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Binding properties and evolution of homodimers in protein-protein interaction networks


Binding properties and evolution of homodimers in protein-protein interaction networks
Iaroslav Ispolatov?,1 Anton Yuryev,1 Ilya Mazo,1 and Sergei Maslov?2
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Ariadne Genomics Inc., 9700 Great Seneca Highway, Suite 113, Rockville, Maryland 20850, USA?

arXiv:q-bio/0501004v1 [q-bio.GN] 4 Jan 2005

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Department of Physics, Brookhaven National Laboratory, Upton, New York 11973, USA
(Dated: February 9, 2008)

Abstract
We demonstrate that Protein-Protein Interaction (PPI) networks in several eucaryotic organisms contain signi?cantly more self-interacting proteins than expected if such homodimers randomly appeared in the course of the evolution. We also show that on average homodimers have twice as many interaction partners than non-self-interacting proteins. More speci?cally the likelihood of a protein to physically interact with itself was found to be proportional to the total number of its binding partners. These properties of dimers are are in agreement with a phenomenological model in which individual proteins differ from each other by the degree of their “stickiness” or general propensity towards interaction with other proteins including oneself. A duplication of self-interacting proteins creates a pair of paralogous proteins interacting with each other. We show that such pairs occur more frequently than could be explained by pure chance alone. Similar to homodimers, proteins involved in heterodimers with their paralogs on average have twice as many interacting partners than the rest of the network. The likelihood of a pair of paralogous proteins to interact with each other was also shown to decrease with their sequence similarity. This all points to the conclusion that most of interactions between paralogs are inherited from ancestral homodimeric proteins, rather than established de novo after the duplication. We ?nally discuss possible implications of our empirical observations from functional and evolutionary standpoints.

Corresponding author, E-MAIL slava@ariadnegenomics.com, FAX(240) 453-6208. Corresponding author, E-MAIL maslov@bnl.gov, FAX (631) 344-2918. ? Permanent address: Departamento de Fisica, Universidad de Santiago de Chile, Casilla 302, Correo 2, Santiago,
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Chile

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I.

INTRODUCTION

Many functionally important proteins such as receptors (G-protein coupled receptors (Milligan et al. 2003), tyrosine kinase receptors (Ronnstrand 2004)), enzyme complexes (Marianayagam et al. 2004), ion channels (Simon and Goodenough 1998) and transcriptional factors (Amoutzias et al. 2004) are homo- or hetero-dimers. For example, almost 70% of enzymes listed in the Brenda database (http://www.brenda.uni-koeln.de/) can self-interact to form dimers or higher-order oligomers. As another example, G-protein coupled receptors (Milligan et al. 2003), chemokine (Mellado et al. 2001), cytokine (Langer et al. 2004), and tyrosine kinase receptor (Ronnstrand 2004) families all use oligomerization as a step in the pathway activation in response to an agonist (Marianayagam et al. 2004). The examples of multi-protein complexes containing homodimers include proteasome (Bochtler et al. 1999), ribosome (Matadeen et al. 1999), nucleosome (Bentley et al. 1984). The function of most ?lamentous proteins of the cytoskeleton such as actin, myosin, spectrin, tubulin, etc, relies on their oligomerization or polymerization. The ability to self-interact confers several structural and functional advantages to proteins, including improved stability (Hattori et al. 2003, Dunbar et al. 2004) control over the accessibility and speci?city of active sites (Marianayagam et al. 2004), and increased structural complexity. In addition, self-association can help to minimize genome size, while maintaining the advantages of modular complex formation. Protein assembly into heterodimers has the combinatorial effect of producing multiple species with different af?nity to its substrates and other biophysical characteristics, giving the cell an instrument for ?ne-tuning its regulatory responses. Even bigger variety of complexes contain (or are formed by) the interacting paralogs, such as spliceosome (Mura et al. 2001), acting promoting complex Apr2/3, membrane receptors (Rubin and Yarden 2001), and transcription factors (Amoutzias et al. 2004). While many speci?c dimerizing proteins are well studied and their biological and structural properties have been established, little is known about an overall topological in?uence and highlevel statistical properties of dimer distribution in protein networks. The protein networks have recently become a subject of extensive research by biologists as well as by scientists from other ?elds interested in networks and graphs (see, for example, (Spirin and Mirny 2003, Amoutzias et al. 2004, Wagner 2003, Maslov and Sneppen 2002, Wuchty et al. 2003, Kim et al. 2002). Among various studied types of protein-protein networks, a binding, or physical interaction networks have several appealing properties that make them a popular research subject: they are undi-

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rected, Boolean, and the most extensive ones, in principle spanning over all proteins present in a given organism. Several universal features of the binding networks are believed to be established fairly well. Examples include an apparent broad (scale-free) degree distribution (Wagner 2003 and references therein), suppression interactions between high-degree (hub) proteins (Maslov and Sneppen 2002), a higher than randomly expected number of tightly linked sub-graphs or cliques (Spirin and Mirny 2003), and evolutionary conservation of such tightly linked sub-graphs (Wuchty et al. 2003). In this paper we describe a systematic empirical study of topological properties of the physical interaction network properties in the neighborhood of homodimers (self-interacting proteins) as well as heterodimers formed by paralogous proteins.

II.

BASIC OBSERVATIONS

We have assembled and analyzed the protein-protein interaction (binding) networks from four organisms: the baker’s yeast S. cerevisiae, the nematode worm C. elegans, the fruit ?y, D. melanogaster,and the human H. sapiens (see Materials and Methods for details). The most apparspecies yeast worm ?y human Ntotal 6713 22268 26148 25000 – 50000 NPPI 4876 3137 6962 5331 Ndimer 179 89 160 1045 k 6.6 ± 0.2 3.3 ± 0.1 5.9 ± 0.1 5.7 ± 0.1 k
dimer

12.4 ± 1.2 13.1 ± 2.2 14.2 ± 1.2 14.0 ± 0.6

TABLE I: Estimated total number of proteins Ntotal , number of proteins involved in the protein-protein interaction networks NPPI , the number of dimers or self-interacting proteins Ndimer , the average network degree (the number of neighbors) k over all NPPI , and the average degree k proteins.
dimer

of self-interacting

ent observation that follows from the network data (Table I) is that the number of self-interacting proteins in all four organisms is substantially higher than one would expect purely by chance. Indeed, in a network with N proteins (each having at least one interaction), a straightforward estimate assuming equal af?nity to itself and other proteins, suggests that a protein with the connectivity (degree) k would have a probability to bind to itself equal to k/N. The total number of 3

dimers then will be the sum of this expression over all proteins, which is the average connectivity,
N i=1

ki /N ≡ k . As Table I shows, the actual number of dimers is 25-200 times higher than

expected based on this simple-minded hypothesis. The abundance of dimers in all species suggests that their functional importance has been preserved through the evolution. In support of this conclusion we note that self-interacting proteins also have about twice as many interaction partners compared to non-dimers (Table I). Indeed, the number of interaction partners of a protein was shown before to be positively correlated with its probability to be essential for the survival of the cell and to be conserved in the course of evolution (Wuchty et al. 2003). Sometimes the ease with which proteins form self-interactions has purely structural (as opposed to functional) origin explained e.g. by the domain swapping model (Bennet et al. 1994) Indeed, in the fully folded state the individual structural components of a protein are expected to make multiple binding contacts with each other. A pair of identical (or homologous) proteins then might be able to use the same set of contacts to physically interact with each other if they encounter each other in a partially unfolded state. It is interesting to note that average degrees of dimers are about equal to each other in all four organisms studied here. Average degrees of all proteins in the network are also quite close to each other (an anomalously low k ? 3 of the worm network is explained in the Materials and Methods section). At present it is unclear if this apparent similarity is just a coincidence or has some deeper explanations. In any case, the inter- and intra-species comparison of these networks with each other indicate that the data for protein-protein interaction in any of these organisms are far from saturation and a considerable number of new interactions is expected to be added to these networks in the future.

III.

LINEAR SCALING

To better understand connectivity patterns of homodimers in the protein interaction network, we studied how the likelihood of a protein to interact with itself Pdimer (k) depends on its overall number of binding partners (degree) k. Pdimer (k) was obtained by dividing a properly binned degree histogram of all homodimers by the degree histogram of all proteins in the network. Fig. 1 shows Pdimer (k) vs k measured in the ?y data based mainly on the species-wide twohybrid dataset of (Giot et al. 2004). As one can see, the probability of self-interaction linearly 4

10

0

10 Pdimer(K) 10

?1

?2

10

?3

10

0

10 K

1

10

2

FIG. 1: The likelihood Pdimer (k) of a ?y protein to self-interact plotted vs its degree k in the PPI network. The dashed line is the linear ?t Pdimer (k) = 0.0035k.

increases with the degree in the protein network (the dashed line on the log-log plot in Fig. 1 has slope 1). The proportionality coef?cient of this linear increase can be interpreted as the probability pself ? 3.5 × 10?3 that a given edge of a physical interaction network starting at a certain protein ends up connecting this node with itself. It is approximately 25 times larger than the probability pothers = 1/7000 ? 1.4 × 10?4 that it will instead connect with a randomly selected other node among approximately 7000 proteins present in the ?y interaction dataset. This is consistent with a larger than expected number of homodimers discussed above. The observation that the likelihood of a protein to interact with itself linearly increases with the total number of its interaction (binding) partners (Fig. 1) contains an important information about the general mechanisms of such interactions. We conjecture that every protein i can be characterized by a unique intrinsic parameter that we would refer to as its “stickiness” σi . This parameter quanti?es protein’s overall propensity towards forming physical interactions. We further assume

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that both the probability of a protein to interact with itself as well as its probability to interact with other proteins are proportional to this stickiness (albeit with different coef?cients as we saw above) and thus should linearly depend on each other. This rather plausible conjecture of the existence of a “universal propensity towards interactions” of individual proteins in an organism thus explains both the linear scaling in Fig. 1 and our original observation that self-interacting proteins in several organisms tend to have higher than average number of binding partners in the physical interaction network (Table I). Indeed, by considering the homodimers, we automatically pick proteins with higher than average stickiness and thus end up with a subset of proteins characterized by a higher than average number of binding partners k. It is important to emphasize that the proposed “stickiness” of a protein should not be interpreted literally, that is as the ability of a protein to unspeci?cally bind other proteins. In fact, all interactions in our datasets (with the exception of false positives) come from speci?c functionally relevant bindings between proteins. Instead, one should view the “stickiness” as a complex quantitative characteristic of a protein which has contributions from such properties as the number and nature of its constituent domains, the hydrophobicity of its surface, the number of copies of the protein per cell, the extent of its evolutionary conservation, the overall level of a “cooperativity” of the functional task it is involved, etc. In some of our datasets (e.g. human), which are based on a large number of small-scale experiments instead of a single genome-wide assay, the “stickiness” of a protein may also correlate with its overall popularity, i.e. the number of publications it was studied in. Fig. 2 shows the correlation between the propensity towards self-interactions and the number of binding partners in the human dataset. Here, as for the ?y (see Fig. 1), Pdimer (k) has a region < of linear k-dependence. However, here this region is limited to small values of k ? 10. For larger values of k, Pdimer (k) starts to show saturation effects and completely saturates at 1 for k > 100. The saturation is expected to follow a linear region as obviously no probability could exceed 1. Moreover, it can be qualitatively described by the following simple model. Suppose that each of the k interaction links starting at a given protein with a probability pself ends at the same protein, while with a probability 1 ? pself it selects some other protein target. Then the chances that none of the k links results in the formation of the homodimer are (1 ? pself )k , while a homodimer is formed with a probability Pdimer (k) = 1 ? (1 ? pself )k . (1)

For k ? 1/pself this expression yields a linear k-dependence for Pdimer (k), as it was observed for 6

10

0

Pdimer(K)

10

?1

10

?2

10

0

10

1

10 K

2

FIG. 2: The likelihood of a human protein to self-interact. Dashed and dot-dashed lines are ?ts with the Eq. (1) and pself = 0.035 and pself = 0.055 correspondingly. The second value provides the best ?t overall, while the ?rst value better ?ts the low k region.

the ?y data (Fig. 1). This general formula also ?ts Pdimer (K) nicely over the whole range of k (see dashed lines in the Fig. 2). The ?t with this formula provides an estimate of a propensity towards self-interactions among human proteins: pself ? 0.03 ? 0.06 which is some 10 times higher than in our ?y dataset. This is why the saturation of Pdimer (k) is clearly visible in human but not in the ?y. However, due to a vast differences in the extent of coverage and sources of the data describing protein-protein interactions in the human (interacting protein pairs extracted from abstracts indexed in PubMed) and the ?y (a genome-wide two-hybrid assay), different values of pself do not have to re?ect actual differences between these two organisms.
(h)

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IV. EVOLUTION OF HOMODIMERS AND INTERACTING PARALOGS

Interacting paralogous proteins (paralogous heterodimers) are often thought (see, for example, Amoutzias et al. 2004) to be closely related to the self-interacting proteins or homodimers. Indeed, a duplication of a homodimer encoding gene in evolution results in an appearance of a new pair (or several pairs for larger families) of interacting paralogous proteins. Such interaction links between paralogs could be destroyed with time as accumulation of mutations in the constituent proteins changes their three-dimensional shapes. A binding between a pair of non-homodimeric paralogous proteins may also appear de novo after duplication event. Relative importance of these two mechanisms of formation of paralogous heterodimers are not universally agreed on (see e.g. Wagner 2003 for a point of view favoring the de novo formation). In this section we study pairs of interacting paralogs present in our datasets. The purpose of this study is twofold: Therefore the purpose of this section is twofold: ? We ?rst make a number of empirical observations favoring the hereditary nature of interactions between paralogs and con?rming the relationship between most of such heterodimers and their homodimeric ancestors. ? We then use a set of proteins interacting with their paralogous partners to con?rm and extend our empirical observations about homodimers discussed in the previous section. Due to an incomplete and noisy nature of essentially any data describing genome-wide PPI networks there is only partial overlap between sets of homodimers and interacting paralogs. Thus the addition of interacting paralogs to the set of homodimers allows us to considerably improve the statistics of our analysis. We ?rst just count the number of linked paralogous pairs nlinked paralogs in each data set. If most links between paralogs were indeed inherited from homodimeric ancestors, nlinked paralogs should be signi?cantly higher than nlinked random the number of links one expects to ?nd between the same number Nparalogous pairs of randomly selected pairs of non-paralogous proteins. Indeed, as we demonstrated in the previous sections all four organisms included in our study are characterized by an unusually large number of homodimers. If on the other hand most links between paralogous proteins were established de novo after the duplication there is no reason to expect the number of such links to be unusually large compared to a random set of protein pairs. The results presented 8

species yeast ?y worm human

Nparalogous pairs 3409 12991 3480 21562

nlinked paralogs 251 142 105 1280

nlinked random 4±2 11 ± 3 3±2 24 ± 5

k

linked paralogs

k

dimer

14.3 ± 1.9 11.1 ± 1.0 5.8 ± 0.9 10.2 ± 0.6

12.4 ± 1.2 14.2 ± 1.2 13.1 ± 2.2 14.0 ± 0.6

TABLE II: The number of linked pairs of paralogous proteins nlinked paralogs , the number of linked pairs nlinked paralogs expected by pure chance alone, the average degree k interact with some of their paralogs , and the average degree k
dimer linked paralogs

of proteins known to

of self-interacting (dimer) proteins.

in Table II strongly support the hereditary origin of most paralogous heterodimers: for all species nlinked paralogs is much larger than nlinked random (by several orders of magnitude.) This a strong evidence for the hereditary rather than the de novo origin of the paralog-paralog links. Another strong argument for the hereditary hypothesis follows from Fig. 3. This ?gure reveals that the further paralogs diverge in their amino-acid sequences, the smaller is the probability of them to be linked to each other. This suggests that typically pairs of linked paralogs gradually loose inherited interactions rather than establish new ones. Thus we conclude that most interacting paralogs present in our data were created by duplication of homodimeric proteins. A ?nal argument in support of this conclusion is that the average number of binding partners of interacting paralogs k of homodimers k (see Tables I,II). Given that most paralogous heterodimers were at some point formed from homodimers, one might assume that most proteins involved in such heterodimeric complexes are homodimers. However, it is far from being the case (see Table III). Such discrepancy is caused by two reasons, one purely evolutionary while another anthropogenic. ? As a result of substitutions in its amino-acid sequence any protein might loose its ability to interact with its paralog or to homodimerize. From Fig. 2 one can see that many ancient duplicates of homodimers have lost links to their ancestors. ? The experimental data are far from being complete and many links, including selfinteractions, are simply not registered. The comparison between sets of homodimers and 9
dimer linked paralogs

is indistinguishable from that

and is some 2 ? 3 times higher than the average over the whole network

Fig. 3

10

0

yeast fly worm human

Plinked paralogs(s)

10

?1

10

?2

30%

50%
s

70%

90%

FIG. 3: The probability for two paralogous proteins to bind to each other Plinked paralogs vs their sequence similarity s for (top to the bottom) human, yeast, worm, and ?y. Even the most distant paralogs are more likely to interact with each other than a randomly selected pair of proteins. Such randomly expected probability is equal to 1.1 × 10?3 in the human, 1.3 × 10?3 in the yeast, 1.1 × 10?3 in the worm, and 0.8 × 10?3 in the ?y dataset.

interacting paralogs may in principle be used to crudely estimate the completeness of our knowledge of a protein network in a given organism.

V. DISCUSSION

Above we demonstrated that self-interacting proteins tend to have connectivity signi?cantly above the average in the protein-protein interaction network. This phenomenon appears univer-

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species yeast worm ?y human

NPPI 4876 3137 6962 5331

NPPI?p 1682 1578 2951 3840

Nl?p 321 143 169 1548

Ndimer 179 89 160 1045

Nd?p 67 47 59 789

Nd?l?p 36 13 17 460

TABLE III: Numbers of certain types of proteins for yeast, worm, ?y, and human: NPPI - proteins present in the network, NPPI?p - network proteins with at least one paralog present in the network Nl?p - proteins linked to at least one of their paralogs, Ndimer - homodimers, Nd?p - homodimers that have at least one paralog among network proteins, Nd?l?p - homodimers linked to at least one of their paralogs.

sally in protein-protein interaction networks of all four model organisms studied above. As a related phenomenon we found that interacting paralogs also have increased connectivity, likely because most of them are descendants of ancient self-interacting proteins. We also have shown that numbers of homodimers and interacting paralogs are both higher than expected by pure chance alone. We unify these phenomena by introducing a “stickiness” as a measure of protein propensity for binding. Both the propensity of proteins towards self-interactions and the degree of a protein in the protein-protein interaction network are proportional to this parameter. However, the dimerization probability apparently has a larger proportionality coef?cient. This is not very surprising given a multitude of functional roles dimers (or polymers) play in living cells. Dimerizing and oligomerizing proteins are ubiquitous in all organisms and are present in the most evolutionary conserved protein complexes (Marianayagam et al. 2004). On the evolutionary side, we have con?rmed that most links between paralogs are most probably inherited from their dimerizing ancestors. This does not exclude a possibility that some of these links are formed after duplication as a result of random mutations, but the relative number of such de novo created links is relatively small. This conclusion has several implications for the network topology. If a given dimerizing protein has duplicated several times, it leads to an appearance of a fully interconnected complex or clique of paralogous heterodimers. In reality, some links inside this complex are lost due the divergence of sequences of paralogous proteins. Such loss of links may split a higher-order clique into several lower-order ones or make it just a densely (yet not fully) interconnected motif. A higher density of links around dimers caused

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by these remaining heterodimeric links may provide a qualitative explanation to the empirically observed abundance of highly interconnected motifs and cliques in protein networks (Spirin and Mirny 2003). Several simple models of network growth and evolution due to gene duplications followed by subsequent functional divergence of the resulting pair of paralogous proteins lead to networks with an unrealistic bipartite topology in which descendants of a particular protein never interact with their paralogs (Kim et al. 2002). Introduction of a large number of heterodimers to the ancestral network in these models generates frequent links between paralogs which in the end gives rise to more realistic network topologies. Finally, we would like to speculate on a general role that the highly connected self-interacting proteins might play in the cell. A single protein molecule can simultaneously bind only a limited number of partners, at most equal to the number of its functional domains. On the other hand, most biological processes require many different proteins in numbers far greater than the binding capacity of a single protein molecule. The protein components of large signaling or biochemical pathways do not form large stable complexes containing all proteins simultaneously. Yet all the necessary molecules must be in a physical proximity to each other to form a functional module. This contradiction poses a question: how so many different proteins could co-localize in a cell to correctly perform a physiological function? A possible solution to this question involves highly connected self-interacting proteins serving as self-organizing centers for co-localization of the pathway components. The self-interaction (oligomerization) of such proteins might function as a general mechanism for sensing protein concentration (Marianayagam et al. 2004) Indeed, a random increase of a local concentration of monomers leads to their oligomerization and subsequently to the increase in the concentration of binding sites for other pathway components, increasing in turn their effective concentration.

VI.

MATERIALS AND METHODS

The protein interaction data for all four species were obtained from the Biological Association Network databases available from Ariadne Genomics (http://www.ariadnegenomics.com/). The database for H. sapiens was derived from the Ariadne Genomics ResNet database, constructed from the various literature sources using Medscan. Medscan is the Ariadne Genomics’ proprietary natural language processing technology (Novichkova et al. 2003, Daraselia et al. 2003). The databases for the baker’s yeast S. cerevisiae, the nematode worm C. elegans, 12

and the fruit ?y, D. melanogaster were constructed by combining the data from published high-throughput experiments with the literature data obtained using Medscan technology. For more details on the construction of these databases please refer to the PathwayAssist manual (http://www.ariadnegenomics.com/products/pathway.html). Most of the PPI interactions among ?y proteins (20496 out of 20595 or 99.5%) are extracted from a single system-wide two-hybrid study (Giot et al. 2003), while most of worm interactions (5286 out of 5309 or 99.5%) are from a large-scale two-hybrid study (Li et al. 2004). An abnormally small average degree in the worm PPI network compared to that of other organisms might be explained by the fact that, unlike in the yeast (Ito et al. 2001) and the ?y (Giot et al. 2003) cases, the high-throughput two-hybrid assay of worm proteins was not truly genome-wide. Indeed, in (Li et al. 2004) the authors experimentally investigated interactions of only 1873 baits (out of some 22000 worm proteins) against genome-wide libraries of preys. This resulted in an identi?cation of 4027 distinct pairs of interacting proteins which were subsequently extended to include a certain number of in-silico predicted “interologs”. The average degree of these tested 1873 baits (or rather 632 of them that we found among our network proteins) is approximately equal to 5.4. Not only it is much higher than the average degree 3.3 reported for all worm network proteins, but it is also remarkably close to the 5.7 ? 6.6 range found in the other three organisms. Lists of paralogous pairs and their sequence similarities for all four species studied here were obtained by the following procedure. Amino-acid sequences of individual proteins were obtained from the RefSeq database (http://www.ncbi.nlm.nih.gov/RefSeq/). For each organism, the sequences were compared against themselves using the BLASTp program with the expectation value cutoff equal to 0.001 (Altschul et al. 1990). A global alignment similarity was then computed by adding together numbers of similar amino-acids from all non-overlapping locally aligned segments and dividing this number by the geometric average of two protein lengths. Thus gaps between the aligned segments were considered to have zero similarity. In a case of overlapping segments we took the one with the highest percent of similarity. We estimated that about 2% of the true homologs are not recovered by this approach due to an incompleteness of the BLASTp output for local alignment. Another sacri?ce for quicker calculation is an underestimation of the global alignment score by 5-10% compared to more precise calculation after alignment using the CLUSTALW algorithm (Thompson et al. 1994). To avoid including pairs of proteins similar over only one of their domains we further restricted our set to only protein pairs with the similarity higher than 30%. At the end all protein pairs that 13

have been aligned by BLAST but omitted from the ?nal paralog list due to failing the similarity cutoff were searched for having common paralogs. If a common paralog was found, the pair was reinstated in the paralog list, even though its similarity is lower than the 30% cutoff.

VII.

ACKNOWLEDGMENT

This work was supported by 1 R01 GM068954-01 grant from NIGMS. Work at Brookhaven National Laboratory was carried out under Contract No. DE-AC02-98CH10886, Division of Material Science, U.S. Department of Energy.

VIII.

REFERENCES

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