electrostatic clustering and free energy calculations ...electrostatic clustering and free energy...

Electrostatic Clustering and Free Energy Calculations Provide

a Foundation for Protein Design and Optimization

RONALD D. GORHAM JR., CHRIS A. KIESLICH, and DIMITRIOS MORIKIS

Department of Bioengineering, University of California, Riverside, CA 92521, USA

(Received 5 September 2010; accepted 24 November 2010; published online 8 December 2010)

Associate Editor Angelique Louie oversaw the review of this article.

Abstract—Electrostatic interactions are ubiquitous in pro-teins and dictate stability and function. In this review, wediscuss several methods for the analysis of electrostatics inprotein–protein interactions. We discuss alanine-scanningmutagenesis, Poisson–Boltzmann electrostatics, free energycalculations, electrostatic similarity distances, and hierarchi-cal clustering of electrostatic potentials. Our recently devel-oped computational framework, known as Analysis ofElectrostatic Similarities Of Proteins (AESOP), incorporatesthese tools to efficiently elucidate the role of electrostaticpotentials in protein interactions. We present the applicationof AESOP to several proteins and protein complexes, forwhich charge is purported to facilitate protein association.Specifically, we illustrate how recent work has shaped theformulation of electrostatic calculations, the correlation ofelectrostatic free energies and electrostatic potential clusteringresults with experimental binding and activity data, the pHdependence of protein stability and association, the design ofmutant proteins with enhanced immunological activity, andhow AESOP can expose deficiencies in structural models andexperimental data. This integrative approach can be utilizedto develop mechanistic models and to guide experimentalstudies by predicting mutations with desired physicochemicalproperties and function. Alteration of the electrostatic prop-erties of proteins offers a basis for the design of proteins withoptimized binding and activity.

Keywords—Alanine scan, Poisson–Boltzmann equation,

Continuum electrostatics, Solvation, Electrostatic potential,

Hierarchical clustering.

INTRODUCTION

Electrostatic interactions play a key role in manybiological processes.10,26,42,44,49 Proteins are comprisedof ionizable amino acids, which contain titratablegroups whose ionization states are dependent on their

physicochemical properties and the physicochemicalproperties of the surrounding environment. The dis-tribution of whole and partial charges throughout thethree-dimensional structure of a protein determines itselectrostatic properties, and governs how the proteinwill interact with its binding partners. It is well knownthat several intermolecular forces, including van derWaals, hydrophobic, and electrostatic interactions,contribute to association and stability of protein com-plexes. For excessively and oppositely charged proteins,association is divided into recognition and binding,according to the two-step model (Fig. 1a).25,28,38,49 Inthe recognition step, long-range electrostatic interac-tions cause electrostatic steering, accelerating the for-mation of an encounter complex and orientation ofcomplementary binding sites. In the binding step, theprotein interface is desolvated and side chains areoptimally rearranged through short-range interactions(polar and nonpolar) to stabilize the bound complex.

In recent years, computational methods have rap-idly evolved and become an integral part of the anal-ysis of protein–protein interactions. Depending on theaccuracy of the underlying physics, algorithm effi-ciency, and parameterization, computational tech-niques can provide an excellent complement toexperimental techniques and methods. Since theadvent of computational analysis of proteins and theirinteractions, researchers have shown interest in devel-oping methods to accurately calculate electrostaticforces between proteins. Molecular dynamics (MD)simulations1,12,26,45 often incorporate explicit solva-tion, in which proteins are surrounded by water mol-ecules and ions. These complete atomistic models offeran accurate picture of the electrostatic forces andenergetics involved in protein–protein interaction, butare computationally expensive, especially for largesystems. Alternatively, implicit solvation models offera more efficient analysis of electrostatics, since solvent

Address correspondence to Dimitrios Morikis, Department of

Bioengineering, University of California, Riverside, CA 92521, USA.

Electronic mail: [email protected]

Annals of Biomedical Engineering, Vol. 39, No. 4, April 2011 (� 2010) pp. 1252–1263

DOI: 10.1007/s10439-010-0226-9

0090-6964/11/0400-1252/0 � 2010 The Author(s). This article is published with open access at Springerlink.com

1252

molecules are not explicitly modeled and dynamic ef-fects are not directly incorporated.1,11,12

In this review, we present an overview of a newcomputational framework for electrostatics calcula-tions. This review is not intended to be comprehensivein nature and focuses mainly on improvement, vali-dation, and application of electrostatic calculationsfrom work in our group, with representative applica-tions. Our Analysis of Electrostatic SimilaritiesOf Proteins (AESOP)24 computational frameworkincorporates alanine-scanning mutagenesis, Poisson–Boltzmann (PB) electrostatics, electrostatic free energycalculations, and hierarchical clustering in an effort tounderstand and compare the electrostatic nature ofprotein families, including homologs and mutants. Wepresent herein the computational basis for AESOP,and specific applications that exemplify its predictivecapability for protein design and optimization.

METHODS

Alanine-Scanning Mutagenesis

Our computational methods for evaluation of elec-trostatics begin with an atomic-resolution three-dimensional structure of a protein or protein complex.Structures are obtained from the protein data bank(PDB),4 as determined by either X-ray crystallographyor nuclear magnetic resonance (NMR) spectroscopy.For proteins without an experimentally determined

structure, we can use homology modeling to model thestructure of the protein based on a sequence alignmentusing proteins with known structure and similarsequence as templates. Two most convenient criteriafor similarity are (a) an identity of at least 25% for asequence size greater than 100 amino acids and (b) anexpectation (E) less than1024,which gives the likelihoodthat similarities are due to chance.29

Alanine-scanning mutagenesis has long beenregarded as an important experimental tool in probingprotein function by delineating the contribution of themutated amino acids in specific biological processes. InAESOP, we use computational alanine scans to observethe effects of specific ionizable amino acids on theelectrostatic potential distribution and associativeproperties of proteins and protein complexes. Muta-tions of charged residues at physiological pH (arginine,lysine, glutamic acid, aspartic acid, and histidine) toalanine introduce perturbations in the electrostaticpotential distribution of the protein, with minor alter-ations in protein structure or integrity. AESOP utilizesthe R software package36 for structure editing, calcu-lation, and electrostatic analyses. AESOP performsalanine mutations by simply removing the side chainatoms of ionizable residues, with the exception of Cb.For electrostatics calculations, we typically limit ala-nine scans to mutants of ionizable residues only, sincethese mutations have the largest effects on Coulombicinteractions and electrostatic potentials. However,AESOP can be used to analyze mutation of any residueto alanine, since dipole moments and partial chargescan alter the distribution of electrostatic potential. Inaddition, mutation of any residue can affect the shapeof the dielectric and the ion accessibility surfaces of theproteins (see below). Besides alanine, mutations to anyother residue are also possible.

PB Electrostatics

PB calculations represent the forefront of electro-static analysis using implicit solvation in proteins.2,19,26

Since solvent molecules and ions are not explicitlymodeled, PB calculations can efficiently determineelectrostatic potential distributions and electrostaticfree energies of proteins. AESOP utilizes the grid-basedAdaptive PB Solver (APBS)3 for all electrostatics cal-culations. At low ionic strengths (including physiolog-ical ionic strength of 150 mM), the linearized PBequation provides a sufficient approximation for thecalculations of electrostatic potentials of proteins, givenby (in SI units):

�e0r � er rð Þru rð Þ þ e0er rð Þj2 rð Þu rð Þ ¼XN

i¼1Qid r� rið Þ:

ð1Þ

FIGURE 1. (a) Scheme illustrating the two-step model ofprotein association. (b) Thermodynamic cycle for calculationof electrostatic free energy of association and solvation. Thetop horizontal process represents association in a referencestate (without water and ions) and the bottom horizontalprocess represents association in a solvated state in thepresence of ions. Three vertical processes show solvation ofeach free protein (A and B) and the protein complex (AB). Thedielectric coefficients ep and es correspond to protein andsolvent, respectively. The ion accessibility parameter, j,depends on ionic strength.

Electrostatic Clustering and Free Energy 1253

In Eq. (1), u(r) is electrostatic potential in units ofkBT/e (kB the Boltzmann constant, T the absolutetemperature, and e the magnitude of electron charge),er(r) the dielectric coefficient (relative electrostaticpermittivity with respect to vacuum), e0 the electro-static permittivity of vacuum, j2(r) the ion accessibilityparameter for ±1 counter ions (related to a modifiedinverse Debye screening length), Qi the fixed proteinith charge at atom position ri (to a total of N charges),and the d function denotes the position of charges. Theion accessibility parameter allows for the incorpora-tion of ionic strength into the calculation of electro-static potential. In PB calculations, dielectriccoefficient, ion accessibility, and charge must bedefined at each grid point, in order to solve for elec-trostatic potential. Charges are assigned based on theatomic structure, and dielectric and ion accessibilityvalues are assigned based on solvent accessible and ionaccessible molecular surfaces, respectively. Typically,the solvent and ion accessible surfaces are calculatedby the union of the center points of spherical probeswith 1.4 and 2.0 A radii, corresponding to the molec-ular radii of water and ions, respectively.

PB calculations are highly sensitive to parameterselection. Previous analyses have shown that freeenergy values calculated using PB electrostatics varysignificantly with protein dielectric and choice ofdielectric boundary,13,15,39,42,43 thus it becomesimportant to determine the proper selection ofparameters, based on the application. In addition,since proteins are calculated in a discretized space,electrostatic potential calculations are sensitive to gridresolution.15

Electrostatic Similarity and Clustering

It is of interest to compare the distribution of elec-trostatic potential for different proteins. It is a well-known principle of biochemistry that protein structureis directly related to function. AESOP is centered onthe idea that electrostatically similar proteins will havesimilar associative properties, and in turn will yield asimilar biological function. Many methods of com-paring electrostatic properties of molecules have beendeveloped, and recently applied to proteins. Carboet al.6 developed a similarity index to compare theelectron density of small molecules. More recently,additional electrostatic similarity indices (ESIs) byHodgkin and Richards,18 Reynolds et al.,37 andPetke34 have been developed to compare the electro-static potential distribution of two molecules.

While ESI measures were originally developed forthe comparison of small molecules, Wade et al. adap-ted the measures and paved the way for application toproteins.5,47,50,52 Certain issues arise when dealing with

such large biomolecules, most importantly how to treatthe protein interior. Large or globular proteins tend tohave polar character on their surfaces, whereas theinterior or core is largely hydrophobic in nature due tosolvent exclusion. When very low dielectric coefficientsare used to model the protein interior, the electrostaticpotential values in that region are much larger thanobserved outside the protein. Some similarity indicesare highly sensitive to large values in the protein inte-rior, and thus give disproportionate weight to thesevalues. Wade et al. proposed the use of a skin region(Skin) when comparing grid points for calculation ofsimilarity indices,47 such that only those values ofelectrostatic potential that fall between a radius of3–7 A from the protein surface are included in thecalculation. This comparative scheme eliminates elec-trostatic potential values inside the protein, as well asthose outside the Debye length (~7 A at 150 mM ionicstrength), which are thought not to have a significanteffect on protein–protein association. Our group hasexamined the efficacy of a shell comparative scheme(Shell), which includes all potential values outside thesolvent-accessible surface of the protein, and a whole-box scheme (WB), which includes all potential valuescalculated within the entire grid.22 The results of ouranalysis are discussed below.

In order to compare proteins and protein mutantsbased on electrostatic potential distribution and elec-trostatic similarity, AESOP utilizes hierarchical clus-tering21 with average linkage to generate dendrogramsof mutants for comparison. ESIs (discussed above) areconverted to electrostatic similarity distances (ESDs),in which identical electrostatic potentials haveESD = 0, with ESD increasing with increasing dis-similarity.

CDP ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1�

PuA i; j; kð ÞuB i; j; kð ÞffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

uA i; j; kð Þ2q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiP

uB i; j; kð Þ2q

vuut ; ð2Þ

DP ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� 2

PuA i; j; kð ÞuB i; j; kð Þ

PuA i; j; kð Þ2 þ

PuB i; j; kð Þ2

s; ð3Þ

LDP ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1� 1

N

X

N

2uA i; j; kð ÞuB i; j; kð ÞuA i; j; kð Þ2þuB i; j; kð Þ2

s; ð4Þ

LD ¼ 1

N

X

N

juA i; j; kð Þ � uB i; j; kð Þjmax juA i; j; kð Þj; juB i; j; kð Þjð Þ: ð5Þ

In Eqs. (2)–(5), uA(i,j,k) and uB(i,j,k) represent thecalculated electrostatic potential at grid point (i,j,k) fortwo compared proteins (A and B), respectively, andN represents the total number of grid points used in

GORHAM JR. et al.1254

electrostatic calculations. The equations above com-pare dot products (correlation dot-product: CDP; dot-product: DP; and localized dot-product: LDP) anddifference (localized difference: LD) with differentnormalizations, according to the ESIs mentionedabove.5,6,18,34,37,47 The ESDs given above are used inAESOP to cluster mutants and homologous proteinsbased on electrostatic similarity,22 and a comparativeanalysis of their application is discussed later.

Free Energy Calculations

PB electrostatic potential calculations can easily betranslated into electrostatic free energy values forproteins. APBS calculates free energy based on thedistribution of electrostatic potential within and sur-rounding the protein, according to:

Gelec ¼1

2

Xqiui; ð6Þ

where qi and ui are the charge and electrostaticpotential at each grid point, respectively. For proteincomplexes for which an atomic-resolution structure isavailable, we can calculate association free energyvalues based on a thermodynamic cycle, shown inFig. 1b. Intuitively, protein association can be repre-sented by the bottom horizontal process (DGsolu), withsolvent (eS = 78.54) and ionic strength (I = 150 mM)being modeled. It is well known that while electrostaticinteractions between proteins are often favorable, theirstabilizing effect is counterbalanced by desolvation.17

The effects of desolvation of each free protein andcomplex are incorporated into free energy calculationsvia the vertical processes in Fig. 1b. The top of thecycle depicts each protein and their association in areference state (DGref), in which solvent and ions arenot modeled. In order to incorporate the effects ofboth association and solvation, DDGsolvation values arecalculated, which incorporate both horizontal bindingand vertical solvation processes. The described freeenergy values are calculated according to:

DGref ¼ GrefAB � Gref

A � GrefB ; ð7Þ

DGsolu ¼ GsoluAB � Gsolu

A � GsoluB ; ð8Þ

DDGsolvation ¼ DGsolvationAB � DGsolvation

A � DGsolvationB

¼ DGsolu � DGref: ð9Þ

Since APBS uses a grid-based method to solve thelinearized PB equation, whole and partial atomiccharges in the protein are distributed to neighboringgrid points for calculation. This discretization canlead to self-energies and grid artifacts. In order toseparate free energies into association and solvation

components, care must be taken to eliminate gridartifacts and erroneous self-energies that arise as aresult of numerical solution of the PB equation. Sub-traction of the top horizontal process (reference state)from the bottom horizontal process (solvated state)will likely cancel these artifacts, presuming the struc-tures of the separated components and their positionswithin the grid are identical to their respective coor-dinates in the complex in each case. In order to accu-rately calculate free energy of association in a solvatedstate, the APBS external program Coulomb is typicallyused to calculate nongrid-based free energy of eachprotein based on Coulombic potential, according to:

DGCoulombic ¼ GCoulombicAB � GCoulombic

A � GCoulombicB :

ð10Þ

An adjusted free energy quantity can be calculatedfor association in a solvated environment by incorpo-rating nongrid-based Coulombic energy calculations,as shown below:

DGsolution ¼ DDGsolvation þ DGCoulombic: ð11Þ

The free energy values in Eqs. (9)–(11) are incorpo-rated intoAESOP to compare the relative association ofproteins and protein mutants, in the absence of erro-neous self-energies and grid artifacts.9,15 PB free energycalculations represent a method of quantitatively pre-dicting biological activity, which is an important factorin the design and optimization of proteins.

APPLICATIONS

Protein Design Using Electrostatics

Based on the two-step model for protein associa-tion, it can be reasoned that mutations that alter theelectrostatic character of a protein can have a dramaticeffect on binding without resulting in substantialstructural changes. This hypothesis is based on theessential role of long-range electrostatic interactionsduring recognition of excessively and oppositelycharged proteins, and has major implications for pro-tein design. By utilizing this hypothesis and the per-turbative methods of the AESOP framework, it ispossible to computationally design protein analogswith tailored associative properties. We applied thisapproach to the design of novel analogs of the viralprotein, VCP,41,52 which is an important example ofviral mimicry used for immune system evasion. VCP isthe complement control protein (CCP) of the vacciniavirus, and is composed of four excessively chargedCCP modules. CCP modules are small compact do-mains consisting primarily of beta-sheets, which arestabilized by two disulfide bonds. CCPs are typically


composed of multiple CCP domains connected byflexible linkers. VCP is capable of mimicking humancomplement regulators to initiate factor I-mediateddegradation of C3b, one of the central proteins ofcomplement activation. VCP has a highly relatedhomolog, SPICE, which is produced by the morepotent variola (smallpox) virus. Despite having anearly identical sequence that differs by only 11 aminoacids, VCP and SPICE differ by up to 1000-fold intheir ability to regulate the complement system. Inorder to rationalize this significant gain in function, wecomputationally generated a series of VCP analogsbased on charged amino acid substitutions found inSPICE. Simple Coulombic calculations were initiallyused to determine the effect of the mutations on theelectrostatic potential of VCP, and visual comparisonwas used to identify analogs predicted to have functionsimilar to SPICE.41 Experimental binding and func-tional assays were performed and confirmed the pre-dicted activities of a series of 12 computationallypredicted constructs.41 Among them, a VCP analogconsisting of only two glutamic acid-to-lysine muta-tions was found to have similar activity to SPICE. Amore rigorous analysis, including MD simulations, PBelectrostatics, ESD clustering, covariance analysis ofcorrelated and anti-correlated modular motions, andapparent pKa calculations, was also performed tofurther elucidate the correlations between the overallpositive charge of VCP and binding ability.52 Theclustering results comparing the VCP analogs andSPICE reconfirmed our earlier predictions that chan-ges in the electrostatic potential of VCP are responsiblefor the improved function of SPICE.52

We have also applied this design approach to thestudy of another CCP, Kaposica of Kaposi’s sarcoma-associated herpesvirus, which has a function similar toVCP and SPICE.35 In this analysis, we used homologymodeling to generate a structure for Kaposica, whichwas used to analyze the electrostatic potential of theentire protein and each of the four CCP modulesindividually. PB electrostatic calculations were used todesign a series of mutants with the goal of altering theoverall positive potential of Kaposica or of each of itsmodules and linkers. One novel approach employed inthe design of Kaposica analogs included chargereversal of individual CCP modules, which was used toelucidate the importance of the electrostatic characterof each module. This was achieved by performing PBelectrostatic calculations on each CCP module alone todetermine which combination of basic-to-acidicmutations would produce a predominantly negativespatial distribution of electrostatic potential, whileintroducing the fewest changes. These electrostaticcalculations guided experimental studies in which thedesigned analogs were synthesized and analyzed. The

binding ability of the Kaposica analogs was evaluatedusing surface plasmon resonance, while factor Icofactor activity for C3b/C4b and C3-convertase decayaccelerating activity were measured to examine thefunctionality of each analog. Comparison of electro-static calculations and experimental data providedevidence in support of the importance of the electro-static potential of individual CCP modules, and the useof electrostatic calculations in protein design.

Validation and Improvement of ElectrostaticsCalculations

Due to the complexity of biomolecular electrostat-ics, several assumptions and approximations, such asimplicit solvation as discussed above, are often used.Another such approximation that is often made whenperforming electrostatic perturbation calculations is toignore the effects of dynamics before and after muta-tion. To evaluate the effects of dynamics on electro-static calculations of the AESOP framework, weperformed an analysis on the barnase–barstar complexwhich incorporated alanine-scanning mutagenesis,electrostatic clustering and free energy calculations, aswell as MD simulations.22 Since ionizable residues aretypically solvent exposed, structural changes followingmutation are expected to only occur locally and aretherefore considered to be negligible. However, weobserved that slight structural rearrangements in thebarnase–barstar complex, which occurred during a10-nsMD trajectory, resulted in ~100 kJ/mol differencein the solvation free energy of association. In contrast,we also observed that the conformation of the parentstructure had little to no effect on the correlation of freeenergies of association with experimental binding abil-ities nor on the clustering results, since each mutant wascompared relative to the same starting structure. Post-mutation relaxation, incorporated by using 5 ns MDsimulations for each experimentally tested mutant, onlyprovided minor improvement in the correlation of freeenergies of association with experiment. This studyshowed, at least for the barnase–barstar complex, that arigid-body assumption is reasonable.

In addition to dynamic relaxation considerations,the selection of parameters in PB calculations is asubject of controversy in protein electrostatic analysis,particularly how to treat the protein interior.Researchers have reported the use of internal proteindielectric coefficients ranging between 2 and 40, andsometimes higher depending on the system.42 Othergroups have suggested the use of a radially dependentdielectric function, in which a very low value is used torepresent the central core of the protein, and valuesbecome higher toward the protein surface.33,43,48

Recently, we performed PB free energy calculations


using dielectric coefficients of 2, 10, 20, and 40 for theprotein interior.15 In addition, we examined the effectsof ionic strength, PB linearization, and grid resolutionon calculated free energy values. We calculatedDGCoulombic, DGsolution, and DDGsolvation values foralanine mutants of five different protein complexeswith available experimental binding and kinetic data,obtained from the Alanine Scanning Energetics Data-base.46 These complexes represent a diverse dataset,varying in size, net charge, and biological function.Our results showed that for excessively and oppositelycharged proteins, both DGCoulombic and DDGsolvation

values correlated well with experimental data for allvalues of protein dielectric. Solution free energy valuestypically did not correlate well at low protein dielectric(eP = 2), but the correlation increased significantly asprotein dielectric was increased. The strongest corre-lations were observed using eP = 40, which pro-vides support for using higher dielectric values (eP �20–40), particularly for calculations involving protein

complexes. The higher dielectric coefficient likelyaccounts for the highly polar protein interfaces thatbecome buried upon complex formation, as well asminor structural rearrangements and surface alterationsupon mutation. Our data also showed that Coulombicenergies usually performed comparably to PB freeenergies, suggesting the use ofDGCoulombic as an efficientinitial predictor of relative protein association.15

Finally, we evaluated several comparative gridschemes (WB, Shell, and Skin) and ESD measures thathave been proposed for electrostatic clustering analy-sis.22 We performed a thorough comparison of ninecomparative grid scheme/ESD combinations forthe electrostatic clustering of barnase alanine-scanmutants. Since free energies of association are the goodpredictors of binding ability, the clustering methodsthat are able to closely group mutations with similarfree energies of association are thought to provide thebest predictions in the absence of a cocrystal structure.Figure 2 contains dendrograms for the clustering of

FIGURE 2. Dendrograms for the electrostatic clustering of barnase alanine-scan mutants based on: (a) WB–DP; (b) WB–LD;(c) Skin–DP; and (d) Skin–LD. Electrostatic potentials were calculated using ionic strengths corresponding to 0 mM ion concen-tration and eP 5 2. Colored circles indicate the free energy change upon mutation for each alanine mutant relative to the parent(white circle). The color code is as follows: red for 2500 to 2201 kJ/mol, yellow for 2200 to 21 kJ/mol, cyan for 1 to 200 kJ/mol,and blue for 201 to 400 kJ/mol.


barnase mutants based on four clustering methods,and the colored circles indicate the relative free energyof association for each mutant. Inspection of thesedendrograms shows that WB–DP is unable to properlycluster mutants with similar predicted effects onbinding, while the remaining three methods performequally well. This is due to the fact that DP relies ontaking the product of electrostatic potential values,which gives disproportionate weight to values in thelow-dielectric region of the protein interior, rather thanthe region of interaction outside the solvent-accessiblesurface of the protein. The WB–LD method providesaccurate predictions without needing to define skinboundaries, and therefore provides a simpler and moreefficient approach. Also, it should be noted that in thisstudy, we used single-alanine mutations, which intro-duce small changes in electrostatic potential distribu-tion, but may have substantial effects on bindingdepending on the location of the residue substitution.The results from such a comparison based on theelectrostatic clustering of homologous proteins, whichinclude multiple mutations and sometimes lowsequence identity, may be quite different due to asubstantial increase in the differences between elec-trostatic potentials.

Clustering and Free Energy of Single-Alanine Mutants

Our group has utilized AESOP for clustering andfree energy calculations of numerous systems, partic-ularly protein complexes involved in complementimmunity, including unpublished work. A specificexample of clustering and free energy calculationsinvolves EfbC and Ehp, proteins secreted on the sur-face of Staphylococcus aureus which contribute toimmune evasion by the bacterium. Both proteins bindcomplement fragment C3d, and disrupt several pro-cesses in complement immune activation and regula-tion.14,40 Since EfbC and Ehp are excessively basic(+7e and +11e) and bind to an acidic region on C3d,electrostatics is shown to strongly influence associa-tion. The results of our work for C3d–EfbC are shownin Fig. 3.14 It is evident that mutations of acidic resi-dues to alanine (acidic mutants) and basic residues toalanine (basic mutants) cluster together, respectively.In addition, we observe a high degree of correlationbetween clustering and free energy (DDGsolvation), asfree energy values are similar within each cluster in thedendrogram. Our results also show that mutationslocated away from the protein–protein interface cansignificantly enhance complex association, suggestingthat the global distribution of electrostatic potentialsurrounding the protein will govern the formation ofan encounter complex between C3d and EfbC. Inaddition, our analysis with EfbC-homolog Ehp

indicates that electrostatic potential may be responsiblefor its increased potency (based on experimental data)16

compared to EfbC. We plan to utilize our initial elec-trostatic analysis of C3d–EfbC and C3d–Ehp in thedesign of a therapeutic to combat S. aureus infection.

We applied a similar analysis to several other proteinsystems as well. Specifically, we recently examined theC3d–CR2 interaction.9,24 The results gave credibility tothe recent controversy over the cocrystal structure ofC3d–CR2.20 With the incorporation of recently pub-lished experimental data, the correlation between cal-culated and experimental free energies is poor, despiteexcessive charge playing a role in complex formation.Our results are consistent with the possibility that thepublished structure is not physiological, but ratheran artifact of crystallographic conditions. Similarly,

FIGURE 3. Clustering and free energy results for C3d–EfbC.(a) Clustering of EfbC mutants at 0 mM ion concentration andeP 5 2. The color of the line to each mutant in the dendrogramindicates the type of mutation. Mutations of positive aminoacids are in blue, mutations of negative amino acids are inred, and mutations of neutral amino acids are in gray. (b) Freeenergy (DDGsolvation) values of C3d–EfbC complex mutants at0 mM ion concentration and eP 5 2. The white, red, and bluevertical regions correspond to the line coloring of (a). Thecolored circles within the plot represent the distance of eachamino acid to C3d, as indicated in the legend. The black circlerepresents the parent complex. A horizontal shaded boxindicates mutations with a free energy value of 650 kJ/mol ofthe parent.


calculations with a docking model structure of Epstein-Barr virus glycoprotein 350–CR2 (gp350–CR2) yieldeda similar finding (unpublished results). Relatively poorcorrelations between calculated and experimental freeenergy values brought the integrity of the model intoquestion, especially considering the model was con-structed using experimental data as constraints. TheC3d–CR2 and gp350–CR2 show the efficacy of AESOPthrough negative results.

Clustering of Homologous Proteins and Domains

The AESOP analysis of homologous proteins posesdifferent challenges due to an increase in the electro-static diversity among protein analogs, when comparedto alanine scan mutants. Substantial differences inamino acid composition (sequence identity), localstructure, and charge distribution are possible withinhomologous families, despite having quite similarfunctions. One such system to which the AESOPframework has been applied is a family of Arabidopsislipid transfer proteins (LTPs).7 In this study, electro-static clustering was used to elucidate the uniquefunctionality of one specific analog, Arab_LTP5. Theunique character of Arab_LTP5 was believed to be due

to its excessive positive charge (+14e), and the effectsof this excessive charge could be manifested inArab_LTP5’s amino acid sequence, charge distribu-tion, or spatial distribution of electrostatic potential.Figure 4 provides examples of three different types ofclustering in which LTP/LTP-like proteins were com-pared on the basis of (a) sequence similarity, (b) three-dimensional charge distribution, and (c) electrostaticsimilarity (Shell–DP method). These dendrogramsshow that neither sequence similarity nor charge dis-tribution is sufficient for comparing this homologousfamily of proteins. Of these three types of comparisons,only the comparison of spatial distributions of elec-trostatic potential was able to illustrate the uniquecharacter of Arab_LTP5.7

We have also applied the AESOP methods toanother type of homologous protein family, the homol-ogous CCP domains of complement regulator factorH.23 In this study, homology modeling and electro-static calculations were used to analyze the electro-static diversity of the CCP domains of factor H, withthe goal of further developing our model for the role ofelectrostatics in complement regulation. Figure 5illustrates the clustering results for electrostatic com-parison of the 20 CCP modules of factor H based on

FIGURE 4. Dendrograms for the clustering of 20 LTP/LTP-like proteins based on (a) sequence identity; (b) charge distribution;and (c) ESD Shell–DP. Electrostatic potentials were calculated using ionic strengths corresponding to 50 mM ion concentrationand eP 5 2. Isopotential contours at two axial rotations are included for each LTP/LTP-like protein. The color code for the iso-potential contours is blue for positive and red for negative electrostatic potential. Isopotential contours are plotted at 61 kBT/e.


the WB–LD clustering method. The dendrogram ofFig. 5 was generated using homology models for 9CCP domains, while the remaining 11 structuresoriginated from a combination of NMR and X-raycrystallographic structures obtained from the PDB.The use of the AESOP clustering methods allowed forthe prediction of factor H contacts, including specificinteractions with C3b macroglobulin (MG) domainsand nonspecific interactions with polyanion-rich sur-faces, which are important for factor I-mediated deg-radation of C3b.23 Electrostatic clustering analysis alsoprovided insight into the pathobiology of involvementof specific factor H modules in disease.

Ionization Free Energy and pH Dependence

We have applied electrostatic methods for deter-mining pH and ionic strength dependence for protein

properties, such as net charge (titration curves), sta-bility (folding–unfolding transition), and association.32

We have studied the pH and ionic strength dependenceof charge and stability of C3d and CR2 and of theC3d–CR2 complex, an important protein complex thatacts as a link between innate and adaptive immuni-ties.30,32,51 Calculations were based on a thermody-namic cycle for pH-dependent association, in whichassociation free energy is decomposed into a processthat incorporates the ionization properties of aminoacids and a process with neutral amino acids.32,51 Theresults showed good agreement between calculatedionization free energies of association and experimen-tal pH- and ionic strength-dependent associationkinetics, and provided a decomposition of electrostaticand nonpolar contributions to association free ener-gies.51 An earlier study30 had postulated the effects oflong-range electrostatics in C3d–CR2 association usingcrystallographic structures. The study by Zhang et al.51

used MD simulations to assess the significance ofelectrostatic potential fluctuations and CR2 modularmotions in binding, and provided the detailed matrixof short/medium-range intra- and inter-molecularinteraction energies. In addition, that study51 showedthat ionization free energies of association for a seriesof C3d and CR2 mutants were predictive of relativeexperimental binding abilities. A subsequent study9

showed good correlations between calculated ioniza-tion free energies of association and electrostatic freeenergies of association at physiological pH. The dif-ference between the two free energy calculations wasthat the former includes the pH dependence of ioni-zation and takes into account the apparent pKa valuesof amino acids, whereas the latter used the presumedionization states of ionizable amino acids at physio-logical pH. The presumed ionization states are chargedaspartic and glutamic acids, lysines and arginines,and charged termini, whereas histidines, tyrosines,and nondisulfide-bonded cysteines are neutral, unlessselected to be charged based on apparent pKa pre-cal-culation. It iswell known that the pKavalues of ionizableamino acids within the protein can be shifted signifi-cantly compared to those of free amino acids in solution.The magnitude and direction (positive or negative) ofthe shifts depends on the local electrostatic (Coulombicand solvation) microenvironment. These types of shiftsare particularly important for amino acids involved inbinding and catalysis. Many reviews on ionizationproperties of proteins and the calculation of apparentpKa values have been published, including one of ourswith examples from systems we have with worked in thepast,49 and we will not elaborate further here.

We have studied the pH and ionic strength depen-dence of stability of the 10th type III domain of humanfibronectin (FNfn10).27 This type of calculation is

FIGURE 5. Dendrogram for the electrostatic clustering of the20 CCP modules of factor H based on WB–LD. NMR or X-raycrystallographic structures were used for 11 CCP domainsand homology models were used for 9 CCP domains. Elec-trostatic potentials were calculated using ionic strengthscorresponding to 0 mM ion concentration and eP 5 2. Isopo-tential contours at four axial rotations are included for eachCCP module. The color code for the isopotential contours isblue for positive and red for negative electrostatic potential.Isopotential contours are plotted at 61 kBT/e.


possible by using a thermodynamic cycle that modelsthe pH dependence of the folding–unfolding transitionin a charged and neutral state, by taking into accountthe pH dependence of amino acid ionization whencalculating charges.27,32,49,51 In agreement with exper-imental data, the calculations showed that at high ionicstrength, FNfn10 is more stable at low pH comparedto neutral pH.27 This was attributed to unfavorableinteractions in a triplet of acidic residues that becomeweaker at high ionic strength, as Coulombic interac-tions are screened by solvent ions, or at low pH, asacidic amino acids become neutralized. Upon mutationof the central acidic residue, the calculations showedincreased stability in agreement with experimentaldata.27 This study demonstrates the utility of electro-statics-based computational predictions for the designof proteins with tailored stabilities. In the case ofFNfn10, higher stability provides a better scaffold forthe attachment of novel antibody mimics (termedmonobodies). The same study served as a medium tocompare the effect of backbone and side chain flexi-bility on calculated pH- and ionic strength-dependentstabilities and to assess the accuracy and precision ofcalculated apparent pKa values. This was accom-plished by using an NMR ensemble of structures forthe calculations and NMR-derived pKa values ofacidic amino acids for comparison with experimentaldata.27 We have also examined the titration curves andpH dependence of stability of two homologous plantproteins, SCA1 and SCA2, and discussed the findingsin view of experimental data and functional models.8

In summary, calculated titration curves provide pHdependencies of charges and protein isoelectric points.Calculated stability curves provide the pH range ofprotein functionality. Calculated stability curves forprotein complexes provide the pH dependencies ofionization free energies of association. The calculatedpH-dependent processes discussed here take intoaccount the ionization states of amino acids, whichdepend on favorable and unfavorable Coulombicinteractions and favorable solvation or unfavorabledesolvation effects. PB-based calculations of ionizationproperties are an excellent predictive medium of theeffect of mutations in protein function, especially whenthe processes of binding and catalysis are involved, andin protein design when pH and ionic strength depen-dencies are of importance.

Electrostatic Design of Peptide-Based Inhibitors

PB electrostatic calculations are a useful tool inpeptidic and peptidomimetic inhibitor design, in caseswhere design is based on peptides derived from nativeprotein sequences. This is possible when the nativeproteins are excessively charged and binding to

receptors is driven by electrostatic complementarity.The interaction of HIV-1 gp120 with the humanreceptor CCR5 takes place through a positivelycharged variable loop (V3 loop) in gp120 and a nega-tively charged N-terminal domain in CCR5. Thiselectrostatic mechanism contributes in mediating viralentry and modulating biological activity in the humanhost cell. The V3 loop has variable positive net char-ges, depending on HIV-1 strains, thus it is of interest toexamine the effect of charge on the inhibition ofgp120–CCR5 interaction. We have shown using aseries of V3 loop-derived peptides that there is anexcellent correlation between calculated electrostaticpotentials and experimental binding and inhibitiondata.31 We studied a series of peptides with variableexcess of positive net charge in the range of +1 to +9,and found that as the positive electrostatic potentialincreased, the peptide binding and inhibition abilityincreased. Interestingly, a peptide with scrambledpositive charges showed similar binding affinity andinhibitory activity as the parent peptide from which itwas derived.31 The parent peptide had sequence from aviral strain and net charge +5, whereas the modifiedpeptide had similar sequence, but with scrambledpositions for lysine and arginine residues to a total netcharge of also +5. In both cases, parent-viral andmodified peptides, the patterns of spatial distributionsof electrostatic potentials were similar. Given thenotorious flexibility and mobility of the V3 loop, whichis evidenced by the lack of observation of usableelectron densities in crystal structures of free gp120,and our findings, we suggested that a possible avenuefor anti-HIV drug design may not be based on struc-ture but on the electrostatic properties of the V3 loopsequence. This approach may be an efficient way todesign a drug which will account for the ability of HIVto mutate, by simultaneously targeting the numerousstrains with variable sequences and flexible structures,but with positive charges at the V3 loop.

PERSPECTIVES

In this review, we discussed a number of tools forthe analysis of electrostatics in proteins and proteincomplexes. The newly developed AESOP computa-tional framework provides an integrative approach forelucidating the role of specific charged residuesimportant for protein interaction and function. Wehave illustrated how different applications of AESOPhave both improved calculation of electrostatic effectsin proteins and shown the efficacy of computationalmethods to elucidate implications of electrostatics inbinding and biological function. This computationalframework can be used to analyze electrostatic data for


mechanistic studies to understand basic biologicalfunction. It can also be used to guide experimentalstudies by providing a basis for the design of proteinmutants and homologs with optimized functions. Suchstudies form a foundation for the design of proteintherapeutics and biotechnology products.

OPEN ACCESS

This article is distributed under the terms ofthe Creative Commons Attribution NoncommercialLicense which permits any noncommercial use, distri-bution, and reproduction in any medium, provided theoriginal author(s) and source are credited.

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