Electronic Structure, Binding Energy, and Solvation Structure of the Streptavidin-BiotinSupramolecular Complex: ONIOM and 3D-RISM Study

Qingbin Li,†,‡ Sergey Gusarov,† Stephane Evoy,†,§ and Andriy Kovalenko*,†,‡

National Institute for Nanotechnology, 11421 Saskatchewan DriVe, Edmonton, Alberta, T6G 2M9, Canada, andDepartment of Mechanical Engineering and Department of Electrical and Computer Engineering, UniVersity ofAlberta, Edmonton, Alberta, Canada T6G 2R3

ReceiVed: March 24, 2009; ReVised Manuscript ReceiVed: May 26, 2009

We studied the electronic structure of the binding site of the streptavidin-biotin complex by using the ONIOMmethod at the HF/STO-3G:UFF level and obtained the solvation structure of the complex by using the statistical-mechanical, three-dimensional molecular theory of solvation (aka three-dimensional reference interaction sitemodel, 3D-RISM-KH). All the streptavidin residues located within 3 Å of the biotin residue were includedin the quantum mechanical (QM) layer. In total, 16 residues including biotin with 274 atoms were in the QMlayer, in which five residues are responsible for the hydrophobic interactions and nine residues for the hydrogen-bonding/electrostatic interaction with biotin. We found a geometry change of the urea moiety of the biotinbound in the network of van der Waals and polar interactions. Compared to the isolated biotin, the bridgingC-C bond of the biotin urea moiety in the binding site increases in length as a result of the π-σ interactionwith the surrounding streptavidin Trp residues. This extends the previous picture of the geometry changefrom the ureido group to the whole bicyclic urea moiety. We have evaluated the performance of 15 densityfunctional methods and 11 basis sets by single point calculation for the binding energy of the optimizedcooperative binding complex structure. Closest to the experimental value of 18.3 kcal/mol is the binding freeenergy of 19.6 kcal/mol obtained for the AN model at B3LYP/6-31G(d):UFF//HF/STO-3G:UFF level. Thehybrid DFT methods with enhanced assessment for nonbonded interactions such as PBE1PBE, MPW1B95,and MPWB1K can also give accurate binding energy with the use of diffuse functionals (i.e., mPWB1K/6-31+G(d)). The 3D hydration structure of the unliganded streptavidin and the streptavidin-biotin complexobtained by using the 3D-RISM-KH molecular theory of solvation shows there is one immobilized watermolecule at the biotin urea moiety, acting as a water bridge between the sulfur and the nitrogen of the NHgroup close to Ser45. This suggests that, in the docking process, biotin replaces six of the seven water moleculesattached to the unliganded streptavidin binding site, and one remaining water molecule is squeezed into thegap between the Btn, Tyr43, Ser45, Trp92, and Trp79 residues in the binding pocket.

Introduction

The unusually strong noncovalent interactions of thestreptavidin-biotin complex stood out from the empiricaltendency of maximum, -1.5 kcal/mol free energy contribu-tions per non-hydrogen atom, as concluded by Kollman andco-workers for a wide variety of macromolecule-smallmolecule interactions.1 The binding free energy of this system(18.3 kcal/mol)2 is one of the strongest noncovalent bindingsbetween a protein and a small ligand in an aqueous solution3

and has led to many practical applications such as sequester-ing, sensor design, and the architecture control of supramo-lecular constructs.4-8 Accurate prediction of the cooperativeeffect of the hydrogen bonding, hydrophobic effect, van derWaals, and electrostatic interactions in this system has beena subject of much interest. Despite the progress made in theunderstanding and quantifying the origin of the bindingenergetics and dynamics of the streptavidin-biotin complexfrom both experimental9-18 and computational studies,19-23

its detailed binding structure and accurate binding energy atthe quantum mechanical level, including the role of im-mobilized water, remain to be learned. Addressing thesepoints is the subject of the present paper.

In 1989, Weber, Salemme, and co-workers studied the crystalstructure of the streptavidin-biotin complex and suggested thatits strong binding is due to dipole reorientation, hydrogenbonding, and disorder-order transitions, with the hydrogenbonding to the ureido ring system of biotin dominating in thestabilization of the complex.3 A series of site-directed mutagen-esis experiments were carried out later on by Stayton, Stenkamp,and co-workers,10-16 which reported the following: (i) Theyquantitatively verified the importance of both hydrogen-bondingresidues and van der Waals interaction residues (Tryptophan);(ii) They explained that the region of Trp 120 could act as ajoint cap for the binding site upon the binding of streptavidinand biotin, and in turn, contribute to the free energy due to morehydrogen bonds and hydrophobic interaction around the valeratemoiety. In 2004, Williams et al. contended that the largefree energy of biotin binding to streptavidin is the property ofthe whole positively cooperative system, with a widely delo-calized structural tightening derived from the biotin-inducednoncovalent interactions within streptavidin.24

* Corresponding author. Phone: (780) 641-1716. Fax: (780) 641-1601.E-mail: andriy.kovalenko@nrc-cnrc.gc.ca.

† National Institute for Nanotechnology.‡ Department of Mechanical Engineering, University of Alberta.§ Department of Electrical and Computer Engineering, University of

Alberta.

J. Phys. Chem. B 2009, 113, 9958–99679958

10.1021/jp902668c CCC: $40.75 2009 American Chemical SocietyPublished on Web 06/22/2009

Significant increase of computational power and the develop-ment of theoretical methodology in the recent decade givescomputation and theory a new opportunity to comprehensivelyaddress this particular application. In 1992, Miyamoto andKollman performed molecular dynamics (MD)/free energyperturbation simulations and concluded that the nonpolar vander Waals/dispersion effects of the tryptophan resides Trp79,Trp92, Trp108, and Trp120 play a major role in the high bindingfree energy of the complex compared to that of the electrostaticcontribution of the hydrogen bonding screened by watersolvent.19,20 Their predictions were used later by Stayton,Stenkamp, and co-workers to design the site-directed mutagen-esis experiment.11,13-16 In 2001, Chipot and Dixit re-examinedthe system by using MD simulation in a new simulationenvironment with the CHARMm param22 force field and gavea more balanced evaluation of the hydrogen bonding and vander Waals contributions.21 In 2003, Zhang et al. studied thesystem by using a new computational approach called molecularfractionation with conjugate caps (MFCC). They calculated thebinding energies (at HF/3-21G level) to be almost 30 kcal/mollarger than those given by a force field for the same system.22

Very recently, along with our investigation of this system, Houkand DeChancie reported a binding study of the streptavidin-biotincomplex to re-evaluate the hydrogen-bonding interaction byusing a cluster model and ab initio methods, including solvationof biotin and bound water molecules at the protein binding site.23

Much effort has also been devoted to developing methodologyto accurately predict a noncovalent binding system in an aqueoussolution. Some recent refinement of density functional theory(DFT) methods has been focused on such improvement ofdescribing nonbonded interactions. Perdew et al. advanced thelocal density approximation up to the exact exchange andcorrelation functional, PBE1PBE, by using a nonempiricalapproach.25 Cohen and Handy introduced the O exchangefunctional,26 whereas Xu et al. developed the X exchangefunctional27 to construct the popular B3LYP28 method. Basedon the modified Perdew and Wang exchange functional(MPW)29 and Becke’s 1995 correlation functional (B95),30 Zhaoand Truhlar developed the hybrid meta density functionalmethods MPW1B95 and MPWB1K.31 All these modern DFTmethods have shown enhanced assessment for nonbondedinteractions.27,31,32

Upon the above-mentioned elaborate work, there still are threeconsiderable gaps in the basic understanding of the streptavidin-biotin system that we address in this report. First, despite anumber of works describing the structure and orientation ofparticular residues in the binding site as well as the coarse-grained structure of the binding pocket, there is no structurepublished to date of the whole cooperative binding site at abinitio quantum mechanical level. Second, although the perfor-mance of the existing density functional methods for nonbondedinteractions has been tested for particular interactions, it hasnot been benchmarked for the whole coupled system withcorrelated multiple interactions including the hydrogen bonding,hydrophobic effect, van der Waals, and electrostatic interactions.Third, the role of immobilized water molecules in the strepta-vidin-biotin bonding pocket in solution has not been clear sofar.

Resolving both the solvation structure and thermodynamicsof protein in molecular details is challenging in both experimentand molecular simulations. This task is readily feasible by usingstatistical-mechanical, three-dimensional molecular theory ofsolvation, also known as the three-dimensional referenceinteraction site model (3D-RISM).33-37 This theory is capable

of predicting such phenomena and properties as self-assemblyand conformational stability of synthetic organic supramolecularnanoarchitectures (organic rosette nanotubes) in differentsolvents,38,39 supramolecular chirality of rosette nanotubes drivenby structural solvent molecules and controlled by the composi-tion of a solvent mixture,39 stability of microtubules in solution,40

water and rare gas binding to protein pockets,41-44 thermody-namics of protein hydration45-47 and its essential role in proteinfolding,48 volumetric effects on protein binding,44 partial molarvolume changes on conformational transitions of biomoleculesin solution,49-53 and the effect of cosolvent on protein dena-turation under pressure.53

In this work, we study the electronic structure of the bindingsite of the streptavidin-biotin complex by using the ONIOMmethod at the HF/STO-3G:UFF level followed by a single pointbenchmark calculation of the interaction energies by usingvarious DFT methods and basis sets. We then obtain thestructure hydration of the liganded and unliganded streptavidinby using the 3D molecular theory of solvation.

1. Models

The crystallographic structure of the streptavidin/biotinmonomer was obtained from the Brookhaven database (PDB)structure 1stp.9 This truncated form incorporates residues13-133 of the native 159-residue streptavidin chain and isbelieved to have the binding energy same or similar to thealternative longer versions of the protein.19,20 Note that thiscrystallographic structure has the “open” form, which meansthe effect of the joint cap around residue Trp120 on the bindingenergy is not included.

1.1. Amber Model. All protons were removed from thecrystallographic structure since the proton naming conventionused in PDB does not match IUPAC specifications. The missinghydrogen atoms and the C-terminal oxygen in Val133 were thenreloaded by Leap in the AMBER package.54 (The structure builtcontains 1775 atoms.) After the subsequent minimization usingthe generalized Born (GB) model of solvation for 2500 stepsin the AMBER package, all residues located within 3 Å of thebiotin residue were selected as the quantum layer. In total, thereare 16 residues with 272 atoms, including biotin (Btn), Asn23,Leu25, Ser27, Tyr43, Ser45, Val47, Gly48, Asn49, Trp79,Ser88, Thr90, Trp92, Trp108, Leu110, and Asp128. Figure 1demonstrates the structure of the AMBER model of thestreptavidin-biotin complex. A cartoon representation is usedfor the protein, and the QM layer part is presented in theCorey-Pauling-Koltun (CPK) drawing model. Biotin is shownin the van der Waals (VDW) drawing model to distinguish itfrom streptavidin residues in the QM layer.

Figure 1. Structure of the AMBER model. A cartoon representationis used for streptavidin with the QM layer presented in CPK drawing.Biotin is shown in VDW drawing to distinguish it from the streptavidinresidues in the QM layer.

Streptavidin-Biotin Supramolecular Complex J. Phys. Chem. B, Vol. 113, No. 29, 2009 9959

1.2. Amber Neutralized (AN) Model. Biotin is modeledin the AMBER model in the anionic state with the partialatomic charges taken from Miyamoto and Kollman.19 Thiscomplex system has an overall charge of -3 when assigningdefault charge states from the Duan et al. (ff03) force fieldin AMBER55 to the residues of streptavidin. To avoid anunrealistic electronic repulsion of charged residues in thebinding energy due to the lack of solvation effect in theONIOM calculation, we neutralized the system by assigninga protonated state to Btn (QM layer), Asp128 (QM layer),and Val133 (MM layer). All other QM layer residues fromthe AMBER model remain in the QM part, thus, constituting1778 atoms in total with 274 atoms in the QM layer for theAN model. There are 26 boundary conditions between theQM and the MM layers created upon this selection procedure,and all cuts are on the peptide bonds.

1.3. Gaussview Neutralized (GN) Model. Besides theAMBER package, Gaussview was used to build the secondneutral model. The PDB file was processed with the followingsteps: (1) Missing hydrogen atoms were added to the PDBstructure by Gaussview when loading; (2) Bound water mol-ecules were removed from the crystal structure manually; (3)For consistency, the histidine residues in the complex were allset neutral, as in the previous two models, and protonated stateswere assigned to Btn, Asp128, and C-terminated Val133 toneutralize the whole system for the subsequent ONIOMoptimization; (4) Constituents of the QM level of this modelwere carefully selected so as not only to include all functionalgroups for binding interactions but also to put the boundariesmostly on sp3 hybridized C-C bonds. Finally, the GN modelhas exactly the same atoms as the AN model but with fewer,197 atoms, in the QM layer. In this procedure, 20 boundaryconditions are created.

2. Theoretical Methods

2.1. Geometry Optimization. Most calculations were per-formed with the Gaussian 03 software package,56 except forthe preliminary minimization of the AMBER model in theAMBER 9 package.54 In vacuo geometry optimizations wereperformed for both the neutralized systems, AN and GN models.A quantum mechanical description for the active binding siteat the Hartree-Fock (HF) level of theory, using the standardSTO-3G basis set, was combined with the Universal Force Field(UFF) molecular mechanical treatment for the rest of the protein.The size of the system and the extremely flat potential energysurface (PES) due to the noncovalent interactions in complexsystems make geometry optimization the most expensive task.As a consequence of the extremely flat PES, the most commonfailure in the optimization was that the maximum and rmsdisplacements were higher than their threshold values 0.002 and0.001 au, respectively; even though the maximum and rms forceswere lower than the default thresholds 0.00045 and 0.0003 au.The following protocol was used to overcome these failures inthe optimization: (1) Loose convergence criteria of 0.01 au forthe maximum step size and 0.0017 au for the rms force wereused for initial optimization; (2) Full convergence for forceswith the default fine integration grid was achieved, giving thegeometries of conformations with settled forces; and (3)Frequency calculation was done for these structures, and thesecond derivative was used to further optimize them untilsatisfying full convergence criteria for both displacements andforces.

The binding energy of streptavidin-biotin was calculatedfrom the equation:

in which the structure of the streptavidin-biotin complex wasoptimized for the whole complex, and the structures of separatestreptavidin and biotin were taken to be the same as in theoptimized complex and kept fixed throughout the calculations.To compare with the experimental values of the binding freeenergy, we added the free energy corrections obtained with theharmonic frequencies that were computed using the analyticalsecond derivative formulas available in GAUSSIAN 03. Sincethere is no solvation environment available in GAUSSIAN 03for the ONIOM system, we isolated the QM part of the ONIOMsystem and terminated it with hydrogen atoms at all theboundaries. Then, the polarizable continuum model (PCM)treatment was applied to the isolated QM parts of streptavidin,biotin, and their complex to account for the effect of watersolvent on the binding energy. As follows from the energybreakdown in ONIOM, the redundant term Einterior border

PCM corre-sponding to the energy of solvation of the interior borderbetween the QM and the MM parts of the ONIOM systemcancels out, giving precisely the required solvation term in thebinding energy of the complex:

Below we show both the model and the extrapolated energiesfor the ONIOM system; the extrapolated energies are correctedfor thermal free energies using the standard 3N-6 harmoniccontributions from the frequency run. The estimates for thebinding energies are finally obtained after the corrections to thesolvation energies.

2.2. Evaluation of the Performance of Different ElectronicStructure Theories. We computed the single point molecularenergies to evaluate the accuracy of different methods andbasis sets for the ONIOM system using structures from theoptimized AN model. 16 levels of electronic structure theorywere used. Other than Hartree-Fock (HF) based methods,15 density functional theory (DFT) methods were employed:three local density approximation (LDA) methods (SPL,SVWN, SVWN5),57-61 four generalized gradient approxima-tion (GGA) methods (PW91PW91,62 mPWPW,29 PBEPBE,25

BLYP63,64), six hybrid DFT methods (B3LYP,28 B3P86,28,65

B3PW91,28,65 MPW1PW,29 PBE1PBE,25 O3LYP26), and twohybrid meta DFT methods (MPW1B95, MPWB1K).31 Table1 lists the hybrid parameters and the corresponding exchangeand correlation functionals of the Hybrid DFT methods weselected. It should be mentioned that the computationresourcesavailablewerenotsufficient toapply theMøller-Plessetsecond-order perturbation method (MP2) to this large systemeven for a single point calculation. We tested 11 basis sets:eight Pople basis sets (3-21G, 6-31G, 6-31G(d), 6-31G(d,p),6-31G+(d), 6-311G, 6-311G(d), 6-311G(2df,p))56,66 and threeDunning basis sets (cc-pVDZ, cc-pVTZ, aug-cc-pVDZ).67,68

2.3. 3D Molecular Theory of Solvation. To study thesolvation structure of the streptavidin and biotin system,including the area near the binding dock, we employed the3D-RISM-KH35-37 integral equation theory. The details of the

Ebinding ) EcomplexONIOM - Ebiotin

QM - EstreptavidinONIOM

Ebindingsolvation ) Ecomplex

PCM - EstreptavidinPCM - Ebiotin

PCM

) (Einterior borderPCM + Ebinding site+biotin

PCM )complex -

(Einterior borderPCM + Ebinding site

PCM )streptavidin - EbiotinPCM

) Ebinding site+biotinPCM - Ebiotin

PCM - Ebinding sitePCM

9960 J. Phys. Chem. B, Vol. 113, No. 29, 2009 Li et al.

method have been given in the literature, and here we providea brief outline only. The 3D-RISM equation:33-37

is coupled with the 3D version of the closure approximationproposed by Kovalenko and Hirata (3D-KH closure):35,37

where hγuv(r) is the 3D total correlation function, which is related

to the 3D distribution function gγuv(r) ) hγ

uv(r) + 1 giving thenormalized probability of finding site γ of solvent moleculesat position r around the solute molecule, and cγ

uv(r) is the3D direct correlation function, which has the asymptotics ofthe solute-solvent site interaction potential: cγ

uv(r) ∝ - uγuv(r)/

(kBT), where kBT is the Boltzmann constant times thetemperature. The superscripts “u” and “v” denote the soluteand solvent molecules, respectively, and site subscript indicesR and γ enumerate all sites on all sorts of solvent molecules.The solvent susceptibility �Rγ

vv (r) ) ωRγvv (r) + FRhRγ

vv (r),representing a response of the solvent to an external fieldexerted by the solute supramolecule, splits up into theintramolecular and intermolecular correlations. The intramo-lecular term is represented by the intramolecular matrix ωRγ(r)) δRγ + (1 - δRγ)δ(r - lRγ)/(4πlRγ

2 ) determined by thegeometry of solvent molecules with site-site separations lRγ,whereas the intermolecular part is given by the totalcorrelation functions of pure solvent hRγ

vv (r) times the solventnumber density FR. In advance to the 3D-RISM-KH calcula-tion, the site-site correlations hRγ

vv (r) are obtained from thedielectrically consistent RISM theory69 coupled with the KHclosure (DRISM-KH).33 The convolution in eq 1 is calculatedby using the 3D fast Fourier transform technique with thelong-range electrostatic asymptotics of all the correlationfunctions, both radial and 3D ones, separated out and

evaluated analytically, which provides correct calculation ofboth the solvation structure and thermodynamics.36,37

Water solvent at ambient temperature T ) 300 K and physicaldensity F ) 0.99705 g/cm3 is represented with the SPC/E watermodel.70 We used the AMBER parameter set, force field 03,for the interaction site charges and Lennard-Jones parametersof the protein.

The 3D-RISM-KH integral eqs 1-2a were solved on a gridof 512 × 256 × 256 points in a rectangular supercell of size256 × 128 × 128 Å3. The box dimensions are chosen to betwice as large as the size of the protein macromolecule so as toaccommodate enough space of approximately several solvationshells around it. This ensures elimination of the effect of thesupercell periodicity artifacts on the solvation structure at shortrange (with the long-range electrostatic asymptotics treated fullyanalytically).33,37 Further refinement of the grid size resolutionto better than 0.5 Å does not significantly change the solvationstructure obtained. The eqs 1-2a are solved for the 3D sitedirect correlation functions cγ

uv(r). They are converged to arelative root-mean-square accuracy of 10-5 by using themodified direct inversion in the iterative subspace (MDIIS)accelerated solver.33,71

3. Results and Discussion

3.1. Geometry Optimization. The optimized structures ofthe AN and GN models we obtained are shown in Figure 2.The QM layer (model part of the system) is presented with ballsand sticks, and the MM layer is shown with wire frame. Biotinis highlighted in the model part to distinguish it from thestreptavidin residues in the QM layer.

The more detailed nonpolar van der Waals and polarinteraction networks between biotin and the related residues of

TABLE 1: Energy Expressions from the Hybrid DensityFunctional Theories Used in the Calculations

hybridmethods hybrid parameters with corresponding functional

B3LYP 0.20 Ex (HF) + 0.80 Ex (Slater) + 0.72 Ex (B88) +0.19 Ec (VWN) + 0.81 Ec (LYP)

B3P86 0.20 Ex (HF) + 0.80 Ex (Slater) + 0.72 Ex (B88) +1.0 Ec (VWN) + 0.81 Ec (P86)

B3PW91 0.20 Ex (HF) + 0.80 Ex (Slater) + 0.72 Ex (B88) +1.0 Ec (PW91, local) + 0.81 Ec (PW91, nonlocal)

mPW1PW 0.25 Ex (HF) + 0.75 Ex (Slater) + 0.75 Ex (mPW) +1.0 Ec (PW91)

PBE1PBE 0.25 Ex (HF) + 0.75 Ex (Slater) + 0.75 Ex (PBE) +1.0 Ec (PW91, local) + 1.0 Ec (PBE, nonlocal)

O3LYP 0.1161 Ex (HF) + 0.9262 Ex (Slater) + 0.8133 Ex(OPTX) + 0.19 Ec (VWN5) + 0.81 Ec (LYP)

MPW1B95 0.31 Ex (HF) + 0.69 Ex (Slater) + 0.69 Ex (mPW) +1.0 Ec (B95)

MPWB1K 0.44 Ex (HF) + 0.56 Ex (Slater) + 0.56 Ex (mPW) +1.0 Ec (B95)

hγuv(r) ) ∑

R∫ dr′cR

uv(r - r′)�Rγvv (r′) (1)

gγuv(r) ) {exp(dγ

uv(r))

1 + dγuv(r)

forfor

dγuv(r) e 0

dγuv(r) > 0

(2a)

dγuv(r) ) -

uγuv(r)

kBT+ hγ

uv(r) - cγuv(r) (2b)

Figure 2. Structure of the optimized streptavidin-biotin bingingcomplex obtained by using the two-layers ONIOM method. (a) ANmodel and (b) GN model. The QM layer (model system) is shown inball and stick, and the MM layer is shown in wire frame representation.Biotin is highlighted to distinguish from the streptavidin residues inthe QM layer.

Figure 3. Nonpolar van der Waals interaction network between biotinand related residuals of streptavidin from the optimized AN model.

Streptavidin-Biotin Supramolecular Complex J. Phys. Chem. B, Vol. 113, No. 29, 2009 9961

streptavidin from the AN model are explicitly shown in Figures3 and 4, respectively. The residues responsible for nonpolar vander Waals interaction in this model are Leu25, Gly48, Trp79,Trp92, Trp108, and Leu110. As shown in Figure 3, the isopropylof Leu25 is coordinated to the center of the biotin ureido group,whereas Trp92 and Trp108 sit beside the tetrahydrothiophenering, forming a sandwich structure. The remaining residues,including Gly48, Trp79, and Leu110 are packed around thelinear valeryl chain of biotin.

The most polar interactions in Figure 4 are the hydrogenbonds of: in particular, Asn23, Ser27, and Tyr43 with the biotinureido oxygen; Ser45 and Asp128 with the two biotin ureidoNH; Thr90 with the biotin sulfur; and Asn49 and Ser88 withthe biotin valeryl oxygen. The only exception is residue Val47,which forms the electrostatic interaction between the Val47 acyloxygen and the hydrogen on the biotin valeryl chain. All thedistances of the polar interaction bonds obtained for theoptimized structure are reported in Figure 4. The participationof the biotin ureido ring plays an important role for polarinteractions. The sp3 hybridized biotin ureido oxygen forms atetrahedral geometry with the C-O bond length of 1.25 Å. Thebond length of the three hydrogen bonds to the correspondinghydrogen atoms in Asn23, Ser27, and Tyr43 is 1.88, 1.68, and1.68 Å, respectively. The hydrogen bonds between the biotinureido NH groups and the corresponding residues feature ahydrogen bridge to Ser45 with RNH ) 1.06 Å and RHO ) 1.51Å and a looser connection to Asp128 with RNH ) 1.03 Å andRHO ) 1.97 Å. The length of the remaining weaker hydrogen-bonding ranges are from 1.90 to 2.50 Å.

The network of nonpolar van der Waals and polar interactionsbetween biotin and the related residues of streptavidin from theGN model are also exhibited in Figure 5. The nonpolar van derWaals interaction network is quite similar to that for the ANmodel, whereas only five out of the nine bonds, due to polarinteractions that were found in the AN model, are present inthis GN model system. The residues involved in polar interac-tions in the GN model are Asn23, Ser27, Ser45, Val47, andAsp128. The length of the bonds due to polar interactions weobtained for the optimized GN model are shown in Figure 5,where the C-O bond length to the urea oxygen is 1.23 Å and1.79, 1.65 Å from the urea oxygen to the hydrogen atoms inAsn23 and Ser 27, respectively. The hydrogen bonds coordi-nated to the biotin ureido NH groups features RNH ) 1.06 Å

and RHO ) 1.50 Å for Ser45 and RNH ) 1.03 Å and RHO ) 2.04Å for Asp128.

Geometry Change of the Urea Moiety in Biotin. As a resultof the coupled multiple interactions, the geometry change ofthe urea moiety from isolated to bound biotin is important tounderstand its high affinity. It has been reported that thesepositively cooperative interactions work in a nonadditive way,making a stronger overall binding affinity than the sum of theindividual interactions.23,24,72,73

Figure 6 shows the optimized backbone structures of abicyclic urea unit of the isolated biotin (a), bicyclic urea unitof biotin bound in the AN model (b), bicyclic urea unit of biotinbound in the GN model (c), and the conjugate base of thebicyclic urea unit with deprotonation at Ser45 side (d). To beconsistent, the isolated biotin and its conjugate base are allcomputed at the HF/STO-3G level. The bond length of ureidooxygen to carbon increases from 1.215 to 1.249 and 1.233 Åfor the AN and GN models, respectively. The C-N bonddecreases from 1.442 to 1.369 Å in the AN model and from1.442 to 1.375 Å in the GN model.

For the hydrogen-bonding induced mutual polarization, it wasdemonstrated in the previous experimental work that the C-Obond lengthens and correspondingly the C-N bond shortenswith the strength increase of the hydrogen bonding to the ureaoxygen of biotin.74 Along with our investigation, DeChancieand Houk performed a theoretical study of hydrogen bondcooperativity between the biotin urea moiety and five strepta-vidin hydrogen-bonding residues by using a simplified clustermodel (methanol for Ser27 and Ser45, phenol for Tyr43, acetatefor Asp128, and formanide for Asn23) at higher theoretical level(B3LYP/6-31+G(d,p)). A significant polarization of the C-Obond and C-N bond of the ureido moiety was also reported.23

Our optimized structures of biotin at the streptavidin bindingsite for the AN and GN models are all in agreement with theseobservations.

More importantly, for the combined polar (hydrogen bondingand electrostatic) and nonpolar (van der Waals) interactionsincluded in our system, we observed a new geometrical change,namely an increase in the bridging C-C bond length in thebicyclic ring from 1.556 to 1.570 and to 1.571 Å for the ANand GN models, respectively. As a consequence, we have thecorresponding shortening of the bonds beside the bridging C-Cbond in the tetrahydrothiophene ring. For example, in the ANmodel the C-O, C-N, and bridging C-C bond lengths change

Figure 4. Polar interaction network between biotin and related residualsof streptavidin from the optimized AN model. Broken lines mark theintermolecular hydrogen bonding (or associative electrostatic interactionwith Val 47). The numbers give the bond length in Å.

Figure 5. Polar and nonpolar van der Waals interaction networkbetween biotin and related residuals of streptavidin from the GN model.Broken lines mark intermolecular hydrogen bonding (or associativeelectrostatic interaction with Val 47). The numbers give the bond lengthin Å.

9962 J. Phys. Chem. B, Vol. 113, No. 29, 2009 Li et al.

by 0.034, -0.073, and 0.015 Å, respectively. It is important tonote that even in the conjugate base (Figure 6d), the elongatedbridging C-C bond has not been seen so far, indicating thatthe elongation originates from the π-σ interaction between theTrp residues around the urea group. This evidence extends thegeometry change from mainly the ureido group to the wholebicyclic urea moiety.

Since the AN model demonstrates a more complete polarinteraction network between biotin and related residues ofstreptavidin, this model is selected as a testing system for thefollowing evaluation of the performance of different ab initiomethods and basis sets regarding the binding energy.

3.2. Effects of Different Levels of Theory on the BindingEnergy. For the first evaluation, the effects of basis sets andmethods on the binding energy of the ONIOM system wereinvestigated by using the optimized structure from the AN modeland the theoretical methods mentioned in Section 2.2. Table 2lists the 11 basis sets tested with the HF method and the 16methods tested with the 6-31G(d) basis set. Table 3 comparesthe effect of basis sets on the binding energy from single pointcalculations based on the optimized structure from the ANmodel. The energies shown are the model and extrapolatedenergies, the latter presented for comparison. It follows fromTable 3 that the polarization functions on heavy atoms areessential for these noncovalent interactions. When polarizationfunctions on heavy atoms are in place, the affinity drops from71.2 to 55.4 kcal/mol for the Pople double-� basis set (6-31Gto 6-31G(d)) and from 68.1 to 54.2 kcal/mol for the Pople

triple-� basis set (6-311G to 6-311G(d)). The effect of addingpolarization functions on hydrogen is not very obvious (56.1vs 55.4 kcal/mol for 6-31G(d)). Diffuse functions drop theaffinity from 55.4 to 50.5 kcal/mol for the Pople double-�6-31G(d) and from 57.1 to 47.6 kcal/mol for the Dunningdouble-� cc-pVDZ. For the Pople basis sets, switching fromdouble-� 6-31G to triple-� 6-311G does not make a very bigdifference (71.2 to 68.1 kcal/mol). For the Dunning basis set,switching from double-� to triple-� results in an affinity dropfrom 57.1 to 42.0 kcal/mol. This big difference could beexplained by the increase of polarization functions from DZ toTZ, since they are included in the Dunning basis sets. Figure 7plots the binding energy to give a clearer sense and includes

Figure 6. Comparison of the optimized backbone structure of the bicyclic urea unit of biotin in: (a) isolated biotin; (b) biotin bound in the bindingpocket of the AN model; (c) biotin bound in the binding pocket of the GNmodel; and (d) the conjugate base. The structures are optimized at theHF/STO-3G level.

TABLE 2: Basis Sets and Methods Used in the Calculations

basis set basis set sizea method

SZ 1 HFSTO-3G 2664/888 LDA

DZ 2 SPL1 3-21G 2664/1626 3 SVWN52 6-31G 3852/1626 4 SVWN3 6-31G(d) 4728/2502 GGA4 6-31G(d,p) 5190/2964 5 PW91PW915 6-31+G(d) 5312/3086 6 mPWPW6 cc-pVDZ 5936/2818 7 PBEPBE7 AUG-cc-pVDZ** 8012/5040 8 BLYP

TZ Hybrid Methods8 6-311G 4580/2368 9 B3LYP9 6-311G(d) 5456/3098 10 B3P8610 6-311G(2df,p) 8254/5312 11 B3PW9111 cc-pVTZ 10402/7424 12 mPW1PW

13 PBE1PBE14 O3LYP15 MPW1B9516 MPWB1K

a Number of primitive Gaussians/number of contracted Gaussiansfor model system in AN model only.

TABLE 3: Single Point Energy for the Optimized ANModel Obtained by Using the HF Method and DifferentBasis Sets

extrapolated ONIOMenergy (au)

binding affinity(kcal/mol)

basis set complex biotin streptavidin model extrapolated

3-21G -7299.825212 -1113.061213 -6186.595116 97.6 106.06-31G -7337.316116 -1118.661591 -6218.541022 62.9 71.26-31G(d) -7340.304045 -1119.025388 -6221.190425 47.0 55.46-31G(d,p) -7340.668068 -1119.058878 -6221.519817 47.7 56.16-31+G(d) -7340.499760 -1119.043931 -6221.375383 42.1 50.5cc-pVDZ -7340.997138 -1119.106115 -6221.800084 48.7 57.1AUG-cc-

pVDZ**-7341.417721 -1119.155481 -6222.186430 39.2 47.6

6-311G -7338.915740 -1118.847743 -6219.959394 59.8 68.16-311G(d) -7341.820386 -1119.199948 -6222.534010 45.9 54.26-311G(2df,p) -7342.549745 -1119.278428 -6223.190268 42.5 50.8cc-pVTZ -7342.890850 -1119.320839 -6223.503124 33.6 42.0

Figure 7. Effect of a basis set on the interaction energy of theoptimized streptavidin-biotin complex (AN model).

Streptavidin-Biotin Supramolecular Complex J. Phys. Chem. B, Vol. 113, No. 29, 2009 9963

the results of the model energies. Note that the addition of thelow layer (UFF part) to the model system (QM part) results inan 8 kcal/mol binding energy increase.

To evaluate the performance of different density functionalsin comparison with the experimental binding free energy, wecalculated the free energy and solvation energy corrections. Theresults are presented in Table 4. Both the corrections areperformed at HF/STO-3G level using the GAUSSIAN 03package. As mentioned in the Theoretical Methods Section, theharmonic frequencies were computed by using the ONIOMsystems for the thermal free energy correction, and the solvationenergy correction was done by calculating the binding affinitydifference for the isolated QM models without and with watersolvent described using the polarizable continuum model (PCM).

Table 5 makes a comparison of the results for the bindingenergy obtained from different methods with the use of the6-31G(d) basis set. Overall, the generalized gradient approxima-tion (GGA) methods feature an approximately 50 kcal/molimprovement over the local density approximation (LDA). Mostof the GGA methods employed here achieved a decent accuracyfor the binding energy of this noncovalent system, whereas theBLYP, mPWPW, and B3PW91 methods slightly underestimatedthe binding energy, while others slightly overestimated it. Theonly exception is O3LYP, with Handy’s OPTX modificationof Becke’s exchange functional, which gave nonaffinity of thisnoncovalent binding system after correction. We further studiedthis issue, and it is addressed below. The commonly usedB3LYP hybrid method leads to the closest description ofnoncovalent binding energy (19.6 kcal/mol) among all themethods. Next to it stands the mPW1PW method giving 20.1kcal/mol. Modern hybrid DFT methods, such as PBE1PBE,MPW1B95, and MPWB1K, with enhanced assessment fornonbonded interactions (run with the use of the 6-31G(d) basisset as well) overestimated the binding energy by about 10 kcal/

mol compared to the experimental data. Figure 8 illustrates witha graph the performance of different methods for the ONIOM,free and binding energies (after the solvation correcton), incomparison with the experimental data.

We note the poor performance of the O3LYP functional onthe binding energies. It has been reported in the originalassessment conducted by Hoe et al.75 that a major deficiencyof the O3LYP functional is the lack of accuracy for diffusesystems or weakly bonded systems. A subsequent evaluationof this functional for the G3/05 test set of experimental energiesby Curtiss et al.76 revealed that the O3LYP functional produces

TABLE 4: Free Energy and Solvation Energy Correction for the Optimized NA Model

energy (au) energy (kcal/mol)

theory complex biotin streptavidin binding affinity correction

Free Energy (ONIOM Model)HF/STO-3G:UFF -7248.213986 -1105.626677 -6142.491734 60.0 -thermal free energies -7232.801212 -1105.357263 -6127.390946 33.3 -26.7

Solvation Energy (QM Model)HF/STO-3G -7249.230305 -1105.626676 -6143.521421 51.6 -(PCM)water) -7249.3286 -1105.650607 -6143.640005 23.8 -27.7

TABLE 5: Single Point Energy for the Optimized AN Model Obtained by Using the 6-31G(d) Basis Set and DifferentElectronic Structure Methods

extrapolated ONIOM energy (au) binding affinity (kcal/mol)

method complex biotin streptavidin extrapolated energy free energya binding energyb

HF -7323.207879 -1116.621841 -6206.373796 133.2 106.5 78.8SPL -7323.612714 -1116.670206 -6206.730585 133.0 106.3 78.6SVWN5 -7345.338267 -1119.213236 -6225.910053 134.9 108.2 80.5SVWN -7380.848388 -1123.807679 -6256.900837 87.8 61.1 33.4PW91PW91 -7382.489310 -1124.008960 -6258.366732 71.3 44.6 16.9mPWPW -7374.833065 -1123.042849 -6251.654315 85.3 58.6 30.9PBEPBE -7380.682266 -1123.788362 -6256.786099 67.6 40.9 13.2B3LYP -7383.396748 -1124.089547 -6259.189324 74.0 47.3 19.6B3P86 -7403.529218 -1126.460718 -6276.946028 76.8 50.1 22.4B3PW91 -7380.698054 -1123.779052 -6256.814991 65.3 38.6 10.9mPW1PW -7381.733687 -1123.934187 -6257.680771 74.5 47.8 20.1PBE1PBE -7375.351495 -1123.131686 -6252.087548 83.0 56.3 28.6O3LYP -7380.830845 -1123.814987 -6256.936080 50.1 23.4 -4.3MPW1B95 -7380.270769 -1123.809378 -6256.330652 82.0 55.3 27.6MPWB1K -7379.949666 -1123.778732 -6256.037797 83.5 56.8 29.1

a HF/STO-3G vibrational frequencies were used for the thermal free energy corrections. b The solvation energy correction applied.

Figure 8. Effect of an electron correlation approximation on theinteraction energy of the optimized streptavidin-biotin complex (ANmodel).

9964 J. Phys. Chem. B, Vol. 113, No. 29, 2009 Li et al.

substantial errors for hydrogen-bonded complexes. To testpossible improvement of the energy accuracy due to cancellationof errors, we took the HF, O3LYP, and mPWB1K methods withthe 6-31G(d) and 6-31+G(d) basis sets for further verification.The performance of these six levels of approximation waschecked in the single point calculations for the optimized ANand GN models based on the following: (i) effect of the fourhydrogen bonds on the binding energy in the AN model, whichare absent in the GN model; (ii) accuracy of O3LYP for differentsystems; and (iii) use of diffuse functionals to diminish thediscrepancy of the binding energy calculated at the mPWB1K/6-31G(d):UFF//HF/STO-3G:UFF level with the experimentaldata.

Table 6 shows the single point energies for the differentmodels obtained from the above six levels of approximationwe tested. A comparison of the binding free energies of theAN and GN models shows the lack of four hydrogen bonds inthe GN model results in a drop in the binding energy byapproximately 10 kcal/mol (around 36%) for the HF methodand by 16 kcal/mol (around 32%) for the mPWB1K method.However, with the O3LYP method the energy differencebetween the AN and GN models is negligible, which meansthat O3LYP does not adequately represent the four hydrogenbonds present in the AN but absent in GN model. Adding thediffuse functional to the AN and GN systems affects the threemethods differently. For the HF and mPWB1K methods, thediffuse functional on heavy atoms results in a drop of about17% and 19% in the binding energy, repectively. However, forO3LYP, a 72% drop in the binding energy occurs with thediffuse functional for both the neutralized models. We concludefrom this study that, the O3LYP functional is not suitable todescribe the binding energy of this noncovalently bondedsystem. For the hybrid DFT methods with enhanced assessmentof nonbonded interactions, such as MPWB1K, the use of diffusefunctionals can drop the binding energy by about 10 kcal/mol,and thus, it gives a more accurate binding energy compared tothe experiment.

Other than the binding free energies of the streptavidin-biotinsystemcalculatedearlierfrommolecularmechanicalsimulations,19-21

the only computational study at the QM level of binding energyfor the whole system was performed by Zhang and co-workers22

by using the MFCC approach at the HF/3-21G level. Theycalculated the binding energies to be about 116 kcal/mol basedon the PDB database crystal structure. Among all the theorieswe tested for the optimized structure, B3LYP/6-31G(d) producesthe best agreement with the experimental binding free energy.The closest values obtained are 19.6 kcal/mol at the B3LYP/6-31G(d):UFF//HF/STO-3G:UFF level and 20.1 kcal/mol at themPW1PW/6-31G(d):UFF//HF/STO-3G:UFF level for the ANmodel.

3.3. 3D Solvation Structure. We studied the solvationfeatures of the streptavidin-biotin complex by using the 3D-RISM-KH molecular theory of solvation. The geometry of the

AN model was used, and the deprotonated states were assignedto Btn, Asp128, and Val133 in order to apply the force field 03parameter set. Figure 9 illustrates the 3D solvation structure ofstreptavidin by showing the 3D distribution function of wateroxygen, gO

uv(r) in the isosurface representation. We depicted theisosurfaces of gO

uv(r) > 4, that is, the area where the probabilitydensity of finding a water molecule is four times larger than inthe bulk solvent.

To calculate the average number of water molecules N aroundthe binding site in the streptavidin-biotin complex and thenonbound streptavidin, we integrated the 3D density distributionof water oxygen over the binding site cavity volume VB:

where F is the number density of bulk ambient water. Thebinding site cavity volume VB in the above integral was specifiedas a rectangular box 2 Å larger on each side of the box than thesize of the biotin urea moiety. The x, y, and z sizes of the boxwere 7.9, 6.8, and 5.2 Å, respectively. The integration showsthat on average there is one water molecule in this box aroundthe biotin urea moiety of the streptavidin-biotin complex andthere is roughly seven water molecules in the same volumeof the unliganded streptavidin. The number of such structuralwater molecules in the unliganded streptavidin is in excellentagreement with the previous crystallographic studies.3 It shouldbe pointed out that, in the recent computational study of thebiotin and streptavidin binding with MD simulations, Houk andDeChancie also predicted seven bound water in the unligandedstreptavidin binding pocket.23

Figures 10 and 11 show the isosurface representation of thewater oxygen density distribution function drawn at a level ofgO

uv(r) > 12 to visualize the local maxima, which determine themost possible hydration sites of the unliganded and ligandedstreptavidin. We identified two local maxima for the bindingsite of the unliganded streptavidin below called as sites 1 and2. The structural water at site 1 is located next to the sp3

hybridized oxyanion of the biotin ureido group, and it bridgesthe amide of Asn23 and the hydroxyls of Ser27 and Tyr43,respectively. Site 2 is situated in between Val47, Ser27, andSer45 and coordinated to the amide group of Val47. Accordingto the solvation structure obtained, the structural water at site 1might be essential in stabilizing the fold of nonbinding strepta-vidin by connecting the amide of Asn23 to the hydroxyls ofSer27 and Tyr43.

TABLE 6: Single Point Energy for Different Models(kcal/mol)

energy of AN model energy of GNmodel

model extrapolated model extrapolated

HF/6-31G(d) 47.0 55.4 30.3 36.2HF/6-31+G(d) 42.1 50.5 26.2 32.1O3LYP/6-31G(d) 41.7 50.1 32.9 38.8O3LYP/6-31+G(d) 24.8 33.2 17.6 23.5mPWB1K/6-31G(d) 75.2 83.5 51.7 57.6mPWB1K/6-31+G(d) 66.5 74.9 44.3 50.2

Figure 9. Isosurface representation of the solvation shell aroundstreptavidin. The surfaces show the areas of the 3D water oxygendistribution function g(r) > 4.

N ) ∫VB

FgOuv(r)dr

Streptavidin-Biotin Supramolecular Complex J. Phys. Chem. B, Vol. 113, No. 29, 2009 9965

Figure 11 shows the location of high-density water at theliganded streptavidin binding site, which can hold one structuralwater molecule at most. As follows from the water oxygen andhydrogen distribution peaks at this hydration site surroundedby Btn, Tyr43, Ser45, Trp92, and Trp79, this immobilized watermolecule is most probably arranged as a water bridge hydrogenbonded to the sulfur atom of the urea moiety and the nitrogenatom of the NH group close to Ser45. The water oxygen atomis coordinated to the hydrophobic part of the Tyr 43, Trp92,and Trp79 residues.

A comparison of the solvation structure of the unligandedand liganded streptavidin suggests that the water molecule at

hydration site 1 might hold the three surrounding residues inthe unliganded streptavidin apart from each other, thus con-tributing to stabilization of the conformation of the unligandedstreptavidin. In the docking procedure, the Btn molecule canreplace only six out of the seven water molecules situated atthe binding site of the unliganded streptavidin. The remainingone water molecule, very likely from hydration site 1 of theunliganded streptavidin, might be squeezed into the gap amongBtn, Tyr43, Ser45, Trp92, and Trp79 residues in the bindingpocket. In a subsequent study, we plan to use the 3D moleculartheory of solvation to further resolve the binding free energycontributions of the one trapped water molecule and the sixwater molecules released from the binding pocket in the biotin-streptavidin complex. One needs to mention that Houk andDeChancie compared the solvation structure of avidin to thatof streptavidin using MD simulation and concluded that thegreater affinity of the avidin to streptavidin complex is achieveddue to the weakening of the binding interactions with waterrather than the stronger interactions with biotin.23 Our resultsfor the solvation structure in the binding pocket of theunliganded and liganded streptavidin obtained from the statisti-cal-mechanical, 3D molecular theory of solvation are in goodagreement with this observation.

4. Conclusions

The strong noncovalent interactions of streptvidin-biotinsystem are a nontrivial challenge for computational chemistry.Our best model contains all the streptavidin residues within 3Å of the biotin (Btn) residue in the quantum (QM) layer. Intotal, 16 residues including Btn with 274 atoms were describedat the QM layer, in which five residues are responsible for thehydrophobic interaction and nine residues for the hydrogen-bonding/electrostatic interaction with Btn. Compared to isolatedBtn, a geometry change of the urea moiety in the bound Btnoccurs in the network of both nonpolar van der Waals and polarinteractions: the C-O bond gets longer and, correspondingly,the C-N bond gets shorter; and the bridge C-C bond getslonger and the neighboring C-C bonds in the tetrahy-drothiophene ring get shorter. In the AN model, for example,the C-O, C-N, and bridge C-C bond length changes are0.034, -0.073, and 0.015 Å, respectively.

We have evaluated the performance of 11 basis sets and 15density functionals, including the recently refined DFT func-tionals with an improved description of nonbonded interactions,by the single point calculation for the binding energy using theoptimized cooperative binding complex structure. The modernhybrid density functional methods with enhanced assessmentfor nonbonded interactions, such as PBE1PBE, MPW1B95, andMPWB1K, produced overestimated values that were about 10kcal/mol higher than that of the experimental binding energyof 18.3 kcal/mol. This gap could be eliminated by employingdiffuse functionals. The B3LYP method with the 6-31G(d) basisset yielded a quite good value of 19.6 kcal/mol for the ANmodel.

The solvation structure of the streptavidin-biotin system wasstudied by using the statistical-mechanical, 3D-RISM-KHmolecular theory of solvation. Integration of the 3D densitydistribution of water oxygen over the binding pocket shows thatthere are about seven water molecules in the binding pocket ofthe unliganded streptavidin and one water molecule around theBtn ureido group of the streptavidin-biotin complex. Thisimmobilized water molecule acts as a water bridge between thesulfur and the nitrogen in the NH group close to Ser45 in theurea unit of Btn. We identified two high-density hydration sites,

Figure 10. Isosurface representation of the solvation shell around thebinding pocket of the unliganded streptavidin. The surfaces show theareas of the 3D water oxygen distribution function g(r) > 12. The arrowsindicate the location of high-density water sites 1 and 2. The QM layeris represented in the CPK drawing.

Figure 11. Isosurface representation of the solvation shell around thebinding pocket of the streptavidin-biotin complex. The surfaces showthe areas of the 3D water oxygen distribution function g(r) > 6. Thearrow indicates the location of a high-density water site. The QM andBtn layers are represented in CPK and VWD drawings, respectively.

9966 J. Phys. Chem. B, Vol. 113, No. 29, 2009 Li et al.

sites 1 and 2, coordinated to the amide of Asn23 and hydroxylsof Ser27 and Tyr43, respectively, which are considered to beessential in stabilizing the fold of the unliganded streptavidin.

Acknowledgment. This work was supported by the NationalResearch Council (NRC) of Canada. Q.L. thanks Dr. TakeshiYamazaki and Dr. Stanislav Stoyanov for valuable discussionsand for help in the 3D-RISM calculations. Computations weresupported in part by the Centre of Excellence in IntegratedNanotools (CEIN) at the University of Alberta. The Gaussiancomputations were performed using the Gaussian commerciallicense of the National Research Council of Canada.

References and Notes

(1) Kuntz, I. D.; Chen, K.; Sharp, K. A.; Kollman, P. A. Proc. Natl.Acad. Sci. U.S.A. 1999, 96, 9997.

(2) Swamy, M. J. Biochem. Mol. Biol. Int. 1995, 36, 219.(3) Weber, P. C.; Ohlendorf, D. H.; Wendoloski, J. J.; Salemme, F. R.

Science 1989, 243, 85.(4) Wilchek, M.; Bayer, E. A. Methods Enyzmol. 1990, 184, 5.(5) Dixon, R. W.; Radmer, R. J.; Kuhn, B.; Kollman, P. A. J. Org.

Chem. 2002, 67, 1827.(6) Bontempo, D.; Maynard, H. D. J. Am. Chem. Soc. 2005, 127, 6508.(7) Suci, P. A.; Klem, M. T.; Arce, F. T.; Douglas, T.; Young, M.

Langmuir 2006, 22, 8891.(8) Edgar, R.; Mckinstry, M.; Hwang, J.; Oppenheim, A. B.; Fekete,

R. A.; Giulian, G.; Merril, C.; Nagashima, K.; Adhya, S. Proc. Natl. Acad.Sci. U.S.A. 2006, 103, 4841.

(9) Weber, P. C.; Wendoloski, J. J.; Pantoliano, M. W.; Salemme, F. R.J. Am. Chem. Soc. 1992, 114, 3197.

(10) Chilkoti, A.; Tan, P. H.; Stayton, P. S. Proc. Natl. Acad. Sci. U.S.A.1995, 92, 1754.

(11) Freitag, S.; Le Trong, I.; Klumb, L.; Stayton, P. S.; Stenkamp, R. E.Protein Sci. 1997, 6, 1157.

(12) Chu, V.; Freitag, S.; Le Trong, I.; Stenkamp, R. E.; Stayton, P. S.Protein Sci. 1998, 7, 848.

(13) Freitag, S.; Le Trong, I.; Chilkoti, A.; Klumb, L. A.; Stayton, P. S.;Stenkamp, R. E. J. Mol. Biol. 1998, 279, 211.

(14) Klumb, L. A.; Chu, V.; Stayton, P. S. Biochemistry 1998, 37, 7657.(15) Le Trong, I.; Freitag, S.; Chu, V.; Stayton, P. S.; Stenkamp, R. E.

Acta Crystallogr. 2003, D59, 1567.(16) Hyre, D.; Le Trong, I.; Freitag, S.; Stenkamp, R. E.; Stayton, P. S.

Protein Sci. 2000, 9, 878.(17) Gonza’lez, M.; Bagatolli, L. A.; Echabe, I.; Arrondo, J. L. R.;

Argaran∼a, C. E.; Cantor, C. R.; Fidelio, G. D. J. Biol. Chem. 1997, 272,11288.

(18) Williams, D. H.; Stephens, E.; Zhou, M. J. Mol. Biol. 2003, 329,389.

(19) Miyamoto, S.; Kollman, P. A. Proteins: Struct., Funct., Genet. 1993,16, 226.

(20) Miyamoto, S.; Kollman, P. A. Proc. Natl. Acad. Sci. U.S.A. 1993,90, 8402.

(21) Dixit, S. B.; Chipot, C. J. Phys. Chem. A 2001, 105, 9795.(22) Zhang, D. W.; Xiang, U.; Zhang, J. Z. H. J. Phys. Chem. B 2003,

107, 12039.(23) DeChancie, J.; Houk, K. N. J. Am. Chem. Soc. 2007, 129, 5419.(24) Williams, D. H.; Stephens, E.; O’Brien, D. P.; Zhou, M. Angew.

Chem., Int. Ed. 2004, 43, 6596.(25) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett 1996, 77,

3865.(26) Cohen, A. J.; Handy, N. C. Mol. Phys. 2001, 99, 607.(27) Xu, X.; Goddard, W. A. Proc. Natl. Acad. Sci. U.S.A. 2004, 101,

2673.(28) Becke, A. D. J. Chem. Phys. 1996, 104, 1040.(29) Adamo, C.; Barone, V. J. Chem. Phys. 1998, 108, 664.(30) Becke, A. D. J. Chem. Phys. 1996, 104, 1040.(31) Zhao, Y.; Truhlar, D. G. J. Phys. Chem. A 2004, 108, 6908–6918.(32) Zhao, Y.; Truhlar, D. G. J. Chem. Theory Comput. 2005, 1, 415–

432.(33) Beglov, D.; Roux, B. J. Chem. Phys. 1995, 103, 360.(34) Kovalenko, A.; Hirata, F. Chem. Phys. Lett. 1998, 290, 237.(35) Kovalenko, A.; Hirata, F. J. Chem. Phys. 1999, 110, 10095.(36) Kovalenko, A.; Hirata, F. J. Chem. Phys. 2000, 112, 10391.(37) Kovalenko, A. Three-Dimensional RISM Theory for Molecular

Liquids and Solid-Liquid Interfaces. In Molecular Theory of SolVation;Hirata, F., Ed.; Kluwer: Dordrecht, The Netherlands, 2003; pp 169-275.

(38) Moralez, J. G.; Raez, J.; Yamazaki, T.; Motkuri, R. K.; Kovalenko,A.; Fenniri, H. J. Am. Chem. Soc. Commun. 2005, 127, 8307.

(39) Johnson, R.; Yamazaki, T.; Kovalenko, A.; Fenniri, H. J. Am. Chem.Soc. 2007, 129, 5735.

(40) Drabik, P.; Gusarov, S.; Kovalenko, A. Biophys. J. 2007, 92, 394.(41) Imai, T.; Hiraoka, R.; Kovalenko, A.; Hirata, F. J. Am. Chem. Soc.

Communications 2005, 127, 15334.(42) Imai, T.; Hiraoka, R.; Kovalenko, A.; Hirata, F. Proteins: Struct.,

Funct., Bioinf. 2007, 66, 804.(43) Imai, T.; Hiraoka, R.; Seto, T.; Kovalenko, A.; Hirata, F. J. Phys.

Chem. B 2007, 111, 11585.(44) Imai, T.; Isogai, H.; Seto, T.; Kovalenko, A.; Hirata, F. J. Phys.

Chem. B 2006, 110, 12149.(45) Imai, T.; Harano, Y.; Kinoshita, M.; Kovalenko, A.; Hirata, F.

J. Chem. Phys. 2006, 125, 024911.(46) Imai, T.; Kovalenko, A.; Hirata, F. Mol. Simul. 2006, 32, 817.(47) Imai, T.; Kovalenko, A.; Hirata, F. Chem. Phys. Lett. 2004, 395,

1.(48) Imai, T.; Harano, Y.; Kinoshita, M.; Kovalenko, A.; Hirata, F.

J. Chem. Phys. 2007, 126, 225102.(49) Imai, T.; Ohyama, S.; Kovalenko, A.; Hirata, F. Protein Sci. 2007,

16, 1927.(50) Imai, T.; Takekiyo, T.; Kovalenko, A.; Hirata, F.; Kato, M.;

Taniguchi, Y. Biopolymers 2005, 79, 97.(51) Imai, T.; Harano, Y.; Kovalenko, A.; Hirata, F. Biopolymers 2001,

59, 512.(52) Harano, Y.; Imai, T.; Kovalenko, A.; Kinoshita, M.; Hirata, F.

J. Chem. Phys. 2001, 114, 9506.(53) Yamazaki, T.; Imai, T.; Hirata, F.; Kovalenko, A. J. Phys. Chem.

B 2007, 111, 1206.(54) Case, D. A.; et al. Amber 9; The Scripps Research Institute: La

Jolla, CA, 2006.(55) Duan, Y.; Wu, C.; Chowdhury, S.; Lee, M. C.; Xiong, G.; Zhang,

R.; Cieplak, P.; Luo, R.; Lee, T. J. Comput. Chem. 2003, 24, 1999–2012.(56) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb,

M. A.; Cheeseman, J. R. ; Montgomery J. A., Jr.; Vreven, T.; Kudin, K. N.;Burant, J.C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci,B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.;Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.;Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox,J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.;Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.;Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.;Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels,A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.;Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.;Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz,P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al.Laham, M. A.;Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson,B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian03 reVisionB.01, Gaussian Inc.: Pittsburgh, PA, 2003.

(57) Hohenberg, P.; Kohn, W. Phys. ReV. 1964, 136, B864.(58) Kohn, W.; Sham, L. J. Phys. ReV. A: At., Mol., Opt. Phys. 1965,

140, 1133.(59) Slater, J. C. The Self-Consistent Field for Molecules and Solids.

In Quantum Theory of Molecules and Solids; Vol. 4; McGraw-Hill: NewYork, 1974.

(60) Perdew, J. P.; Zunger, A. Phys. ReV. B: Condens. Matter Mater.Phys. 1981, 23, 5048.

(61) Vosko, S. H.; Wilk, L.; Nusair, M. Can. J. Phys. 1980, 58, 1200.(62) Perdew, J. P. in Electronic Structure of Solids ’91, Ed. Ziesche, P.

and Eschrig, H. (Akademie Verlag, Berlin, 1991) 11.(63) Becke, A. D. Phys. ReV. A: At., Mol., Opt. Phys. 1988, 38, 3098.(64) Lee, C.; Yang, W.; Parr, R. G. Phys. ReV. B: Condens. Matter

Mater. Phys. 1988, 37, 785.(65) Perdew, J. P. Phys. ReV. B: Condens. Matter Mater. Phys. 1986,

33, 8822.(66) Frisch, M. J.; Pople, J. A.; Binkley, J. S. J. Chem. Phys. 1984, 80,

3265.(67) Dunning, T. H., Jr. J. Chem. Phys. 1989, 90, 1007.(68) Woon, D. E.; Dunning, T. H., Jr. J. Chem. Phys. 1995, 103, 4572.(69) Perkyns, J. S.; Pettitt, B. M. J. Chem. Phys. 1992, 97, 7656–7666.(70) Berendsen, H. J. C.; Postma, J. P. M.; van Gunsteren, W. F.;

Hermans, J. In Intermolecular Forces; Pullman, B. Ed.; Reidel: Dordrecht,1981, p. 331.

(71) Kovalenko, A.; Ten-no, S.; Hirata, F. J. Comput. Chem. 1998, 20,928.

(72) Masunov, A.; Dannenberg, J. J. J. Phys. Chem. B 2000, 104, 806.(73) Steiner, T. Chem. Commun. 1997, 727.(74) Blessing, R. H. J. Am. Chem. Soc. 1983, 105, 2776.(75) Hoe, W.; Cohen, A. J.; Handy, N. C. Chem. Phys. Lett. 2001, 341,

319.(76) Curtiss, L. A.; Redfern, P. C.; Raghavachari, K. J. Chem. Phys.

2005, 123, 124107-1.

JP902668C

Streptavidin-Biotin Supramolecular Complex J. Phys. Chem. B, Vol. 113, No. 29, 2009 9967