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PROTEINS: Structure, Function, and Genetics 30:249–263 (1998)
Structural Modeling of the Complex Between
an Acetylcholine Receptor-Mimicking Antibody
and Its Snake Toxin Antigen
Catherine Tenette-Souaille and Jeremy C. Smith*
Section de Biophysique des Protéines et des Membranes, DBCM, CEA-Saclay, Gif-sur-Yvette, France
ABSTRACT
The antibody Ma2-3 neutralizes the functional, acetylcholine receptor binding activity of its antigen, neurotoxin a, and
exhibits several other properties in common
with the receptor itself. We present here the
results of calculations examining the threedimensional structure of the toxin a:Ma2-3
complex. The antigen structure, determined by
nuclear magnetic resonance spectroscopy,1 was
docked to models of the variable fragment of
the antibody combining site2 by using a method
based on surface complementarity and maximization of buried surface area3,4 while taking
into account the possibility of conformational
change on complexation. Extensive experimental information on the location of the functional epitope was incorporated into the analysis and used to screen candidate geometries of
the complex resulting from the modeling. Eight
plausible structures that are in accord with
the experimental data were derived. Common
structural features of the models are discussed, and residues of the antibody-combining site that are expected to play important
roles in complexation are identified. In particular, three epitope residues that, according to
mutagenesis experiments, make particularly
strong contributions to the binding, interact
excentrically and do not make contact with the
central loops of the combining site, L3 and H3.
Proteins 30:249–263, 1998. r 1998 Wiley-Liss, Inc.
Key words: antibody-antigen complex; snake
toxin; protein docking
INTRODUCTION
The structural characterization of protein-protein
complexes in general, and antibody-antigen complexes in particular, presents a major challenge to
structural biology. Although hundreds of antibodies
have been sequenced,5 only approximately 60 antibodies and 10 antibodies complexed with protein
antigens have been determined crystallographically,
and the rate that X-ray structures are being solved
lags behind that of sequence generation.6 Among the
reasons for this lag are the time-consuming nature of
the crystallographic process and the fact that the
r 1998 WILEY-LISS, INC.
obtention of crystals suitable for structural analysis
is sometimes not possible. Consequently, there is a
need to develop noncrystallographic methods capable of providing information on the three-dimensional (3-D) structures of antibodies, antigens, and
their complexes.
Among the methods that can be applied are molecular modeling and simulation. Computational methods exist for calculating structures of antibody combining sites, given the primary sequence, and for
determining the structures of protein-protein complexes, given the structures of the isolated proteins.
Some of the methods for combining site modeling use
energy calculations and involve techniques such as
uniform search in internal coordinate space,7,8 random generation of backbone conformations,9 Monte
Carlo simulation,10 and high-temperature molecular
dynamics.11 These methods have provided useful
models in several cases. A procedure combining
energy calculations with screening of the database of
existing structures also has been developed and has
given satisfactory results for the structure prediction
of two antilysozyme antibodies.12 Several methods
for the calculation of protein-protein complex geometries, starting from the structures of the isolated
molecules have been developed13,14 and have succeeded in some cases. Notable among the successes
are those of six groups that accepted a recent challenge to determine the b-lactamase inhibitory protein:TEM-1 b-lactamase association and correctly
predicted the general mode of association.15
Ideally, a combination of the above methods would
enable the structure of any antibody: protein antigen
complex to be derived, given the primary sequence of
the antibody and the 3-D structure of the antigen.
However, no single method of antibody structure or
protein-protein complex structure calculation has
proved to be completely reliable. The combining site
generation methods have modeled the shorter
complementarity determining region (CDR) loops
more accurately than the longer ones, with typical
RMS deviations from crystal structures of approxi-
*Correspondence to: Jeremy C. Smith, Section de Biophysique des Protéines et des Membranes, DBCM, CEA-Saclay,
91191 Gif-sur-Yvette, France.
Received 10 January 1997; Accepted 2 July 1997
250
C. TENETTE-SOUAILLE AND J.C. SMITH
mately 1 Å for the shorter loops but sometimes
greater than 2 Å for the longer ones. Similarly,
protein-protein docking predictions are still fraught
with difficulties, as evidenced by the failure of three
different methods to identify uniquely the pancreatic
trypsin inhibitor:trypsin complex.4,16,17
The chances of successful structure prediction can
be enhanced by incorporating information from experiments that identify residues important for the
binding interaction and thus can be used to screen
candidate structures obtained from the modeling
procedures. This approach is used in this study, in
which we examine the structure of the complex of the
monoclonal IgG2a-k antibody, Ma2-3 with its antigen,
neurotoxin a from Naja nigricollis (Kd 5 1.9 3 1029
M18 ). Toxin a binds to the nicotinic acetylcholine
receptor (AChR), blocking transmission at the neuromuscular junction. Site-directed mutagenesis experiments have defined residues important in binding to
AChR.19 The epitope of Ma2-3 on toxin a has also
been delineated by using nuclear magnetic resonance (NMR) spectroscopy,20 chemical modification,18 and site-directed mutagenesis.21 The functional site and epitope largely overlap. In accord
with this result, it was found that Ma2-3 is a
neutralizing antibody, preventing binding of toxin a
to AChR.21 Ma2-3 also recognizes and neutralizes all
the native short toxins tested.18 These results raise
the question of to what extent, if at all, Ma2-3 might
mimic the AChR cholinergic binding site. This possibility was discussed in recent work that showed that
1) like AChR, Ma2-3 elicits anti-AChR antibodies,
which in turn elicit antitoxin antibodies; 2) the
region 106-122 of the a-chain of AChR shares 66%
primary structure identity with CDR regions of
Ma2-3; and 3) 8 of the 10 epitope residues of the
homologous erabutoxin a also belong to the 10residue epitope recognized by AChR.21
The following data were incorporated in the present docking analysis: 1) the solution structure of the
antigen, toxin a determined by NMR spectroscopy,1
2) the results of extensive modeling of the combiningsite of Ma2-3,2 and 3) the results of three sets of
experiments, performed to map the Ma2-3 epitope:
chemical modification of Lys and Trp residues,18 the
determination, using NMR, of the H-D exchange
rates of labile amide hydrogens in toxin a, free and
bound to the antibody,20 and binding experiments on
site-directed mutants of the homologous erabutoxin
a from Laticauda semifasciata.21
In what follows, the NMR results on the structure
of isolated toxin a and the modeled structures of
Ma2-3 are used as input for an algorithm that
generates protein-protein complexes based on surface complementarity and the hydrophobic effect.3,4
The complexes generated are screened for consistency with the experimental functional epitope mapping data. Eight complexes that satisfy the modeling
and experimental criteria are found. The eight com-
plexes have structural features in common. In particular, the models suggest that the main interactions that determine the binding affinity are made
away from the central loops, H3 and L3.
METHODS
Common properties of antibody-antigen association have been described.22,23 Immune recognition is
based largely on structural complementarity of the
proteins, but conformational changes may take place
on association.24–26 Therefore, the approach used
here is based largely on structural complementarity
but makes some allowance for conformational change.
Input Structural Data
Antigen
NMR work resulted in eight plausible structures
of toxin a.1 The average of these structures was used
as a starting point for this study. This structure was
refined by performing minimizations of the potential
energy of the hydrated toxin, using the program
CHARMM.27 The hydrating water molecules were
generated by solvating the toxin in a large water box
and removing water molecules lying either closer
than 2.6 Å to any heavy atom or farther than 6.0 Å
from all atoms of the protein. In two initial minimizations the water molecules were free to move whereas
the toxin heavy atoms were harmonically restrained
to their initial positions with a force constant of 50,
then 25 kcal · mol21 · Å22. In the third minimization,
the toxin backbone atoms were restrained by a harmonic potential of force constant 5 kcal · mol21 · Å22,
whereas the water molecules and toxin sidechain
atoms were free to move. The eight NMR toxin
structures and the energy-minimized average structure are shown in Figure 1. The polypeptide chain of
the toxin is organized into three adjacent loops
forming a large b-sheet that emerges from a globular
core containing four disulphide bonds. The toxin can
be described as having two opposite faces. The face
closest to the C-terminal loop is slightly convex. The
backbone variation among the eight structures is
very low, whereas side-chain orientations are different in all structures for residues 29–34, corresponding to the tip of loop 2.
Antibody
In previous work, described in detail in Ref. 2,
structural modeling was performed on the isolated
Ma2-3 variable fragment. Three different tried and
tested methods of combining site generation—
uniform conformational sampling,7 high-temperature molecular dynamics,11 and a combined algorithm12—were used with relaxed acceptance criteria
to generate a large number of geometries. These
structures were clustered into 13 classes, from which
four thermally interconvertible conformations were
selected as being most likely to be populated in
solution. In this study, to increase the likelihood of
STRUCTURAL MODELING OF TOXIN a-Ma2-3 COMPLEX
251
TABLE I. List of the Epitope Residues Identified by
Site-Directed Mutagenesis on Toxin a
Gln7
Arg33
Fig. 1. Superposition of the eight NMR structures (fine lines) of
toxin a (PDB code 1NEA1) and the average structure (bold line).
Loops 1, 2, and 3 are from left to right. The concave side of the
protein side faces the viewer. The disulfide bridges are represented with a broken bold trace. The numbering scheme common
to all short snake toxins is used in the present work.
capturing the correct antibody conformation and to
allow for possible conformational changes of the
antibody on complexation, all 13 derived structural
classes were used in the docking calculations with
the antigen.
Epitope mapping
The Ma2-3 epitope on toxin a has been probed
with three sets of experiments:
(1) With the use of affinity chromatography and
proton 2D-NMR spectroscopy, H-D exchange
rates of the labile amide hydrogens of the toxin a
were determined, unbound, and bound to the
antibody.20 Eight amides had a protection factor
larger than 10, a value considered significant
compared with the errors incurred in the exchange measurements. These amides are in Gln6,
Lys15, Lys26, Val28, Ile36, Ile37, and Arg38,
suggesting that the Ma2-3 epitope is localized
largely on loop 2 of toxin a.
(2) Chemical modification of residues in toxin a and
in the homologous erabutoxin a was performed.18
Erabutoxin a is another short curaremimetic
toxin, with primary and tertiary structures very
Lys27
Ile36
Trp29
Glu38
Asp31
Lys47
His32
Ile50
close to that of toxin a.1 Residue 18 is deleted in
toxin a, but this deletion results in only minor
structural differences, far from the functional
epitope.28 The chemical modification experiments, performed on Lys residues 15, 27, 47, and
51 and Trp29, revealed that the sites by which
the toxin binds to Ma2-3 contain at least the two
terminal amino groups at position 27 and 47 and
the indole group at position 29.18
(3) The epitope of erabutoxin a has been subjected to
extensive mutational analysis, with a view to
identifying the residues whose mutations affect
the stability of the protein-antibody complex.21
This strategy has been used in a number of
cases, and the results match structural analyses.29–32 More than 70% of the positions of erabutoxin a have been modified by site-directed mutagenesis and the affinity for Ma2-3 subsequently
determined.19,21 As far as possible, the mutations
were chosen to maximize the change in the
chemical nature of the residues while minimizing the likelihood that structure would change
significantly. Circular dichroism spectra of the
mutants were identical to the native protein.
Moreover, several of the mutants were subjected
to X-ray crystallographic analysis, and no detectable structural change was observed. It was
concluded that substantial differences in binding
affinities were unlikely to be due to structural
changes in the antigen.21
In Ref. 32 it was observed that residues whose
mutations result in more than a tenfold affinity
decrease in a protein-antibody complex belonged to
the epitope identified by X-ray analysis. Mutations
at 10 positions in the erabutoxin led to an Ma2-3
affinity constant ratio between the mutant and native species larger than 10 (see Table I). These
positions are occupied by the same residues in toxin
a, except at position 32 where a histidine is found.
These residues form a contiguous surface on the
concave face of the toxin, shown in Fig. 2. The three
residues identified by chemical modification in Ref.
18 were included among the 10 identified by mutagenesis. The surface area covered by the identified
epitope is approximately 700 Å2, a value comparable
with other protein-protein complexes.22
The observed affinity constant decreases were
higher than 500-fold in three cases: Gln7, Trp29, and
Glu38, with two mutations of Glu38 leading to
decreases of nearly four orders of magnitude, corresponding to decreases of nearly 5 kcal/mol in the
252
C. TENETTE-SOUAILLE AND J.C. SMITH
A
Fig. 2. Epitope of toxin a. A: Residues
identified by chemical modification, NMR spectroscopy, and site-directed mutagenesis are
numbered. B: Space-filling model of toxin a
with, in green, functional epitope identified by
site-directed mutagenesis.
B
STRUCTURAL MODELING OF TOXIN a-Ma2-3 COMPLEX
Fig. 3.
253
Definition of the six coordinates defining the relative positions of the two proteins.
dissociation free energy. These three residues are
spatially close to each other, forming a compact
cluster. Presumably, Gln-7, Trp-29, and Glu-38 form
an ‘‘energy core’’ for interaction of Ma2-3 with the
toxin. This is in accord with several experimental
and theoretical studies on protein-protein interactions that suggest in many cases of protein-protein
recognition a limited number of core residues, three
or four, contribute the major part of the affinity.30,33–38
Docking Procedure
The algorithm used to dock the proteins was that
of Refs. 3 and 4. It is based on low-resolution shape
complementarity and buried surface area considerations. Both molecules are considered as rigid bodies, and each amino acid is represented as a sphere,
placed at the side-chain centroid. The relative position of the two molecules is described by six degrees
of freedom: five angles and one distance (see Fig. 3).
For each geometry generated, an energy, EB, is
calculated by using the equation EB 5 E* 2 gB*. E*
represents molecular overlap. 2 gB* represents the
hydrophobic free energy due to burial of the surface
area B*. B* is estimated with an analytical approximation.39 The constant, g is taken equal to 50
cal/mol · Å2.4
This initial positioning algorithm is low resolution
in that the residues are treated as spheres. Consequently, although the backbone geometry is expected
to significantly influence the results of these calculations, side-chain conformation is expected to be less
important. The backbone tracing of the antigen
shows little variation among the eight NMR-derived
geometries (see Fig. 1). Therefore, to reduce the
combinatorial computational load, only the minimized average NMR structure of the antigen was
used in all calculations. However, the 13 modeled
antibody structures do manifest backbone conformational variations.2 Each of these structures was
considered a priori to be equally likely to exist in the
complex, and all were included in the docking. The
same docking protocol was followed by using each of
the 13 isolated Ma2-3 models. The toxin a was
roughly positioned above the combining site of each
Ma2-3 model, and geometries of the complex were
produced in two ways: by uniform sampling (with a
grid size of 10°) and by using Monte Carlo calculations, as described in Ref 4.
First screening and clustering
More than 3 3 106 solutions were obtained. These
were subjected to two screening and clustering procedures. In the first, orientations yielding values of B*
254
C. TENETTE-SOUAILLE AND J.C. SMITH
greater than 1200 Å2 were sorted according to EB and
clustered: solutions were considered to belong to the
same cluster if their latitude and longitude values
were within 5° of the average orientation of the
cluster and their spin angles x differed by less than
10°. The geometry with minimum energy EB within
each cluster was retained for subsequent analysis.
In the majority of crystallographic antibodyprotein antigen complexes five of the six CDR loops
make contact with the antigen. Therefore, solutions
were retained for which all 10 experimentally identified toxin epitope residues make contact with the
antibody, and at least five of the six hypervariable
loops make contact with the toxin. To determine the
contacts, the surface accessibilities of each of the 10
residues defining the functional epitope and all
residues from the combining site were calculated. A
relaxed criterion was used because the side-chain
positions had not been optimized: residues were
considered as participating in the interface if their
accessible surface area in the isolated protein was
reduced by at least 20% in the complex. For each
retained model, the surface area buried at the toxin
a-Ma2-3 interface was recalculated, at atomic detail,
with the Lee and Richards algorithm40 using a probe
radius of 1.4 Å.
Second clustering and screening
The retained solutions were clustered further to
group together models with similar toxin orientations but different antibody structures. Solutions
with latitudes and longitudes within 10° were clustered together. Two quantities were calculated and
used to choose a representative structure from each
cluster. One of these was the energy EB. The other is
a low-resolution, short-range scoring function for
electrostatic complementarity, Eel, calculated by representing the residues with the same, simplified
model that was used during the docking procedure,41
i.e., as spheres of radii ri centered at a distance Ri
from their corresponding Ca atoms. Eel is the sum
over the interface of terms Ei,j, between residues i
and j, given by:
5
0
Ei j 5 I(i, j )
di, j
if
di, j $ (ri 1 Ri ) 1 (rj 1 Rj ) 1 d
if
di, j , (ri 1 Ri ) 1 (rj 1 Rj ) 1 d
where di,j is the distance between the Ca atoms. The
interaction matrix, I(i,j) is given in Table II. To
soften the positional dependence of the function, the
distance allowance was increased by d 5 1.0 Å.
Twenty structural families were obtained at this
stage. The energies EB and Eel were calculated for
each model. Thirteen of the 20 families contained
more than one model. In 11 of these the same model
possessed the minimum value of both energies, and
this model was selected for further refinement. For
each of the other two groups, the complex was
TABLE II. Matrix Used for the Electrostatic
Interaction Calculations
Positive
Negative
Polar
Apolar
Positive*
Negative†
Polar‡
Apolar§
110
210
110
210
210
210
0
0
0
0
*Lys, Arg.
†Asp, Glu.
‡Asn, Gln, Ser, Thr, Tyr, His.
§Ala, Cys, Ile, Val, Phe, Gly, Leu, Pro, Trp, Met.
TABLE III. Results of the Docking Calculations
Between Toxin a and the 13 Antibody Fv Models
Antibody
1
2
3
4
5
6
7
8
9
10
11
12
13
Total
B* .1200 Å2
Clustering*
Filtering†
2974
3079
3005
3620
3324
3361
3582
3423
2969
3558
2751
3114
2892
41,585
127
117
129
136
132
117
119
129
125
115
119
134
114
1613
6
4
9
0
5
1
1
0
1
8
4
5
7
51
*Number of clusters.
†Number of solutions in which at least 5 Ma2–3 CDRs and the
10 functional epitope residues participate in the interface.
retained that possessed the largest energy gap with
the second-lowest energy complex for that criterion
for which it had the lowest energy. CDR loops L1 and
H2 were in poor, unusual conformations in certain of
the models of the isolated antibody generated in the
previous work.2 Models of the complexes in which
these loops remained solvent exposed, and thus
probably flexible, were retained. Two of the 20
models, in which loops in unusual conformations
made significant contacts with the toxin, were rejected.
Refinement of the atomic-detail models
In the final stage of the calculations the interface
side chains of the 18 remaining models were positioned by using energy minimization and molecular
dynamics calculations with CHARMM, parameter
set 22. In these calculations all residues farther than
11 Å from the interface were kept fixed. Side chains
of all residues having at least one atom less than 9 Å
from an atom of the other molecule were free to
move. A soft harmonic constraint was applied to the
main-chain atoms of these residues and to all atoms
of residues between 9 and 11 Å from the interface.
Three consecutive molecular dynamics calculations
were performed for each of the 18 models. In the
STRUCTURAL MODELING OF TOXIN a-Ma2-3 COMPLEX
Fig. 4.
255
Distribution of the angular parameter values of the 51 selected orientations.
first, the toxin was translated 2 Å away from Ma2-3
along the axis between the molecular centers of
mass. In the second and third, the toxin was translated back to its initial position in successive 1-Å
steps. In each of the three runs 200 steps of steepest
descent minimization was performed followed by
heating to 400 K in 2 ps and finally running 5 ps
further molecular dynamics without temperature
control. Subsequently, the system was relaxed by
cooling to approximately 0 K in 2 ps and energy
minimized with the Adopted Basis Set Newton Raphson algorithm in CHARMM.
Several properties of the resulting atomic detail
models were examined. Among these were the antigen-antibody interaction energies, calculated as the
sum of van der Waals and electrostatic energies of
the CHARMM potential function. Another energy
also was evaluated, DGAT, which estimates the solvation free energy of the complex, i.e., the free energy
in transferring the complex from solution to the gas
phase. DGAT was calculated by using the empirical
relation of Eisenberg and McLachlan42: DGAT 5
oN
k51DskAk where where Dsk is the solvation parameter and Ak the accessible surface area of atom k. The
atomic solvation parameters used were those in Ref.
43.
RESULTS AND DISCUSSION
Generation and Preliminary Screening
of Models
In Table III are listed the numbers of complexes
with B* greater than 1200 Å2 for each of the 13
antibody models, together with the numbers of complexes retained after the first clustering and screen-
256
C. TENETTE-SOUAILLE AND J.C. SMITH
TABLE IV. Number of Residues of Each Antibody
CDR* in Contact With a Toxin Residue. Models With
5 or 6 CDRs Contacting Are in Boldface
Complex
L1
L2
L3
H1
H2
H3
Total
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
3
6
3
4
4
2
1
1
0
4
3
2
0
0
0
0
0
0
7
0
0
0
0
4
7
5
1
4
1
7
6
5
5
0
3
6
1
2
2
3
5
1
1
1
3
4
3
1
0
0
1
3
0
1
1
3
1
1
0
2
1
1
3
1
2
1
2
2
2
3
3
2
0
6
7
3
1
0
0
1
6
4
8
0
1
1
0
8
2
0
8
3
2
2
2
8
5
7
6
5
4
4
6
6
6
4
7
6
20
20
15
13
13
17
15
16
19
22
21
15
15
14
14
18
15
15
*CDR limits are those used for the Fv modeling.2
ing procedure. This procedure resulted in the elimination of approximately 99% of the solutions with B*
greater than 1200 Å2, leaving 51 models. Figure 4
shows the distributions of the relative orientations of
the molecules in these 51 models. The f1, f2, u1, and
u2 values are distributed relatively narrowly, whereas
the spin angle x is dispersed, with only one region,
[230°:60°], being relatively unpopulated. This reflects the fact that, although the proximity of the
epitope to the combining site is known, the relative
orientation is not. The second clustering, performed
without differentiating between antibody models,
led to 20 families containing between one and eight
members. Representative structures were chosen
from each family, as described in Methods, leaving
18 retained solutions.
Analysis of the 18 Selected Complexes
The 18 models were refined at atomic detail by
using energy minimization and molecular dynamics
calculation as described in Methods. The resulting
structures were analyzed to characterize features in
common.
The paratope
A list of intermolecular contacts made by each
Ma2-3 CDR in each side-chain refined model is given
in Table IV. Figure 5 shows the number of times each
Ma2-3 residue contacts the antigen, summed over
the 18 refined models. The total number of residues
making contact in each model varies from 13 to 22,
distributed over 4–6 CDRs. In 18 of the 20 models
most of the contacts are found to involve only one or
two CDRs, the exceptions being models 4 and 10.
Loop H3 was contacting in all 18 models and H1 in
all but one of them. The other loops, L1, L2, L3, and
H2, are less frequently implicated, making contacts
in 7, 5, 3, and 6 models, respectively. Figure 6 shows
a view from above the Ma2-3 combining site. The
accessible surface area of loop L3 is approximately
250 Å2, small compared with that in the only other
crystallographic structure with an eight-residue L3
loop: HyHEL5 (430 Å2 ).44 The relatively low accessible surface area of this loop is consistent with it
forming part of the paratope in only 3 of the 18
models of the complex.
Those residues of any given CDR making contact
with the antibody are mostly the same ones in each
model. For the central loops, L3 and H3, these are
the residues most exposed to solvent.2 In loop L1,
AsnL31 and its adjacent environment make contact,
and in loop H1 the segment H31-H33 makes contact.
In the models in which L2 and H2 make contact,
almost all the residues participate approximately
equivalently.
Framework residues also make a number of contacts with the toxin, between 1 and 12 depending on
the model. The framework residues most frequently
implicated are TyrL49, the region between loops L1
and L2 around TyrL67, the N-terminal segment of
the VH domain, and the region H26-H30, near loop
H1. H26-H30 form the loop joining CDR H1 with the
preceding b-strand: these residues belong to the
hypervariable region H1 defined by Chothia and
Lesk.45 All of the above framework regions are near
the combining site and have been found to participate in antigen interactions in complexes with known
structures.
Antibody-combining sites are often rich in aromatic residues, particularly Tyr and Trp.23,46 In the
Ma2-3 modeling there was a ring of Tyr residues of
approximately 15 Å diameter at the top of the
combining site, encircling H3. Two framework residues, TyrL49 and TyrL67, are part of this ring and
make contact with the antigen in some of the models.
The hypervariable loops contribute the other five Tyr
residues of the ring: L50 (loop L2), L92 (loop L3), H32
and H33 (loop H1), and H52 (loop H2). One Trp (H50)
is also nearby. These residues frequently make contacts with the antigen in the models.
The epitope
The experimental mapping of the epitope on the
toxin has shown that at least 10 of its residues
contribute significantly to the interaction with Ma2-3.
Figure 7 shows the number of contacts made by each
toxin residue, again summed over all 18 refined
complexes. The 10 identified functional epitope residues are those most frequently implicated, together
with Thr45. Six other residues make contact with
the antibody in at least 9 of the 18 models. Six of the
seven not previously identified residues are on the
same face of the toxin as the identified functional
epitope residues: Asn5, Gln10, and Lys15 in loop 1;
STRUCTURAL MODELING OF TOXIN a-Ma2-3 COMPLEX
257
Fig. 5. Number of contacts made by the Ma2-3 residues with toxin a in the 18 selected models.
Limits of the CDRs are indicated by a bold trace.
Tyr25 in loop 2; and Pro44 and Thr45 in loop 3 (see
Fig. 3). The seventh, Gly49, is at the top of loop 3.
Apart from Lys15 = Ala, mutations of these residues
did produce affinity constant decreases relative to
the native protein, although the changes observed
(DKd , 6.0 nM) were not sufficiently large to warrant inclusion in the epitope based on the mutational
data alone.21
Selection of Eight Final Models
The docking energies, EB, and electrostatic energies, Eel, of the 18 complexes, calculated at low
resolution, i.e., with the residues modeled as spheres,
prior to the molecular dynamics side-chain positioning, are listed in Table V, together with their buried
surface areas calculated at atomic detail. EB varies
from 285 to 260 kcal · mol21, Eel from 2105 to 245
kcal · mol21 and the buried surface area from 1450 to
2350 Å2. EB and Eel were uncorrelated with the
surface area (data not shown), and the minimum
value of each property was found in different complexes.
Atomic detail properties of the 18 side-chain optimized models are given in Table VI. The buried
surface areas calculated at atomic detail are significantly smaller than those calculated at low resolution (listed in Table V), and the values calculated
with the all-atom model are approximately 10%
larger than with the heavy atom representation.22
For all but one model (complex 5), the heavy-atom
buried surface areas are in the interval seen experimentally (1600 6 350 Å2 ). For this, and other reasons stated below, complex 5 was eliminated from
the list of candidate models.
The antibody-antigen interaction energies vary
considerably among the complexes, from 2324.9
kcal · mol21 (complex 12) to 2119.2 kcal · mol21 (complex 5), but the solvation free energies less so, from
557.7 kcal · mol21 (complex 10) to 482.1 kcal · mol21
(complex 12). The buried surface area is roughly
proportional to DGAT and roughly inversely proportional to Eint (data not shown). As a consequence of
this and the fact that the interaction and solvation
energies cannot simply be summed, the models
cannot be ranked on a single energy scale. Discrimination between the models using the atomic detail
criteria in Table VI is thus difficult.
The energy minimization and molecular dynamics
procedures were accompanied by small structural
rearrangements. These, together with examination
of the complexes at finer detail, led to the rejection of
several complexes due to the absence of contacts by
critical epitope residues. The contacts made by the
functional epitope toxin residues in each of the
258
C. TENETTE-SOUAILLE AND J.C. SMITH
Fig. 6. Space-filling representation of the Ma2-3 combining site (framework, light gray; L1,
magenta; L2, cyan; L3, blue; H1, orange; H2, yellow; H3, red).
TABLE V. Fv Model, Interaction Energy EB,
Electrostatic Term Eel Calculated at Low
Resolution, and Buried Surface Area Calculated
With an All-Atom Representation, of the 18 Models
of the Complex Obtained After Clustering
and Screening
EB
Eel
BSA*
Complex Antibody (kcal · mol21) (kcal · mol21) (Å2)
Fig. 7. Number of contacts made by the toxin residues with the
antibody in the 18 selected models. Residues of the functional
epitope are in bold.
models are listed in Table VII. Table VII permits the
elimination of five models: 3, 7, 5, 10, and 17, for
which residues strongly implicated in the functional
epitope do not interact with the antigen. In models 3
and 7, Glu38 does not interact with the antibody and
in models 5 and 10 Gln7 does not interact. The
experimental mutagenesis data indicate that the
contribution of these residues to the binding to
Ma2-3 is critical,21 and it is probable that they make
direct contacts. Similarly, model 17 was rejected due
to the absence of a contact between Ile50 and Ma2-3.
For models 12 and 13, in which functional epitope
residues Ile50 and Asp31 are listed in Table VII as
not contacting the antibody, the cavities between
these residues and the antibody were significantly
smaller than a water molecule, and these models
were thus retained. In complex 5 residue Lys47, at
the periphery of the epitope, is unable to make
contact with the antibody, providing yet another
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
1
1
1
2
2
3
3
3
5
5
7
10
10
10
12
12
13
13
271.8
268.7
264.3
265.3
261.5
274.7
273.0
261.8
267.1
264.8
264.8
277.4
270.6
267.4
282.7
274.3
273.1
269.9
278.6
260.6
266.0
268.9
281.7
247.6
262.4
257.1
2101.5
281.1
276.7
264.2
282.7
288.5
273.0
296.9
273.3
273.4
2031
2055
1921
1955
1493
2182
2177
1816
1886
1812
2259
2301
2297
2171
2167
2041
2250
2250
*BSA, buried surface area.
reason to reject this model. Models 5 and 13–18
involve contacts with less than 5 CDRs and were
eliminated on this basis.
The eight remaining models are shown in Figure
8. In the functional epitope-mapping experiments
STRUCTURAL MODELING OF TOXIN a-Ma2-3 COMPLEX
259
TABLE VI. Properties of 18 Models of Ma2–3-toxin a Complex After MD Refinement
Complex
BSA*
(Å2)
Eint†
(kcal · mol21)
DGAT
(kcal · mol21)
Contact
residues‡
Hydrogen
bonds§
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
1933 (1804)
1997 (1749)
1893 (1656)
1725 (1483)
1338 (1162)
1988 (1816)
2022 (1862)
1622 (1473)
1614 (1493)
1940 (1749)
2074 (1825)
2114 (1903)
2118 (1983)
2172 (1943)
1925 (1716)
1817 (1695)
2161 (1945)
2078 (1839)
2286.1
2251.1
2210.9
2195.4
2119.2
2226.2
2285.2
2194.6
2232.5
2256.0
2251.0
2324.9
2195.8
2271.1
2193.2
2205.3
2263.9
2182.1
2518.7
2501.9
2510.0
2527.0
2554.0
2519.3
2507.4
2540.9
2549.7
2557.7
2504.8
2482.1
2488.9
2503.8
2488.4
2502.9
2510.8
2511.3
18 1 26
22 1 23
17 1 19
18 1 19
9 1 14
22 1 24
25 1 24
14 1 20
16 1 21
15 1 25
21 1 26
21 1 24
20 1 22
24 1 26
20 1 23
20 1 19
23 1 23
19 1 23
16
14
10
13
4
12
15
12
14
13
10
18
7
12
10
6
11
12
*Surface area buried at the interface, calculated with an all-atom representation. The value in brackets
was calculated with the heavy atoms only.
†Interaction energy calculated as the sum of the intermolecular van der Waals and electrostatic terms.
‡Number of toxin and Ma2–3 residues that make a contact across the interface. Two residues are
considered in contact if at least one pair of heavy atoms is at a distance less than the sum of their van der
Waals radii plus 0.5 Å.
§Number of interface hydrogen bonds, identified with QUANTA,48 with a maximal distance between the
acceptor and the donor of 3.5 Å and a maximal angle X-A . . . D of 110°.
TABLE VII. Description of the Contacts Made by the Functional Epitope Toxin Residues
Complex
Gln7
Lys27
Trp29
Asp31
His32
Arg33
Ile36
Glu38
Lys47
Ile50
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
h
h
v
h
—
h
h
h
h
—
h
h
h
h
v
v
h
h
h
h
h
h
v
h
h
h
h
h
h
h
v
h
h
h
h
h
h
v
h
v
v
v
h
v
h
h
v
v
v
h
h
v
h
v
h
h
v
h
h
v
h
h
h
h
h
h
—
h
h
h
h
v
v
h
v
v
h
h
h
h
h
v
v
h
v
h
v
v
v
v
h
h
h
v
h
h
h
h
h
h
h
h
h
h
h
h
h
h
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
h
h
—
h
h
h
—
h
h
h
h
h
h
v
v
h
v
h
h
h
h
h
—
h
h
h
h
h
h
h
h
h
h
h
h
h
v
v
v
v
v
v
v
v
v
v
v
—
v
v
v
v
—
v
h, hydrogen bond; v, van der Waals contact; —, no contact. Most satisfactory models are in boldface. See footnotes of Table VI.
three residues were found to have an affinity constant decrease on mutation greater than 500: Gln7,
Trp29, and Glu38. These large changes suggest that
these three residues might form the energy core of
the interaction with the paratope. Glu7 and Glu38
are indeed found to make hydrogen bonds with the
antigen in all of the models, although their paratope
partner residues vary according to the model. Trp29
hydrogen bonds in only two complexes. The energy
core residues did not interact with the central CDR
loops L3 and H3 in any of the models. The absence of
an L3 interaction is probably related to the relatively
low accessible surface area of this loop. H3 does
make contact with the antigen in all models (see
Table IV) but never with the energy core residues.
This may be due to the fact that, in the isolated
260
C. TENETTE-SOUAILLE AND J.C. SMITH
Fig. 8. Views of the eight final models for the complex. The color scheme for the space-filling representation of the antibody is given in
Figure 6. The toxin backbone is represented as a green wire. The numbering of the complexes corresponds to Tables 4–7. Top panel: top
left, complex 1; top right, complex 2; bottom left, complex 4; bottom right, complex 6. Bottom panel: Top left, complex 8; top right, complex 9;
bottom left, complex 11; bottom right, complex 12.
STRUCTURAL MODELING OF TOXIN a-Ma2-3 COMPLEX
antibody models, the most accessible segment of loop
H3 (H101–H104) contains small residues with poor
hydrogen-bonding capabilities, Gly-Ala-Thr-Ala. This
is in contrast with other antibodies where large
residues such as aromatics or charged residues are
commonly found in this segment.46
One or two salt bridges are found in each of the
models of the complex. The Ma2-3 CDR loops contain
three positively charged residues: LysL24, ArgL54,
and LysH59. All three are surface exposed in the
models derived for the isolated antibody-combining
site but are not near the top of the combining site.
Residues located at these positions in the sequence
rarely have been involved in direct interactions with
antigens in known complexes.46 Although LysL24
does not interact with the antigen in any of the
models, the possibility that the other two residues do
interact cannot be completely excluded from the
present modeling, because ArgL54 makes contact in
three models and LysH59 in one.
AspH31 is the only negatively charged residue
mostly accessible to solvent in the models of isolated
Ma2-3. This residue makes hydrogen bonds to the
antigen in six of the eight models, and four of these
are salt bridges (with either Lys15 or Lys47). The
three other negatively charged residues, AspL32,
AspL91, and AspH108, are mostly buried in the
isolated antibody models (relative accessibility to
solvent ,0.2) and form intraprotein hydrogen bonds.
However, the models of the isolated antibody do not
exclude the interaction of these residues with the
antigen, and AspL32 and AspL91 are in positions in
the sequence that interacts with antigen in some
known complexes.46 AspL32 bonds to hydrogen in
three of the eight models, AspH108 in one, and
AspL91 in none.
CONCLUSION
Ma2-3 has so far resisted all attempts at crystallization, either with or without its antigen. However,
this study illustrates how, in the absence of crystallographic data, the combination of molecular modeling
with experiment can lead to progress in the understanding of the 3-D structural properties of an
antibody-antigen complex. Eight models of the toxin
a-Ma2-3 complex were selected from a starting set of
3 3 106 generated configurations, based on surface
complementarity, buried surface area, and consistency with extensive epitope mapping data. The
eight models show certain common characteristics.
In particular, they possess the property that the
three residues that, according to site-directed mutagenesis experiments, are most strongly implicated in
the binding do not interact with the central loops H3
and L3.
The problem of how to choose between generated
models of a protein-protein complex is particularly
261
difficult. One is confronted with the fact that no
particular energy or scoring scale has proved to be
completely reliable. This difficulty will be lessened
no doubt as computational power increases and our
understanding of the basic chemical principles of
molecular association improve, and the development
of reliable methods for predicting the structure of
antibody combining sites and their antigen complexes is clearly of fundamental as well as practical
interest. In the meantime we have adopted an
approach in which the model building is guided by
energetic considerations, but relaxed acceptance criteria are used to take into account the uncertainties
involved. This reduces the chance that the correct
complex geometry will escape the screening. However, it requires the use of other assumptions to
grade the quality of the models. These were based on
experiment and assumed that those 10 residues
identified as being part of the functional epitope are
actually in contact with the antibody and that at
least five of the six CDR loops of the antibody are in
contact with the antigen. Although these assumptions hold in most cases, they are not 100% reliable.
Consequently, to examine the reliability of the models proposed and to distinguish between them will
require further experimentation.
Crystallization attempts for the complex and the
isolated antibody are being pursued. However, less
direct experiments also can be performed, involving,
for example, site-directed mutagenesis of the antibody. In particular, mutations of those regions of the
CDRs that are predicted to be in contact with the
antigen can be made and antigen-binding affinities
assessed. Mutations of the ring of Tyr residues (into
Phe and Ser, for example) would provide useful
information. Among the charged residues, ArgL54
and AspH31 are the most solvent accessible and are
the closest to the center of the combining site.
Mutation of AsnL31 would allow the role of loop L1 to
be examined and SerL52, AlaH54, and SerH55 would
test loops L2 and H2. These experiments should
permit the elimination of some of the models and are
now in progress.47
ACKNOWLEDGMENTS
We thank our colleagues at the Département
d’Ingénierie des Protéines et des Membranes, CEASaclay, for having stimulated our interest in this
project, for numerous discussions, and for performing complementary experimental work. We thank in
particular Karine Janon, Sophie Zinn-Justin (who
also provided assistance with the graphics), Frédéric
Ducancel, and André Ménez.
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