neutralization y111.2 1.9CT }u CT, CT }u CT CEP fit y110.4 1.1CT }u CT, CT }u CT }CH , neutralization y112.5 3.23

CT }u N, CT }u N }H, neutralization y113.3 4.0CT }u N, CT }u N CEP fit y114.5 5.2CT }u N, CT }u N }CH , neutralization y111.2 1.93

( ) ( [[ ( ) ] ] )B Test molecule B N- N-methyl-N- 2-pyridinylmethyl amino carbonyl -Val-methylamide , interaction energy= y73.8 kcal / mol

CT }u N, CT }u N }H, neutralization y73.9 0.1CT }u N, CT }u N CEP fit y72.5 y1.3CT }u N, CT }u N }CH , neutralization y73.3 y0.53

CT }u N, CT }u C }H, neutralization y73.3 y0.5CT }u N, CT }u C CEP fit y72.5 y1.3CT }u N, CT }u C }CH , neutralization y73.2 y0.63

CT }u CR, CT }u C }H, neutralization y73.7 y0.1CT }u CR, CT }u C CEP fit y73.2 y0.6CT }u CR, CT }u C }CH , neutralization y72.4 y1.43

( ) ( ( ) ( ) )C Test molecule C N- 5-isoquinolyloxyacetyl -methylthioalanine- 2-phenyl ethyl amide , interaction energy= y75.9 kcal / mol

CT }u C, CT }u C }H, neutralization y75.9 0.0CT }u C, CT }u C CEP fit y75.7 y0.2CT }u C, CT }u C }CH , neutralization y78.5 2.63

( ) ( )D Test molecule D N-propionate-methylthioalanine-allophenylnorstatine-thioproline-tert-butylamide ,interaction energy = y143.2 kcal / mol

CT }u C, CT }u CT, C }u CP }H, neutralization y145.9 2.7CT }u C, CT }u CT, C }u CP CEP fit y142.3 y0.9

CT }u C, CT }u C }H, neutralization y144.3 1.1CT }u C, CT }u C CEP fit y141.6 y1.6

CT }u C, C }u CP }H, neutralization y144.2 1.0CT }u C, C }u CP CEP fit y143.0 y0.2( ) ( )E Test molecule E Ace ]Ser ]Leu ]Asn ]Nme , interaction energy = y115.3 kcal / mol

CT }u C, CT }u C }H, neutralization y116.4 1.1CT }u C, CT }u C CEP fit y116.6 1.3

C }u N, C }u N }H, neutralization y113.8 y1.5C }u N, C }u N CEP fit y108.3 y7.0

aThis interaction energy is for the whole molecule ]enzyme complex.bFragmentation schemes are shown in Figure 2.c This interaction energy is for the reassociated molecule ]enzyme complex.d The difference is between the enzyme ]whole molecule interaction energy and the enzyme-reassociated molecule interactionenergy.

ªr eassoc w ho l e 2Ž .m r m , was 1.1 for the diol overlap and1.0 for the extended overlap. The hydration freeenergies are larger than that calculated for thewhole molecule by 2.1 kcalrmol for the diol over-

lap and 3.4 kcalrmol for the extended overlap ascompared with 0.25 kcalrmol for the CEP fitmethod and 0.76 kcalrmol using —H neutraliza-

Ž .tion Table IA . The enzyme]molecule A interac-


YOUNG ET AL.

( )FIGURE 3. A The diol group is overlapping for these( )two fragments of molecule A. B The overlap is extended

( )and includes the diol group and the Phe side chains. CThese residues are used to test the average overlapmethod of reassociation and the neutral blocking group

( )method for Ace ]Ser ]Leu ]Asn ]Nme molecule E . Onlyin the neutral blocking group method are the groupsdenoted by dashed parallelograms constrained to beneutral.

tion energies are larger than that with the wholemolecule by 3.0 kcalrmol and 3.2 kcalrmol, forthe diol overlap and extended overlap, respec-tively. The corresponding value for the CEP fitmethod is 1.1 kcalrmol and for —H neutralization

Ž .is 1.9 kcalrmol Table III, part A . For molecule A,the average overlap method yields worse resultsthan —H neutralization and CEP fit.

Another test of the average overlap method isperformed on a peptide. The fragments chosen areeach amino acid of molecule E, with the addition

Ž .of acetyl and N-methyl blocking groups Fig. 3C .An example of the overlap using molecule E is asfollows. Upon reassociation, the methyl carbon ofthe acetyl blocking group of leucine overlaps thealpha carbon of the serine residue, and the alpha

carbon of the leucine residue is overlapped byterminal methyl carbons in blocking groups ofboth the serine and asparagine residues. All of theintervening backbone atoms overlap. The EP RMSdifference for this reassociation method and frag-mentation scheme is 1.01 kcalrmol, smaller by lessthan 0.2 kcalrmol than the CEP fit method ofTable I, part E. In this case, the overlapping frag-ment scheme and averaging method show only aslight advantage as evaluated by the EP RMSdifference. The dipole moment ratio is 1.0 and thefree energy of hydration of the reassociatedmolecule is larger than that of the whole moleculeby 0.14 kcalrmol, as compared with 0.34 kcalrmolfor the CEP fit method and 0.41 kcalrmol for the—H neutralization method. However, the en-zyme]molecule E interaction energy is larger thanthe enzyme]original molecule interaction energyby 1.9 kcalrmol. The corresponding values for the—H neutralization method and for the CEP fitmethod are 1.1 kcalrmol and 1.3 kcalrmol, respec-tively. For molecule E, the average overlap methodyields results comparable to —H neutralizationand CEP fit; however, the interaction energy com-parison is worse for the average overlap method.Based on these results for molecules A and E, the—H neutralization and the CEP fit methods arelikely to be more reliable for reassociation than theaverage overlap method.

NEUTRAL BLOCKING GROUPS

The use of neutral blocking groups has beenemployed for amino acid charge calculations.9

Thus, we examine this method on test molecule Ewhich is a peptide. The neutral blocking groupsare designated by the dashed parallelograms inFigure 3C. The EP RMS difference for this methodis 1.23 kcalrmol; the dipole moment ratio is 1.0;the free energy of solvation is y35.54 kcalrmol;and the interaction energy is y116.8 kcalrmol. All

Žof these values are comparable to those parts E of.Tables I, II, and III of the CEP fit and —H neutral-

ization methods.

Application to HIV-1 ProteaseDiastereomer Inhibitors

Having studied five test molecules that wereobtained by truncation of HIV PR, we now extend

Ž .our calculations to the full size inhibitors Fig. 4 .Interaction energies of three diastereomers are cal-

VOL. 18, NO. 4530


FIGURE 4. The RR, RS, and SS inhibitors differ only in(the chirality at the diol the diol comprises the two central

)hydroxyl groups . The partitions used in the partialcharge calculation are represented by dashed lines.

culated and compared to binding affinity experi-Ž .ments. These three diastereomers are RR A76889 ,

Ž . Ž .RS A77003 , and SS A76928 with inhibition con-stants17 K of 112 pM, 12 pM, and 11 pM, respec-i

Ž .tively, and corresponding RTln K values ofiy14.1, y15.5, and y15.6 kcalrmol at 378C.17 Wechose to study diastereomers because the effects ofentropy and hydration on binding are expected todiffer very little for the three. A complete calcula-tion of the free energy of binding is beyond thescope of this article, but the calculated interac-tion energies should reproduce the trend: RR )RS , SS.

Partitions for the partial charge calculation areplaced between each valine C and carbonyl car-a

bon as shown by the dashed lines in Figure 4.Ž .Interaction energies Table IV were calculated us-

Žing CHARMm 22 and AMBER 4.0 including crys-.tallographic water molecules with DFTrDZVPD

CEP fit reassociated partial charges for the in-hibitors. The order of binding is reproduced byboth CHARMm and AMBER. In CHARMm, thevan der Waals energies are the dominant term. InAMBER, the coulomb energies dominate slightly.

TABLE IV.HIV-1 Protease-Inhibitor Interaction Energies.

aComplex vdW Coulomb Total

CHARMm 22RR y104.12 y59.01 y163.13RS y104.51 y85.25 y189.76SS y113.73 y76.96 y190.69

AMBER 4.0RR y67.34 y68.29 y135.63RS y71.58 y96.40 y167.98SS y73.47 y93.03 y166.50

a van der Waals energy.

This agreement of the interaction energies with thetrend in binding may be entirely fortuitous. Theeffect of hydration should reduce the magnitude ofthese numbers considerably, and efforts to adaptthe use of the boundary element method to calcu-late hydration energies for such large systems areunderway.

Conclusions

Earlier work3, 4 shows that the use of an ex-tended basis set with diffuse functions is requiredto find partial charges which reproduce experi-mental dipole moments well. The calculation ofpartial charges for molecules on the order of 50]60nonhydrogen atoms using this basis set is at pres-ent intractable. This study represents our first stepin understanding the errors introduced by parti-tioning and reassociation of a molecule in calculat-ing atomic partial charges using a large basis set.We have compared various fragmentation schemesand reassociation methods to obtain atomic partialcharges for these molecules. This work has shownthat errors in the electrostatic potential introducedby fragmenting a tripeptide at the peptide bondare two to five times larger than for the alphacarbon—carbonyl carbon bond. This was antici-pated due to the polar nature of the peptide bond.In general, the expectation, that errors introducedby partitioning of carbon—carbon bonds would besmaller than those from partitioning ofcarbon—nitrogen bonds, was realized. Overall, theCEP fit method works slightly better than the —Hneutralization method. For peptides, the neutralblocking group method9 was also tested and foundto be comparable to the CEP fit method.

The results indicate that our solvation calcula-tions are less sensitive to errors in the chargedistribution than calculations of the electrostaticpotential at the van der Waals surface shells. Thesensitivity of interaction energy calculations tothese errors is more selective. That is, not only dothe portions of the charge distribution at the lig-and]target interface dominate the result, but also,certain portions of this interface, such as regionscontaining highly charged groups, can magnifyerrors in the charge distribution. As the largesterrors are usually near the partitions, the partitionscan sometimes be chosen based on knowledge ofthe target structure. For example, with the targetHIV PR, the ligand partitions should be madeaway from the active-site aspartic acid residues inthe bound structure. Further reduction of these


YOUNG ET AL.

errors will come from a better representation ofinterfragment polarization effects and will mostlikely be incorporated using some type of CEP fitmethod.

Acknowledgments

We thank Dr. John Erickson and Dr. T. N. Bhatfor crystallographic coordinates. We thank Mr.Robert Lebherz for a prompt upgrade of Gaussian92 to include the DFT code. We thank Dr. JackCollins for sharing his expertise with AMBER, Dr.Greg Tawa for insightful discussions, and Ms.Lucyna Lubkowska for chemical nomenclature.Special thanks are extended to the staff of theBiomedical Supercomputing Center, FCRDC, Fred-erick, MD, for their assistance and for access to theCray Y-MP supercomputer. The contents of thispublication do not necessarily reflect the views orpolicies of the Department of Health and HumanServices, nor does mention of trade names, com-mercial products, or organizations imply endorse-ment by the U.S. government.

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building molecular charge distributions from fragments: application to hiv-1 protease inhibitors

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