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Proc. Natl. Acad. Sci. USA
Vol. 96, pp. 8477–8482, July 1999
Biophysics
A systematic study of low-resolution recognition in
protein–protein complexes
ILYA A. VAKSER*
†
,OMAR G. MATAR
‡
, AND CHAN F. LAM
‡
*Department of Cell and Molecular Pharmacology and
‡
Department of Biometry, Medical University of South Carolina, 171 Ashley Avenue,
Charleston, SC 29425
Edited by Peter G. Wolynes, University of Illinois at Urbana-Champaign, Urbana, IL, and approved May 26, 1999 (received for review
April 13, 1999)
ABSTRACT A comprehensive nonredundant database of
475 cocrystallized protein–protein complexes was used to
study low-resolution recognition, which was reported in ear-
lier docking experiments with a small number of proteins. The
docking program
GRAMM was used to delete the atom-size
structural details and systematically dock the resulting mo-
lecular images. The results reveal the existence of the low-
resolution recognition in 52% of all complexes in the database
and in 76% of the 113 complexes with an interface area >4,000
Å
2
. Limitations of the docking and analysis tools used in this
study suggest that the actual number of complexes with the
low-resolution recognition is higher. However, the results
already prove the existence of the low-resolution recognition
on a broad scale.
Protein–protein interactions play a central role in protein
function. Because these interactions are determined by the
structure of the components that form the complex as well as
by the physicochemical properties of the environment, studies
of these factors are important for better understanding of
protein functions and for the subsequent application of this
knowledge to protein engineering and drug design.
Computer modeling makes it possible to perform direct
computational experiments to study fundamental principles of
protein interactions in a way that often would be impossible in
‘‘real’’ experiments. What is the role of the large-scale struc-
tural motifs (e.g., the main-chain fold) in protein recognition?
A direct experiment to determine this role would be to
eliminate the small, atom-size structural elements and test the
recognition properties of the remaining structure. Such an
experiment (1–3) is clearly feasible only computationally (in
silico). Studies of large-scale recognition factors include cor-
relation of the antigenicity of surface areas with their acces-
sibility to large probes (4), role of the surface clefts (5),
automatic binding site identification based on geometric cri-
teria (6, 7), study of the ‘‘low-frequency’’ surface properties
(8), and ‘‘fuzzy’’ binding-site descriptors (9, 10). Several pro-
tein-recognition techniques use smoothed potential functions
(11–14), which effectively are equivalent to the averaging of
the contribution of neighboring atoms and, thus, to the
‘‘smoothing’’ of the local structural elements. Studies of pro-
tein binding (15, 16) and energy landscapes in protein folding
(17) and protein interactions (18, 19) confirm the existence of
nonlocal recognition preferences.
Progress in understanding the principles of protein recog-
nition leads to better computational methods for protein
docking (20–22). The principal drawback of the existing
docking methodologies is sensitivity to structural inaccuracies.
One example of such inaccuracies is conformational changes
upon the formation of the complex (23, 24). A major obstacle
to the docking of protein structures obtained with modeling is
significant errors in these structures (25). This aspect is
especially important in view of the current progress in genome
sequencing. Most of the resulting protein structures will have
to be modeled rather than determined experimentally (26).
Thus, the structure-based functional studies will require com-
putational techniques capable of docking large numbers of
protein models of limited accuracy within reasonable compu-
tational time. In short, the docking methods needed for global,
genome-scale studies have to be fast and have to tolerate
structural inaccuracies on the order of a few angstroms, even
at the expense of substantially lower precision in the docking
results.
The program
GRAMM (1, 27, 28) has been shown to ade-
quately address these issues in a number of tests (2, 24, 29, 30).
The procedure allows docking at variable ‘‘resolutions,’’ de-
pending on the accuracy of the structural components to be
docked. The high-resolution docking yields high-precision
results and is relatively slow (hours of computational time).
The low-resolution docking is fast (several seconds of cpu
time) and may tolerate structural inaccuracies on the order of
7 Å, which is a precision characteristic of many protein models
(31–33). However, it can predict only complex’s gross features,
which may serve as a starting point for a more detailed study.
The essence of the procedure is the reduction of protein
structures to digitized images on a three-dimensional grid. The
structural elements smaller than the step of the grid are not
present in the docking. Thus, the procedure provides a con-
venient tool to eliminate smaller (e.g., atom-size) details. This
feature is the source of tolerance to structural inaccuracies. At
the same time, it makes possible the study of the role of the
low-resolution recognition factors in protein complexes.
The low-resolution recognition was studied earlier with
GRAMM on a limited number of protein complexes (2). The
results show the existence of preferences to the correct struc-
ture of the complex even at the resolution of 7 Å. The limited
number of test cases, however, did not allow broader conclu-
sions to be drawn about the existence of such factors in general.
In the present study, a comprehensive nonredundant data-
base of crystallized protein–protein complexes (I.V. and A.
Sali, unpublished data) was used to determine the existence of
the low-resolution recognition. This database provided an
opportunity for a systematic study of protein recognition by
using structural data presently available for this purpose. All
details smaller than 7 Å were eliminated from the protein
structures.
GRAMM was able to determine the existence of the
low-resolution recognition in 52% of the complexes with
interface area ⬎1,000 Å
2
and in 76% of the complexes with
interface area ⬎4,000 Å
2
. Our inability to detect the low-
resolution recognition in the remaining complexes does not
The publication costs of this article were defrayed in part by page charge
payment. This article must therefore be hereby marked ‘‘advertisement’’ in
accordance with 18 U.S.C. §1734 solely to indicate this fact.
PNAS is available online at www.pnas.org.
This paper was submitted directly (Track II) to the Proceedings office.
†
To whom reprint requests should be addressed at: Department of Cell
and Molecular Pharmacology, Medical University of South Carolina,
173 Ashley Avenue, PO Box 250505, Charleston, SC 29425. e-mail:
vakseri@musc.edu.
8477
mean that these complexes do not have this property. The fact
that
GRAMM, like any other procedure, has limited capabilities
suggests that the actual percentage of complexes with the
low-resolution recognition is higher.
METHODS
The details of the GRAMM docking approach are described in
refs. 1 and 27. The method involves (i) a projection of the two
molecules on a three-dimensional grid; (ii) the calculation,
using Fourier transformation, of a correlation function that
assesses the degree of surface overlap and the penetration on
relative shifts of the molecules in three dimensions; and (iii)a
scan of the relative orientations of the molecules in three
dimensions. The algorithm provides a list of correlation values
that indicate the extent of geometric match between the
surfaces of the molecules; each of these values is associated
with six numbers describing the relative position (translation
and rotation) of the molecules. The procedure is thus equiv-
alent to a six-dimensional search but is much faster by design.
The overlap of the molecular images is equivalent to the
intermolecular energy E calculated with a step-function po-
tential (14).
E ⫽
冘
i,j
E共r
ij
兲, E(r
ij
) ⫽
再
U,0⬍ r
ij
ⱕ R
⫺ 1, R ⬍ r
ij
ⱕ 2R
0, r
ij
⬎ 2R
where E is the energy, U is the height of the repulsion part of
the potential, R is the range of the potential (the grid step), and
r
ij
is the distance between atoms i (receptor) and j (ligand).
Because the molecules are represented by grid images, no
structural details smaller than the step of the grid are taken
into account in the calculations. Thus, in the low-resolution
docking, a sparse grid with ⬇7 Å grid step eliminates all
atom-size details.
RESULTS
Database of Complexes. The database included 475 com-
plexes from the Protein Data Bank (34). A structure was
considered a protein–protein complex if it consisted of more
than one chain of 30 or more residues. For convenience, the
larger and the smaller proteins within a complex were called
‘‘receptor’’ and ‘‘ligand,’’ respectively. The database is nonre-
dundant in that no complex has both the receptor and the
ligand homologous to the receptor and the ligand of any other
complex in the database. The criterion for the homology was
30% or greater sequence identity. The database had 631
complexes with physical contact between subunits. For the
purpose of this study, only 475 complexes with interface area
⬎1,000 Å
2
were taken. The protein pairs with smaller inter-
faces were not considered, in an attempt to minimize the
number of complexes that are artifacts of crystallization and
thus do not reflect biological functions (35–37).
Docking. Docking was performed by using
GRAMM at low
resolution. The procedure implemented an exhaustive grid
search for the ligand–receptor structure matches. The docking
parameters were: step of the grid, 6.8 Å; repulsion part of the
potential, 6.5; and interval for rotations, 20°. For each com-
plex, the 1,000 lowest-energy matches were analyzed. The
values of the parameters were determined earlier (1) as
FIG. 1. Examples of the distribution of ligand positions. Receptors are shown in green and ligands in yellow, in the crystallographically
determined position within the complex. The 100 lowest-energy ligand positions are shown in red. Matches are clustered primarily inside the binding
area (a), inside and outside the binding area (b), outside the binding area (c), and not clustered (d).
8478 Biophysics: Vakser et al. Proc. Natl. Acad. Sci. USA 96 (1999)
quasi-optimal for the low-resolution docking, based on 10
receptor–ligand complexes. These values were obtained by
largely empirical, nonquantitative considerations and were not
optimized or modified in any other way for the criteria used in
the present study.
The nature of the
GRAMM approach dictates that all struc-
tural details smaller than the grid step (in this study, 6.8 Å) are
deleted from the molecular images. It was shown earlier (14)
that the difference between the low- and the high-resolution
docking is that at high resolution, the low-energy positions of
the ligand are dispersed around the receptor (what is usually
referred to as ‘‘the multiple-minima problem’’), whereas at low
resolution they tend to cluster in the area of the global
minimum (the binding site on the receptor). From the point of
view of molecular shape, this effect has to do with smoothing
smaller structural details, so that only the larger ones, usually
associated with the binding site (e.g., deep cavity in the
enzymes active sites) remain and attract ligand matches with
different ligand orientation. From the point of view of the
intermolecular energy, the transition to lower resolution
means an increase in the potential range (14). This leads to a
long-range, ‘‘mean force’’ potential that averages the contri-
butions of multiple atoms. The potential corresponds to a
smoother energy profile that leaves a smaller number of
minima (ideally one), which leads to the clustering of the
ligand positions in these minima (at the binding sites). Exam-
ples of the actual distribution of the ligand positions are shown
in Fig. 1. In many cases, the clustering occurs in the areas that
are not identified in the crystal structures as binding sites.
Presently, it is not clear whether these clusters correspond to
alternative binding sites.
Basic Assumptions in the Analysis of the Results. For the
analysis of the docking results, we calculated the average
distance of each atom from the center of mass for all proteins
in the database. These average distances r
Ri
and r
Li
were
considered, respectively, as the ‘‘radii’’ of the receptor and the
ligand in the complex i. The average values of such radii for all
receptors r
R
and all ligands r
L
were 25 Å and 23 Å, respectively
(Fig. 2). In this study, for simplicity, we analyzed only the
positions of the center of mass of the ligands. The low-
resolution binding site on the receptor was defined as the area
within 10 Å of the position of the ligand’s center of mass in the
crystal structure (Fig. 2).
The output of
GRAMM docking is a list of ligand’s positions
sorted according to the score of the match. The score is
proportional to the surface overlap (1, 27). At the same time,
it is equivalent to the intermolecular energy calculated with a
simplified potential (14). The basis of the analysis of the
docking results was the assumption that if the ligand–receptor
recognition exists, the low-energy matches are more populated
FIG. 2. Idealized representation of proteins. The receptor is shown
in yellow and the ligand in red. Radii are calculated as the average
distance of all atoms in a protein from its center of mass. The radii
shown are the average radii of all receptors and ligands. The binding
region is defined as the area within 10 Å of the crystallographic
position of the ligand’s center of mass and is shown in green.
FIG. 3. Percent of matches inside the binding area according to the energy rank. The percent is based on the inside/total ratio of the matches
of a given rank (see text). Energy rank is accumulated in the histogram in groups of 10. (a) All complexes. (b) Complexes with interface of
1,000–2,000 Å
2
(Top), 2,000–4,000 Å
2
(Middle), and ⬎4,000 Å
2
(Bottom).
Biophysics: Vakser et al. Proc. Natl. Acad. Sci. USA 96 (1999) 8479
in the binding site than the would-be random ones, whereas the
high-energy matches are distributed randomly regardless of
the position of the binding site.
A Trend Toward the Actual Structure of the Complex.
GRAMM performs an exhaustive grid search, which reports all
possible matches (within the accuracy of the grid), and outputs
the list of matches sorted by energy. Thus, the evidence that the
low-energy matches are better represented in the binding site
than the high-energy ones would indicate a preference toward
the actual structure of the complex. If the number of matches
inside and outside the binding site is n
in
and n
out
, respectively,
then the low-energy matches in the binding site are repre-
sented better than the high-energy ones, if n
l
in
/(n
l
in
⫹ n
l
out
) ⬎
n
h
in
/(n
h
in
⫹ n
h
out
), where l is low energy and h is high energy.
Fig. 3 shows the distribution of the percent of matches in the
binding site p ⫽ 100 䡠 n
in
兾(n
in
⫹ n
out
) for the entire database,
according to the energy of the match. The distribution clearly
shows a strong nonlinear correlation of this percent with the
energy, resulting in an inside/total ratio of the low-energy
matches significantly higher than the inside兾total ratio of the
high-energy ones. The other conclusion is that this difference
in the low-energy and the high-energy matches depends on the
area of the interface in the crystal structures (little difference
for smaller interfaces and substantially bigger difference for
larger interfaces).
As shown in Fig. 3, the trend to smaller inside/total ratio of
the higher-energy matches continues through the entire energy
spectrum (only the first 1,000 lowest-energy matches were
analyzed for each complex). To assess the difference in the
low-energy and the high-energy population objectively, it was
useful to find out actually how high the high-energy values are.
Fig. 4 shows a significant correlation between p
l
based on 100
low-energy matches (rank 1–100) and p
h
based on 100 high-
energy matches (rank 901–1,000, highest-energy analyzed).
This indicates that for a number of complexes, the highest-
energy matches analyzed were still clustered in the binding site.
Thus, for such complexes, the rank of the high-energy matches
that are supposed to be distributed regardless of the binding
site could be well beyond the first 1,000.
The Number of Complexes with Low-Resolution Recogni-
tion. The analysis of total values for the entire database reveals
the general character of and trends in the low-resolution
recognition. However, it does not answer one of the most
intriguing questions, i.e., how many protein complexes follow
the low-resolution recognition? Is it a universal feature or does
it apply only to some proteins? To address this question, one
has to look at the distribution of matches in individual protein
complexes. The analysis of individual complexes in this study
was based on an assumption that the absence of the low-
resolution recognition corresponds to a random distribution of
matches in the docking of low-resolution structures. Thus,
detecting a significantly higher than the would-be random
number of matches in the binding site would indicate the
existence of low-resolution recognition.
An important aspect in such analysis is modeling of the
random matches. The number of matches analyzed for each
complex was 1,000, sorted from low to high energy. As shown
FIG. 4. Correlation of the percent of matches inside the binding
area of low-energy (rank 1–100) and high-energy (rank 901–1,000)
ligand positions. The percent values are calculated for every complex
in the database.
FIG. 5. Distribution of complexes according to the percent of
matches inside the binding site. The total number of matches per
complex is 1,000 (a) and 100 (b) (lowest energy matches).
FIG. 6. Percent of complexes with detected low-resolution recog-
nition. (a) All complexes. (b) Complexes with interface area 1,000–
2,000 Å
2
(Left), 2,000–4,000 Å
2
(Middle), and ⬎4,000 Å
2
(Right).
8480 Biophysics: Vakser et al. Proc. Natl. Acad. Sci. USA 96 (1999)
above, the highest-energy matches in this list, although dis-
tributed with smaller than the low-energy ones inside-binding-
site/total ratio, in a number of complexes were still clustered
in the binding area. Thus, they cannot be considered random.
The option for modeling random matches that was found
feasible, although far from being ideal, is based on two
assumptions: first, the proteins may be roughly considered as
spheres, with the radius equal to the average distance of all
atoms from the center of mass (Fig. 2), and second, the random
matches are uniformly distributed around the receptor. In such
case, the area of the binding site is S
b
⫽
䡠10
2
(Fig. 2), and the
total area available for the matches (a match is positioned in
the ligand’s center of gravity) in a complex i is S
ti
⫽ 4
(r
Ri
⫹
r
Li
)
2
. Fig. 2 shows the average values of r
Ri
and r
Li
.Inour
analysis, however, these radii were calculated and taken into
account individually for each complex. The number of sites
with the area equal to that of the binding site is n ⫽ S
ti
兾S
b
. The
probability of K matches in such site (e.g., the binding site)
could be approximated by a Poisson distribution (38), with the
mean number of matches m ⫽ 1,000兾n and SD m
1/2
. The 2-SD
confidence interval (⬇95% interval) is m ⫾ 2m
1/2
. Thus, if the
actual number of matches in the binding site K is larger than
m ⫹ 2m
1/2
, it is significantly larger than the random one and,
consequently, the low-resolution recognition was considered
detected for this complex.
The distribution of complexes according to the percent of
matches in the binding site is shown in Fig. 5. As can be seen,
a significant number of complexes have a very large percentage
of matches in the binding site. At the same time, many
complexes have no matches in the binding site. Both cases
point to the nonrandom character of the match’s distribution.
In the case of no matches at the ligand–receptor interface, the
matches were usually clustered at different sites, which may be
an indication of alternative binding modes. The analysis of
complexes based on the comparison with the distribution of
the random matches (Fig. 6) determined 52% of all complexes
to have the low-resolution recognition property (37%, 52%,
and 76% of complexes with interface area 1,000–2,000 Å
2
,
2,000–4,000 Å
2
, and ⬎4,000 Å
2
, respectively). Obviously, like
any computational approach, both
GRAMM and the analysis
procedure have limitations in terms of the algorithm, imple-
mentation, choice of parameters, etc. Thus, it is unrealistic to
expect detection of all low-resolution recognition cases. The
actual number of such cases may be significantly higher.
However, we presently do not have a better estimate of this
number.
Complexes Without Established Low-Resolution Recogni-
tion. Examples of complexes in which we did not succeed in
detecting the low-resolution recognition are shown in Fig. 7. In
most such cases, the factors that cause fewer matches in the
crystallographically determined binding sites are clear (e.g.,
alternative binding mode, chain interpenetration, nonbinary
complex). A deeper insight into such special configurations of
complexes would allow one to increase the number of detected
low-resolution recognition cases. Such study would require
multiple sets of docking parameters and more sophisticated
analysis tools. At this point, however, we chose a simple
approach, that in a systematic way confirms the existence of
low-resolution recognition on a broad scale and left a more
comprehensive analysis for future study.
CONCLUSIONS
A comprehensive, nonredundant database of cocrystallized
protein–protein complexes was used to study low-resolution
recognition, which was reported in earlier docking experi-
ments with a small number of proteins. The docking program
GRAMM was used to delete the atom-size structural details and
systematically dock the resulting molecular images. Analysis of
the results revealed the following. (i) The distribution of
matches in the entire database showed that inside-binding-
site/total ratio for the low-energy matches is higher than that
for the high-energy matches, indicating the existence of a
general docking preference toward the actual binding mode
FIG. 7. Examples of complexes with and without detected low-resolution recognition. The receptor is shown in green and the ligand in red. All
structures are in the cocrystallized positions. (a) A complex with established low-resolution. Complexes without detected low-resolution recognition:
disordered termini that are part of the interface (b), interwoven chains (c), an alternative binding mode with the subunit identical to the ligand
shown in blue (d), helix bundles with a cylinder-like low-resolution structure (e), and a ternary complex (f).
Biophysics: Vakser et al. Proc. Natl. Acad. Sci. USA 96 (1999) 8481
and, thus, showing the significance of the low-resolution
recognition. (ii) Significantly higher than random number of
matches in the binding area, indicating the existence of the
low-resolution recognition, was detected in 52% of all com-
plexes (in 37%, 52%, and 76% of complexes with interface area
1,000–2,000 Å
2
, 2,000–4,000 Å
2
, and ⬎4,000 Å
2
, respectively).
Limitations of the docking and analysis tools used in this study
suggest that the actual number of complexes with low-
resolution recognition is higher. However, the results already
prove the existence of the low-resolution recognition on a
broad scale.
The authors thank Dan Knapp and John Hildebrandt for reading the
manuscript and for helpful comments. This work was supported by the
National Science Foundation Computational Biology Activities grant
and the South Carolina兾National Science Foundation Experimental
Program to Stimulate Competitive Research Cooperative Agreement.
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