Analysis on multi-domain cooperation for predicting protein-protein interactions
- Rui-Sheng Wang†1, 2,
- Yong Wang†3,
- Ling-Yun Wu3,
- Xiang-Sun Zhang3Email author and
- Luonan Chen2, 4, 5, 6Email author
© Wang et al.; licensee BioMed Central Ltd. 2007
Received: 18 March 2007
Accepted: 16 October 2007
Published: 16 October 2007
Domains are the basic functional units of proteins. It is believed that protein-protein interactions are realized through domain interactions. Revealing multi-domain cooperation can provide deep insights into the essential mechanism of protein-protein interactions at the domain level and be further exploited to improve the accuracy of protein interaction prediction.
In this paper, we aim to identify cooperative domains for protein interactions by extending two-domain interactions to multi-domain interactions. Based on the high-throughput experimental data from multiple organisms with different reliabilities, the interactions of domains were inferred by a Linear Programming algorithm with Multi-domain pairs (LPM) and an Association Probabilistic Method with Multi-domain pairs (APMM). Experimental results demonstrate that our approach not only can find cooperative domains effectively but also has a higher accuracy for predicting protein interaction than the existing methods. Cooperative domains, including strongly cooperative domains and superdomains, were detected from major interaction databases MIPS and DIP, and many of them were verified by physical interactions from the crystal structures of protein complexes in PDB which provide intuitive evidences for such cooperation. Comparison experiments in terms of protein/domain interaction prediction justified the benefit of considering multi-domain cooperation.
From the computational viewpoint, this paper gives a general framework to predict protein interactions in a more accurate manner by considering the information of both multi-domains and multiple organisms, which can also be applied to identify cooperative domains, to reconstruct large complexes and further to annotate functions of domains. Supplementary information and software are provided in http://intelligent.eic.osaka-sandai.ac.jp/chenen/MDCinfer.htm and http://zhangroup.aporc.org/bioinfo/MDCinfer.
Many proteins involved in signal transduction, gene regulation and other biological activities require interaction with other proteins or cofactors to achieve specific processes [1, 2]. Elucidating protein-protein interactions can provide deep insights into protein functions and intracellular signaling pathways. Owing to the recent rapid advances in high-throughput technologies, protein-protein interaction data of various species are increasingly accumulated from different experiments and deposited in several main databases such as DIP  and MIPS . This collection of protein-protein interaction data results in a rich, but quite noisy and still incomplete source of information [5, 6] which needs to be analyzed and completed by sophisticated computational methods.
In recent years, a number of computational algorithms have been developed to infer protein-protein interactions, such as those methods based on gene fusion (Rosetta Stone) [7, 8], phylogenetic profile , protein structure , and domain information . In particular, inferring protein-protein interactions (PPI) based on domain information, such as association method , probabilistic method [12–14], SVM-based method , and LP-based approach , has attracted much attention due to its clear biological implication and simplicity. In addition to these methods for protein interaction prediction, inferring domain-domain interactions (DDI) by integrating multiple data sources has also been investigated [17–19].
Domain-based protein interaction prediction assumes that proteins are composed by a set of recognition elements which are referred to as domains, and protein-protein interactions are achieved through domain interactions . A typical procedure for these methods includes two steps. Firstly domain interactions are inferred from experimental protein interactions, and then new protein interactions are predicted based on the inferred domain interactions according to either a probabilistic or deterministic model. The difference between probabilistic and deterministic models is whether or not they are based on the probabilistic formula describing the relations between domain interactions and protein interactions . Most existing algorithms consider domain-domain pairs as the basic units of protein-protein interactions, and these domain-domain interactions are assumed to be independent. However, such an assumption is actually not biologically reasonable because two or more domains may cooperatively interact with another domain . In addition, there are many superdomains where two domains always appear together in individual proteins to mediate the interactions. Given the close relations between two domains in a superdomain, the independence assumption of domain-domain interactions does not generally hold. For example, domain 4 of RNA polymerase Rpb1 (PF05000) and domain 1 of RNA polymerase Rpb1 (PF00623) constitute a superdomain, and they always appear together in individual proteins such as YOR341W, YDL140C and YOR116C, and have many common domain interaction partners .
Recently, Han et al. studied domain combinations in protein interactions [22, 23]. In their work, the appearance frequencies of domain combinations in a set of interacting and non-interacting protein pairs are counted to construct AP (Appearance Probability) matrices [22, 23] which provide useful information about the distribution of multi-domain interactions. For example, among the listed 300 domain combination pairs with high appearance probability values (top300) which are counted based on the total 5826 protein interaction pairs in yeast, there are 246 two-domain pairs, 44 three-domain pairs and 10 four and above domain pairs. Such statistical result indicates that many domains are closely correlated and tend to appear in interacting protein pairs together. In addition, Wang and Caetano-Anolles  used the occurrence and abundance of the molecular interactome of domain combinations to construct global phylogenic trees. When a closely correlated domain combination appears in an interactome, domains in this combination may mediate the interaction simultaneously and cooperatively.
Similar to proteins in a complex which cooperatively bind to each other so as to achieve specific functions , there is also such a cooperation among domains in protein interactions. For example, Klemm and Pabo  found that two unlinked polypeptides corresponding to the POU-specific domain and the POU homeo domain in protein Oct-1 bind cooperatively to the octamer site. Moza et al.  showed that the binding energetics between different hot regions consisting of interfacial residues in a protein-protein interaction are not strictly additive. Cooperative binding energetics between distinct hot regions is significant. They pointed out that cooperativity between hot regions has significant implications for the prediction of protein-protein interactions. When the hot regions are distributed over different domains in proteins, the cooperativity between different hot regions is actually embodied by multi-domain cooperation. Hence, revealing such domain cooperation may provide deep insights into the essential mechanism of protein interactions at the domain level, and can also be further exploited to improve the accuracy of protein interaction prediction.
In this paper, we firstly aim to identify cooperative domains from protein interaction data by extending two-domain interactions to multi-domain interactions. Cooperative domains mean that the strength of their cooperative interaction with some domain is stronger than the corresponding domain-domain interactions. Then, by employing the information of both multi-domains and multiple organisms, we propose a general framework based on a Linear Programming with Multi-domain pairs (LPM) and an Association Probabilistic Method with Multi-domain pairs (APMM), to predict protein interactions in a more accurate manner. Experimental results demonstrate that our approach not only can identify cooperative domains effectively but also has a higher accuracy for predicting protein interactions than the existing methods. Cooperative domains, including strongly cooperative domains and superdomains, were detected from major interaction databases, e.g. MIPS and DIP, and many of them were verified by checking physical interactions from the crystal structures of protein complexes in PDB (Protein Data Bank). These crystal structures of complexes provide intuitive evidences for such cooperation. In addition, comparison experiments in terms of protein/domain interaction prediction also justified the benefit of considering multi-domain cooperation.
The concept of cooperative domains in our work seems to be similar to Han et al.'s "domain combination" [22, 23]. However, there are two fundamental differences between these two concepts. Firstly, the definition of domain combination is not related to domain interaction strength. Each domain combination pair is considered in their approach, no matter what its appearance frequency is in interacting and non-interacting protein pairs. In contrast, the definition of cooperative domains emphasizes "cooperation" and is related to domain interaction strength. By an elaborated variable selection strategy (see Methods), only when the interaction strength of a three-domain pair (D m -D r , D n ) is larger than those of the corresponding two-domain pairs (D m , D n ) and (D r , D n ), this three-domain pair can possibly be a cooperative-domain pair and considered in the model. Secondly, there is no redundant correlation between different domain combinations in our work. For example, if a three-domain pair (D m -D r , D n ) is considered in our method according to the rules of selecting variables (i.e. D m , D r are considered as cooperative domains), the two-domain pairs (D m , D n ) and (D r , D n ) will not be included into the consideration as interacting domains in the same protein pair to eliminate the redundancy, in contrast to the high correlation among Han et al.'s domain combinations [22, 23].
In the following text, Pr(dm, n= 1) represents the probability that domain D m interacts with D n . Pr(dmr, n= 1) represents the probability that domains D m and D r cooperatively interact with D n . Similarly, Pr(dm, nr= 1) represents the probability that domains D n and D r cooperatively interact with D m . Our approach for detecting cooperative domains in protein-protein interactions can be summarized as three steps. First, we extend the conventional probabilistic model for inferring domain interactions to accommodate multi-domain pairs. Then, the interaction probabilities of multi-domain pairs are estimated by the proposed approach. Finally, according to the interaction probabilities of multi-domain pairs, cooperative domains and superdomains are detected. The detailed information on the methodology is given in Methods.
Identification of multi-domain cooperation
Identifying cooperative domains and superdomains
Our method is able to identify biologically meaningful superdomains and putative cooperative domains. We illustrate this feature by using MIPS data set. A cooperative domain pair has a stronger interaction effect than their corresponding two-domain pairs. Therefore, domains D m and D r are cooperative domains if Pr(dm, n= 1) < Pr(dmr, n= 1) and Pr(dr, n= 1) < Pr(dmr, n= 1) from the results of LPM or APMM. From the definitions, domains in a superdomain or in a strongly cooperative-domain pair are expected to have similar biological functions. We applied our approach to protein physical interaction data in MIPS1 (see Methods) to get reliable cooperative-domain interactions.
Superdomains detected by our method from MIPS protein interaction data, where GO annotations are denoted in italic
(1) MutS domain V, ATP binding, damaged DNA binding, mismatch repair
(2) MutS domain III, DNA metabolism
(1) Thiamine pyrophosphate enzyme, C-terminal TPP binding domain, catalytic activity, thiamin pyrophosphate binding
(2) Thiamine pyrophosphate enzyme, central domain, magnesium ion binding, thiamin pyrophosphate binding
(1) Sec23/Sec24 beta-sandwich domain
(2) Sec23/Sec24 zinc finger, COPII vesicle coat, protein binding, intracellular protein transport, ER to Golgi vesicle-mediated transport
(1) Tubulin/FtsZ family, C-terminal domain, protein complex, GTP binding, GTPase activity, protein polymerization
(2) Tubulin/FtsZ family, GTPase domain
(1) Peptidase dimerisation domain, hydrolase activity, protein dimerization activity
(2) Peptidase family M20/M25/M40, metallopeptidase activity, proteolysis
(1) RNA polymerase Rpb1, domain 4, DNA-directed RNA polymerase activity, DNA binding, transcription
(2) RNA polymerase Rpb1, domain 2, nucleus, DNA-directed RNA polymerase activity, DNA binding, transcription
(1) GHMP kinases C terminal
(2) GHMP kinases N terminal domain, ATP binding, kinase activity, phosphorylation
(1) Putative snoRNA binding domain
(2) NOSIC (NUC001) domain
(1) Glyceraldehyde 3-phosphate dehydrogenase, C-terminal domain, NAD binding, glyceraldehyde-3-phosphate dehydrogenase (phosphorylating) activity, glycolysis
(2) Glyceraldehyde 3-phosphate dehydrogenase, NAD binding domain, NAD binding, glyceraldehyde-3-phosphate dehydrogenase (phosphorylating) activity, glycolysis
(1) Ferric reductase NAD binding domain
(2) FAD-binding domain
Cooperative domains detected by our method from MIPS protein interaction data, where GO annotations are denoted in italic
Cooperative domains (Interactor I)
(1) Protein kinase domain, ATP binding, protein kinase activity, protein amino acid phosphorylation
(2) P21-Rho-binding domain
SH3 domain, in a variety of proteins with enzymatic activity
(1) WD domain, G-beta repeat, coordinating multi-protein complex assemblies
(2) F-box domain, mediating protein-protein interactions in a variety of contexts
Skp1 family, dimerisation domain
(1) Bromodomain, interacting specifically with acetylated lysine
(2) SNF2 family N-terminal domain, DNA binding, ATP binding
SWIRM domain, mediating protein-protein interactions
(1) PH domain
(2) PX domain, protein-protein interaction domain, protein binding, phosphoinositide binding, intracellular signaling cascade
Sporulation protein Zds1 C terminal region, suppress the calcium sensitivity of Zds1 deletions
(1) Protein kinase domain, ATP binding, protein kinase activity, protein amino acid phosphorylation
(2) PH domain
SH3 domain, in a variety of proteins with enzymatic activity
(1) SH3 domain, in a variety of proteins with enzymatic activity
(2) Myosin head (motor domain), myosin, ATP binding, motor activity
WH2 motif, actin-binding motif
(1)Pumilio-family RNA binding repeat, DNA binding
(2) RNA recognition motif
AMP-binding enzyme, catalytic activity, metabolism
(1) HEAT repeat, involved in intracellular transport processes
(2) Importin-beta N-terminal domain, nuclear pore, nucleus, cytoplasm, protein transporter activity, protein import into nucleus, docking
Nucleoporin autopeptidase, nuclear pore, transport
(1) AT hook motif, DNA binding motifs
(2) Helicase conserved C-terminal domain, ATP binding, helicase activity, nucleic acid binding
Myb-like DNA-binding domain, nucleus, DNA binding
Strongly cooperative domains detected by our method from MIPS protein interaction data, where GO annotations are denoted in italic
Cooperative domains (Interactor I)
(1) Guanine nucleotide exchange factor for Ras-like GTPases; N-terminal motif, intracellular, regulation of small GTPase mediated signal transduction
(2) SH3 domain, in a variety of proteins with enzymatic activity
Hsp70 protein, involved in different cellular compartments (nuclear, cytosolic, mitochondrial, endoplasmic reticulum, etc
(1) Skp1 family, dimerisation domain
(2) Skp1 family, tetramerisation domain
F-box domain, mediating protein-protein interactions
(1) RNA polymerase Rpb1, domain 5, DNA-directed RNA polymerase activity, DNA binding, transcription
(2) RNA polymerase Rpb1, domain 2, nucleus, DNA-directed RNA polymerase activity, DNA binding, transcription
RNA polymerase Rpb5, C-terminal domain, DNA-directed RNA polymerase activity, DNA binding, transcription
(1) Pumilio-family RNA binding repeat, RNA binding
(2) RNA recognition motif, nucleic acid binding
Seripauperin and TIP1 family, response to stress
(1) EF hand, calcium ion binding
(2) Domain of unknown function (DUF1720), in different combinations with cortical patch components EF hand, SH3 and ENTH
ANTH domain, phospholipid binding
(1) Ubiquitin carboxyl-terminal hydro-lase, cysteine-type endopeptidase activity, ubiquitin thiolesterase activity, ubiquitin-dependent protein catabolism
(2) Rhodanese-like domain
Fes/CIP4 homology domain, regulatory processes
(1) RhoGAP domain, intracellular, signal transduction
(2) PX domain, protein binding, phos-phoinositide binding, intracellular signaling cascade
Sporulation protein Zds1 C terminal region, sporulation, suppress the calcium sensitivity of Zds1 deletions
(1) BAH domain, DNA binding, involved in protein-protein interaction
(2) bromodomain, involved in protein-protein interactions
RNA recognition motif, nucleic acid binding
Verifying cooperative domains by crystal structures
In this section, we verify the detected cooperative domains by checking their physical interactions from the crystal structures of protein complexes in PDB and examine the essential mechanism of protein interactions at the domain level. The complex crystal structures in PDB can be regarded as a gold standard to verify protein interactions and domain interactions. The seq2struct web resource  was used to search sequence-structure links. By focusing on the protein pairs in which proteins are mapped to the same PDB IDs but possess different chain IDs, we found 50 protein pairs with crystal structures that contain cooperative-domain pairs identified by our approach (t-test value is significant by comparing with randomly generated domain pairs).
Furthermore we also revealed some complexes in PDB which are not reported by PROTCOM . For example, three domains Arm, IBB and IBN_N which belong to Armadillo repeat superfamily form a cooperative-domain interaction (PF00514–PF01749, PF03810), and such multi-domain cooperation leads to the complex formed by protein Q02821 (YNL189W) and P33307 (YGL238W) (PDB ID 1wa5, GTP-Binding nuclear protein RAN). Generally, multiple cooperative-domain interactions in an interacting protein pair often correspond to a more complicated complex. The complete list of all the verified cooperative domain interactions by crystal structures in PDB and more detailed information are provided on our web site.
PPI prediction based on multi-domain cooperation
Test on numerical PPI data sets
In addition to identifying superdomains and cooperative domains, our approach has a higher prediction accuracy for protein interactions by exploiting the information of both multi-domains and multiple organisms. In this section, we compared LPM and APMM with the existing methods, such as association based methods (ASNM , ASSOC ), and EM method . Among those existing methods, the ASSOC and EM are developed for the binary interaction data whereas ASNM can be applied to experiment ratio data. We evaluated each method by fivefold cross validation on Ito's experiment ratio data  and assessed the prediction accuracy by root-mean-square error (RMSE) (see Methods).
Comparisons of several methods in terms of RMSE and training time on Ito's dataset
Comparisons of of several methods in term of RMSE and training time on Krogan's yeast extended dataset
Test on binary PPI data sets from multiple organisms
Compared with single organism, data sets from multiple organisms can provide more information, e.g. they cover more domains. In contrast to the existing methods which mainly use the data from single organism, LPM and APMM can employ the data sets from multiple organisms with the consideration of their different reliabilities. In this section, we used binary interaction data from multiple organisms collected by Liu et al.  (see Methods) to compare our approach with the extended EM algorithm  and validate the benefit of multi-domain pairs on binary interaction data.
To examine the effect of cooperative domains on prediction accuracy based on binary interaction data, we used the same training set and directly compared the prediction accuracies of APMM with multi-domain pairs and with only two-domain pairs. The result summarized in Figure 4(b) confirms that APMM with multi-domain pairs has a higher prediction accuracy. The performance of LPM was also confirmed in a similar manner.
Evaluation at domain level and comparison with other methods
In this section, we evaluated our methods at the domain level by comparing the predicted domain interactions with domain interactions in iPfam  and the confidence DDI data in InterDom  (see Methods). The same data set in above section was used as training set.
The overlap of the predicted domain interactions by APMM and LPM with those in iPfam, where λ denotes domain interaction probability, 'Single organism' means the training set of protein interactions is only from yeast, 'Multiple organisms' means the training set is from three organisms: yeast, worm and fly
Single organism (p-value)
Multiple Organisms (p-value)
λ > 0.1
λ > 0.2
99 (< 1e-013)
λ > 0.3
149 (< 1e-013)
λ > 0.4
λ > 0.5
λ > 0.1
λ > 0.2
λ > 0.3
61 (< 1e-013)
λ > 0.4
130 (< 1e-013)
λ > 0.5
49 (< 1e-013)
93 (< 1e-013)
The overlap of the predicted domain interactions by APMM and LPM with those in InterDom, where λ denotes domain interaction probability
Total domain pairs
InterDom overlap (p-value)
λ > 0.1
λ > 0.2
λ > 0.3
3749 (< 1e-013)
λ > 0.4
λ > 0.5
1800 (< 1e-013)
λ > 0.1
λ > 0.2
5844 (< 1e-013)
λ > 0.3
3753 (< 1e-013)
λ > 0.4
λ > 0.5
As for identifying cooperative domains, we made a rough comparison with Han et al.'s domain combination approach [22, 23]. Han et al. provided on their website  a set of 5826 proteins based on which they listed 300 predicted domain combination interacting pairs with top confidence. Among these 300 pairs, there are 246 two-domain pairs, 44 three-domain pairs and 10 four and above domain pairs. We applied our approach to the same dataset and found 34 cooperative-domain pairs (with interaction probability 1.0) among 500 high-scoring domain interactions, 225 among 1000 high-scoring domain interactions, and 635 among 2000 high-scoring domain interactions. Note that in 500 high-scoring domain interactions, the number of cooperative domains is not more than Han's (34/500< 44/300), but when the threshold is lower, we found more cooperative domains. This is mainly due to the difference between the definitions of cooperative domains and domain combinations. In our approach, if a two-domain pair has a stronger interaction, the three-domain pair in the same protein pair will not be included as potential cooperative domains. If two-domain pairs have weaker interactions than the corresponding cooperative-domain interaction, this three-domain pair will be considered and the two-domain pairs will be excluded in the same protein pair. In other words, we eliminate the redundancy between domain combinations, whereas in Han et al.'s method, each domain combination is included.
In this work, cooperative domains, strongly cooperative domains and superdomains in MIPS and DIP were detected, and many of them were verified by the crystal structures in PDB. Functional relations in superdomains and cooperative domains were examined by the terms of GO. Among the detected superdomains, we found that two domains in most of them belong to a same family and have similar or identical functions. Such fact is biologically reasonable because the two domains in a superdomain always appear together in individual proteins and participate in interaction processes simultaneously. It is interesting that many domains that act as superdomains are binding domains, such as snoRNA binding, ATP binding, DNA binding, FAD-binding, NAD-binding, GTP binding, protein binding, and Lum-binding. For cooperative domains, some of them have dissimilar functions partly because domain cooperation needs complementary functions . Cooperative domains tend to be contained in big complicated protein complexes. For example, among cooperative domains with crystal structures, 72% of (36/50) them are involved in large complexes with more than five proteins. This fact to some extent illustrates that multi-domain cooperation can be easily achieved in a multi-protein complex where protein cooperation is prominent.
Multi-domain cooperation information can be explored to reconstruct the structure of a large protein complex. Protein complexes are key molecular entities that integrate multiple gene products to perform cellular functions. Recently, tandem-affinity-purification coupled to mass spectrometry (TAP-MS) which combines affinity tags-based protein purification technique and mass spectrometry for identifying a tagged protein and its interaction partners  has been applied to find the genome-wide screen for complexes [29, 35]. However, although many complexes have now been identified, the detailed interacting relationships among the components are beyond our knowledge because only a few of them have 3D structural information. As pointed in Aloy and Russell , X-ray crystallography provides atomic-resolution models for proteins and complexes, but it is difficult for this technique to obtain sufficient information for the crystallization of large complexes. NMR is generally limited to proteins that have no more than 300 residues. It is therefore necessary and timely to develop new approaches that can reconstruct the structures of complexes based on protein structures and their interaction relationships . The detected cooperative domains in this work can be applied to this problem by combining with docking procedures.
Domains are viewed as the basic functional units of proteins, and it is believed that protein interactions are achieved through domain interactions. Most existing methods for inferring protein interactions from experimental data assume that two-domain pairs are dominating factors for protein interactions. However, like the cooperation of several proteins in a complex, many domains may be cooperative in achieving the interaction of a protein pair. In this paper, we focus on revealing such domain cooperation by considering multi-domain pairs as the basic units of protein interactions. In addition, in contrast to the existing methods which mainly use the data from single organism, data sets for multiple species with different reliabilities were exploited in this paper to make full use of the available information. From the computational viewpoint, this paper provides a general framework based on APMM and LPM to predict protein interactions in a more accurate manner by considering the information of both multi-domain pairs and multiple organisms, which can also be applied to identify cooperative domains. Experiment results demonstrated that our method not only can find superdomains and putative cooperative domains effectively but also has a higher prediction accuracy of protein interactions than the existing methods. Cooperative domains, strongly cooperative domains and superdomains in MIPS and DIP were detected, and many of them were verified by the crystal structures in PDB. Comparison experiments on protein/domain interaction prediction confirm the benefit of considering multi-domain cooperation. More detailed results and software can be found at our website.
In this work, we validated our approach using several types of experiments which employed various experiment data sets as follows.
Binary PPI data
When we test our method for detecting cooperative domains and PPI prediction based on multiple-organism data, we used binary interaction data in which the information is whether two proteins interact or not. In other words, there is not a confidence score for each protein-protein interaction. We collected 4103 physical interactions in yeast from MIPS  (the version is PPI_141105.tab, denoted as MIPS1) and identified superdomains and cooperative domains in this dataset.
For PPI prediction based on multiple-organism data, in order to make comparison convenient, we used the same training data and testing data collected by Liu et al. . These datasets are from yeast S.cerevisiae, worm C.elegans and fly D.melanogaster with respectively 5295, 4714 and 20349 protein interactions. The protein-domain relationships for each protein are extracted from PFAM  and SMART . Among these protein interaction data, only those with domain information were used. In addition, like in Liu et al. , an independent test set including the 3543 yeast physical interaction pairs in MIPS (denoted it as MIPS2) was used as positive examples and the other possible protein pairs, totally 6895215 pairs, as negative examples.
For comparison experiments at the domain interaction level, we used protein-protein interactions and protein domain composition dataset in Riley et al.  and Guimaraes et al. . This set was obtained from the DIP database  and contains 26,032 interactions underlying 11,403 proteins from 69 organisms.
Numerical PPI data
Numerical interaction data are defined as opposite to binary interaction data. It means that each protein-protein interaction has a score to denote the interaction strength. It includes experiment ratio data based on IST  and confidence data by integrating various data sources . IST (Interaction Sequence Tags) was used for decoding interacting proteins in examining two-hybrid interactions. Experiment ratio data based on IST mean that each protein-protein interaction is provided with the number of IST hitting in a certain number of experiments. We conducted cross-validation experiment on numerical interaction data. The first set is a well known dataset– the full data of Ito's dataset . This dataset has 1586 interactions with 1420 proteins containing domain information, and provides the numerical interaction (ratio) data for protein pairs based on the number of IST hits. The other is Krogan's extended dataset . This set has 10265 interactions with 2843 proteins containing domain information. It provides each protein interaction with a confidence score.
Domain sources and DDI data
The domain information for proteins was extracted from Pfam 14.0 . For MIPS1, there are total 1483 Pfam domains involved in 2477 proteins. iPfam database  contains domain-domain interactions confirmed by PDB crystal structures. It has been used as a gold standard set for evaluating predicted domain-domain interactions [17, 19]. In this work, 3034 domain interactions in iPfam (December 2005 version) were used for evaluating domain interaction prediction. In addition, InterDom (version 1.2)  was also used for this purpose. It is a database of putative interacting domains derived from multiple data sources, ranging from domain fusions (Rosetta Stone), protein interactions (DIP and BIND), protein complexes (PDB), to scientific literature (MEDLINE). InterDom 1.2 has 30038 putative domain interactions with different confidence scores.
Protein complex and crystal structure database
Cooperative domains were confirmed using structural data of protein complexes from PDB and PROTOCOM. Protein sequences were mapped from Swiss-Prot/TrEMBL database to their corresponding structure files using the seq2struct web resource . PROTOCOM  is a collection of protein-protein transient complexes and domain-domain structures. It provides the detailed information about protein interactions by identifying the contacted residues, presenting the number of residues on the interface and the list of interfacial residues.
Probabilistic model with multi-domain pairs
In this section, we describe an improved probabilistic model for protein interactions by considering the multi-domain pairs, which is the essential basis of our method.
where Pr( = 1) represents the interaction probability of proteins and in dataset k, and Pr(dm, n= 1) represents the probability that domain D m interacts with D n . Pr(dmr, n= 1) represents the probability that domains D m and D r cooperatively interact with D n . Pr(dm, nr= 1) has a similar meaning. For each protein pair in (1), if there is a cooperative interaction of domains D m - D r with domain D n in the second multiplying term, then (D m , D n ) and (D r , D n ) must be excluded from the first multiplying term in order to maintain the independence assumption; otherwise, (D m - D r , D n ) should be deleted. The third multiplying term for (D m , D r - D n ) should be checked in the same way. Clearly, the first multiplying term represents the effect of two-domain pair interactions while the second and third multiplying terms stand for the effects of cooperative-domain interactions. In next section, we will show how to determine those independent variables.
Note that we extend two-domain interactions only to three-domain interactions because the cooperation involving more than three domains is believed to be rare compared with cases of two and three domains, though theoretically model (1) can be further extended to four-domain pair and above but with the sacrifice of the computational efficiency. Figure 1(b) gives an example for inferring domain interactions from protein interaction and non-interaction data. It indicates that the classical probabilistic model fails to give the correct result for this case while our model can do it by considering multi-domain interactions.
Selection of independent variables
If Rmr, n< Rm, nor Rmr, n< Rr, n, it indicates that the appearance frequency of domain pair Dmr, nin interacting protein pairs is not higher than those of Dm, nand Dr, n. We consider that there is no cooperation between D m and D r in their interacting with D n , so we keep the variables dm, n, dr, nand delete the variable dmr, nin (1).
If Rmr, n≥ Rm, nand Rmr, n≥ Rr, n, for Dm, n
when Rmr, n> Rm, nand Imr, n= Im, n, the appearance frequency of domain pair Dmr, nin interacting protein pairs is higher than those of Dm, nand Dr, n, and furthermore, Dm, ndoes not appear in any other interacting protein pair without D r . Hence, we consider that D m and D r are cooperative when interacting with D n , and thereby the variable dm, nis deleted, but the variable dmr, nis kept in (1);
when Rmr, n= Rm, nand Imr, n= Im, n, it means that D m and D r always appear together in individual proteins. Hence, D m and D r are considered as a superdomain and can be merged to one. For such a case, we delete variable dm, nbut keep the cooperative-domain pair dmr, n.
The operations are performed in the same way for Dr, n. For the case of Figure 1(b), variables for all domain pairs except (D1 - D2, D3) are deleted based on this procedure.
Obviously, the above operations do not cover the case Rmr, n≥ Rm, nand Imr, n< I mn . For this case, we cannot determine if or not there is a cooperative effect of domains D m and D r on their interacting with domain D n since Dm, nalso appears in the interacting pairs without D r , thereby we keep all of them. This may affect the assumption of independence, but there are few such cases. For example, for the date set MIPS1, among 22325 multi-domain pairs, there are only 85 such cases. Hence, by the above variable deletion operations, the assumption can be primarily satisfied. In the following formulation, all the variables appearing in the formula are those kept after the deleting strategy, whereas the probabilities of all deleted variables are set to be zero. Note that, in contrast to the appearance frequency or interaction strength for selecting cooperative domains, the two domains in a superdomain are determined based on their co-occurrence, and the cooperativity are also indirectly confirmed by their identical or similar functions from GO annotations.
Inference of domain interactions
Linear programming with multi-domain pairs
The parameters fp k and fn k can be estimated from experimental data in a similar way as that in Liu et al. .
where is the error for each equality of (5). Model (6) can be solved by any standard LP technique (see Additional file 1).
Solving (6), we can obtain a set of interaction probabilities for domain pairs. Then, new protein interactions can be predicted by these inferred domain interactions through the probabilistic model (1).
Association probabilistic method with multi-domain pairs
where || represents the number of multi-domain pairs in , and is the observed interaction probability between and in the experimental data after considering the false positive and false negative rates. Note that the deleted variables are not counted. From these formula, we can see that all domain pairs have an equal opportunity to contribute the interactions between and for || > 1 under the independence assumption for domain interactions. With these interaction probabilities of domain pairs, we can predict whether a pair of proteins interact or not by the formula (1). The computation of this method is much simple and thus highly efficient. In addition, it does not require any parameter tuning.
We validated our method using several types of experiments with different criteria. For computing the similarity of GO annotations , we adopted a simple method used successfully in Chen et al.  and Wu et al. . In this method, known proteins are assigned with functional annotations by a GO Identification (ID). According to the hierarchical structure of GO annotations, each GO term corresponds to a numerical GO INDEX. The more detailed level of the GO INDEX, the more specific is the function assigned to a protein. The maximum level of GO INDEX is 14. The function similarity between proteins P x and P y is defined by the maximum number of index levels from the top shared by P x and P y . The smaller the value of function similarity, the broader is the functional category shared by the two proteins. The details can be found in Chen et al. .
where P denotes a set of protein pairs (training set or testing set) including interactions and non-interactions. Non-interacting protein pairs may be those not appearing in the observed interaction data or those whose interaction probabilities are below a threshold.
where the number of true positives (TP), true negatives (TN), false positives (FP) and false negatives (FN) are estimated with respect to the given test set.
where n denotes the total number of the predicted domain interactions and N denotes the overlap of the predicted domain interactions with the gold standard set. p represents the probability that a randomly predicted domain pair is in the gold standard set. This measure characterizes the significance of an overlap.
Linear Programming with Multi-domain pairs
Association Probabilistic Method with Multi-domain pairs
Association Numerical Method
Root Mean Square Error
Interaction Sequence Tags
Area Under Curve.
The authors are grateful to the anonymous referees for their valuable comments and suggestions in improving the presentation of the earlier version of the paper. This research work is supported by JSPS under JSPS-NSFC collaboration project, the National Nature Science Foundation of China (NSFC) under grant No.10701080 and the Ministry of Science and Technology, China, under grant No.2006CB503905.
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