Quantum chemical analysis explains hemagglutinin peptide--MHC Class II molecule HLA-DRbeta1* 0101 interactions

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Biochemical and Biophysical Research Communications 323 (2004) 1265–1277

BBRC

Quantum chemical analysis explains hemagglutininpeptide–MHC Class II molecule HLA-DRb1*0101 interactions

Constanza Cardenasa,b,1, Jose Luis Villavecesb,1, Hugo Bohorqueza, Eugenio Llanosb,Carlos Suareza, Mateo Obregona, Manuel Elkin Patarroyoa,*

a Fundacion Instituto de Inmunologıa de Colombia, Carrera 50 No. 26-00, Bogota, Colombiab Grupo de Quımica Teorica, Universidad Nacional de Colombia, Bogota, Colombia

Received 25 August 2004

Available online 15 September 2004

Abstract

We present a new method to explore interactions between peptides and major histocompatibility complex (MHC) molecules

using the resultant vector of the three principal multipole terms of the electrostatic field expansion. Being that molecular interactions

are driven by electrostatic interactions, we applied quantum chemistry methods to better understand variations in the electrostatic

field of the MHC Class II HLA-DRb1*0101–HA complex. Multipole terms were studied, finding strong alterations of the field in

Pocket 1 of this MHC molecule, and weak variations in other pockets, with Pocket 1� Pocket 4 > Pocket 9 � Pocket 7 > Pocket 6.

Variations produced by ‘‘ideal’’ amino acids and by other occupying amino acids were compared. Two types of interactions were

found in all pockets: a strong unspecific one (global interaction) and a weak specific interaction (differential interaction). Interactions

in Pocket 1, the dominant pocket for this allele, are driven mainly by the quadrupole term, confirming the idea that aromatic rings

are important in these interactions. Multipolar analysis is in agreement with experimental results, suggesting quantum chemistry

methods as an adequate methodology to understand these interactions.

� 2004 Elsevier Inc. All rights reserved.

Keywords: Theoretical study; MHC–peptide interactions; Multipolar moments; Electrostatic properties; Quantum chemistry MHC–peptide

interactions

One of the best established facts in the science of mol-

ecules is that all interactions are produced by electro-

static charge interactions [1,2]. The interaction between

the electrostatic fields created by electrons and nuclei

is the source of all chemical and biochemical effects.

Whether they are termed Van der Waals Forces, Hydro-gen Bonds, London Interactions, Hydrophobic Effect,

and so on, they are ultimately produced by the mutual

actions of electrostatic charges stemming from protons

0006-291X/$ - see front matter � 2004 Elsevier Inc. All rights reserved.

doi:10.1016/j.bbrc.2004.08.225

* Corresponding author. Fax: +57 1 4815269.

E-mail addresses: [email protected], [email protected]

(M.E. Patarroyo).

URL: http://www.fidic.org.co.1 Both contributed as first author.

and electrons in the molecules. Whereas it has been use-

ful for empirical purposes to make a distinction between

the above-named ‘‘forces,’’ since they occur on roughly

different experimental realms, it seems useless to keep

such separation for understanding interactions between

specific molecules. It is better to reduce them to forcesthat come from a more fundamental notion governed

by electrostatic charge interactions that are described

computationally by quantum operators.

Nowadays one can move in the direction of under-

standing the multiplicity of effects on the basis of funda-

mental electromagnetic fields since quantum chemical

software has been developed enough so as to carry out

calculations on small biomolecules in reasonable time.This paper is a contribution in this direction.

mailto:[email protected]

1266 C. Cardenas et al. / Biochemical and Biophysical Research Communications 323 (2004) 1265–1277

In an immunological response, one of the most impor-

tant macromolecular interactions is the one taking place

between major histocompatibility complex (MHC) mole-

cules and antigenic peptides. This interaction is regulated

by MHC glycoproteins which, by suitably presenting

antigenic peptides to T-cell receptors, determine thegeneration of an appropriate immune response against a

pathogen [3]. A first set of questions are, why do antigenic

peptides bind to theMHC?What are the causes of strong

binding? What are the causes of selective binding? and

What differences are there among the behaviors of

invariant and polymorphic segments of the MHC?

Human MHC Class II DR molecules are heterodi-

meric structures consisting of an invariant 34 kDa a(HLA-DRa) chain and a highly polymorphic 28 kDa bchain (HLA-DRb). These Class II molecules have re-

stricted distributions among different tissues and play

a key role in antigen presentation to T-helper cells and

the consequent antibody production. Recognizing their

chemical characteristics is thus of vital interest for

achieving the appropriate design of recombinant,

DNA-based or chemically produced sub-unit vaccines.A lot of experimental work has been carried out to

study this interaction; most of which has been aimed

to determine sets of amino acid sequences or epitopes

that are strongly bound and that may be presented by

the MHC molecules [4–7].

Epitopes that may bind strongly have been predicted

for Class I MHC [8–10] molecules, whose interaction

with antigenic peptides is up to now the most studied.Work is still in progress on Class II molecules because,

whilst their interactions share some rules with Class I

molecules, their specific interactions make it necessary

to analyze the governing rules further [11].

Experimental work with Class II molecules has led to

predictive algorithms for these binding sequences or epi-

topes from a statistical point of view [4,12,13]. There are

also computational works, including statistical ap-proaches describing molecular structure or molecular

mechanics calculations, for determining interaction en-

ergy [14,15] Neural networks have also been employed

for determining antigenic peptides for each MHC allele

[16,17]. Among these computational approaches, there

are docking methods that search for optimal comple-

mentarity between two molecules by maximizing simple

forces acting between point entities. These methods aremainly orientated towards analyzing simplifications of

the original molecules, or ‘‘shapes,’’ whether these be ob-

tained from crystallographic studies, solvent accessible

surfaces, Van der Waals surfaces, and such, taking into

account concepts like binding free energy to arrive at pre-

dictions of new stable molecular complexes [18,19].

Several of the aforementioned methods also employ

the determination of electrostatic potential, or chargeparameters, for finding complementarity and interaction

energy, usually obtained by molecular mechanics. These

methods are limited because they leave aside the fact that

molecular interactions follow the laws of quantum

mechanics. Visualizing molecules as rigid bodies having

well-defined geometrical forms and using classical

mechanics approaches are at best coarse approximations

for describing molecular interactions, and work bestwhen thenumbers of parts involvedare large, and thus ap-

proach a statistically groundedmean behavior for the col-

lection of items. Our case is different, since we are looking

at fine-grained interactions of individual components.

Our aim in this work was to study the Class II MHC–

peptide interaction, focusing on the molecules� electro-static behavior by employing methods from quantum

chemistry.We will look for determining factors ruling these

interactions from an electrostatic point of view, under

the hypothesis that the leading factors are electrostatic

in nature and that those peptides interacting strongly

with the MHC should affect the profile of its electro-

static potential, particularly in those regions in the

MHC called Pockets by experimentalists, where the

largest interactions between MHC and peptide havebeen shown to occur. It is assumed that the interaction

of a peptidic fragment with a pocket is relatively inde-

pendent [20–22], and therefore that it is feasible to study

each pocket–peptide interaction separately. This is

clearly a simplification based on experimental results,

but justifiable since we are simply interested in identify-

ing patterns of interaction behaviors.

In this paperwe focus on large variations in the electro-static fields; in a future document we will report on varia-

tions in thewave functions for thesemolecules.Given that

the electric fieldmaybe expanded as a power series ofmul-

tipole moments [23] in which the first terms are the most

important, it becomes meaningful to study these leading

terms (i.e., charge or q, dipole moment or d, and quadru-

pole moment or C) as indicators of the electrostatic land-

scape resulting from amino acid interactions. In a formerstudy we have shown that these terms are excellent dis-

criminators of the properties of amino acids [24].

We began the current research by comparing electro-

static properties of the above-named pockets in presence

and absence of a sequence of amino acids contained in a

well-studied peptide. By making this comparison be-

tween presence and absence of a group of amino acids,

it can thus be seen whether there is any alteration ofpocket electrostatic properties in the HLA-DR molecule

when a peptidic fragment is interacting with it.

The absence of a peptidic sequence in a MHC pocket

shall be labelled as an empty pocket. Of course, these re-

sults cannot be compared to experimental cases, because

no one has managed to produce an MHC complex with

empty pockets that has the same amino acid distribution

in space as an MHC bound to a peptide.This approach provides a good theoretical back-

ground to measure variations in electrostatic properties

C. Cardenas et al. / Biochemical and Biophysical Research Communications 323 (2004) 1265–1277 1267

produced by different peptides. In order to contrast our

findings with experimental knowledge, we selected an

amino acid for comparison purposes that is reported

to fit optimally in each pocket for a specific MHC mol-

ecule. This best-fit case from experimental results we

termed the ideal amino acid for the specific pocket forthe selected MHC. While there is no complete agree-

ment among the experimentalists as to these best peptide

binding sequences to MHC pocket complexes, we

decided to take as reference some experimental data

from Ramensee et al. [13] and Marsh et al. [25] to make

the comparisons in the present study.

We then compared variations in the electrostatic po-

tential of the pocket when the ideal amino acid andflanking terminating amino acids is docked, and when

a different amino acid with the same flanking terminat-

ing amino acids is docked. It is reasonable to expect that

those peptidic fragments (that is, target amino acid plus

flanking terminating amino acids from the original pep-

tidic sequence) produce an alteration in the electrostatic

potential of the pocket similar to that produced by the

ideal peptidic fragment.It is important to underline here that this is a first step

along this line of research, to provide evidence for the

importance of the main aspects of the variations in terms

of differences in electrostatic field.A complete study of the

interactions should include solving the wave function for

themolecular complex formed by theMHCmolecule, the

peptide, and at least two or three layers of solvent mole-

cules, includingwater and electrolytes tomimic biologicalmedium.This is still not possible in reasonable time, sowe

have to apply sound approximations.

In the first place, we do not include solvent. This is jus-

tified by the fact that the same solvent is present in all

cases and one may think of it as a parameter affecting

in similar ways all molecules, so our approach is a ceteris

paribus comparison of the effect of changing the peptide

so as to put into evidence the main features of the inter-action. In second place, we do not use the whole peptide–

MHC complex for the quantum chemical calculations;

instead, we divide this complex into regions centered

around the above-named pockets and study these parts.

Finally, we do not compute the complete electrostatic

field but only its leading terms—charge, dipole, and

quadrupole—which have shown to be sufficient to de-

scribe the main variations due to changes in the aminoacids of the peptide [24,26] These approximations leave

us with a feasible computational problem. To highlight,

the important point of our research is that we find a new

method to explore the interactions between peptides and

MHC molecules. As shown below, our comparisons are

in good agreement with experimental results.

Others [15] have conducted a similar study of the

binding preferences for the same MHC molecule westudy, but applying a methodology grounded in molec-

ular mechanics that permits the simulation of the

MHC–peptide complex in a solvent environment. Their

findings of amino acid binding patterns do not substan-

tially differ from our findings in terms of amino acid

preferences for each pocket. This supports our supposi-

tion that a solvent medium will not change radically the

pattern of binding behavior for our research.

Materials and methods

Defining the studied molecules. The coordinates of the complex

formed by the MHC Class II allele molecule HLA-DRb1*0101 with

the hemagglutinin (HA) peptide crystallized by Stern et al. [27] were

used (1DLH in PDB) to define the position in space of the nuclei

necessary as input for Gaussian�98 calculations. We then focused on

five regions which have been identified by crystallographic coordinate

and site-directed mutagenic analysis of a peptide�s binding regions

called Pocket 1, Pocket 4, Pocket 6, Pocket 7, and Pocket 9.

Each pocket�s conforming amino acid was taken according to

various sources [15,25,27,28]. An additional amino acid from the

remaining MHC residues was added to compensate for charge when

the amino acid in the peptide is charged at the natural pH of 5 for

MHC loading process. Note that the MHC amino acids are not nec-

essarily connected and that they are capped by hydrogen. The amino

acids were numbered according to crystallographic data. To model the

MHC–peptide complex we take the hemagglutinin peptide coordinates

for each pocket according to the amino acid which was directly inside

the pocket and its nearest neighbor amino acids to avoid border effects.

That is, each of the five MHC pockets will be successively occupied by

each of the 20 naturally occurring amino acids flanked on both sides by

nearest neighbor amino acids from the HA peptide sequence that is

supposed to bind to the specific pocket.

Additionally, calculations were done of the pockets without any

peptidic fragment, to serve as reference. This is the ‘‘empty pocket’’

case, as described above.

Table 1 shows amino acids from the a- and b-chains that make up

each pocket, as well as the amino acids from the occupying peptide

sequence. The substituting amino acid, that is to say, the amino acid

that is most engulfed by the pocket amino acids, will be referred to as

‘‘the occupying amino acid.’’

Quantum chemical computations were carried out for each of the

five pockets studied, and occupying amino acid from the hemaggluti-

nin peptide and its flanking neighbors in the peptide. The occupying

amino acid was then systematically changed for each of the 19

remaining naturally occurring amino acids.

Partial optimization of each occupying amino acid�s geometry was

performed during the calculation of the electrostatic properties to al-

low each of the target amino acid side chains to be better accommo-

dated within the pocket. The side chain torsion and valence angles

were the relevant geometrical parameters used for this process. Opti-

mizations were done with the AM1 semi-empirical method and the

Gaussian�98 software [29,30].

Analyzing electrostatic properties: multipole moments. The electro-

static potential of a charged body may be expanded in a power series of

multipole moments according to:

V ðrÞ ¼ 1

4pe0

1

r

ZvqðrÞdsþ 1

r2

ZvqðrÞ cos hds

�

þ 1

r3

ZvqðrÞr2 3

2cos2h� 1

2

� �dsþ � � �

�; ð1Þ

where V (r) is the electrostatic potential at the point in space where the

potential will be measured, r and h are polar coordinates of this point,

e0 is the vacuum permittivity, and ds is the volume infinitesimal within

which V (r) will be evaluate.

Table 1

Pocket composition

Pocket 1

a-Chain I7 F24 F26 F32 W43 A52 S53 F54 E55 D25 D27

b-Chain H81 Y83 V85 G86 F89 T90 V91

Peptide P306 K307 Xaa308 V309

Pocket 4

a-Chain Q9 A10 E11 F24 N62 D25

b-Chain F13 E14 C15 L26 L27 E28 F40 Q70 R71 R72

A73 A74 Y78 C79 R25

Peptide K310 Xaa311 N312

Pocket 6

a-Chain Q9 A10 E11 A61 N62 I63 A64 V65 D66 N69 K67

b-Chain W9 Q10 L11 K12 F13 E28 R29 C30 R71 D66

Peptide N312 Xaa313 L314

Pocket 7

a-Chain V65 N69 D66

b-Chain L11 F13 E28 C30 V38 Y47 W61 Q64 L67 R71 E46

Peptide T313 Xaa314 K315

Pocket 9

a-Chain A68 N69 L70 E71 I72 M73 R76

b-Chain W9 C30 S37 V38 D57 Y60 W61 R29 E59

Peptide K315 Xaa316 A317 T318

Xaa corresponds to the target or occupying amino acid. Additional

amino acids that are added to assure that the molecule is overall

neutral for computational reasons are highlighted in gray (see text).


The three most important terms in this expansion are the monopole

or charge term ð1rRvqðrÞdsÞ, the dipole moment ð 1r2

RvqðrÞr cos hdsÞ, and

the quadrupole moment ð 1r3RvqðrÞr2ð32cos2h� 1

2ÞdsÞ.

These will be the terms used in the present study which will give us

a sound approximation to the electrostatic potential of the complex

MHC–peptide in the neighborhood of each Pocket.

Computing multipole moments. Electrostatic potentials were com-

puted for each pocket separately (both empty and occupied) using the

Gaussian�98 program and a Hartree–Fock method with a 3-21G* basis

set [31,32]. In each case, the computations were performed for the

group of pocket amino acids and a peptidic fragment from the HA

peptide (as seen in Table 1) taking not only the occupying amino acid

but also its nearest neighbors to avoid border effects. All calculations

were carried out on an HP Proliant 8000 computer with six XEON

CPUs and 3GB of RAM.

Mulliken partial charges [33] corresponding to side chain atoms in

each of the MHC-pocket peptidic–fragment complexes (including the

empty case for each pocket) were obtained from these calculations for

each of the peptide amino acids. As we are interested in the differences

in behavior produced by changing a residue, it is reasonable to take

into account only the changes in electrostatic charge in the side chains.

Although Mulliken charges are not very precise, they are easy to

compute and they have shown in several calculations [26] that they

have the same trends as more accurate charges when several molecules

of a set are compared. Besides, the closeness of fit between our results

and experimental data argues for the validity of the approach.

Accordingly, one can use them to see the trends in the electrostatic

landscape of the complex MHC–peptide complex.

The sum of these charges is an approximation to the first term in

the multipole expansion (i.e., to the charge for each of the side chains

of amino acids in the pocket, q). The norms or magnitudes for dipole

(d) and quadrupole (C) moments for the amino acid side chain cor-

responding to each pocket were computed from these charges. A

change was made in the coordinate system for these two calculations,

taking the a carbon in each amino acid as origin because interactions

are related to local multipoles, not to the total multipole of the protein.

The charge q was taken directly from the results of Gaussian 98.

The position vector r used in the following equations for dipole d and

quadrupole C has coordinates (x 0,y 0,z 0) defined as follows for each

amino acid residue with its corresponding a carbon:

x0 ¼ x� xCa;

y 0 ¼ y � yCa;

z0 ¼ z� zCa:

ð2Þ

The dipole moment vector was calculated as follows:

p ¼XNk¼1

qkrk : ð3Þ

The quadrupole moment tensor components were calculated according

to:

Qxixj ¼XNk�1

qk 3xixj � rk2dij� �

;

x1 ¼ xk ;

x2 ¼ yk ;

x3 ¼ zk ;

r2k ¼ x2k þ y2k þ z2k ;

ð4Þ

where q is the charge, r is the nuclei position vector relative to the res-

idue�s a carbon, and N is the total number of atoms in the side chain.

The dipole and quadrupole norms were found as follows:

dk ¼ffiffiffiffiffiffiffiffiffiffiffiffipk � pk

p; ð5Þ

Ck ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiX3

i¼1;j¼1

Q2ij

vuut : ð6Þ

Then, all multipole moments (q, d, and C) were normalized according

to Eq. (7)

xnorm ¼ xi � xmin

xmax � xmin

; ð7Þ

where xi corresponds to the value of each variable (q, d, and C), respec-

tively. The values thus obtained are hence adimensional, lying between

0.0 and 1.0, making comparison between different cases possible.

Computing total differences between occupied and empty pockets.

Data corresponding to amino acids that constitute the pocket were

taken to analyze the effect of a particular occupying amino acid on a

pocket. The difference that each of the target 20 amino acid complexes

has with the empty pocket case was found for each of our multipole

variables, q, d, and C, for each of the MHC amino acid residues, and is

presented in the results.

An idea of the magnitude of the pocket�s global effect on the

electrostatic landscape may be obtained by taking the sum of the

magnitude of these differences between occupied and empty pockets. If

the total addition equals zero, there is total compensation of the effects.

This difference will be initially taken as being the variable measuring

the global differences between the pocket occupied by each of the 20

target amino acids and the empty pocket (without peptide).

Difftot ¼Xi

qio � qieð Þ2 þ dio � dieð Þ2 þ Cio � Cieð Þ2h i1=2

ð8Þ

for i between 1 and the number of residues in the pocket, q is the mag-

nitude of the charge for the respective amino acid residue, d is the norm

of dipole moment for the respective amino acid residue, and C is the

norm of quadrupole moment for the respective amino acid residue.

Subindexes o and e indicate occupied and empty pockets, respectively.

By means of this variable we may globally compare the behavior of

each pocket with regard to different occupying amino acids and we

have thus a measure of how these affect the pocket.

Differences for each of the five pockets. The results of variations in

each of the three leading terms in the differences of multipole moments


were taken to analyze the variations in the electrostatic landscape for

each pocket, this was accomplished by finding the Euclidean distance

of the multipole magnitude differences:

S1 ¼ qo � qeð Þ2 þ do � deð Þ2 þ Co � Cð Þ2h i1=2

: ð9Þ

Subindex o and e indicate the value for occupied and empty pockets,

respectively. q corresponds to Mulliken charge, d to the norm of dipole

moment, and C to the norm of quadrupole moment.

This new variable, S1 is taken as a measurement of the similarity

between the properties of occupying amino acids in each pocket, and

gives us an idea of the perturbation produced by each occupying amino

acid on the pocket�s amino acids. If a particular pocket amino acid is

equally affected by any occupying amino acid, one has evidence that

there is no specificity in the interaction and the dispersion between S1

values for it will be low. On the other hand, a high S1 dispersion would

be evidence of a high specificity.

The range of S1 was computed to analyze these changes in more

detail. This value corresponds to the difference between the largest and

the smallest value in each of the calculated variables and gives a

measure of the dispersion corresponding to the highest effect of the

occupying amino acids in each of the pocket amino acids.

Comparison with ‘‘ideal’’ occupying amino acids. An analysis was

also done for each pocket, taking point-to-point differences between

the values for each pocket occupied by a given amino acid, and that

value when it was occupied by a particular amino acid that we shall

call ‘‘ideal.’’ The latter was taken from Ramensee [13] and Marsh [25],

data taken from experimental data, and are the amino acids that,

according to experiment dock best in the corresponding pocket. This

variable is a similarity measurement of the difference in effect between

various occupying amino acids and the ideal amino acid, and we will

call it Diff 0tot (similar to Eq. (5) but making the difference with the ideal

amino acid instead of empty pocket).

Results and discussion

Results will be presented in two parts: the first corre-

sponds to general findings, in which results for all pock-ets are compared, and the second refers to particular

results for each of the studied pockets.

Total differences

Fig. 1 was obtained from the calculated differences

regarding the interaction with each of the occupying

Fig. 1. Total difference between occupied and empty pockets for each amino

amino acids. Pockets are named P1, P4, P6, P7, and P9 for pockets 1, 4, 6, 7

name.

amino acids (Eq. (3)), showing global effects for each

of the five pockets in the HLA-DRb1*0101 molecule.

Initial analysis of the data shows a relatively large va-

lue for differences when the occupying amino acid is pos-

itively charged (i.e., for arginine, histidine, and lysine)

and a relatively small value for negatively charged ami-no acids (aspartic and glutamic acids). This behavior

was similar in all five pockets (Fig. 1A) and it is assumed

that it is due to this amino acid�s net charge generating

strong electrostatic interactions reflected in the variables

we used. This is confirmed when one analyzes the indi-

vidual data for this amino acid�s interaction with each

pocket where there are extreme values (maximum or

minimum) in most cases for the multipole moments (q,d, and C, data not shown). As they have not been exper-

imentally found to fit into any one of the HLA-

DRb1*0101 pockets, we decided not to consider these

amino acids further in the present work, leaving the

analysis of their behavior for a future study. Fig. 1B is

analogous to Fig. 1A, but leaves aside the charged ami-

no acids.

As may be seen in these two figures, each pocket pre-sents a similar Difftot behavior; most amino acids give

the same difference in magnitude for each pocket with

respect to the empty pocket. A few amino acids behaved

differently in each pocket, according to our composite

variable Difftot.

It is striking that the largest rank of differences was

shown by Pocket 1, confirming what has been found

experimentally found by phage libraries [34] and peptidebinding analysis to these isolated molecules [21] that

Pocket 1 has the strongest peptide binding properties

for this MHC Class II allele [35–37]. The differences

were lesser and more diffuse for the remaining four

pockets.

This can be more clearly observed if the average dif-

ferences for each pocket are taken (Fig. 2A). The aver-

age difference was 2.17 in Pocket 1; 0.44 for Pocket 4;0.35 for Pocket 6; 0.415 for Pocket 7; and 0.422 for

Pocket 9.

acid, for each pocket. (A,B) Total differences with and without charged

, and 9, respectfully. Each amino acid is referred to by its single letter

Fig. 2. Average values of total differences (Difftot) (A) and (B) discriminated by multipolar moments for the pockets of Class II molecule HLA-

DRb1*0101.


These results suggest a first hierarchy for the values

regarding a peptide�s total interaction with the different

Class II MHC HLA-DRb1*0101 molecule pockets:

Pocket 1 � Pocket 4 > Pocket 9 � Pocket 7

> Pocket 6:

This hierarchical behavior was reflected, in turn, in the

values of the differences observed for each pocket. Such

behavior was marked in Pockets 1 and 4 and less

marked in the three other pockets, as seen in Figs. 1A

and B.

It has been experimentally demonstrated that Pocket

1 is the anchoring site for peptide binding to MHC Class

II HLA-DRb1*0101 molecules [35–37]. It is thus themost determinant pocket in the interaction and practi-

cally the only pocket which is indispensable for binding

to these Class II molecules. This completely agrees with

the hierarchy found in this study through multipole

analysis.

Pockets 4 and 9 seem to be more significant in defin-

ing peptide binding and specificity towards the HLA-

DRb1*0101 molecule [34,37] than the two remainingpockets. Pocket 7 is rarely considered to be an anchor-

ing site, while Pocket 6 appears to be more relevant in

some works. Other researchers [38] consider these pock-

ets as only one region for interaction because many of

the residues conforming the pocket region are shared.

The results obtained here show that there is a differ-

ence between empty and occupied pockets, from an elec-

trostatic point of view. Moreover, this differencechanges when the occupying amino acids change, show-

ing that the net effect is localized in some of the pocket�samino acids, as will be seen in more detail below.

When analyzing the change of each multipole mo-

ment (q, d, and C) (Fig. 2B) for each of the pockets, it

was found that each pocket had a defined pattern of

behavior. The most relevant changes for Pocket 1 lie

in quadrupole moments, agreeing with the fact that itis formed by a large number of aromatic residues having

planar symmetry and presenting the highest quadrupole

values. This also agrees with the fact that the occupying

residues that best dock in this pocket are aromatic.

Pockets 4 and 9 did not present predominance in the

changes in any of the three multipole moments. This

may be correlated with the fact that they accept mainly

hydrophobic residues. There is a slight predominance of

changes in charge in Pocket 6 that might have been dueto the presence of a11 glutamic acid and a66 aspartic

acid that are geometrically close to each other [39].

There was a small predominance of changes for the

dipole term in Pocket 7 that might have been due to

the equilibrium between oppositely charged amino acids

and their relative geometrical disposition. In this case, it

is important to bear in mind that this is a shallow region

accepting only ‘‘small’’ residues and that size might bemore important than electrostatic behavior. It is also

important to note that the magnitude of differences is

small in all cases, with the exception of Pocket 1, making

effects less specific. The magnitude of the differences

found confirms the proposed hierarchy.

This hierarchy and in particular the undifferentiated

global behavior of pockets other than Pocket 1 may be

evidence of the essentially promiscuous character ofMHC regarding antigenic molecules, which is requisite

for immunity, because it is important that a single

MHC may be able to capture a large number of patho-

genic molecules, given that human beings have only two

alleles of beta chains to face a large number of possible

pathogens.

Comparative analysis of pockets

Comparison with ideal occupying amino acids

According to Diff 0tot, for each pocket we obtained the

results shown in Table 2. Only amino acids showingslight differences with respect to the ideal ones are

shown, but all other data may be consulted upon

request.

In general, our obtained results agree quite well with

experimental data. In Pocket 1, we have that the more

Table 2

Ideal amino acids for each pocket determined experimentally and in

this study

Pocket Experimental dataa Our theoretical datab

1 Y, F, W, I, L, V Y, F, W, L, I, M, C

4 L, A, I, V, M L, A, S, M

6 A, G, S, T, P A, P, G, T, S

7 L, I, V, Q L, Y, I, C

9 L, A, I, V, N L, A, C, S, N

The common amino acids in the two approaches are underlined, and

the amino acids taken as ‘‘ideal’’ for the comparisons are highlighted in

gray.a According to Ramensee13 and Marsh28.b These are the values obtained in this research.


similar occupying amino acids to tyrosine are aromatic

Phe and Trp. As allelic dimorphism G86V in the b-chainis found in Pocket 1 [40] and as HLA-DRb1*0101 is the

allele being studied (carrying the b86G amino acid in

this position), this means that the best fitting amino

acids are tyrosine, phenylalanine, and tryptophan. Some

other hydrophobic amino acids such as leucine, valine,

and isoleucine are the best fitting into the allele b86V,and they present a certain degree of affinity (although

to a lesser degree) for the b86G allele [41].

In Pockets 4 and 7 the agreement with experimental

found amino acids is rather good. In Pocket 6 it was dif-

ficult to optimize side chain geometries, mainly because

there are two conserved acids, for all Class II molecules,

within this pocket (a11E and a66D) whichwere very close

to each other and whose interaction is stabilized by a net-work of hydrogen bonds [39,42]. This situation prevented

interaction with charged residues or long chains within

this pocket, as it has also been experimentally found

[43]. Optimizing of the target peptide amino acid shifted

the side chains away from the interaction site and the ob-

served results are mainly due to the ‘‘exterior’’ of the

pocket. This effect was present in the case of charged

occupying amino acids and aromatic amino acids.A marked difference between experimental data and

our results was observed in Pocket 9 when the occupying

Fig. 3. Average of S1 for Pocket 1 amino acids. Error bars represent dispersio

represent pocket amino acids that have more specific (that is, differential) in

amino acid was tryptophan. This might have been due

to the fact that its side chain was in very close proximity

with pocket amino acid b9W, giving rise to an unrealis-

tic interaction. There are in some other HLA-DR alleles,

the b57D+/b57D� dimorphism in Pocket 9, and when

this Aspartic acid is present a salt bridge is formed witha76R, determining the non-polar nature of those resi-

dues fitting mainly into this pocket [27,34]. These two

residues a76R, conserved in all Class II molecules, and

b57D, dimorphic, also establish hydrogen bonds with

the main chain of the peptide.

Effect of occupying amino acids on the pocket

Differences for each pocket. In analyzing the differencesfor each pocket with regard to the empty pocket, it was

found that the effects that each amino acid had on the

pocket were particular. It was generally found that each

occupying amino acid affected only some of the amino

acids in each particular pocket. These effects may be sep-

arated into two types of behavior: The first one refers to

the undifferentiated global effect of all occupying amino

acids on some of the pocket�s amino acids. This occurredin the case of a pocket�s amino acids which are found

‘‘outside of the pocket.’’ The second type of behavior,

in which a differential effect was found depending on

the occupying amino acid, was presented by those amino

acids of a pocket properly defining it or which are in di-

rect contact with the occupying amino acid.

Variable S1 (Eq. (9)) was analyzed for each pocket

and each occupying amino acid to observe these behav-iors. In the following graphs the average values of S1 are

seen together with an analysis of the corresponding

range or dispersion for each of the amino acids compos-

ing the pocket, presented as error bars. When the rank is

large, the bar is gray indicating that on that pocket ami-

no acid there is the largest dispersion and, accordingly,

the largest specificity regarding the occupying amino

acids.In Pocket 1 the effect of amino acids a55E and b81H

is the main effect (Fig. 3A), and it is difficult to observe

n. Gray bars are those for which dispersion is higher and consequently

teractions with the target peptide amino acids.


the effect of the other pocket amino acids. Accordingly,

we show a second graph not including them (Fig. 3B).

These amino acids would present a global effect because

they were at the ‘‘entrance’’ to the pocket. b81H is one

of the amino acids establishing a hydrogen bond with

the peptide�s backbone which is conserved in all interac-tions of every peptide with all Class II molecules. This

H-bond has a tremendous impact on the MHC-Class

II molecules–peptide interactions since it has been found

that mutations induced in this residue increase the disso-

ciation rate of the peptide by factors ranging 200-fold,

making it essential to control the peptide–MHC Class

II complexes stability [44]. The pocket amino acids for

which larger dispersions are found are a32F, a43W,a54F, b85V, and b89F all of them situated in the region

properly belonging to the pocket. Clearly, the amino

acids located at the borders of a pocket produce the

strongest interaction but these are generalized or pro-

miscuous, interacting with any binding peptide whereas

the amino acids within a pocket produce weaker but

specific interactions being exclusive and selective for that

specific residue. It seems that this MHC molecule regionhas two functions: (a) strong, general, promiscuous pep-

tide binding at the edges or global effects and (b) weak,

specific binding within the pocket or differential effects.

Fig. 4. Average of S1 for Pocket 4 amino acids. For notation see Fig. 3.

Fig. 5. Average of S1 for amino acids in

In Pocket 4 it was found that pocket amino acid

undergoing a global effect is a62N (which establishes

hydrogen bonds with the peptide�s backbone). This

was also confirmed by the fact that there is low disper-

sion (small max � min differences), meaning that they

were equally affected by any occupying amino acid(Fig. 4). Those amino acids within the pocket producing

a differential effect are in this case a9Q, a11E, b13F,b26L, b7OQ, b71R, b74A, and b78Y (Fig. 4).

Fig. 5 presents results for Pocket 6. The first remark-

able thing is the smaller values for the differences and

the larger dispersion amongst them. Nevertheless, these

results show the two kinds of already-mentioned effects,

i.e., the global effect with pocket amino acids a62N,a69N, and b71R (stabilizing five hydrogen bonds with

the peptide�s backbone), and the differential effects

with a69N, b9W (dimorphic residue that when b9Econtributes to the definition of the polarity of this

pocket in some other class II molecules) and b11Lknown to determine the depth of pocket 6 [45]. In this

pocket the amino acids a62N, a69N present the two

kinds of effects because they are interacting with thebackbone but also with the occupying amino acid

(Fig. 5).

In Pocket 7 a global effect was found on pocket amino

acid a69N (forming two hydrogen bonds with the pep-

tide�s backbone residues), a65V and b11L, and differen-

tial effects on the pocket�s amino acids a69N, b28E, andb61W (the later establishing an hydrogen bond with the

carbonyl atoms of the peptide�s backbone), b67L andb71R (Fig. 6).

Fig. 7 shows the average values of S1 (Eq. (9)) for

Pocket 9. It was once again confirmed that the interac-

tion occurs mainly with some of the pocket�s amino

acids and that there was a global effect on the pocket�samino acid a69N (forming hydrogen bonds with the

peptide�s backbone) and b60Y, and a differential effect

on the pocket�s amino acids a73M, b9W, and b57D,the latter also establishing a hydrogen bond with the

peptide�s backbone (Fig. 7).

Pocket 6. For notation see Fig. 3.

Fig. 6. Average of S1 for amino acids in Pocket 7. For notation see

Fig. 3.

Fig. 7. Average of S1 for amino acids in Pocket 9. For notation see

Fig. 3.

Fig. 8. Average of individual multipolar moments for amino acids in

Pocket 1.


Pocket 4.


Differences for each pocket with individual variables. Indi-

vidual multipoles (q, d, and C) were analyzed regarding

each of the pocket amino acids, observing that the pres-ence of a peptide particularly affected differentially each

of the pocket amino acids with respect to these vari-

ables. There were amino acids presenting large changes

in a particular variable. This is explained in detail for

each pocket in the following section.

Results regarding the average differences for each of

the multipole terms (q, d, and C) in Pocket 1 (Fig. 8)

show the predominant effect on each of the pocket ami-no acids. It can be seen that the leading term is the quad-

rupole moment for aromatic pocket amino acids,

agreeing with the electrostatic nature of aromatic rings.

This confirms the fact that the occupying amino acid

produces different effects on pocket amino acids, depend-

ing on its nature. Fig. 9 shows the average of differences

for eachmultipole moment. In the case of Pocket 4, it was

found that the largest changes were produced in the di-pole moment for amino acids a62N, b26L, and b71R,

as well as in the quadrupole moments of the a62N and

b71R, these two amino acids establishing H-bonds with

the peptide�s backbone. The origin of this change can

be perceived when the electrostatic potential is analyzed,

because there is evidence that some of the atoms become

polarized. For example, the presence of the peptide

makes the asparagine side-chain show strong differences

of electrostatic potential with regard to that of the emptypocket. This can be clearly seen in Fig. 10 where the elec-

trostatic potential for occupied (Fig. 10A) and empty

(Fig. 10B) pocket is shown (the arrows show these strong

modifications according to the electrostatic potential

scale, the figure was constructed with MOLEKEL [46]

upper panel and VMD [47] lower panel).

These effects of charge transfer explain the change in

dipole moment for this amino acid. Similar but weakerelectrostatic differences can be seen for b78Y, b71R (as

pointed out by arrows in Figs. 10A and B), and b79C(not shown in the figure), confirming the two different

effects: the global effect for a62N and the differential ef-

fect for b71R and b78Y. An interaction type p-cationmay be the cause of this charge transfer in b78Y, be-

cause the highest changes are observed when asparagine

or glutamine were the occupying amino acids, whichmay have been interacting through their side chain

amide group. Further studies are currently being carried

out regarding these detailed changes. They are the sub-

ject of a future paper.

Fig. 10. Pocket 4 electrostatic potential of the occupied (A) vs empty Pocket (B). The amino acids with a significant change and the peptide are

indicated with arrows.


Pocket 7.


The changes in each of the multipole terms for this

pocket show that the leading effect in most amino acids

in Pocket 6 concerns the charge, perhaps due to the pres-

ence of a11E and a66D (Fig. 5D), as mentioned before

(Fig. 11).

Differences for each of the multipole terms in Pocket

7 amino acids are presented in Fig. 12. A high predom-

inance of differences in dipole moment in amino acidsb28E and b71R was observed. These two amino acids

were close to each other in a position that could have

been generating a strong induced dipole, due to the

charged nature of their side chains (negative for the glu-

tamic acid and positive for arginine), mediated by the

presence of the peptide that, generally, tends to create

a larger charge delocalization. It has been shown very

recently by X-ray crystallography that b28E, b71R,and a69N establish a hydrogen bond network stabilized

by 4 molecules of water in this Pocket 6/7 area, giving a

pre-eminence to the residues found here and agreeing

completely with our results [35].


Pocket 6.

The observed averages in the differences of individual

multipole terms (q, d, and C) on the pocket�s amino

acids can be seen in Fig. 13. A predominance of the


Pocket 9.


dipole term can be seen on amino acids b60Y and a69Nwhose side chains are directed towards the occupying

amino acid, exhibiting a polarization akin to that

Fig. 14. The figure shows stereo views of the five pockets of HLA-

DRb1*0101. The peptide amino acids are in yellow, with the original

amino acid of HA peptide in red. The pocket�s amino acids that

present a global effect are in purple, and those that display a differential

effect are in pink or blue, accordingly belongs to a or b chain of MHC

molecule.

presented by a62N in Pocket 4. There was a predomi-

nance of charge in amino acid b57D whose side chain

interacted directly with the occupying amino acid

(Fig. 14).

Conclusions

• We have presented a method for theoretically analyz-

ing the interaction between peptides and major histo-

compatibility complex class II interaction based onquantum chemical methods for identifying the elec-

trostatic fields. This approach allows for a determina-

tion of the preference for certain amino acids fitting

into specific pockets, allowing for a more precise

methodology for predicting which amino acids

should fit into which pockets. This method is in good

agreement with experimental data regarding the

order of binding of amino acids to MHC, and allowsus to study this interaction in more detail.

• Ahierarchy regarding the importance ofMHCClass II

HLA-DRb1*0101 molecule pockets has been found,

agreeing with experimentally found values: Pocket

1 � Pocket 4 > Pocket 9 � Pocket 7 > Pocket 6.

• Calculations regarding occupying amino acids similar

to those for the ‘‘ideal’’ ones in each pocket are in

excellent agreement with results found experimen-tally, showing high level of sensitivity in our theoret-

ical approach;

• The interaction in each pocket shows two types of

effects: a global one, presented by those amino acids

from the pocket that interact mainly with the peptide�sbackbone, and a differential effect presented by those

amino acids within a particular pocket specifically

interacting with the lateral chain of the occupying res-idue. The global effect contributes to the docking of the

peptide in the pocket, whereas the differential effect

gives specificity to the pocket and is responsible for

direct interactions with occupying amino acids.

• It is possible to determine the predominating effect in

each pocket and to focus on it for each of the pocket

amino acids, noting whether the interaction is ruled

by changes in charge, in dipole moment or in quadru-pole moment. This leads to the possibility of a

detailed analysis of the interaction that should be car-

ried out further on.

• This is a first approach to the solution of this problem

from the quantum chemistry computational point of

view.

Acknowledgments

The work presented here would not have been possi-

ble without the generous support of the Presidency of

Colombia and the Colombian Ministry of Health.


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Quantum chemical analysis explains hemagglutinin peptide--MHC Class II molecule HLA-DRbeta1* 0101 interactions

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