Global view of the protein universe
, Nir Ben-Tal
, and Rachel Kolodny
Department of Computer Science and Engineering, Polytechnic Institute of New York University, Brooklyn, NY 11201;
Department of Biochemistry and
Molecular Biology, George S. Wise Faculty of Life Sciences, Tel Aviv University, Ramat Aviv 69978, Israel; and
Department of Computer Science, University of
Haifa, Mount Carmel 31905, Israel
Edited by Barry Honig, Howard Hughes Medical Institute, Columbia University, New York, NY, and approved July 2, 2014 (received for review
February 24, 2014)
To explore protein space from a global perspective, we consider
9,710 SCOP (Structural Classification of Proteins) domains with up
to 70% sequence identity and present all similarities among them
as networks: In the “domain network,”nodes represent domains,
and edges connect domains that share “motifs,”i.e., significantly
sized segments of similar sequence and structure. We explore the
dependence of the network on the thresholds that define the
evolutionary relatedness of the domains. At excessively strict
thresholds the network falls apart completely; for very lax thresh-
olds, there are network paths between virtually all domains. In-
terestingly, at intermediate thresholds the network constitutes
two regions that can be described as “continuous”versus “dis-
crete.”The continuous region comprises a large connected compo-
nent, dominated by domains with alternating alpha and beta
elements, and the discrete region includes the rest of the domains
in isolated islands, each generally corresponding to a fold. We also
construct the “motif network,”in which nodes represent recurring
motifs, and edges connect motifs that appear in the same domain.
This network also features a large and highly connected compo-
nent of motifs that originate from domains with alternating alpha/
beta elements (and some all-alpha domains), and smaller isolated
islands. Indeed, the motif network suggests that nature reuses
such motifs extensively. The networks suggest evolutionary paths
between domains and give hints about protein evolution and the
underlying biophysics. They provide natural means of organizing
protein space, and could be useful for the development of strate-
gies for protein search and design.
protein cooccurrence networks
protein similarity networks
How are proteins related to each other? Which physico-
chemical considerations affect protein evolution and how?
A global view of the protein universe may shed light on these
fundamental questions. It could also suggest new strategies for
protein search and design (1–3). However, forming a global
picture of the protein universe is difficult because we have to
piece it together from the many local glimpses that our empirical
data and computational tools provide. In other words, a global
picture needs to portray the relationships among all proteins, yet
we only have evidence of such relationships among several pro-
teins, based on the similarity between their sequences, structures,
and functions. The considerable size of the Protein Data Bank
(4) also complicates this task.
In particular, an intensely debated question is whether protein
space is “discrete”or “continuous”(2, 3, 5–10). These terms are
loosely defined. Discrete implies that the global picture consists of
separate, island-like, structural entities. In the hierarchical protein
domains Structural Classification of Proteins (SCOP) (11) these
entities are termed “folds,”and in the CATH database (12) they
are called “topologies.”Alternatively, “continuous”implies that
the space between these entities is generally populated by cross-
fold similarities (e.g., refs. 2, 5, 6, 9, 13–15). If such similarities are
abundant, then one must account for them when organizing and
searching proteins (5, 8, 16). In support of the abundance of such
similarities is the remarkable success of structure prediction
methods that piece together predictions of protein fragments or
larger protein segments (e.g., ref. 17).
There are different approaches to forming a global view of the
protein universe (18). The most significant efforts are the ones
embodied in the hierarchical classifications CATH and SCOP.
However, a hierarchy implicitly assumes that there are isolated
regions in protein space. An alternative approach is to study the
protein universe via maps––where domains are represented by
points in two or three dimensions, placed so that the distances
between them depend on the dissimilarity between their corre-
sponding domains (e.g., refs. 19–21). By coloring the points
according to domain characteristics, one can visually identify
global properties of the protein universe (19, 20). However, a map
representation in low-dimensional Euclidean space implicitly
suggests that similarity among domains is transitive (i.e., that
similarity within the pairs AB and BC implies that AC is similar
too); we know that this is often not the case (6). Finally, a third
approach to study protein space is via similarity and cooccurrence
networks. In similarity networks, nodes typically represent protein
domains and edges connect similar domains. Several successful
studies of protein space capitalize on such networks (22, 23).
Cooccurrence networks of protein domains, in which nodes rep-
resent domains and edges connect cooccurring domains, were also
studied to better understand protein evolution (24–26).
Here, we study the global nature of the protein universe using
domain and motif networks (Fig. 1). To construct these net-
works, we identify evolutionary relationships among a represen-
tative set of SCOP domains; we relate two domains if they share
a significantly sized part (denoted motif) with similar structure
and sequence. Our analysis reveals that protein space is both
discrete and continuous: SCOP domains of the all-alpha, all-
beta, and alpha +beta classes, in which alpha and beta elements
do not mix, mostly populate the discrete parts, whereas alpha/beta
To globally explore protein space, we use networks to present
similarities among a representative set of all known domains.
In the “domain network”edges connect domains that share
“motifs,”i.e., significantly sized segments of similar sequence
and structure, and in the “motif network”edges connect re-
curring motifs that appear in the same domain. The networks
offer a way to organize protein space, and examine how the
organization changes upon changing the definition of “evolu-
tionary relatedness”among domains. For example, we use
them to highlight and characterize the uniqueness of a class of
domains called alpha/beta, in which the alpha and beta elements
alternate. The networks can also suggest evolutionary paths be-
tween domains, and be used for protein search and design.
Author contributions: N.B.-T. and R.K. designed research; S.N. and R.K. performed re-
search; N.B.-T. and R.K. analyzed data; and N.B.-T. and R.K. wrote the paper.
The authors declare no conflict of interest.
This article is a PNAS Direct Submission.
Freely available online through the PNAS open access option.
To whom correspondence may be addressed. Email: firstname.lastname@example.org or
This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.
August 12, 2014
domains, with alternating alpha and beta segments, mostly pop-
ulate the continuous ones. We also find that recurring motifs are
very abundant; the motifs from the all-alpha and alpha/beta
domains are the more abundant, and the more gregarious ones.
We align all-versus-all in a set of 70% sequence nonredundant
SCOP v.1.72 domains (11) using the structural aligner SSM (27).
For each pair of aligned domains, we calculate the length of the
aligned region, the percent sequence similarity of aligned residues
(using the BLOSUM62 substitution matrix), and the root-mean-
square deviation (rmsd) of these residues. Then, we define cutoffs
for these values and use them to filter the alignments. From the
filtered alignments, we construct the domain network (Fig. 1B)and
the motif network (Fig. 1C). In the domain network, nodes are the
SCOP domains in the dataset, and edges connect pairs of domains
that share a similar motif. In the motif network, nodes are motifs,
and the edges connect pairs of motifs that cooccur in a domain. We
consider length thresholds of 55 and 75 residues, percent similarity
of aligned residues thresholds of 30%, 40%, and 50%, and rmsd
thresholds of 2, 2.5, and 3 Å. We explore how well threshold
combinations reproduce SCOP segregation into folds, i.e., opti-
mally including all domains from the same fold in a connected
component, whereas excluding from it domains of other folds.
Protein Space Includes Continuous and Discrete Regions. The con-
nectivity of the domain network varies depending on the thresh-
olds used to define the evolutionary relationships (Fig. 2 and SI
Appendix, Figs. S1–S4). If we consider the relatively lax thresholds
of 50 residues, 30% sequence similarity, and 3-Å rmsd, then the
resulting domain network is virtually a single connected compo-
nent (including 9,385 or 97% of the domains). For more stringent
thresholds, which we consider to represent evolutionary relation-
ships more faithfully, the network reveals both continuous and
discrete regions of protein space (Fig. 2 and SI Appendix, Figs. S2
and S3). At even more stringent length and similarity thresholds
the network falls apart completely (e.g., SI Appendix,Fig.S4). SI
Appendix,Fig.S5shows the stacked histograms of sizes of the
connected components, of representative networks. Indeed, using
longer length, higher percent similarity, or lower rmsd thresholds
results in a more disconnected network, and places more domains
in smaller components. Importantly, in all these cases, we see a
single exceptionally large connected component.
SI Appendix, Fig. S6 shows the percent of domain pairs with the
same SCOP fold that are in the same connected component in
a domain network (xaxis), versus the percent of pairs that have
a different SCOP fold and that are not connected (yaxis). We
consider all pairs among the all-alpha, all-beta, alpha/beta, and
alpha +beta domains (SI Appendix, Fig. S6A), and all pairs
among the 61% domains that are not alpha/beta (SI Appendix,
Fig. S6B). Notice that when considering the region of protein
space that does not include the alpha/beta domains (SI Appendix,
Fig. S6B), the domain network captures the notion of fold far
better and fairly well overall. As expected, lax thresholds generate
a network with larger connected components, and consequently
the percent of domain pairs with the same fold that are connected
is greater (higher values along the xaxis), but also, there are more
domain pairs of different folds that are (inappropriately) con-
nected (lower values along the yaxis). The thresholds that gen-
erate domain networks that overall best agree with SCOP fold
assignments are either (i) alignments longer than 75 residues,
with percent similarity greater than 30%, and rmsd smaller than
2.5Å, or (ii) alignments longer than 55 residues, percent similarity
greater than 30%, and rmsd smaller than 2 Å.
SI Appendix, Fig. S7 shows the same analysis per SCOP class.
We see that in the all-beta class, and to a lesser extent in the
alpha +beta class, our optimal thresholds can generally identify
SCOP folds and place domains of the same fold in the same
connected component, while still being disconnected from the
domains that are not in that fold (high values along the xand
yaxes). In the alpha/beta class, and to a lesser extent in the all-
alpha class, if we want to successfully connect domains that are
in the same fold (i.e., achieve high values along the xaxis), we
inevitably connect to domains that are not in the same fold
Fig. 1. Constructing the domain and motif net-
works. (A) The aligned protein segments, marked in
colors, are the motifs. (B) In the domain network,
edges connect domains that share similar motifs
(e.g., domain d1wjga_ and d1vlua_ that share the
cyan motif). (C) In the motif network, edges connect
cooccurring motifs (e.g., the orange and cyan motifs
cooccur in the d1vlua_ domain).
www.pnas.org/cgi/doi/10.1073/pnas.1403395111 Nepomnyachiy et al.
(low values along the yaxis). We fail to find threshold combi-
nations that are successful along both axes.
The Continuous Region of the Protein Universe Contains the Alpha/
Beta Domains; the All-Alpha, All-Beta, and Alpha +Beta Domains Are
in the More Discrete Region. Fig. 2 shows the domain network that
best reproduces SCOP’s classification into folds. It is balanced in
that it connects a significant amount of domains to each other
even though it was obtained using conservative thresholds to
represent evolutionary relationships. As the networks obtained
using all other (reasonable) thresholds, the network features
both discrete and continuous regions. For the most part, SCOP
domains of the all-alpha, all-beta, and alpha +beta classes, in
which alpha and beta elements do not mix, populate the discrete
parts (Fig. 2); roughly speaking, in this region the connected
components correspond to SCOP folds (SI Appendix,Fig.S8). In
contrast, the alpha/beta domains, with alternating alpha and beta
elements, populate the large connected component. This contin-
uous region includes domains from most alpha/beta folds, in-
cluding the TIM barrels, NAD(P) binding Rossmanns, FAD/NAD
(P) binding, and many more (SI Appendix, Fig. S8); the domains of
each fold are often found in very close vicinity to each other in the
main connected component. It is known that individual folds
(e.g., TIM barrels) have undergone circular mutations and splicing
within their respective folds (28). Our analysis indicates that the
evolutionary relationships extend beyond the individual fold,
covering, in essence, the entire alpha/beta SCOP class.
If we consider the similarity of sequence and structure as in-
dicative of evolutionary relationships among proteins, Fig. 2 can
be interpreted as collections of evolutionary paths in protein
space. For example, Fig. 3 shows a path passing between
domains from the FAD/NAD(P) binding, TIM barrel, Ross-
mann NAD(P) binding, nucleotide binding, and Flavodoxin
folds. In this network, there is a path between 77% of the alpha/
beta domain pairs, whereas paths between a pair of domains
from the all-alpha, all-beta, and alpha +beta classes are found
only in 10%, 6%, and 8% of the cases, respectively. This is not an
artifact of the different number of domains in the four SCOP
classes: we see similar numbers when we randomly sample 1,000
domains from each SCOP class. The large amount of paths
within the alpha/beta SCOP class suggests that it is particularly
easy to add and delete motifs among them without impeding
structural stability. It could be that evolution took advantage of
this property to design new proteins with novel functions.
Fig. 4 shows the network of 8,219 recurring motifs, obtained
using the same parameters used for the domain network of
Fig. 2. Of these, 994 are nonsingletons. The number of different
domains which are present in a motif is, by definition, greater
than 2, and almost always less than 50 (983, or 99%, of the motifs
that are nonsingletons). In 82% of these cases (810 motifs) all of
the domains in the motif have the same SCOP class; only in 31%
of these cases (311 motifs) do they have the same SCOP fold.
Recurring motifs are very common. We see that the (green)
alpha/beta are the most abundant: the percent (number) of
nonsingleton motifs that are all-alpha, all-beta, alpha +beta, and
alpha/beta is 22%, 4%, 4%, and 55%, (223, 43, 44, and 547),
respectively; 28% (279) of the nonsingleton motifs have an equal
part of two classes. The weak connection between motifs taken
from domains of the alpha/beta and all-alpha classes is mediated
by superimpositions of small domains on excessively large do-
mains. Had these larger domains been divided into smaller
Fig. 2. Global view of protein space via the domain
network. The nodes represent the set of 70% se-
quence nonredundant SCOP domains, colored by
their SCOP class (see color legend); edges connect
between domains that share a motif. Here, two
domains are connected if we found a similarity of at
least 75 residues, with at least 25% sequence simi-
larity, and at most 2.5 Å rmsd. We see that there
are two regions: one is very connected, or continu-
ous, and populated mostly by (green) alpha/beta
domains in which the alpha and beta elements al-
ternate; the other is discrete, composed of many
disconnected components, and populated by the
all-alpha, all-beta, and alpha +beta domains. Only
components with more than 10 domains are shown.
Nepomnyachiy et al. PNAS
August 12, 2014
domains, the vast majority of motifs from the all-alpha domains
would disintegrate from the main connected component.
The Domain Network Reveals the Continuous–Discrete Nature of
Protein Space. The question if protein space is continuous or
discrete has been extensively debated (2, 3, 5–10), and is in-
teresting both fundamentally and for its implications on how
to organize and search protein databases (5, 16). The domain
network allows us to describe “continuous”and “discrete”more
concretely based on the sizes and number of connected com-
ponents. We find that protein space has both discrete and con-
tinuous regions, in agreement with Sadreyev et al. (7), and that
the distinction largely depends on the domains’SCOP class:
continuity is most prevalent among the alpha/beta domains
whereas the region of the all-alpha, all-beta, and alpha +beta
domains is mostly discrete. Skolnick et al. attributed the conti-
nuity to physical properties of proteins and to backbone hydro-
gen bonds in particular (15). That alpha/beta domains are more
interconnected than other SCOP classes suggests that the domains
in this class share unique physicochemical qualities that are yet to
Edges in the domain network are determined using specific
thresholds. More lax thresholds imply more edges and hence a
more connected network; at the extreme case all protein space is
a single connected component. Stricter thresholds imply fewer
edges and hence a less connected network. Also, using a more
sensitive method to identify similarity among domains will reveal
a more connected network. Indeed, the method and the thresholds
for inferring the relationships among domain pairs should fit the
question at hand. We consider “local”relationships that represent
domains closer and further apart in evolution and combine them
into a “global”view of protein space to study its properties.
To connect domain pairs that are likely evolutionarily related,
we verified that the domains share similar structure and se-
quence over a significant number of residues. Skolnick et al. (15)
showed that when relating domain pairs based solely on the
similarity of their structures (and a minimal TM_Score threshold
of 0.4), protein space is essentially a single connected compo-
nent. Our work deals with what happens when we “raise the
metaphorical bar”for relating two domains, and enforce that the
domain pairs are likely evolutionarily related (using a range of
thresholds). Indeed, even in this stricter setting, if the thresholds
are sufficiently lax (namely, at least 50 residues with more than
25% sequence identity and rmsd less than 3 Å) virtually all of
protein space is connected, suggesting that protein space is
evolutionarily (not only structurally) connected. However, if we
consider stricter thresholds, and specifically ones which were
calibrated to best capture the connectivity of SCOP folds, then
protein space disintegrates, and this disintegration is generally in
the region of non–alpha/beta domains.
One could argue that all of fold space is discrete; only each
SCOP class requires different thresholds to disintegrate. Our data
show that this is not the case. To learn this, we focused on each
of the four SCOP classes, and searched for optimal thresholds
resulting in networks that capture SCOP fold connectivity. Recall
that a successful network simultaneously keeps same-fold domains
connected, and disconnects them from domains in different folds.
The success stems directly from the properties of the class of
domains: If a class has a more discrete nature, that is, if its intrafold
similarities are greater than its interfold similarities, then we can
find appropriate thresholds. If, on the other hand, it has a more
continuous nature, then by using increasingly strict thresholds to
relate domain pairs, the domain network will disintegrate, but it
will do so altogether, and lose the property that same-fold domains
remain in the same connected component. Indeed, we see that the
SCOP classes vary in how well the best thresholds capture their
fold connectivity: the all-beta domains have the most discrete
nature, followed by the alpha +beta domains, the all-alpha
domains, and finally the alpha/beta domains that have the most
continuous nature (SI Appendix,Fig.S4).
We construct the dataset of likely evolutionary relationships
using two steps: (i) searching for candidate domain pairs, and
then (ii) verifying that their corresponding subparts satisfy pre-
defined length, sequence similarity, and structure similarity cri-
teria. For the first step, we used the structural aligner SSM (27).
However, structural aligners vary in the relationships that they
identify: some are more sensitive than others (29, 30). Here, we
chose SSM because it was shown to be particularly sensitive (30).
The search procedure can be augmented using additional structural
Fig. 3. “Walking”in the domain network. A putative evolutionary path, to
demonstrate the relationships between connected domains. The path, taken
from the major connected component, passes through eight domains from
five different SCOP folds of the alpha/beta class. The aligned motifs are
marked in orange or cyan; residues shared by the motifs in both directions
along the path are in magenta. The number of residues, rmsd, and percent
sequence similarity (using BLOSUM62) of the aligned motifs are indicated.
www.pnas.org/cgi/doi/10.1073/pnas.1403395111 Nepomnyachiy et al.
aligners [e.g., Matt (29), STRUCTAL (31), or TM_align (15)].
Hopefully, these can identify additional candidate evolutionary
relationships, which we can subsequently subject to the similarity
filters in step (ii).
The Motif Network Reveals the Ubiquitous Reuse of Motifs in Nature.
Previous studies of cooccurrence networks use domains as the
unit element (24, 26, 32, 33). In those networks, nodes represent
domains, and edges connect between cooccurring domains. Our
motif network is similar, only we represent motifs that are smaller
than domains. The distributions of the number of neighbors in
the domain cooccurrence and our motif network are similar (24).
Also, the alpha/beta motifs and domains tend to have more
partners (or a higher rank) in their respective networks (24).
Importantly, we derive the unit element (or nodes) in the
cooccurrence network from the data rather than relying on
predefined (e.g., SCOP–CATH) domains. Domains were used
because they are considered the basic unit of protein evolution
(34). It is assumed that there is only a limited set of them, and
domains from this set are combined to form the set of proteins in
the proteome using genetic mechanisms (24). For example, ge-
netic recombination can cause loss or duplication of parts of
genes, entire genes, or even longer chromosomal regions; mobile
genetic elements (DNA transposons and retro-transposons) can
lead to duplication or deletions (26). It may be, however, as
suggested by Lupas et al., that the basic unit is actually smaller
than a domain (35). Our tools offer a way to further investigate
this idea and demonstrate the abundance of mix-and-join events.
In this respect it is noteworthy that whereas domains are con-
sidered to be autonomous structural units, which are stable on
their own, it may well be that the motifs are not, and that despite
their ability to “hop between domains”they are stable only
within the context of the intact domain. Note that we have used
the same thresholds in the motif and domain networks. These
thresholds are not necessarily the best ones to highlight all sig-
nificant similarity at the subdomain level. Future in-depth study
is required to better understand the properties of motifs and
their networks with more lax thresholds. Regardless of the actual
evolutionary scenario underlying the motif network, the network
lends itself naturally to protein engineering efforts by suggesting
which substructures can replace one another while maintaining
protein foldability. Just like evolution has recycled such motifs so
could protein engineers, enriching the topologies of engineered
proteins and their likelihood of performing new functions.
Alpha/Beta Domains Are Unique. Previous work showed that the
alpha/beta domains are older (19), more stable (36), more fre-
quently involved in domain fusion events (32), and are associated
with high functional diversity (20). Our analysis shows two addi-
tional unique features of these domains: they lie in a tightly con-
nected region of protein space and their motifs mix-and-join with
a wider range of motifs. The tendency of the alpha/beta domains
to easily mix-and-join could explain their functional diversity.
Two alternative explanations for these properties of the alpha/
beta domains and motifs are (i) they existed in ancient evolutionary
history, and were mixed from these entities (35, 37), or (ii ) their
biophysical properties give them a selection advantage. Our
observations do not help in determining which of the two expla-
nations is more likely, and this remains a significant challenge.
We provide tools for navigation in the domain and motif
networks by integrating Cytoscape (38) and PyMOL (39). To
visualize our networks, download the Cytoscape files describing
them at http://cs.haifa.ac.il/∼trachel/domain_motif_networks/.The
networks could be used to theorize about protein evolution, sug-
gest evolutionary pathways between domains, and hence maybe
suggest strategies for protein design.
Dataset. Our dataset consists of 9,710 domains that are 70% sequence
nonredundant from the SCOP database. We filtered away domains whose
structures were not accurately determined [a Summary PDB ASTRAL Check
Index score (40) lower than 0.2]. We aligned all-versus-all domains using the
structural alignment method SSM (27). We parsed the alignments, measured
their length (i.e., number of aligned residues), and calculated the percent of
identical residues, and the percent of similar residues (using the BLOSUM62
matrix). From these data, we constructed and visualized the domain and the
motif networks using Cytoscape (38).
The Domain Network. The nodes in the domain network represent the
domains in the dataset (Fig. 1A); a single edge connects two nodes if we
found a significant alignment of sufficiently many residues, sufficiently low
rmsd, and sufficiently high percent sequence similarity (Fig. 1B). We con-
sidered different thresholds of alignment length (55 and 75 residues), rmsd
(2, 2.5, and 3 Å), and percent sequence similarity (30%, 40%, and 50%).
The Motif Network. The motif graphs offer an alternative representation
of the same alignment data (Fig. 1C). The first step is to identify the nodes
of the motif graph. An alignment, A, matches a set of residues in protein P1
with a set of residues in protein P2; here, we denote these subsections P1A
Fig. 4. Global view of protein space via the motif network. The nodes
represent the set of 8,219 identified motifs, colored by the SCOP class of the
majority of their domains (see color legend; white represents cases where no
SCOP class is the majority); edges connect between motifs that cooccur in
a domain. The motif network was constructed using the set of alignments
that are longer than 75 residues, with more than 25% sequence similarity,
and less than 2.5 Å rmsd (Methods). We see that the alpha/beta (and the all-
alpha) motifs are more common, more gregarious, and form the largest
Nepomnyachiy et al. PNAS
August 12, 2014
and P2A. As evidenced by the alignment itself, P1Aand P2Aare two names
of a similar subsection. This subsection can have additional names: consider
another alignment, B, which matches subsections P1Band P3B. If the resi-
dues in subsection P1Bare actually the same ones as those in P1A, then P1B
and P3Bare also names of this subsection. Thus, we need to identify the
different names (in the example given here: P1A,P2A,P1B,P3B) that describe
similar subsections. To do this, we constructed an auxiliary graph, in which
the nodes are the raw subsections extracted directly from the set of signifi-
cant alignments (two per alignment); in the example described the nodes in
the auxiliary graph will include the nodes P1A,P2A,P1B,P3B. In the auxiliary
graph we connect pairs of subsections associated with each alignment (one
edge per alignment); in the example these will be the edges between P1A
and P2A, and between P1Band P3B. In the auxiliary graph we also connect
(almost) similar subsections of the same domain; in the example given above
this is an edge between P1Aand P1B. For this, we used a threshold of 90%
overlap (e.g., we connected the motifs that represent residues 1–100 and
residues 2–101 of the same domain). Each connected component in the
auxiliary graph is a node in the motif network. In other words, each node in
the motif graph is a set of recurring subsections.
To generate a clearer motif network, we added a few more steps. First,
even when using the 90% overlap threshold, we may suffer from a “drag-
ging”effect, where we start with one subsection, and then via a series of
intermediate subsections that are 90% similar to each other, we reach an-
other subsection of vastly different size. To circumvent this problem, we
greedily split motifs in which the ratio between the longest and shortest
subsection is greater than 1.5. Also, we remove motifs that we identify as
supermotifs of other motifs in the dataset: if motif1 includes subsection PA
and motif2 includes subsection PB, and all residues in subsection PBare also
subsection PA, then we consider motif1 a supermotif of motif2, and remove
it. The edges in the motif network connect motif pairs for which there are
subsections of that domain in both motifs.
Data Visualization. We added an interface to viewing structural information
using PyMOL (39). In the domain network we visualize the domains that
correspond to the nodes, as well as the domain superimpositions that cor-
respond to the edges; the aligned residues are highlighted. In the motif
network an edge is a domain that includes both motifs at its end nodes: we
show the two motifs in cyan and in orange, with the overlapping residues
in magenta; if there is more than one possible domain, the user needs to
choose the one to visualize. For the nodes in the motif network, we visualize
two domains with these motifs superimposed on one another.
ACKNOWLEDGMENTS. We thank Yonatan Bilu, Sarel Fleishman, and Dan
Tawfik for insightful discussions, Varda Wexler for graphics consulting, and
the anonymous reviewers for helpful comments. N.B.-T. acknowledges the
financial support of Grant 1775/12 of the Israeli Centers of Research
Excellence Program of the Planning and Budgeting Committee and the
Israel Science Foundation.
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