 Research article
 Open Access
 Published:
Analysis on multidomain cooperation for predicting proteinprotein interactions
BMC Bioinformatics volume 8, Article number: 391 (2007)
Abstract
Background
Domains are the basic functional units of proteins. It is believed that proteinprotein interactions are realized through domain interactions. Revealing multidomain cooperation can provide deep insights into the essential mechanism of proteinprotein interactions at the domain level and be further exploited to improve the accuracy of protein interaction prediction.
Results
In this paper, we aim to identify cooperative domains for protein interactions by extending twodomain interactions to multidomain interactions. Based on the highthroughput experimental data from multiple organisms with different reliabilities, the interactions of domains were inferred by a Linear Programming algorithm with Multidomain pairs (LPM) and an Association Probabilistic Method with Multidomain 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 multidomain cooperation.
Conclusion
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 multidomains 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.osakasandai.ac.jp/chenen/MDCinfer.htm and http://zhangroup.aporc.org/bioinfo/MDCinfer.
Background
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 proteinprotein interactions can provide deep insights into protein functions and intracellular signaling pathways. Owing to the recent rapid advances in highthroughput technologies, proteinprotein interaction data of various species are increasingly accumulated from different experiments and deposited in several main databases such as DIP [3] and MIPS [4]. This collection of proteinprotein 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 proteinprotein interactions, such as those methods based on gene fusion (Rosetta Stone) [7, 8], phylogenetic profile [9], protein structure [10], and domain information [11]. In particular, inferring proteinprotein interactions (PPI) based on domain information, such as association method [11], probabilistic method [12–14], SVMbased method [15], and LPbased approach [16], has attracted much attention due to its clear biological implication and simplicity. In addition to these methods for protein interaction prediction, inferring domaindomain interactions (DDI) by integrating multiple data sources has also been investigated [17–19].
Domainbased protein interaction prediction assumes that proteins are composed by a set of recognition elements which are referred to as domains, and proteinprotein interactions are achieved through domain interactions [12]. 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 [12]. Most existing algorithms consider domaindomain pairs as the basic units of proteinprotein interactions, and these domaindomain 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 [20]. 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 domaindomain 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 [21].
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 noninteracting protein pairs are counted to construct AP (Appearance Probability) matrices [22, 23] which provide useful information about the distribution of multidomain 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 twodomain pairs, 44 threedomain 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 CaetanoAnolles [24] 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 [1], there is also such a cooperation among domains in protein interactions. For example, Klemm and Pabo [25] found that two unlinked polypeptides corresponding to the POUspecific domain and the POU homeo domain in protein Oct1 bind cooperatively to the octamer site. Moza et al. [20] showed that the binding energetics between different hot regions consisting of interfacial residues in a proteinprotein 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 proteinprotein interactions. When the hot regions are distributed over different domains in proteins, the cooperativity between different hot regions is actually embodied by multidomain 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 twodomain interactions to multidomain interactions. Cooperative domains mean that the strength of their cooperative interaction with some domain is stronger than the corresponding domaindomain interactions. Then, by employing the information of both multidomains and multiple organisms, we propose a general framework based on a Linear Programming with Multidomain pairs (LPM) and an Association Probabilistic Method with Multidomain 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 multidomain cooperation.
Results
In this paper, we investigate domain cooperation in protein interactions by extending twodomain interactions to multidomain interactions. We first define the types of domains and domain pairs, and then describe the main results. Assume that there are M domains D_{1}, …, D_{ M }involved in the experimental interaction data. We use (D_{ m }, D_{ n }) to represent a twodomain pair, one domain in a protein and the other in another protein, and use (D_{ m }D_{ r }, D_{ n }) to denote a generalized pair i.e. a threedomain pair, where D_{ m }and D_{ r }appear in one protein (denoted by D_{ m }D_{ r }) and D_{ n }in another protein. A multidomain pair means a twodomain pair or a threedomain pair. In Figure 1(a), we list all the multidomain pairs in proteins (P_{1}, P_{2}). A cooperativedomain pair (cooperativedomain interaction) implies a generalized pair (D_{ m }D_{ r }, D_{ n }) in which two domains D_{ m }D_{ r }referred as cooperative domains coexist in a protein P_{1} and cooperatively interact with D_{ n }in another protein P_{2}. The cooperativedomain pair should have a stronger interaction effect than the corresponding twodomain pairs (D_{ m }, D_{ n }) and (D_{ r }, D_{ n }). A strongly cooperativedomain pair (strongly cooperativedomain interaction) is a cooperativedomain pair (D_{ m }D_{ r }, D_{ n }) which satisfies that there is an interaction effect of D_{ m }or D_{ r }on D_{ n }only if the domains D_{ m }and D_{ r }appear together. In Figure 1(b), D_{1} and D_{2} are strongly cooperative domains interacting with D_{3} because all other domain pairs involving D_{1} or D_{2} have no interactions. A superdomain implies two 'combined' domains D_{ m }D_{ r }which are special cooperative domains and always appear together in individual proteins. Note that we extend twodomain interactions only to threedomain interactions because the cooperation of more than three domains is believed to be rare compared with the cases of two and three domains according to statistics [22].
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 noninteracting 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 threedomain pair (D_{ m }D_{ r }, D_{ n }) is larger than those of the corresponding twodomain pairs (D_{ m }, D_{ n }) and (D_{ r }, D_{ n }), this threedomain pair can possibly be a cooperativedomain pair and considered in the model. Secondly, there is no redundant correlation between different domain combinations in our work. For example, if a threedomain 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 twodomain 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(d_{m, n}= 1) represents the probability that domain D_{ m }interacts with D_{ n }. Pr(d_{mr, n}= 1) represents the probability that domains D_{ m }and D_{ r }cooperatively interact with D_{ n }. Similarly, Pr(d_{m, nr}= 1) represents the probability that domains D_{ n }and D_{ r }cooperatively interact with D_{ m }. Our approach for detecting cooperative domains in proteinprotein interactions can be summarized as three steps. First, we extend the conventional probabilistic model for inferring domain interactions to accommodate multidomain pairs. Then, the interaction probabilities of multidomain pairs are estimated by the proposed approach. Finally, according to the interaction probabilities of multidomain pairs, cooperative domains and superdomains are detected. The detailed information on the methodology is given in Methods.
Identification of multidomain 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 twodomain pairs. Therefore, domains D_{ m }and D_{ r }are cooperative domains if Pr(d_{m, n}= 1) < Pr(d_{mr, n}= 1) and Pr(d_{r, n}= 1) < Pr(d_{mr, n}= 1) from the results of LPM or APMM. From the definitions, domains in a superdomain or in a strongly cooperativedomain pair are expected to have similar biological functions. We applied our approach to protein physical interaction data in MIPS1 (see Methods) to get reliable cooperativedomain interactions.
Totally we found 5187 twodomain interactions (with nozero interaction probability), 83 superdomains and 650 cooperativedomain pairs, among which 525 pairs are strongly cooperative domain interactions according to the above definition. Some detected (strongly) cooperative domains and superdomains in MIPS1 are respectively listed in Tables 1, 2 and 3. To investigate functional relations of domains in these superdomains and cooperative domains, we listed their Pfam descriptions and GO annotations. GO similarity was computed for two domains both with GO annotations in superdomains (Table 1). From these tables, we can see that two domains in most superdomains and some cooperative domains have similar GO annotations or belong to a same family, which is consistent with our hypotheses, i.e., domains in a cooperativedomain interaction work cooperatively to facilitate specific functions. For instance, two domains in superdomains PF05000PF00623, PF02775PF00205, PF02800PF00044 or PF00488–PF05192 have identical or similar functions at the respective GO levels. For those superdomains without GO annotations, the Pfam descriptions of two domains in most of them are also similar, such as PF08033PF04810, PF03953PF0009 or PF08544PF00288. For cooperative domains, some of them have similar GO annotations of functions, such as PF00806PF00076, where PF00806 is a Pumiliofamily RNA binding repeat and PF00076 is a RNA recognition motif. Both domains are necessary for RNA binding. Some cooperative domains have no GO annotations but belong to same families, such as PF01466–PF03931. Both PF01466 (Skp1, dimerisation domain) and PF03931 (Skp1_POZ, tetramerisation domain) belong to the Skyp1 family. It is interesting that three domains in the strongly cooperativedomain interaction (PF04998PF00623, PF01191) are found to have same functions, and they are all RNA polymerase domains. As another example, we identified cooperative domains PF00036–PF08226, and the Pfam description also supports the combination of PF08226 (DUF1720) with PF00036 (EF hand) [21]. Such facts imply that we can infer the functions of cooperative domains if one of them has known functions. We also applied our approach to DIP data set, and the detected superdomains and cooperative domains are given in Tables IIII (Additional File 1)
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 [26] was used to search sequencestructure 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 cooperativedomain pairs identified by our approach (ttest value is significant by comparing with randomly generated domain pairs).
Figure 2 shows cooperative domains in a complex crystal structure formed by physical interactions of proteins P02994 (ORFs: YBR118W, YPR080W) and P32471 (ORF: YAL003W), where P02994 has three domains and P32471 has one domain PF00736. This complex is also included in the complex database PROTCOM [27]. Interacting protein pairs and their Pfam domain annotations are described in this figure. Clearly, EF1 guanine nucleotide exchange domain PF00736 in P32471 has interactions with all of the domains in P02994. These interactions are verified by the binding sites of PF00736 with the domains in P02994. The cartoon of crystal structure illustrates that all cooperativedomain interactions in (P02994, P32471) are correctly identified and supported by the interfacial residues involved in the interaction. The interfacial residues are picked out by a simple rule, i.e. their Cα atoms are within the distance threshold 10Å, which is consistent with the more accurate computation given in PROTCOM. This example provides an intuitive evidence for the cooperation among domains in the interaction of P02994 and P32471.
Furthermore we also revealed some complexes in PDB which are not reported by PROTCOM [27]. For example, three domains Arm, IBB and IBN_N which belong to Armadillo repeat superfamily form a cooperativedomain interaction (PF00514–PF01749, PF03810), and such multidomain cooperation leads to the complex formed by protein Q02821 (YNL189W) and P33307 (YGL238W) (PDB ID 1wa5, GTPBinding nuclear protein RAN). Generally, multiple cooperativedomain 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 multidomain 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 multidomains and multiple organisms. In this section, we compared LPM and APMM with the existing methods, such as association based methods (ASNM [16], ASSOC [11]), and EM method [12]. 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 [28] and assessed the prediction accuracy by rootmeansquare error (RMSE) (see Methods).
The performance of each method in terms of RMSE and elapsed training time for fivefold crossvalidation is summarized in Table 4. In order to check the effect of cooperative domains on the accuracy, here we computed RMSE only on those protein pairs containing cooperativedomain pairs. RMSE comparison results on all protein pairs are given in Table IV and Table V (Additional file 1). From Table 4 we can see that the performances of EM and ASSOC methods on experiment ratio data are not good since their training and testing errors are very high. ASNM which is an extension of ASSOC has much better results than ASSOC. LPM has a lower training and testing error than the methods based on twodomain pairs. Table 4 also indicates that APMM has the lowest error in both training and testing prediction of protein interactions. In addition, there is no significant increase on the computation time when multidomain pairs are included.
The results for Ito's dataset in five rounds are not so consistent because there may exist bias in five divided subsets due to the small size of this dataset. Another larger dataset used for crossvalidation is Krogan's confidence data [29] (see Methods). We used this set to test if or not various methods can correctly predict the interaction confidence of protein pairs. The result is summarized in Table 5, from which we can see that for the confidence prediction, our approach (LPM and APMM) employing multidomain pairs again has better performance both in training and in testing than other methods. LPM generally has less training error than APMM but its testing error is slightly higher than that of APMM. An example to illustrate the effect of cooperative domains on the prediction accuracy is given in Additional file 1. We also made a direct comparison of our approach based on twodomain pairs and multidomain pairs, and the results are summarized in Figure 3. We can see that LPM based on multidomain pairs in training and testing has less prediction error in each round of fivefold cross validation than LPM based on only twodomain pairs. APMM also has such a tendency except the first round in testing. Such results further confirm the benefit of considering multidomain interactions.
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. [14] (see Methods) to compare our approach with the extended EM algorithm [14] and validate the benefit of multidomain pairs on binary interaction data.
Based on the same test set and training set, it is convenient to compare our methods and the extended EM [14]. The training sets respectively consist of protein interactions from single organism (yeast) and multiple organisms. Based on yeast protein interaction dataset, we found 4556 twodomain interactions (with nozero interaction probability), 94 superdomains, 652 cooperative domain pairs, among which 640 pairs are strongly cooperativedomain interactions. In the protein interaction dataset of three organisms, we detected 34123 twodomain interactions (with nozero interaction probability), 259 superdomains and 5633 cooperativedomain interactions, where 5400 are strongly cooperative. Among the cooperativedomain interactions in yeast and three organisms, 117 pairs are yeastspecific. With these domain interactions, the prediction accuracy of proteinprotein interactions is measured by the receiver operating characteristic (ROC) curve, which is a plot of the true positive rate (sensitivity) against the false positive rate (1–specificity) for different thresholds. The result is plotted in Figure 4(a), from which we can see that APMM has a higher prediction accuracy than the extended EM algorithm on multipleorganism data. The AUC values of APMM, EM trained on multipleorganism data and EM trained on singleorganism data are respectively 0.766, 0.701 and 0.611. This result indicates that APMM is also effective on binary interaction data. LPM has a similar performance as APMM which is not shown here.
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 multidomain pairs and with only twodomain pairs. The result summarized in Figure 4(b) confirms that APMM with multidomain 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 [30] and the confidence DDI data in InterDom [31] (see Methods). The same data set in above section was used as training set.
The comparison results of the predicted domain interactions by LPM and APMM with those in iPfam are summarized in Table 6 with the significance of the overlap (pvalue) computed by comparing with randomly predicted domain pairs (see Methods). We can see that domain interactions predicted by our approach have a significant overlap with iPfam and domain interactions predicted from multipleorganism data have larger overlap with iPfam owing to exploiting more information. Note that the overlap proportion is not so big. This is mainly because the amount of data in iPfam is highly incomplete and many domain interactions do not appear in iPfam.
The comparison results of the predicted domain interactions by LPM and APMM with those in InterDom are summarized in Table 7 with pvalues, which shows that the overlap with InterDom is significant and the interaction probabilities of predicted domain pairs are positively correlated with those in InterDom, i.e. a higher threshold corresponds to a higher mean confidence score. In addition, when selecting the same number of top highscoring predicted domain interactions, the prediction result exploiting multipleorganism data has a much higher mean confidence score than that based on singleorganism data, which is shown in Figure 5.
The domain interactions in iPfam have been used as a gold standard set to evaluate the predicted domaindomain interactions [17, 19]. We conducted a comparison experiment to evaluate the performance of our approach and the methods in Riley et al. [17] and Guimeraes et al. [19] based on the number of highscoring domaindomain interactions confirmed by the gold standard set. Specifically, three methods (APMM in our work, DPEA in [17], PE in [19]) were applied in a same training set (DIP data, see Methods) and we checked the overlap of the predicted domaindomain interactions with iPfam by selecting a same number of highscoring predicted domain interactions. The results based on 3005 highscoring predicted domain interactions (provided by Riley et al. [17] and Guimeraes et al. [19]) are listed in Figure 6, where PE(1) denotes PE approach with network reliability 60% (LPscore ≥ 0.4, pwscore ≤ 0.1) and PE(2) denotes PE approach with network reliability 50% (LPscore ≥ 0.4, pwscore ≤ 0.1). APMM(1) means APMM based on multidomain pairs and APMM(2) means APMM based on twodomain pairs. From Figure 6, we can see that our method has a comparable result with PE and a better performance than DPEA in terms of DDI prediction. Of course, this comparison result suffers from the incompleteness of the data in iPfam. Compared with APMM based on twodomain pairs, APMM based on multidomain pairs has a slightly smaller iPfam overlap. This is because when our methods include multidomain pairs, according to the definition of cooperative domains and the rule of selecting variables, some twodomain pairs are replaced with cooperativedomain pairs. At the same time, the current gold standard set only contains twodomain interactions. The distribution of the iPfam overlaps is shown in Figure 7 which indicates that our method can be an important complement since there is a large proportion of predicted DDIs not covered by other methods. Note that except twodomain interactions, our method can also infer cooperativedomain interactions.
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 [32] 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 twodomain pairs, 44 threedomain pairs and 10 four and above domain pairs. We applied our approach to the same dataset and found 34 cooperativedomain pairs (with interaction probability 1.0) among 500 highscoring domain interactions, 225 among 1000 highscoring domain interactions, and 635 among 2000 highscoring domain interactions. Note that in 500 highscoring 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 twodomain pair has a stronger interaction, the threedomain pair in the same protein pair will not be included as potential cooperative domains. If twodomain pairs have weaker interactions than the corresponding cooperativedomain interaction, this threedomain pair will be considered and the twodomain 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.
Discussion
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, FADbinding, NADbinding, GTP binding, protein binding, and Lumbinding. For cooperative domains, some of them have dissimilar functions partly because domain cooperation needs complementary functions [33]. 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 multidomain cooperation can be easily achieved in a multiprotein complex where protein cooperation is prominent.
Multidomain 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, tandemaffinitypurification coupled to mass spectrometry (TAPMS) which combines affinity tagsbased protein purification technique and mass spectrometry for identifying a tagged protein and its interaction partners [34] has been applied to find the genomewide 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 [36], Xray crystallography provides atomicresolution 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 [37]. The detected cooperative domains in this work can be applied to this problem by combining with docking procedures.
As an example, Figure 8 illustrates how to reconstruct the RNA Polymerase IITFIIS complex (PDB ID 1y1v) by our approach at protein, domain and atomic levels respectively with the following five steps. In the first step, from the information of TAPMS, there are total 13 different proteins (P04050, P08518, P16370, P20433, P20434, P20435, P34087, P20436, P27999, P22139, P38902, P40422, P07273) in this complex as its subunits (Figure 8(a)). Then, in the second step, according to Pfam and protein sequences, all possible domains for each protein in terms of Pfam architectures can be obtained (Figure 8(b)). There are 30 domains involved in this complex, so it is infeasible to clearly explain the interaction relationships between domains and proteins only by twodomain pairs (total 1435 pairs). In the third step, cooperative domain interactions are obtained by performing our approach on protein interaction data, which provide valuable information (Figure 8(c)). In the fourth step, physical interactions of those 13 proteins in the complex can be predicted at the protein level (see Figure 8(d), where thick lines denote the physical interactions realized by cooperative domain interactions and thin ones are realized by twodomain interactions). In the fifth step, the interactions between protein pairs are further examined at the domain levels based on complex structure information. For example, by examining the domain interactions between proteins P08518 (seven domains) and P16370 (two domains), we found that all of domains in the two proteins cooperatively interact with other domains except PF04566, as shown by a 3D structure from PDB in Figure I (Additional file 1). On the other hand, it is easy to estimate the interaction relations between proteins by considering cooperative domains. For example, proteins P04050 and P08518 probably have the strongest interaction because they have many cooperativedomain interactions. By further combining our method with a protein docking procedure (for searching the interacting areas of domains) [38], the detailed interactions at atomic level can be identified, which makes it possible to construct the stable and coherent crystal structure of a complex.
Conclusion
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 twodomain 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 multidomain 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 multidomain 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 multidomain cooperation. More detailed results and software can be found at our website.
Methods
Data sources
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 multipleorganism 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 proteinprotein interaction. We collected 4103 physical interactions in yeast from MIPS [4] (the version is PPI_141105.tab, denoted as MIPS1) and identified superdomains and cooperative domains in this dataset.
For PPI prediction based on multipleorganism data, in order to make comparison convenient, we used the same training data and testing data collected by Liu et al. [14]. These datasets are from yeast S.cerevisiae, worm C.elegans and fly D.melanogaster with respectively 5295, 4714 and 20349 protein interactions. The proteindomain relationships for each protein are extracted from PFAM [21] and SMART [39]. Among these protein interaction data, only those with domain information were used. In addition, like in Liu et al. [14], 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 proteinprotein interactions and protein domain composition dataset in Riley et al. [17] and Guimaraes et al. [19]. This set was obtained from the DIP database [3] 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 proteinprotein interaction has a score to denote the interaction strength. It includes experiment ratio data based on IST [28] and confidence data by integrating various data sources [29]. IST (Interaction Sequence Tags) was used for decoding interacting proteins in examining twohybrid interactions. Experiment ratio data based on IST mean that each proteinprotein interaction is provided with the number of IST hitting in a certain number of experiments. We conducted crossvalidation experiment on numerical interaction data. The first set is a well known dataset– the full data of Ito's dataset [28]. 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 [29]. 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 [21]. For MIPS1, there are total 1483 Pfam domains involved in 2477 proteins. iPfam database [30] contains domaindomain interactions confirmed by PDB crystal structures. It has been used as a gold standard set for evaluating predicted domaindomain 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) [31] 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 SwissProt/TrEMBL database to their corresponding structure files using the seq2struct web resource [26]. PROTOCOM [27] is a collection of proteinprotein transient complexes and domaindomain 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 multidomain pairs
In this section, we describe an improved probabilistic model for protein interactions by considering the multidomain pairs, which is the essential basis of our method.
Assume that in the protein interactions of K species (or data sets), there are N_{ k }proteins in dataset k respectively denoted by ${P}_{1}^{K}$, …, ${P}_{{N}_{k}}^{k}$k = 1, …, K, with M domains in all of these proteins represented by D_{1}, …, D_{ M }. Let ${P}_{i}^{k}$ also denote a set of domains in the protein i of dataset k. Define ${P}_{ij}^{k}$ to represent a protein pair (${P}_{i}^{k}$, ${P}_{j}^{k}$) and D_{ m, n }to represent a domain pair (D_{ m }, D_{ n }). We also introduce a symbol D_{m, rn}for a cooperativedomain pair (D_{ m } D_{ r }, D_{ n }) to represent the case that domains D_{ m }and D_{ r }in protein ${P}_{i}^{k}$ cooperatively interact with domain D_{ n }in protein ${P}_{j}^{k}$. D_{m, rn}has a similar implication. In our probabilistic model, ${P}_{ij}^{k}$ is also used to represent the set of domain pairs including all multidomain pairs in ${P}_{i}^{k}$, and ${P}_{j}^{k}$ i.e.,
Let the interaction between ${P}_{i}^{k}$ and ${P}_{j}^{k}$ (between D_{ m }and D_{ n }) be represented by a random variable ${p}_{ij}^{k}$ (d_{m, n}). Accordingly we introduce random variables d_{mr, n}to denote whether domains D_{ m }and D_{ r }cooperatively interact with domain D_{ n }or not. The probabilistic model [12, 13] for inferring protein interactions has two basic assumptions. One is that domain interactions in each protein pair are independent. The other is that two proteins interact if and only if there is at least one interacting domain pair in this protein pair. In the improved model, we also make these assumptions, but extend twodomain interactions to multidomain interactions. Therefore, the interaction probability of ${P}_{i}^{k}$ and ${P}_{j}^{k}$ is given by
where Pr(${p}_{ij}^{k}$ = 1) represents the interaction probability of proteins ${P}_{i}^{k}$ and ${P}_{j}^{k}$ in dataset k, and Pr(d_{m, n}= 1) represents the probability that domain D_{ m }interacts with D_{ n }. Pr(d_{mr, n}= 1) represents the probability that domains D_{ m }and D_{ r }cooperatively interact with D_{ n }. Pr(d_{m, 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 twodomain pair interactions while the second and third multiplying terms stand for the effects of cooperativedomain interactions. In next section, we will show how to determine those independent variables.
Note that we extend twodomain interactions only to threedomain 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 fourdomain 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 noninteraction 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 multidomain interactions.
Selection of independent variables
In order to make the variables of model (1) independent with each other, we will delete dependent variables among d_{m, n}, d_{mr, n}and d_{r, n}according to the following strategy. Define
where I_{ mn }is the number of interacting protein pairs in the training set that contain domain pair D_{m, n}, and N_{m, n}is the total number of protein pairs in the training set that contain D_{m, n}. R_{mr, n}and R_{r, n}are similarly defined. For variables d_{m, n}, d_{mr, n}and d_{r, n}, the variable deletion strategy is described by the following procedure.

1.
If R_{mr, n}< R_{m, n}or R_{mr, n}< R_{r, n}, it indicates that the appearance frequency of domain pair D_{mr, n}in interacting protein pairs is not higher than those of D_{m, n}and D_{r, 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 d_{m, n}, d_{r, n}and delete the variable d_{mr, n}in (1).

2.
If R_{mr, n}≥ R_{m, n}and R_{mr, n}≥ R_{r, n}, for D_{m, n}

when R_{mr, n}> R_{m, n}and I_{mr, n}= I_{m, n}, the appearance frequency of domain pair D_{mr, n}in interacting protein pairs is higher than those of D_{m, n}and D_{r, n}, and furthermore, D_{m, n}does 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 d_{m, n}is deleted, but the variable d_{mr, n}is kept in (1);

when R_{mr, n}= R_{m, n}and I_{mr, n}= I_{m, 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 d_{m, n}but keep the cooperativedomain pair d_{mr, n}.
The operations are performed in the same way for D_{r, n}. For the case of Figure 1(b), variables for all domain pairs except (D_{1}  D_{2}, D_{3}) are deleted based on this procedure.
Obviously, the above operations do not cover the case R_{mr, n}≥ R_{m, n}and I_{mr, 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 D_{m, n}also 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 multidomain 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 cooccurrence, and the cooperativity are also indirectly confirmed by their identical or similar functions from GO annotations.
Inference of domain interactions
Linear programming with multidomain pairs
Before predicting protein interactions, we need firstly to infer domain interactions from multiple datasets. Owing to experiment noises, each protein interaction dataset has a false positive rate fp^{k}and a false negative rate fn^{k}·fp^{k}= Pr(${o}_{ij}^{k}$ = 1${p}_{ij}^{k}$ = 0), fn^{k}= Pr(${o}_{ij}^{k}$ = 0${p}_{ij}^{k}$ = 1). where ${o}_{ij}^{k}$ = 1 if the interaction between proteins ${P}_{i}^{k}$ and ${P}_{j}^{k}$ is observed in the dataset and ${o}_{ij}^{k}$ = 0 otherwise. Thus the probability that proteins ${P}_{i}^{k}$ and ${P}_{j}^{k}$ in dataset k are observed to be interacting in the experiments is related with the real interaction probability in the following way:
The parameters fp^{k}and fn^{k}can be estimated from experimental data in a similar way as that in Liu et al. [14].
With the basic probabilistic model (1) and the formula (3), we have
Pr(${o}_{ij}^{k}$ = 1) when two proteins (${P}_{i}^{k}$, ${P}_{j}^{k}$) interact and 0 otherwise in the binary PPI data. For numerical interaction data we can set Pr(${o}_{ij}^{k}$ = 1)as the ratio of interactions between proteins ${P}_{i}^{k}$ and ${P}_{j}^{k}$ in a series of experiments. Note that the left side may be greater than 1 due to the incomplete interaction information in binary experiment data. For such a case we can normalize them first. Let x_{m, n}= ln(1 Pr(d_{m, n}= 1)), x_{mr, n}= ln(1  Pr(d_{mr, n}= 1)), x_{m, nr}= ln(1  Pr(d_{m, nr}= 1)) and ${\beta}_{ij}^{k}=\mathrm{ln}(1\frac{\mathrm{Pr}({o}_{ij}^{k}=1)f{p}^{k}}{1f{n}^{k}f{p}^{k}})$. By the similar technique adopted in Hayashida et al. [16], then the above equalities can be written as
This is a set of linear equalities. If we can find x_{m, n}, x_{mr, n}and x_{m, nr}(x_{m, n}≤ 0, x_{mr, n}≤ 0 and x_{m, nr}≤ 0) satisfying (5) for all observed protein interaction data, the domain interaction probabilities Pr(d_{m, n}= 1), Pr(d_{mr, n}= 1) and Pr(d_{m, nr}= 1) fully consistent with the training data can be obtained. However, it is usually impossible to satisfy all constraints owing to the noise and incompleteness of experimental data. In such a case it is natural and reasonable to minimize the total error with respect to L_{1} norm. Therefore we can obtain the following Linear Programming with Multidomain pairs (LPM):
where ${\epsilon}_{i,j}^{k}$ 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 multidomain pairs
Numerical experiments show that LPM performs well, but is computationally expensive for large scale problems. Therefore, we introduce a faster probabilistic method based on statistics. This method is based on a generalization of Association Probabilistic Method [13] with multidomain pairs (APMM). It estimates the interaction probabilities of multidomain pairs in the following way:
where ${P}_{ij}^{k}$ represents the number of multidomain pairs in ${P}_{ij}^{k}$, and ${\rho}_{ij}^{k}$ is the observed interaction probability between ${P}_{i}^{k}$ and ${P}_{j}^{k}$ 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 ${P}_{i}^{k}$ and ${P}_{j}^{k}$ for ${P}_{ij}^{k}$ > 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.
Evaluation measures
We validated our method using several types of experiments with different criteria. For computing the similarity of GO annotations [40], we adopted a simple method used successfully in Chen et al. [41] and Wu et al. [42]. 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. [41].
For protein interaction prediction on numerical PPI data, we use rootmeansquare error (RMSE) to measure the difference between the observed probability values and the predicted probability values:
where P denotes a set of protein pairs (training set or testing set) including interactions and noninteractions. Noninteracting protein pairs may be those not appearing in the observed interaction data or those whose interaction probabilities are below a threshold.
For protein interaction prediction on binary PPI data, we use sensitivity and specificity to evaluate the performance of a method. Specifically, given a set of interacting protein pairs as positive set and a noninteracting protein pair set as negative set, sensitivity and specificity (denoted by SN and SP) are respectively defined as
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.
The evaluation of the predicted domain interactions in this work is based on the overlap with the gold standard set iPfam. We adopted binomial cumulative distribution function to compute the significance of the overlap (pvalue) by comparing with randomly predicted domain pairs:
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.
Abbreviations
 PPI:

ProteinProtein Interaction
 DDI:

DomainDomain Interaction
 LPM:

Linear Programming with Multidomain pairs
 APMM:

Association Probabilistic Method with Multidomain pairs
 EM:

Expectation Maximization
 LP:

Linear Programming
 ASNM:

Association Numerical Method
 RMSE:

Root Mean Square Error
 IST:

Interaction Sequence Tags
 AUC:

Area Under Curve.
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Acknowledgements
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 JSPSNSFC 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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RSW and YW designed and implemented the algorithm. LYW and XSZ gave some helpful suggestions on the experiments. LC proposed the main idea and gave many helpful suggestions for the manuscript. All authors wrote and approved the manuscript.
RuiSheng Wang, Yong Wang contributed equally to this work.
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Keywords
 Domain Interaction
 Protein Pair
 Domain Pair
 Interfacial Residue
 Interaction Probability