lafont proteins 2007

Protein–Protein Recognition and Interaction Hot Spots inan Antigen–Antibody Complex: Free Energy DecompositionIdentifies ‘‘Efficient Amino Acids’’Virginie Lafont,1,2 Michael Schaefer,3 Roland H. Stote,4 Daniele Altschuh,2 and Annick Dejaegere1*1Structural Biology and Genomics Department, UMR 7104, Institut de Genetique et de Biologie Moleculaire et Cellulaire, CNRS/INSERM/ULP, F-67404 Illkirch Cedex, France2UMR7175-LC1 CNRS/ULP, ESBS, Parc d’Innovation, 67412 Illkirch Cedex, France3Laboratoire de Chimie Biophysique, Institut le Bel, Universite Louis Pasteur, 67000 Strasbourg, France4Laboratoire de Biophysicochime Moleculaire, Institut de Chimie, LC3-UMR7177, Universite Louis Pasteur,67070 Strasbourg Cedex, France

ABSTRACT The molecular mechanics Poisson–Boltzmann surface area (MM/PBSA) method wasapplied to the study of the protein–protein complexbetween a camelid single chain variable domain(cAb-Lys3) and hen egg white lysozyme (HEL), andbetween cAb-Lys3 and turkey egg white lysozyme(TEL). The electrostatic energy was estimated bysolving the linear Poisson–Boltzmann equation. Afree energy decomposition scheme was developed todetermine binding energy hot spots of each complex.The calculations identified amino acids of the anti-body that make important contributions to the inter-action with lysozyme. They further showed the influ-ence of small structural variations on the energeticsof binding and they showed that the antibody aminoacids that make up the hot spots are organized insuch a way as to mimic the lysozyme substrate.Through further analysis of the results, we definethe concept of ‘‘efficient amino acids,’’ which can pro-vide an assessment of the binding potential of a par-ticular hot spot interaction. This information, inturn, can be useful in the rational design of smallmolecules that mimic the antibody. The implicationsof using free energy decomposition to identifyregions of a protein–protein complex that could betargeted by small molecules inhibitors are discussed.Proteins 2007;67:418–434. VVC 2007Wiley-Liss, Inc.

Key words: MM/PBSA; molecular dynamics; macro-molecular electrostatics; protein engi-neering; drug design; antibodies;camelids

INTRODUCTION

For a wide range of biological processes, including anti-body–antigen interactions, hormone–receptor interac-tions, signal transduction, and regulation, the formationof stable protein–protein complexes is of fundamental im-portance. Interfering with or modulating the formation ofthese complexes therefore offers attractive opportunitiesfor therapeutic intervention. However, the development ofsmall molecules that modulate protein–protein interac-

tions is difficult.1 There are several examples of naturalmolecules that bind at protein interfaces2 and a growingnumber of synthetic compounds that are aimed at per-turbing protein–protein interactions (for a recent review,see Ref. 3). Progress in developing synthetic compoundswill benefit greatly from improved understanding of theenergetics and dynamics of protein–protein recognition.Our current understanding of protein–protein interac-tions is based on structural analysis of protein–proteincomplexes mostly determined by crystallography, on vari-ous biophysical characterizations of protein–protein com-plexes that give insight into the kinetics and thermody-namics of protein–protein association,4 and on biochemi-cal analyses that help identify amino acids important forrecognition.

An important concept that has emerged in the lastyears is the notion of interaction energy ‘‘hot spots,’’ whichis the idea that a handful of amino acids at the bindinginterface make a dominant contribution to the binding af-finity.5,6 Mutation studies, mostly alanine scanning stud-ies, have indeed shown7 that only a few mutations [native? Ala] affect the free energy of binding by more than2 kcal/mol. This has led to a distinction between the func-tional epitope (i.e. ‘‘hot spot residues) and the structuralepitope (all residues that participate in the interface).8

The Supplementary Material referred to in this article can be foundat http://www.interscience.wiley.com/jpages/0887-3585/suppmat/

Virginie Lafont’s current address is Department of Biology, JohnsHopkins University, 3400 North Charles Street, Baltimore, MD21218-2685.

Michael Schafer’s current address is Novartis Pharma AG, Kly-beckstrasse 141, 4057 Basel, Switzerland.

*Correspondence to: Annick Dejaegere. Structural Biology andGenomics Department, UMR 7104, Institut de Genetique et de Biolo-gie Moleculaire et Cellulaire, CNRS/INSERM/ULP, BP 10142,F-67404 Illkirch Cedex, France. E-mail: [email protected]

Grant sponsor: French Ministry of Defense, Centre National de laRecherche Scientifique, Institut National de la Sante et de la Recher-che Medicale, and Universite Louis Pasteur, Strasbourg, France.

Received 20 May 2006; Revised 6 September 2006; Accepted 15 Sep-tember 2006

Published online 26 January 2007 in Wiley InterScience (www.interscience.wiley.com). DOI: 10.1002/prot.21259

VVC 2007 WILEY-LISS, INC.

PROTEINS: Structure, Function, and Bioinformatics 67:418–434 (2007)

However, much remains to be understood of the role ofresidues surrounding the hot spots in creating a favorablebinding environment, on the balance between electro-static, van der Waals, and hydrophobic interactions in theformation of complexes, in entropic contributions to bind-ing, and in the role of molecular flexibility on the bindingprocess.Computational and theoretical methods permit the sys-

tematic analysis of individual amino acid contributions tothe formation of protein complexes.9–13 They provide awealth of information that are complementary to experi-ments and allow the determination of the structural andenergetic consequences of mutations, as well as a betterunderstanding of the physical mechanism and origin ofthe intermolecular interactions that drive binding. Freeenergy simulations methods14–16 have been successfullyused to predict the effect of point mutations on binding af-finity in macromolecular complexes (for a recent review,see Ref. 17). Computational cost, however, puts practicallimitations on the number of point mutations that can beanalyzed by free energy simulations for a given complex.Systematic analysis of the contribution of all amino acidsto the stability of macromolecular complexes have mostlyrelied on different empirical free energy functions11,12 aswell as on all-atom molecular mechanics methods usingimplicit representation of the solvent (so called MM/PBSAor MM/GBSA methods18). The MM/PBSA method hasbeen used to systematically analyze the contribution of allamino acids to the formation of several macromolecularcomplexes. For computational efficiency, these analyseswere performed on a single structure of the complex.10,19

The generalized Born model for electrostatics has alsorecently been applied to the free energy decomposition inprotein–protein complexes.13,20,21 The generalized Bornmodel is faster, but introduces additional approximationsin the electrostatics treatment with respect to numericalsolutions of the Poisson–Boltzmann equations. In thepresent work, we develop a computationally tractable, yetreliable, free energy decomposition protocol that can beused to identify amino-acids that have a dominant role inbinding. In the MM/PBSA approach presented here, weuse solutions to the Poisson–Boltzmann equation toobtain the electrostatic contribution to binding. This is incontrast to other recent applications of the methodol-ogy13,20,21 where the Generalized Born model wasemployed. In addition, multiple conformations from mo-lecular dynamics trajectories are used in the analysis.The protocol is used to analyze molecular recognition in

the complex between a camel single chain antibody vari-able domain (cAb-Lys3) and its antigen lysozyme.22,23 Therecombinant protein cAb-Lys3 is a single variable domain.Single domain antigen binding fragments can be gener-ated from the variable domain of Camelidae heavy chainantibodies. Indeed, the Camelidae possess, in addition toclassical IgG molecules, a large fraction of naturallyoccurring heavy chain antibodies that are devoid of lightchains.24 These single domains preserve the ability tobind specifically and with high affinity to their antigens.These small antibodies, also called VHH or nanobodyTM

are minimally sized, stable, and highly soluble, and there-fore offer a number of benefits in medical and biotechno-logical applications (for a recent review, see Ref. 25). Highaffinity VHH can be obtained after immunization of lla-mas and dromedaries with specific antigens.23,26 Alterna-tively, phage antibody libraries can be used.27,28 VHHsthat inhibit several enzymes22,23,26,28–31 have been identi-fied, as well as VHH that target antigens specific ofhuman tumors32,33 or specific of infectious agents.34

VHHs against a mouse anti-DNA monoclonal antibodythat are competitive binders of the original DNA antigenhave also been recently identified and are shown to beuseful for molecular mimicry studies.35 VHHs against pro-teins of interest in human disease have potential diagnos-tic33 or therapeutic32 applications. Camelidae VHHs arenot only able to recognize a wide range of target proteins,their high stability and small size makes them amenableto structural studies, and an increasing number of VHH–antigen structures are available (for recent examples seeRefs. 36–38). The structural information from these com-plexes is potentially useful for the development of smallmolecule mimicks of the VHH.39 For this to be realized,however, it is important to identify the important interac-tions in the VHH–antigen complex. From an experimentalanalysis alone, this is not necessarily evident. In this pa-per, we show, for the VHH cAb-Lys3–lysozyme complex,that an interaction energy hot spot exploited in the anti-body–lysozyme complex is also used by the N-acetyl gluco-samine (NAG) ring of saccharide substrates in subsite Cof the lysozyme binding pocket. We support the results ofthe free energy decomposition approach by the mutationalanalysis of four VHH positions. We further introduce theconcept of amino acid efficiency and show the potential offree energy decomposition in extracting useful informa-tion for drug design.

MATERIALS ANDMETHODS

We developed a protocol based on the MM/PBSAmethod,13,18,40 in which conformations extracted from mo-lecular dynamics simulations are processed by a combina-tion of methods using a simplified description for the sol-vent to give an estimate of binding free energy. Individualcontributions of each amino acid to the complex formationare estimated and important amino acid ‘‘hot spots’’ areidentified.

Structures

The coordinates of the camel single-domain VH anti-body–lysozyme complexes were obtained from the ProteinData Bank.41 Two structure files containing hen egg whitelysozyme as the antigen were obtained: 1MEL (solved at2.5 A resolution)22 and 1JTT (solved at 2.1 A resolution).42

A third structure file containing the coordinates for thecomplex of the same antibody with turkey egg white lyso-zyme as the antigen was also obtained from the ProteinData Bank: 1JTP (solved at 1.9 A resolution).42 For thestructures 1MEL and 1JTP, there are two complexes perasymmetric unit, antibody chain A with lysozyme chain L

419INTERACTION HOT SPOTS IN ANTIGEN–ANTIBODY COMPLEX

PROTEINS: Structure, Function, and Bioinformatics DOI 10.1002/prot

and antibody chain B with lysozyme chain M. As there aresignificant structural differences between the two com-plexes,42 calculations were carried out for each complex(AL and BM).The hydrogen atoms were added to the crystal structure

using the HBUILD module43 of the CHARMM44 program(version 29a1); the all atom parameter set of CHARMM2245

was used for all calculations. Each structure was sub-jected to an energy minimization of 5000 steps using thesteepest descent algorithm and 5000 steps using theadopted basis Newton Raphson algorithm. Harmonic con-straints, added initially to prevent any large perturbationof structure, were gradually reduced over the course ofthe minimization. The final steps of the minimizationwere done without constraints. The minimization wasstopped when the gradient of the energy was less than10!4 kcal mol!1 A!1. A distance dependent dielectric of 4r,where r is the distance between two atoms, and a non-bonded cutoff of 13 Awere used during minimization.

Determination of Protonation State

The pKa of titratable groups were determined for boththe isolated proteins and for the complexes using contin-uum electrostatic as described by Schaefer et al.46 Themethod assumes that electrostatic effects dominate theinfluence of the surroundings on the pKa of titratablegroups. The change in pKa of titratable residues betweenthe solution value (where experimental values for aminoacid side chains are used) and the value in the protein in-terior is then calculated using continuum electrostatics.We used the UHBD program47 to calculate the free energyof different states of protonation and a series of c-shellscripts46 to obtain the titration curves. The protonationstates of selected residues were determined at physiologi-cal pH of 7.4. Residues located at the interface of the com-plex are those which are the most susceptible to undergoshifts in pKa when the complex is formed. Therefore wedetermined the protonation state of acidic and basic resi-dues that are buried upon complexation, i.e. residues thathave a solvent accessible surface area difference betweenthe complex and the free molecules larger than 10 A2. Theprotonation states of these residues were determined inthe complex and in the two separated proteins. The proto-nation states of all other titratable groups were put totheir standard values. A dielectric constant of 80 was usedfor the solvent. Two values of the internal dielectric con-stant for the protein were tested (4 and 20) and both gavesimilar results in terms of whether particular groups wereprotonated or not at a pH of 7.4.

Molecular Dynamic Simulations

Molecular dynamic simulations were done using theCHARMM44 program and the all atom parameter set ofCHARMM22.45 The minimized protein–protein complexeswere solvated in a 933 633 63 A box of TIP3P water. Mo-lecular dynamic simulations were performed at constanttemperature using the Nose–Hoover method48,49 withperiodic boundary conditions. Bond lengths involving

bonds between heavy atoms and hydrogen atoms wereconstrained using SHAKE.50 With the protein–proteincomplex fixed, the water was equilibrated for 6 ps at 300K. The constraints were removed and the entire systemwas again equilibrated for 6 ps. A time step of 1 fs wasused in the simulation and structures were collected every10 fs. Van der Waals interactions were truncated at a cut-off distance of 12.5 A using a switch function. Electrostaticinteractions were truncated at 12.5 A using a shift func-tion. All simulations contain between 35,500 and 35,700atoms, which includes about 3800 atoms for the proteincomplex. Six trajectories ranging from 180 to 300 ps inlength were generated using different starting structuresand initial conditions. The different simulations per-formed are listed in Table I. The purpose of the simula-tions was to generate multiple structures to improve thestatistical sampling of the binding energy calculations.

Free Energy Calculations and Free EnergyDecomposition

Free energy was estimated according to a MM/PBSAapproach,18 in which the free energy is calculated accord-ing to the following equation:

Gmolecule " EMM #GPBSA ! TSMM $1%

where EMM is the total molecular mechanical energy;GPBSA, the solvation free energy; and TSMM, the entropy.The molecular mechanical energy contains an electro-static term, a van der Waals term, and an internal energyterm. The solvation free energy is divided into two contri-butions: the electrostatic contribution and the nonpolar(or hydrophobic) contribution.

GPBSA " GPB #Gnp $2%

For the purpose of the present study, we calculated only asubset of terms entering the MM/PBSA Eq. (1), namelythe total electrostatic contribution, the van der Waals con-tribution, and the nonpolar, or hydrophobic, contribution

TABLE I. MD Simulations Done forConformational Sampling

Complex PDB ID ChainsHIS111

Trajectory{ps}

cAb-Lys3/HEL MEL AL HSD 180cAb-Lys3/HEL MEL AL HSE 180cAb-Lys3/HEL MEL BM HSE 240cAb-Lys3/HEL JTT AL HSE 250cAb-Lys3/TEL JTP AL HSD 180cAb-Lys3/TEL JTP BM HSE 300

Details for four simulations of the cAb-Lys3/Hen egg-white lysozymecomplex, two simulations of the cAb-Lys3/Turkey egg-white lysozymecomplex. For each PDB crystallographic structure, both complexes ofchains A#L and of chains B#M were used. The protonation state forthe residue His 111 was determined, see text (HSD/HSE: protonationon Nd/Ne, respectively). For the complex of chains A#L in PDB entryMEL (cAb-Lys3/HEL), trajectories were run for each of the two proto-nation states of His 111 (HSE and HSD).

420 LAFONT ET AL.


to the free energy. As we neglect conformational changeupon complexation (see later), there are no changes to theinternal energy terms. The binding free energy was thenestimated according to the following equation:

DG " DEelec # DEvdw # DGelecsolv # DGnp

solv $3%

where DEelec and DEvdw are the electrostatic and van derWaals contributions to the energy of the complex forma-tion, respectively; DGelec

solv and DGnpsolv are the electrostatic

and nonpolar contributions related to solvation, respec-tively.Equation 3 neglects conformational entropy contribu-

tions to the thermodynamics of binding. We did not esti-mate this term because our main goal was to apply thismethod to identify residues that play a dominant role instabilizing the bound complex rather than obtaining aquantitative account of the binding thermodynamics.Although methods have been proposed to analyze individ-ual contributions to conformational entropies,51,52 theirgeneralization in the present context would entail a signif-icant and unnecessary computational cost. Another sim-plification introduced concerns the neglect of conforma-tion changes between the bound and unbound proteins. Inthe absence of an experimental structure for the unboundantibody, the structures of the unbound proteins weretaken from that of the complex. There are experimentalindications that the antibody–antigen association is domi-nated by enthalpy and occurs without large structuralrearrangements.53,54 These simplifications preclude cal-culations of absolute values of the binding free energy;however, they are expected to be satisfactory in the con-text of identifying interaction energy ‘‘hot spots’’ in theprotein–protein complex, which is the goal of the presentstudy. Similar simplifications have been adopted by otherauthors.10,19,55,56 Each contribution to the binding freeenergy entering Eq. (3) was decomposed as a sum of indi-vidual contributions per residue, as described later.

van der Waals contributions

The van der Waals energy was calculated by the 6-12Lennard-Jones potential of the CHARMM22 force field.The individual contributions to the van der Waals interac-tion energy of each residue of the antibody was estimatedas one half the interaction with the set of lysozyme resi-dues located in a 12.5 A cutoff distance, and vice versa forlysozyme. The division by two ensures that the sum ofindividual contributions gives the total van der Waalsinteraction energy of the complex.

Electrostatic contributions

The total electrostatic energy of a macromolecular sys-tem can be partitioned into contributions from interac-tions between pairs of atomic partial charges of the macro-molecule and from the interactions of individual partialcharges with the solvent.In a process such as protein association, there is always

interplay between favorable and unfavorable contribu-

tions. For example, there is always a destabilizing contri-bution due to the loss of favorable interactions betweencharged and polar residues and the solvent molecules(desolvation). In addition, there is a change in the num-ber, and the environment, of pair-wise interactions result-ing from complex formation, which counterbalances theunfavorable desolvation term.

We used the UHBD program47 to solve the linearizedPoisson–Boltzmann equation using a finite-differencemethod (FDPB). A shell script, which includes interfacesto UHBD, was used to compute the electrostatic bindingfree energy of binding of the two molecules. The boundarybetween the solute and solvent regions with differentdielectric constants is determined by the molecular sur-face. van der Waals radii and charges of atoms areobtained from parameters of the force field CHARMM22.A dielectric constant of 80 was used for the solvent and 1for the protein (the value of 1 for the protein dielectric con-stant is used when conformational averaging is per-formed; for the single calculation on the X-ray structure ofthe cAbLys3-HEL, a value of 4 was used for the proteindielectric constant10). The final mesh grid on whichcharges are located and on which the electrostatic poten-tial is calculated has a grid spacing of 0.35 A.

The electrostatic contribution was decomposed by resi-dues. This decomposition is possible because the linearPoisson–Boltzmann equation is used, which permits asuperposition of the electrostatic potential at point i bythe sum of potentials created by each individual charge.

DGelec "X

i2C

1

2qi/

complexi

!X

i2A

1

2qi/

antibodyi #

X

i2L

1

2qi/

lysozymei

8>>>>:

9>>>>; $4%

This equation shows that the total electrostatic energy ofa complex C (antibody # lysozyme) is calculated by sum-ming over all charges, the product of the charge qi and thepotential /i at the position of the charge. The potential /i

is obtained by solving the linear Poisson–Boltzmann (PB)equation using the program UHBD. The contribution ofone residue j to the electrostatic free energy of complexformation is estimated by summing over all charges qiusing the potentials /i created at the position i by theatomic charges of residue j:

DGelecj "

X

i2C

1

2qi/

j2Ci !

X

i2A

1

2qi/

j2Ai #

X

i2L

1

2qi/

j2Li

8>>>>:

9>>>>; $5%

where j belongs either to A (antibody) or to L (lysozyme).Such decompositions were first used to interpret contin-

uum electrostatic calculations for solvation of phosphor-anes in water,57 and a decomposition scheme similar toequation (4) was first applied to proteins by Hendsch andTidor.10 However, in earlier free energy decompositionwork based on the Poisson–Boltzmann method, only a sin-



gle conformation of the protein–protein complex was usu-ally used,10,19,58 which is not the case here.

Nonpolar contributions

The nonpolar contributions to the free energy of bindingare taken to be proportional to the loss in solvent accessi-ble surface area.

DGnp " g SAScomplex ! SASantibodyunbound # SASlysozyme

unbound

! "! "$6%

The radii of protein atoms are obtained from the parame-ters of the force field CHARMM22. We used CHARMM forcalculating the accessible surface with a probe radius of1.4 A. We determined the accessible surface of eachresidue in the free molecules and in the complex and thenwe calculated the accessible surface area differencebetween the free molecule and the complex for eachresidue. A value of 5 cal mol!1 A!2 was used13,20,21 for theconstant g.

Selection of Structures for the FreeEnergy Decomposition

Past free energy decomposition analysis based on theMM/PBSA or MM/GBSA methods have been performedusing either a single experimental structure9,10 or an en-semble of conformations extracted from moleculardynamic simulations.13,56 It is known that the differentenergy terms used in the MM/PBSA method fluctuate sig-nificantly with small changes in structure linked to ther-mal fluctuations.59 It is therefore necessary to use an en-semble of structures rather than one experimental struc-ture in free energy decompositions based on the MM/PBSA scheme. Obtaining converged values of binding freeenergies for quantitative assessment of binding thermody-namics entails significant computational effort.13 Theintention of the present work was to reliably identifythose amino acids that play a dominant role in binding,and to obtain a semi-quantitative estimate of their contri-butions to the binding thermodynamics. We, therefore,developed a protocol that uses only a limited number ofconformations extracted from molecular dynamics trajec-tories for the free energy decomposition, but that allowssufficient sampling to reduce artifacts linked to the use ofa single conformation. For the system studied, severalcrystal structures were available (cf. Structures Section).These structures were used as starting points for shortmolecular dynamics trajectories. Thus, significant confor-mational differences would be taken into account by usingthe different initial structures and the MD simulationswould give small thermal fluctuations around the crystalstructure. Ten conformations were extracted from the MDtrajectories for analysis. The structures were notextracted at regular time intervals, but selected using aprotocol that was designed to cover a large, representativerange of individual MM/PBSA energy terms. The compo-nent of the binding free energy that shows the largestfluctuations with small changes in structures is the elec-

trostatic Coulomb term. We therefore computed the Cou-lomb interaction energy in vacuo between the proteincAb-Lys3 and lysozyme for all conformations saved fromthe MD trajectory (coordinates were collected every 0.1 psfrom the MD). The Coulomb electrostatic interactionenergy in vacuo was calculated using the CHARMM pro-gram. A dielectric constant of 1 and a nonbonded cutoff of12.5 A was used, with a shift truncation function for elec-trostatics. The conformations were clustered in ten groupsthat had similar values of the electrostatic interactionenergy, and that were distributed evenly between the low-est and highest values recorded for the electrostatic inter-actions over the course of the trajectory. One conformationwas extracted from each cluster (with vacuum interactionenergy closest to the cluster average value). Eachextracted conformation was then postprocessed using theMM/PBSA procedure. The total free energy and its indi-vidual components were then obtained for each trajectoryas a weighted average over the conformations extracted,with higher weight given to conformations extracted frommore populated clusters (i.e. the weight of a conformationis proportional to the ratio of the number of conformationswith that energy to the total number of conformationsextracted from the MD trajectory). This procedure reducesthe computational cost of performing MM/PBSA calcula-tions while allowing an estimate of the effect of conforma-tional variation on the decomposition analysis. While theenergy used for selecting the conformations was the vac-uum electrostatic term, which differs from the solventterm computed by continuum electrostatics, the two termsshow a significant statistical correlation, so that confor-mations that show large variation in vacuum energy alsoshow significant variation in solution energy (data notshown,60), hence the interest of the simplified protocol.

A standard deviation of each amino acid contribution isalso calculated. The statistical weight of the conformationis taken into account in computing the standard devia-tion.61 When results from different simulations using dif-ferent starting structures are averaged, the total numberof conformations in all trajectories is used to normalizethe weight of each individual conformation in the average.

Amino Acid Efficiency

We define the amino acid efficiency as the free energycontribution of each amino acid divided by its number ofnonhydrogen atoms (i.e. 4 for Gly, 5 for Ala, 14 for Trpetc.). This definition is similar in spirit to the definition ofligand efficiency62 which is defined as the binding affinityper heavy atom. When extending the notion to aminoacids within a macromolecule, we also considered thatsome amino acids may be partially or even fully buried inunbound proteins. We therefore tested an alternative defi-nition of the number of atoms as the solvent accessibleatoms rather than all heavy atoms. The effective numberof solvent accessible atoms was computed in the followingway: for each of the 20 amino acid, AA, a tripeptide Gly-AA-Gly was constructed in extended conformation andthe solvent accessible surface of the amino acid in the tri-

422 LAFONT ET AL.


peptide was computed. The radii of amino acids atomswere obtained from the CHARMM force field andCHARMM program was used for calculating the accessi-ble surface with a probe radius of 1.4 A. The solvent acces-sible surface of each amino acid of the unbound proteinwas computed using the same procedure. Then an effec-tive number of atoms (Neffect) for each amino acid withinthe protein was computed as

Neffect " Nheavy &Sprot

Speptide

# $% &# 1 $7%

In this equation, Nheavy is the number of heavy atoms inthe amino acid; Sprot, the solvent accessible surface of theamino acid in the unbound protein; Speptide, the solvent ac-cessible surface of the amino acid in the tripeptide. If theamino acid is completely buried in the unbound protein(Sprot " 0), the effective number of atoms is set to one.The amino acid efficiency was calculated in two ways:

first by dividing the free energy contribution of eachamino acid by the effective number of atoms (Neffect), andsecond, by dividing the free energy contribution by thenumber of heavy atom (Nheavy). The results were com-pared and they were not found to be significantly differentbetween the two procedures. The data using Neffect arepresented in the Supplementary Material and the aminoacid efficiency calculated by dividing the free energy bythe number of heavy atoms was used in the analysis of theresults presented.

Mutations and Binding Affinity MeasurementsProduction of VHHmutants

The cAb-Lys3-pHEN6 vector29 containing the gene forthe expression of the recombinant cAb-Lys3 with a C-ter-minal His6 was a kind gift from Drs. M. Lauwereys and S.Muyldermans (Laboratorium voor Ultrastructuur, Brus-sels). The mutations T28A, T28D, T28K, D73S, D73R,D73K, Y118F, and I29T were introduced by standard sitedirected mutagenesis techniques. All mutant genes wereconfirmed by nucleotide sequencing. The proteins wereexpressed and purified as described by Lauwereys et al.29

Affinity measurements

The interaction of the wild type or mutant cAb-Lys3with either TEL or HEL was analyzed using a Biacore1

2000 instrument (Biacore AB, Uppsala, Sweden) asdescribed previously.63 Briefly, all experiments were car-ried out at 258C in HBS-EP buffer (10 mMHEPES pH 7.4,150 mM NaCl, 3.4 mM EDTA with 0.005% SurfactantP20). TEL or HEL were immobilized on a CM5 sensor sur-face using the amine coupling chemistry as described.63

The active concentrations of the antibody fragments weremeasured by injecting the samples on a surface containinghigh levels of lysozyme in conditions of total mass trans-port.64 The reaction rate was recorded 15 s after injection,and used to calculate the active cAb-Lys3 concentrationbased on a previously established calibration curve. Forkinetic measurements, the WT and mutant cAb-Lys3 mol-

cules were injected at different concentrations on a controlsurface and on a surface containing low levels of immobi-lized lysozyme. The injection and postinjection phaseslasted between 3 and 5 min. The surfaces were regener-ated with 50 mM HCl. Data were fitted globally with theBIAevaluation 3.1 software (Biacore AB), using the Lang-muir binding model.

RESULTS

Free Energy Decomposition for the AntibodycAb-Lys3

Here, we report the results concerning the contributionof the camelid single chain variable domain (cAb-Lys3) tototal binding free energy of the complex with hen eggwhite lysozyme (HEL) and turkey egg white lysozyme(TEL). The cAb-Lys3 single variable domain fragmentbinds to HEL and TEL with nanomolar affinity.65 On av-erage, the solvent accessible surface of the antibody thatis buried on binding is 998 A2 for the HEL and 945 A2 forthe TEL complex. To identify those amino acids that makesignificant interactions in the bound complex, the freeenergy decomposition scheme was applied to the cAb-Lys3/HEL and cAb-Lys3/TEL complexes. In all, 6 simula-tions were run of the different complexes and the MM/PBSA analysis was applied to all trajectories following theprocedure outlined in Methods. The results presentedhere in detail are average results over the different anti-gens, HEL and TEL, respectively. The decompositionresults, presented in Figs. 1–3, are for the cAb-Lys3/HELcomplex. A comparison to the results obtained for the cAb-Lys3/TEL complex is given in Supplementary Material.

In cAb-Lys3, the residues that contact lysozyme belongto the Complementary Determining Regions (CDRs) (asdefined in Ref. 67; see also Ref. 22). The results show thatamino acids that constitute the CDRs make the most im-portant contributions to the binding interactions, whilethe framework region of the antibody (defined as the anti-body without the CDRs) makes mostly negligible contribu-tions (see Fig. 1 and Table II). The residues of the CDRsdo not, however, contribute uniformly to the binding inter-actions (see Fig. 1). The third Complementary Determin-ing Region (CDR 3), which is particularly long in the cAb-Lys3 and inserts in the lysozyme active site,22 makes thedominant contribution to binding (see Fig. 1 and Table II);in particular, a contiguous stretch of seven residues (Thr101 - Ile 102 - Tyr 103 - Ala 104 - Ser 105 - Tyr 106 - Tyr107) is shown to contribute 75% of the total binding freeenergy, while it contributes only 57% of the buried cAb-Lys3 surface.

An analysis of the binding in terms of electrostatic, vander Waals and hydrophobic (based on surface area) contri-butions (see Fig. 2 and Table II) shows that for cAb-Lys3,binding is dominated by the van der Waals interactions,while the hydrophobic (surface area) contribution issmaller. The relative contributions of the three CDRs andof the framework region to the hydrophobic term areroughly correlated with their respective van der Waalscontributions.



Overall, the electrostatic contribution of the cAb-Lys3 tobinding is about zero, which results from the compensa-tion between (#4 kcal/mol) unfavorable electrostatic con-tributions of CDR’s 1 and 2 and favorable contributions ofa few amino acids in CDR3. The standard deviation on theelectrostatic contribution is comparatively large (seeTable II), which is expected, given the magnitude of theCoulomb and the solvation free energy terms that areinvolved. In the small seven residue sequence of CDR 3that dominates the binding energy, some of the residueshave favorable electrostatic contributions to binding, par-

ticularly in the cAb-Lys3/HEL complex. Although moreextensive conformational sampling would be required toget a quantitative assessment of the electrostatic contri-bution for these residues, it is striking (cf. Fig. 2) that thissequence of residues emerges as the only region wherefavorable electrostatic contributions are found. This favor-able region of cAb-Lys3 is shown in Fig. 1b.

Free Energy Decomposition for Lysozyme

The analysis of the contributions of lysozyme to thebinding energetics reveals important qualitative differen-ces with respect to the cAb-Lys3 (cf. Figs. 3 and 4 andTable II). Lysozyme buries on average a solvent accessiblesurface of 900 A2 for HEL and 822 A2 for TEL upon com-plex formation.

The amino acids that make a dominant contribution tobinding are not contiguous, but form two discontinuouspatches around amino acids 58-63 and 106-109 (seeFig. 3b). The residues that make the most favorable con-tributions to binding contribute only 42% of the buried ly-sozyme (HEL) surface (50% of TEL). As for cAb-Lys3, thefavorable interactions of these residues are dominated bythe van der Waals contribution (cf. Table II and Fig. 4).These residues line the binding pocket into which theCDR3 of cAb-Lys3 inserts (cf. Fig. 3b and discussion givenbelow).

Lysozyme (HEL) contains several charged residues ator near the binding interface that become buried uponbinding. An analysis of the binding in terms of electro-static, van der Waals, and hydrophobic contributions (seeFig. 4 and Table II) shows that several charged residues(D52, R73, and R112) have large unfavorable electrostaticterms. Although some of them make important interac-tions with cAb-Lys3 amino acids (see later), the interac-tion term is not important enough to compensate for theirdesolvation, and as a result, the total electrostatic contri-bution of these amino acids is positive (see Figure 4).While small local conformational differences between the

Fig. 1. (a) Net binding energy contribution by residue of the antibodyfor the cAb-Lys3/hen egg white lysozyme complex. The values reportedare averages of the total contribution DG, as estimated from Eq. (3). Theresults are presented for residues belonging to complementary determin-ing region (CDR1 from Pro 31 to Gly 35, CDR2 from Ala 50 to Gly 66, andCDR3 from Asp 99 to Asp 121) and for residues of the framework regionwith a contribution different from zero. Averages are calculated over allstructures extracted from the trajectories (MEL AL HSD, MEL AL HSE,MEL BM, and JTT). Units: kcal/mol. (b) Antibody surface colored accord-ing to the total energetic contribution of each residue. Coloring from green(favorable) to red (unfavorable) with contributions in the range from!7.74 to #7.13 kcal/mol. Figure generated using the program GRASP.66

The residues with the most favorable or unfavorable contributions arelabeled.

Fig. 2. Decomposition of the total energetic contribution of antibodyresidues presented in Figure 1a. The electrostatic (ELEC in blue), thenonpolar (SAS in red) and the van der Waals (VDW in yellow) contribu-tions, as defined in Methods, are displayed separately for selected resi-dues (see Figure 1a for selected residue). Units: kcal/mol.

424 LAFONT ET AL.


complexed and uncomplexed lysozyme may modulate themagnitude of this term, the desolvation effect explains, inlarge part, why the electrostatic contribution is large andpositive for lysozyme (about #36 ' 6 kcal/mol, average ofHEL and TEL; see Table II).This is an important difference with the cAb-Lys3,

where such large positive contributions were notobserved. As a result, although unfavorable electrostaticinteractions are compensated by the favorable nonpolarones, the contribution of lysozyme to the binding ener-getics is small when compared with that of cAb-Lys3. The

relative contribution of lysozyme to the total binding freeenergy is only about 15% (cf. Table II, !7 kcal/mol from atotal of !52 kcal/mol for HEL, and !6 kcal/mol out of atotal of !38 kcal/mol for TEL). The observation that thedifference in total contribution to binding between the twopartners is directly linked to the difference in electrostaticinteraction also results from the fact that, by definition(see Methods), the van der Waals interactions are sharedequally between the two proteins, and that the differencein buried surface area between two proteins in a complexis very small.68 Electrostatic desolvation, on the otherhand, is strongly dependent on the individual structureand charge distribution of each partner, and large differ-ences can be observed for two proteins in a complex asdemonstrated here. Although the absolute values of theantibody and lysozyme contributions to binding differbetween the HEL and TEL complexes (see Table II), therelative magnitudes of the individual contributions arevery similar.

Comparison of the Different Structures

We studied three experimental structures of the cAb-Lys3 in complex with HEL, and two of the complex withTEL. The three HEL complex structures differ signifi-cantly by a rigid body rotation of one protein with respectto the other42 and both the sequence and the internalstructure of the lysozyme monomer are different in theTEL and in the HEL complex structures. The RMS differ-ences between the different protein–protein complexes (inboth the crystal structures and structures obtained fromthe MD trajectory) are given in Table 1 of SupplementaryMaterial.

With these differences, it is possible to test the robust-ness of the free energy decomposition scheme with respectto changes in sequence and in conformation space. Theshort MD simulations that were run for each structurewere used to generate ensembles of conformations andthus to reduce statistical error. We are then able to obtaina more general understanding of the recognition processin that our results are less dependent on the specificthree-dimensional structure.

A comparison of the results for the two lysozymes (seeFig. 5) shows that the interaction energy hot spots are thesame in the two complexes; similar results are obtainedfor the antibody (see Fig. 1 of Supplementary Material).However, some charged amino acids of the interface, suchas Asp 48 and Arg 73 (HEL) or Lys 73 (TEL), show signifi-cantly different binding energy contributions for the fivestructures of the complex (three structures for HEL andtwo structures for TEL). These differences can beexplained either structurally or based on the lysozymesequences. For example, Asp 48 of lysozyme can formfavorable interactions with Tyr 106 of cAb-Lys3, but it issituated in a loop and shows larger structural fluctuationsthan other amino acids. Hence its contribution variesconsiderably between the different structures. Likewise,Arg 73 (HEL) or Lys 73 (TEL) are in a region of the pro-tein–protein interface that shows significant structural

Fig. 3. (a) Net binding energy contribution by residue of the HEL lyso-zyme for the cAb-Lys3/hen egg white lysozyme complex. The valuesreported are averages of the total contribution DG [cf. Eq. (3)]. The resultsare presented for residues with a contribution different from zero. Theaverages were calculated over all structures extracted from the trajecto-ries of the different initial structures (MEL AL HSD, MEL AL HSE, MELBM, and JTT). Units: kcal/mol. (b) Projection of the total energetic contri-bution of each residue onto the lysozyme surface. The residues are col-ored from green (favorable contributions) to red (unfavorable contribu-tions). The values range from !7.74 to #7.13 kcal/mol. The picture wasprepared using the program GRASP66. The residues with the most favor-able or unfavorable contributions are noted. [Color figure can be viewedin the online issue, which is available at www.interscience.wiley.com.]



variations. These results underline the need to exercisecaution when interpreting the results from a free energydecomposition for a single crystallographic structure. Theconformational sampling applied in this study yields amean value with a standard deviation for each contribu-tion; the standard deviation is a useful first indication ofthe dependence of the results on small structural changes.

For example, in the cAb-Lys3/HEL complex, the confor-mational sampling clearly helps discriminating the truehot spot residues from amino acids that have favorablebut highly fluctuating contributions (see Fig. 1 of Supple-mentary Material). These results suggest that, whenever

TABLE II. Individual Contributions to the Binding Energy for the cAb-Lys3/HEL Complex (top part) and thecAb-Lys3/TEL Complex (lower part)

ELEC SAS VDW TOTAL

CHICKENCDR1 {P31-G35} 1.3 ' 1.2 !0.1 ' 0.04 !2.9 ' 0.9 !1.8 ' 2.2CDR2 {A50-G66} 2.6 ' 2.6 !0.7 ' 0.1 !6.4 ' 1.2 !4.6 ' 3.9CDR3 {D99-D121} !3.8 ' 5.5 !3.4 ' 0.2 !26.9 ' 2.0 !34.0 ' 7.7HOT SPOT {T101-Y107} !6.4 ' 4.6 !2.8 ' 0.2 !23.6 ' 1.9 !32.8 ' 6.7FRAME {all without CDRs} 0.3 ' 5.3 !0.7 ' 0.3 !4.0 ' 1.9 !4.4 ' 7.4cAb-Lys3 {all antibody} 0.4 ' 4.5 !5.0 ' 0.2 !40.2 ' 3.6 !44.8 ' 8.3Lysozyme: N46, I58, N59, W62,W63, N103, A107, W108, V109

!1.8 ' 2.1 !1.9 ' 0.1 !20.6 ' 1.1 !24.3 ' 3.3

Lysozyme: D48, D52, R61, R73, R112 29.5 ' 6.3 !1.5 ' 0.1 !9.6 ' 1.7 18.4 ' 8.1HEL {all lysozyme} 37.4 ' 7.0 !4.5 ' 0.3 !40.2 ' 3.6 !7.2 ' 10.9

Total 37.8 ' 8.6 !9.5 ' 0.5 !80.4 ' 7.2 !52.0 ' 16.2TURKEYCDR1 {P31-G35} 2.6 ' 0.8 !0.2 ' 0.03 !2.1 ' 0.5 0.3 ' 1.3CDR2 {A50-G66} 3.7 ' 1.2 !0.7 ' 0.04 !5.0 ' 0.4 !2.1 ' 1.7CDR3 {D99-D121} 1.8 ' 3.9 !3.4 ' 0.2 !26.9 ' 1.7 !28.5 ' 5.8HOT SPOT {T101-Y107} 1.1 ' 2.9 !2.8 ' 0.1 !23.8 ' 1.7 !25.5 ' 4.7FRAME {all without CDR’s} 0.4 ' 0.6 !0.4 ' 0.1 !2.0 ' 0.3 !2.0 ' 1.0cAb-Lys3 {all antibody} 8.5 ' 4.7 !4.7 ' 0.2 !36.0 ' 2.0 !32.3 ' 6.8Lysozyme: N46, I58, N59, W62, W63,

N103, A107, W108, V1090.02 ' 1.9 !2.1 ' 0.1 !20.0 ' 1.2 !22.08 ' 3.2

Lysozyme: D48, D52, R61, R73, R112 30.1 ' 3.3 !1.3 ' 0.1 !8.8 ' 0.7 20.0 ' 4.1TEL {all lysozyme} 34.3 ' 3.3 !4.2 ' 0.2 !36.0 ' 2.0 !5.8 ' 5.5

Total 42.8 ' 7.4 !8.9 ' 0.3 !72.1 ' 3.9 !38.1 ' 11.6

All contributions are averages over the structures extracted from several molecular dynamics trajectories, as described in the Methods section.The contributions for CDRs (Complementary Determining Regions) 1 to 3, for the hot spot residues (T101 to Y107 for cAb-Lys3), for the frame-work (residues not in the CDR regions of cAb-Lys3, FRAME), for the entire antibody (cAb-Lys3), for lysozyme (HEL or TEL), for the hydrophobicpatches in lysozyme, and for charged residues in lysozyme are obtained by summing over the specified residues. All energies are in kcal/mol.

Fig. 5. Comparison of results obtained for the two complexes cAb-Lys3/hen egg white lysozyme (red) and the cAb-Lys3/turkey egg whitelysozyme (green). The contributions plotted are averages of total contri-butions of lysozyme residues. The two lysozymes differ by only sevenresidues. The sequence used in this plot is the one for the chicken egg-white lysozyme. Amongst the residues shown in the graph, the followingsequence differences in the turkey egg-white lysozyme are found: Q41H,R73K, V99A, and D101G. The averages were calculated over all trajecto-ries generated for each complex. The standard deviation for each residueis shown. [Color figure can be viewed in the online issue, which is avail-able at www.interscience.wiley.com.]

Fig. 4. Decomposition of the total energetic contribution of lysozymeresidues presented in Figure 3a. The electrostatic (ELEC in blue), thenonpolar (SAS in red) and the van der Waals (VDW in yellow) contribu-tions are displayed separately for selected residues (see Fig. 3a forselected residue). Units: kcal/mol. [Color figure can be viewed in theonline issue, which is available at www.interscience.wiley.com.]

426 LAFONT ET AL.


available, averaging over several experimental structuresis likely to increase the significance of the results obtainedfrom the decomposition scheme.

Mutational Analysis of Four cAb-Lys3 Positions

To further investigate the importance of using confor-mational averaging when calculating a free energy decom-position, 4 amino acids of the antibody, identified as mak-ing nonzero contributions to binding free energy by a freeenergy decomposition calculation on a single crystal struc-ture, were mutated as specified in Methods. These wereThr 28, Asp 73, and Tyr 118, which, in the cAbLys3-HELcrystal structure (BM complex), have total contributionsto the binding free energy of !1.1, !0.5 and !2.3 kcal/molrespectively. Thr 28 and Asp 73 were replaced by residuesthat lead to important modifications of size and/or charge(T28A, T28D, T28K, D73S, D73R, and D73K), while amore conservative change was made at position 118(Y118F), to avoid large structural effects of the mutation.Residue Ile 29, which was identified as important for bind-ing, was mutated to Thr as a positive control. The kineticsof the interaction of the wild type and eight cAbLys3mutants with either HEL or TEL were measured by Bia-core. Kinetic parameters, expressed as percentage of thosemeasured for the interaction of HEL or TEL with theunmodified cAb-Lys3, are compared in Figure 6. Exceptfor the I29T change, which produced a 3- to 4-fold increasein koff, other changes had no measurable effect on interac-

tion kinetics. From the computational analysis, contribu-tions from Thr 28, Asp 73, and Tyr 118 showed large fluc-tuations with conformational averaging and yielded smallbinding averages (see Fig. 1a and Fig. S1 in Supplemen-tary material). However, contributions from individualstructures can be important, as is shown by the largeerror bars.

DISCUSSIONStructural Analysis of the Binding EnergyHot Spots

A useful aspect of the free energy decomposition schemepresented here is that it not only identifies the bindingenergy hot spots, but also gives insight into the nature ofthe key interactions.

The amino acids from the cAb-Lys3 (see Figs. 1 and 2and Table II) that make the most favorable contributionsto binding (between !2 and !8 kcal/mol) form a contigu-ous stretch of residues in the CDR3: Thr 101 - Ile 102 - Tyr103 - Ala 104 - Ser 105 - Tyr 106 - Tyr 107 (one additionalimportant amino acid is Ile 29 from CDR1), while for lyso-zyme, the most favorable interactions are made by Asn46- Ile 58 - Asn 59 - Trp 62 - Trp 63 - Asn 103 - Ala 107 -Trp 108 - Val 109 (see Figs. 3 and 4 and Table II), whichare grouped together spatially.

For a more detailed analysis, we determined whetherthe favorable interactions of the hot spot residues are pre-dominantly van der Waals or electrostatic in nature andwhether they face each other on the two partners of thecomplex. Concerning cAb-Lys3, the hot spot interactionsare mainly nonpolar. The important amino acids fromCDR3 make favorable contributions to the interactionenergy via the solvent accessible surface, or hydrophobicterm and via the van der Waals interactions. Some ofthese important van der Waals interactions are madewith amino acids on lysozyme that are also, correspond-ingly calculated as making important contributions. Forexample, the side chain of Ala 104 of cAb-Lys3 fills ahydrophobic pocket lined by the side chains of Ile 58, Ala107, and Trp 108 of lysozyme. Particularly favorable vander Waals interactions are also made by Trp 62 of lyso-zyme. This amino acid not only makes an important con-tact with a hot spot residue from cAb-Lys3 (Ile 102 fromCDR3), but it also makes contacts with several aminoacids from CDR1 (Ile 29 and Tyr 32) and CDR2 (Gly 54),which have smaller van der Waals contributions to thebinding energy. The large contribution of Trp 62 (lyso-zyme) arises from its central position at the protein–pro-tein interface that allows a large number of van der Waalscontacts.

Thus the size of the amino acid and the shape of the con-tact surface plays an important role and in some cases avan der Waals hot spot is located on one of the proteins,whereas there is no dominating van der Waals contribu-tion arising from the reciprocal residues on the other pro-tein. Thus, even though van der Waals interactions areshared equally between the two proteins, at the residuelevel, the hot spots are not necessarily symmetrical.

Fig. 6. Comparison of kinetic on-rate (a) and off-rate (b) parametersfor the interaction between the WT or mutant cAb-Lys3 with HEL (darkgrey) or TEL (light grey). Rate parameters are expressed as percent of thewild type value. Measurements were repeated 2–3 times for the WT cAb-Lys3 and mutants T28K, I29T, and D73S, for which error bars are shown.



Even though van der Waals interactions have an impor-tant contribution to hot spots, some important electro-static interactions can also be identified. The electrostaticcontribution is favorable for cAb-Lys3 residues Tyr 103 -Ala 104 - Ser 105 - Tyr 106, which are involved in a hydro-gen bond network with several residues from lysozyme.The most favorable electrostatic interactions are made bythe two tyrosine residues; they can be further decomposedinto side chain and main chain contributions. As can beseen from Figure 7, the dominant contributions are madeby the side chain for Tyr 103 (the main chain also makes afavorable, but less important, contribution) and by themain chain for Tyr 106. Examination of the structuresindicates that the Tyr 103 side chain hydroxyl groupmakes an H-bond with Arg 112 from lysozyme, while theTyr 106 main chain NH makes an H-bond with the car-boxyl group of Asp 52 from lysozyme. The favorable contri-bution of these H-bonds is directly linked to the strongelectrostatic potential created by the charged amino acidson lysozyme. Remarkably, the free energy decompositionfor lysozyme (see Figs. 3 and 4) yields unfavorable electro-static contributions to the binding free energy for Arg 112and Asp 52. This is due to the large desolvation penaltyupon binding for the charged side chains of these residues.The fact that electrostatic interactions are not alwaysfavorable to binding has been noted in other free energydecomposition studies.13,19,21,58 In this particular exam-ple, it can be seen that Arg 112 and Asp 52, although notfavorable themselves, create a favorable environment forTyr 103 and Tyr 106 on the cAb-Lys3, and thus have animportant role in the formation of the complex. The othercharged amino acid on lysozyme that has a large unfavor-able desolvation contribution is Arg 73. Arg 73 is notinvolved in hydrogen bonds with amino acids on cAb-Lys3, and its binding energy contribution shows largerfluctuations than those of Arg 112 and Asp 52 (seeFig. 3a).

In contrast to the unfavorable electrostatic contribu-tions calculated for Arg 112 and Asp 52 of lysozyme, asmall favorable contribution is found for Trp 63 of lyso-zyme, which interacts with Tyr 103 main chain from cAb-Lys3. Thus, even though the electrostatic interaction fromthe main chain of Tyr 103 of cAb-Lys3 is smaller than theinteraction made by its side chain (cf. Fig. 7), the mainchain H-bond yields a favorable binding energy contribu-tion both on cAb-Lys3 and on lysozyme. Two additionalamino acids of lysozyme make favorable (although smallerthan those found in cAb-Lys3) electrostatic contributions:Asn 59 (HEL: !1.7 kcal/mol) and Ala 107 (HEL: !0.6 kcal/mol), see Figure 4. An analysis of the structures showsthat Asn 59 and Ala 107 are engaged in hydrogen bondswith Ala 104 of cAb-Lys3 (cf. Figure 9), and this buriednetwork of H-bonds is particularly favorable.

Comparison of Experimental andComputational Data

The conclusions of the calculations were challengedwith both existing and new mutational studies of cAb-Lys3. While the existing studies mainly focus on residuesidentified here as ‘‘hot spot,’’ we chose to focus on fourpositions with a calculated small contribution to bindingenergy.

Existing experimental studies include replacements ofresidues Thr 101 (by L,S,P) and Ser 105 (by N,H,Q,A,G,P,M) from CDR3 of cAb-Lys3 for a quantitative struc-ture-activity study,53 and replacements of residues fromCDR1 and CDR2 to revert to the germ line sequence.54

The replacements at positions 101 and 105 had variedeffects, the largest losses in binding affinity being 120-foldfor the T100P change, and 100-fold for the S105Qchange.53 In particular, the mutation S105A resulted in a10-fold loss in experimental binding affinity (i.e. a changeof 1.4 kcal/mol in binding affinity), which is in reasonableagreement with the computed binding free energy contri-bution of !4.8 ' 2.3 kcal/mol for the serine as a whole (i.e.including main chain contributions that are not lost uponmutation to Ala). Multiple mutations were introduced inCDR1 and CDR2 so that the influence of individualchanges is not known.54 Thermodynamic data howevershow a role of residues from CDR1 and CDR2 forenthalpic stabilization of the bound complex during matu-ration,54 which is in agreement with the results of thepresent calculations that show that CDR1 and CDR2make favorable van der Waals interactions with lysozymeand thus play a role in stabilizing the complex.

To investigate whether positions with small, but non-zero, computed contributions can nevertheless influencebinding, we targeted residues Thr 28, Asp 73, and Tyr118. The residue Ile 29, which is identified as important inCDR1, was taken as a positive control. None of the muta-tions at positions 28, 73, and 118 had a measurable effecton binding kinetics (see Figure 6), while the mutation atposition I29 (I29T) increased koff 3- to 4-fold, thus result-ing in a loss of binding affinity. These experimentalresults support the validity of our computational ap-

Fig. 7. Decomposition of the electrostatic contributions into side chainand main chain components for the antibody in the cAb-Lys3/hen eggwhite lysozyme complex. The values represented are averages of theelectrostatic contribution of backbone (yellow) and side chain (blue) ofantibody residues. (see Fig. 1a for selected residues). The average wascalculated over all the trajectories done with the different initial structures(MEL AL HSD, MEL AL HSE, MEL BM, and JTT). Units: kcal/mol.[Color figure can be viewed in the online issue, which is available at www.interscience.wiley.com.]

428 LAFONT ET AL.


proach. In particular, the mutations data support oursimplified conformational averaging scheme, and showthat the three amino acids tested, which showed largefluctuations in the computed contribution, do not influ-ence binding, while their contribution was non negligibleif only one experimental X-ray structure is used.

Experimental vs. Computational Hot Spots

The comparison of the experimental data to the compu-tational results raises some important issues. Amino acidsthat are found to play an important role in binding are of-ten referred to in the computational literature as ‘‘bindingenergy hot spots,’’ irrespective of whether the quantitycalculated is the change in binding free energy uponmutating the residue to alanine, or a related but differentquantity. In this paper, we used the term hot spot foramino acids that make significant individual contribu-tions (<!1.5 kcal/mol) to the total binding free energy, asdescribed in Material and Methods. It is therefore usefulto clarify the relationship between ‘‘hot spots’’ as dis-cussed in the present computations and ‘‘hot spots’’obtained by alanine scanning experiments.Experimentally, binding energy hot spots are often

defined as residues that, when mutated to alanine, giverise to a significant drop in the binding affinity (typically,changes in binding free energy larger than 1.5 kcal/mol).7

As discussed in Ref. 69, mutations to alanine can affectthe binding affinity by both changing the structure and/orfree energy of the unbound partners as well as those ofthe bound complex. This combination of effects compli-cates the interpretation of alanine scanning experiments,and consequently their exploitation in, for example,designing small molecule inhibitors that mimic importantinteractions. An advantage of computational approachesis that the energetic contributions can be separated in amanner that is not attainable experimentally. For exam-ple, as done in the present study, it is possible to analyzethe energetic contribution of an amino acid withoutresorting to explicit mutation to alanine.This is an important aspect of the present calculations,

which is to identify binding energy hot spots and, thus,free energy decomposition is used rather than explicitmutation to alanine. Individual amino acid contributionsto binding presented in Figs. 1, 2, 3, 4, 7 are therefore notthe same quantity as the change in free energy uponmutating the residue to alanine. If a direct comparison toAla-scanning experiments was desired, it would be possi-ble to calculate free energy changes upon mutating a resi-due to alanine by constructing the mutant and reevaluat-ing the free energy of binding.11,70 A full estimate of thefree energy change should also consider the structuralconsequences of mutating a specific amino acid to alanine,both in the complex and in the unbound partners.Another difference with experimental alanine scanning

data is that single amino acid free energy contributions tobinding, as computed here, include contributions to thebinding energy from main chain atoms. They are obtainedby writing the total electrostatic, van der Waals and sur-

face area (hydrophobic solvation) terms as a sum overindividual amino acid contributions (as described in Mate-rial and Methods). The decomposition is performed insuch a way that the sum of all individual contributionscorresponds to the total free energy (cf. Eq. 1). Decompos-ing into individual amino acid contributions implies thatpairwise interactions (such as van der Waals and electro-static) are divided equally between the interacting aminoacids i.e. if for example the van der Waals interactionenergy between amino acids A and B amounts to !4 kcal/mol, a contribution of !2 kcal/mol will be attributed to Aand !2 kcal/mol to B, and likewise for electrostatic inter-actions. It must be noted that in the continuum descrip-tion of the solvent that is used here, desolvation (whetherelectrostatic or hydrophobic) is a self-energy term and isthus naturally decomposed in individual contribu-tions.57,71

The earlier-mentioned differences between computa-tional free energy decomposition and experimental ala-nine scanning data should be kept in mind when compar-ing computational and experimental hot spot residues.

Fig. 8. Bar graph of the amino acid efficiency. Each free energy contri-bution (Electrostatic (ELE), nonpolar solvation (SAS), van der Waalsenergy (VDW), and total DG (TOT)) of amino acids is divided by the num-ber of nonhydrogen atoms. The results are presented for the residueshaving the most efficient amino-acids in the interaction for the antibody(top graph) and for the lysozyme (bottom graph). See Methods for details.[Color figure can be viewed in the online issue, which is available atwww.interscience.wiley.com.]



The two approaches nevertheless give convergent infor-mation i.e. when the free energy decomposition identifiesa residue as making a large favorable contribution tobinding, one can expect that mutating this residue to ala-

nine will be detrimental to the binding affinity (unless thecontribution is made by main chain atoms). Significantcorrelations between experimental free energy changesupon mutating a residue to alanine and free energy

Fig. 9. Structural comparison of the lysozyme–cAb-Lys 3 complex and lysozyme-N-acetyl glucosamine(NAG) ring complex. The similarity between the hydrogen bond network formed between A107 and N59 of ly-sozyme and A104 of cAb-Lys3 (upper picture) and the network formed between A107 and N59 of lysozymeand NAG is shown. This network involves efficient amino acids of the lysozyme-cAb-Lys3 complex, and showsthe energetic mimicry of the substrate (see text for details). [Color figure can be viewed in the online issue,which is available at www.interscience.wiley.com.]

430 LAFONT ET AL.


decomposition based on MM/GBSA have indeed beenreported.13 In contrast, a computed unfavorable contribu-tion to binding does not necessarily mean that mutatingthe residue to alanine will increase the binding affinity.As discussed earlier, charged amino acids such as Asp 52and Arg 112 from lysozyme have a positive (unfavorable)contribution, yet most likely they have a structural role instabilizing important residues from cAb-Lys3.

Efficient Amino Acids and Ligand Binding

A different, instructive way to identify amino acids thathave an important role in binding is to compute the‘‘amino acid efficiency,’’ a quantity that we define here inanalogy to ligand efficiency. Ligand efficiency is defined asthe ratio of affinity to molecular size, a common measureof size being the number of nonhydrogen atoms. Thenotion of ligand efficiency has recently attracted a consid-erable interest in drug design studies,62,72 particularly inthe context of fragment based drug design. In fragmentbased drug design, the goal is to find small molecularbuilding blocks that bind to a medicinal target. Subse-quently, several building blocks can be linked or itera-tively increased in size while keeping the molecularweight in the ‘‘druggable’’ range.73 Small ligands withhigh binding efficiency are thus sought as a good startingpoint for lead identification and drug design.By analogy with this concept, we identified ‘‘efficient

amino acids’’ of the binding interface between cAb-Lys3and lysozyme by dividing the free energy contribution ofeach amino acid by its number of nonhydrogen atoms (i.e.4 for Gly, 5 for Ala, 14 for Trp etc.). An alternative defini-tion of amino acid efficiency, based on the solvent accessi-ble surface of the amino acids in the unbound proteinswas also tested. The results are not significantly differentfrom the simple definition mentioned earlier. (See Meth-ods and Supplementary Material for details).Amino acid efficiency can provide an assessment of the

binding potential of a particular hot spot interaction. Indrug design strategies aimed at protein–protein interfa-ces, the identification of efficient amino acids could helpidentify key interactions and prioritize the region of theprotein–protein interface that could be targeted by smallmolecules. To gain physical insight in the origin of theamino acid efficiency, we divided each individual compo-nent of the binding free energy, as well as the total per res-idue free energy of binding, by the corresponding numberof heavy atoms (see Fig. 8). The most efficient amino acidsare Ala 104 and Ser 105 on cAb-Lys3 and Asn 59, Trp 62and Ala 107 on lysozyme. In general, the efficiency of theamino acids on the antibody is better than on lysozyme,and the van der Waals contribution is the dominantenergy term for efficient binding. A notable exception isAsn 59 from lysozyme, where electrostatic and van derWaals interactions contribute equally. Structurally, theligand efficiency of Trp 62 from lysozyme is linked to itsposition as a central residue anchoring amino acids fromCDR 1, 2, and 3 of cAb-Lys3. The three amino acids Ala104 (cAb-Lys3), Asn 59, and Ala 107 (lysozyme) make a

network of hydrogen bonds and hydrophobic contacts (seeFigure 9) that make them particularly efficient. Theseinteractions closely resemble65 those made by lysozymesubstrates, in particular the N-acetyl glucosamine ring(NAG) in subsite C of the binding pocket. The acetamidosubstituent of NAG in site C exhibits low temperature fac-tor and a well defined electron density74 and the saccha-ride in site C has been shown to make energetic contribu-tions to binding that are more favorable than the saccha-rides bound to other sites within the lysozyme bindingpocket.75 Thus the cAb-Lys3 not only is a structural mimicof the lysozyme substrate, but it also exploits bindingenergy hot spots in a similar way as the substrate. Thisfurther shows that identifying binding hot spots or con-versely efficient amino acids can pinpoint regions of theprotein–protein interface that can be targeted by syn-thetic ligands.

CONCLUSIONS

In this work, we analyzed the binding interface betweenthe single chain variable antibody domain (VHH) cAb-Lys3 and its antigen lysozyme, using a free energy decom-position based on Poisson–Boltzmann electrostatics, vander Waals interactions, and a hydrophobic surface areaterm. We considered conformational flexibility of the com-plex explicitly by using several experimental structuresas starting points and performing short molecular dynam-ics simulations on each structure. We selected ten confor-mations from each molecular dynamics simulation thatsample representative values of the Coulomb interactionenergies between the proteins and performed the freeenergy decomposition on each conformation; the resultsrepresent averages over each individual calculation. Thisprotocol was shown to be able to discriminate betweenconsistently favorable interactions that give rise to bind-ing hot spots on one side, and interactions that vary sig-nificantly with small changes in structures on the otherside. The reliability of the free energy decomposition withrespect to using a single crystal structure is improved,while avoiding the large computational cost of a freeenergy simulation method. The predictive ability of theprocedure was subsequently tested by point mutations ofamino acids of the interface; and it was shown that aminoacids that have a contribution to binding when only onecrystal structure is used, but that show large fluctuationswhen using the proposed conformational sampling proto-col, can be mutated without influencing binding affinity.

The analysis of the complex has shown that electro-static interactions do not systematically favor bindingbecause of the compensation between protein desolvationand protein–protein interactions when forming macro-molecular complexes. van der Waals interactions, as ex-pected, systematically favor complex formation. This is inagreement with studies using similar methods on differ-ent complexes.10,13,19,21,58 To identify amino acids thatplay a particularly important role in the protein–proteininterface, we defined and computed the amino acid effi-ciency, i.e., the free energy contribution divided by the



number of heavy atoms in the amino acid. The analogousconcept of ligand efficiency is commonly used in drugdesign, but to our knowledge, it has not been applied toprotein–protein interactions. The efficient amino acidscorrespond to binding energy hot spots, and they originatemainly from efficient van der Waals packing of key resi-dues on the interface. Electrostatic interactions make animportant contribution to a binding energy hot spot ofthree neutral amino acids on the interface that form a net-work of hydrogen bonds, Asn 59 and Ala 107 of lysozyme,and Ala 104 of cAb-Lys3. The formation of networks ofhydrogen bonds that stabilize protein–protein interac-tions has been noticed previously.19 It shows that contin-uum electrostatics using point charges from a classicalforce field, despite its simplified description of the hydro-gen bond,76,77 can identify favorable electrostatic interac-tions in a context where, on average, protein–proteinhydrogen bonds are not contributing or even unfavorableto binding.Interestingly, the amino acids from cAb-Lys3 identified

as efficient are structural mimics of the lysozyme saccha-ride substrate, and they interact with amino acids of lyso-zyme that are also identified as efficient. Our analysisthus establishes that the antibody not only is a structuralmimic of the substrate,65 but that it exploits key interac-tions that are consistent with those of a small moleculesubstrate. This indicates that the free energy decomposi-tion method presented in this work can be used to guideantibody engineering, and that it can also serve as a toolfor designing small molecule inhibitors of protein–proteininteractions with potential therapeutic impact.

NOTE ADDED IN PROOF

In a recent study (Thanos, CD, DeLano WL, Wells, JA.Hot spot mimicry of a cytokine receptor by a small mole-cule Proc Natl Acad Sci USA 2006;103:15422–15427) theligand efficiency of a protein-small molecule and protein-protein complex were compared. However, the ligand effi-ciency was defined as the total binding free energy dividedby the number of contact atoms, which differs from thedefinition of amino acid efficiency as described here.

ACKNOWLEDGMENTS

We thank IDRIS (Institut du Developpement et desRessources en Informatique Scientifique) and CINES(Centre Informatique National de l’Enseignement Super-ieur) for generous allowance of computer time, Drs SergeMuyldermans and M. Lauwereys for the kind gift of thecAbLys3-pHEN6 vector and Julien Gras and ElyetteMartin for programming assistance.

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lafont proteins 2007

Technology

proteinprotein association

free energy of binding

electrostatic energy

handful of amino acids

hot spot residues

institut national

genetique et

illkirch cedex