BACKGROUND
many proteins involved in signal transduction, gene regulation and other biological activities require interaction with other proteins or cofactors to achieve specific processes  <cit> .
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  <cit>  and mips  <cit> .
this collection of protein-protein interaction data results in a rich, but quite noisy and still incomplete source of information  <cit>  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   <cit> , phylogenetic profile  <cit> , protein structure  <cit> , and domain information  <cit> .
in particular, inferring protein-protein interactions  based on domain information, such as association method  <cit> , probabilistic method  <cit> , svm-based method  <cit> , and lp-based approach  <cit> , 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  by integrating multiple data sources has also been investigated  <cit> .
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  <cit> .
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  <cit> .
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  <cit> .
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  <dig> of rna polymerase rpb <dig>  and domain  <dig> of rna polymerase rpb <dig>  constitute a superdomain, and they always appear together in individual proteins such as yor341w, ydl140c and yor116c, and have many common domain interaction partners  <cit> .
recently, han et al.
studied domain combinations in protein interactions  <cit> .
in their work, the appearance frequencies of domain combinations in a set of interacting and non-interacting protein pairs are counted to construct ap  matrices  <cit>  which provide useful information about the distribution of multi-domain interactions.
for example, among the listed  <dig> domain combination pairs with high appearance probability values  which are counted based on the total  <dig> protein interaction pairs in yeast, there are  <dig> two-domain pairs,  <dig> three-domain pairs and  <dig> 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  <cit>  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  <cit> , there is also such a cooperation among domains in protein interactions.
for example, klemm and pabo  <cit>  found that two unlinked polypeptides corresponding to the pou-specific domain and the pou homeo domain in protein oct- <dig> bind cooperatively to the octamer site.
moza et al.
<cit>  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  and an association probabilistic method with multi-domain pairs , 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 .
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.
RESULTS
in this paper, we investigate domain cooperation in protein interactions by extending two-domain interactions to multi-domain interactions.
we first define the types of domains and domain pairs, and then describe the main results.
assume that there are m domains d <dig>  …, dm involved in the experimental interaction data.
we use  to represent a two-domain pair, one domain in a protein and the other in another protein, and use  to denote a generalized pair i.e.
a three-domain pair, where dm and dr appear in one protein  and dn in another protein.
a multi-domain pair means a two-domain pair or a three-domain pair.
in figure  <dig>  we list all the multi-domain pairs in proteins .
a cooperative-domain pair  implies a generalized pair  in which two domains dm-dr referred as cooperative domains coexist in a protein p <dig> and cooperatively interact with dn in another protein p <dig>  the cooperative-domain pair should have a stronger interaction effect than the corresponding two-domain pairs  and .
a strongly cooperative-domain pair  is a cooperative-domain pair  which satisfies that there is an interaction effect of dm or dr on dn only if the domains dm and dr appear together.
in figure  <dig>  d <dig> and d <dig> are strongly cooperative domains interacting with d <dig> because all other domain pairs involving d <dig> or d <dig> have no interactions.
a superdomain implies two 'combined' domains dm-dr which are special cooperative domains and always appear together in individual proteins.
note that we extend two-domain interactions only to three-domain 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  <cit> .
the concept of cooperative domains in our work seems to be similar to han et al.
's "domain combination"  <cit> .
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 , only when the interaction strength of a three-domain pair  is larger than those of the corresponding two-domain pairs  and , 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  is considered in our method according to the rules of selecting variables , the two-domain pairs  and  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  <cit> .
in the following text, pr represents the probability that domain dm interacts with dn.
pr represents the probability that domains dm and dr cooperatively interact with dn.
similarly, pr represents the probability that domains dn and dr cooperatively interact with dm.
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 dm and dr are cooperative domains if pr <pr and pr <pr 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 mips <dig>  to get reliable cooperative-domain interactions.
totally we found  <dig> two-domain interactions ,  <dig> superdomains and  <dig> cooperative-domain pairs, among which  <dig> pairs are strongly cooperative domain interactions according to the above definition.
some detected  cooperative domains and superdomains in mips <dig> are respectively listed in tables  <dig>   <dig> and  <dig>  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 .
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 cooperative-domain interaction work cooperatively to facilitate specific functions.
for instance, two domains in superdomains pf05000-pf <dig>  pf02775-pf <dig>  pf02800-pf <dig> or pf00488–pf <dig> 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 pf08033-pf <dig>  pf03953-pf <dig> or pf08544-pf <dig>  for cooperative domains, some of them have similar go annotations of functions, such as pf00806-pf <dig>  where pf <dig> is a pumilio-family rna binding repeat and pf <dig> 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–pf <dig>  both pf <dig>  and pf <dig>  belong to the skyp <dig> family.
it is interesting that three domains in the strongly cooperative-domain interaction  are found to have same functions, and they are all rna polymerase domains.
as another example, we identified cooperative domains pf00036–pf <dig>  and the pfam description also supports the combination of pf <dig>  with pf <dig>   <cit> .
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 i-iii
2-1-2-5-11-27-1
1-1-2-12-1-8
1-1-3-16-18-6
1-1-3-39-16-3-16
2-1-2-5-11-1-4-9-1-5-1
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  <cit>  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  <dig> protein pairs with crystal structures that contain cooperative-domain pairs identified by our approach .
furthermore we also revealed some complexes in pdb which are not reported by protcom  <cit> .
for example, three domains arm, ibb and ibn_n which belong to armadillo repeat superfamily form a cooperative-domain interaction , and such multi-domain cooperation leads to the complex formed by protein q <dig>  and p <dig>  .
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 , and em method  <cit> .
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  <cit>  and assessed the prediction accuracy by root-mean-square error  .
the performance of each method in terms of rmse and elapsed training time for fivefold cross-validation is summarized in table  <dig>  in order to check the effect of cooperative domains on the accuracy, here we computed rmse only on those protein pairs containing cooperative-domain pairs.
rmse comparison results on all protein pairs are given in table iv and table v .
from table  <dig> 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 two-domain pairs.
table  <dig> 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 multi-domain 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 cross-validation is krogan's confidence data  <cit>  .
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  <dig>  from which we can see that for the confidence prediction, our approach  employing multi-domain 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  <dig>  we also made a direct comparison of our approach based on two-domain pairs and multi-domain pairs, and the results are summarized in figure  <dig>  we can see that lpm based on multi-domain pairs in training and testing has less prediction error in each round of fivefold cross validation than lpm based on only two-domain pairs.
apmm also has such a tendency except the first round in testing.
such results further confirm the benefit of considering multi-domain 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.
<cit>   to compare our approach with the extended em algorithm  <cit>  and validate the benefit of multi-domain 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  <cit> .
the training sets respectively consist of protein interactions from single organism  and multiple organisms.
based on yeast protein interaction dataset, we found  <dig> two-domain interactions ,  <dig> superdomains,  <dig> cooperative domain pairs, among which  <dig> pairs are strongly cooperative-domain interactions.
in the protein interaction dataset of three organisms, we detected  <dig> two-domain interactions ,  <dig> superdomains and  <dig> cooperative-domain interactions, where  <dig> are strongly cooperative.
among the cooperative-domain interactions in yeast and three organisms,  <dig> pairs are yeast-specific.
with these domain interactions, the prediction accuracy of protein-protein interactions is measured by the receiver operating characteristic  curve, which is a plot of the true positive rate  against the false positive rate  for different thresholds.
the result is plotted in figure  <dig>  from which we can see that apmm has a higher prediction accuracy than the extended em algorithm on multiple-organism data.
the auc values of apmm, em trained on multiple-organism data and em trained on single-organism data are respectively  <dig> ,  <dig>  and  <dig> .
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 multi-domain pairs and with only two-domain pairs.
the result summarized in figure  <dig> 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  <cit>  and the confidence ddi data in interdom  <cit>  .
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  <dig> with the significance of the overlap  computed by comparing with randomly predicted domain pairs .
we can see that domain interactions predicted by our approach have a significant overlap with ipfam and domain interactions predicted from multiple-organism 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  <dig> with p-values, 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 high-scoring predicted domain interactions, the prediction result exploiting multiple-organism data has a much higher mean confidence score than that based on single-organism data, which is shown in figure  <dig>
the domain interactions in ipfam have been used as a gold standard set to evaluate the predicted domain-domain interactions  <cit> .
we conducted a comparison experiment to evaluate the performance of our approach and the methods in riley et al.
<cit>  and guimeraes et al.
<cit>  based on the number of high-scoring domain-domain interactions confirmed by the gold standard set.
specifically, three methods  were applied in a same training set  and we checked the overlap of the predicted domain-domain interactions with ipfam by selecting a same number of high-scoring predicted domain interactions.
the results based on  <dig> high-scoring predicted domain interactions  are listed in figure  <dig>  where pe denotes pe approach with network reliability 60%  and pe denotes pe approach with network reliability 50% .
apmm means apmm based on multi-domain pairs and apmm means apmm based on two-domain pairs.
from figure  <dig>  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 two-domain pairs, apmm based on multi-domain pairs has a slightly smaller ipfam overlap.
this is because when our methods include multi-domain pairs, according to the definition of cooperative domains and the rule of selecting variables, some two-domain pairs are replaced with cooperative-domain pairs.
at the same time, the current gold standard set only contains two-domain interactions.
the distribution of the ipfam overlaps is shown in figure  <dig> 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 two-domain interactions, our method can also infer cooperative-domain interactions.
as for identifying cooperative domains, we made a rough comparison with han et al.
's domain combination approach  <cit> .
han et al.
provided on their website  <cit>  a set of  <dig> proteins based on which they listed  <dig> predicted domain combination interacting pairs with top confidence.
among these  <dig> pairs, there are  <dig> two-domain pairs,  <dig> three-domain pairs and  <dig> four and above domain pairs.
we applied our approach to the same dataset and found  <dig> cooperative-domain pairs  among  <dig> high-scoring domain interactions,  <dig> among  <dig> high-scoring domain interactions, and  <dig> among  <dig> high-scoring domain interactions.
note that in  <dig> high-scoring domain interactions, the number of cooperative domains is not more than han's , 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.
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, 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  <cit> .
cooperative domains tend to be contained in big complicated protein complexes.
for example, among cooperative domains with crystal structures, 72% of  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  which combines affinity tags-based protein purification technique and mass spectrometry for identifying a tagged protein and its interaction partners  <cit>  has been applied to find the genome-wide screen for complexes  <cit> .
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  <cit> , 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  <dig> 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  <cit> .
the detected cooperative domains in this work can be applied to this problem by combining with docking procedures.
as an example, figure  <dig> illustrates how to reconstruct the rna polymerase ii-tfiis complex  by our approach at protein, domain and atomic levels respectively with the following five steps.
in the first step, from the information of tap-ms, there are total  <dig> different proteins  in this complex as its subunits ).
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 ).
there are  <dig> domains involved in this complex, so it is infeasible to clearly explain the interaction relationships between domains and proteins only by two-domain pairs .
in the third step, cooperative domain interactions are obtained by performing our approach on protein interaction data, which provide valuable information ).
in the fourth step, physical interactions of those  <dig> proteins in the complex can be predicted at the protein level , where thick lines denote the physical interactions realized by cooperative domain interactions and thin ones are realized by two-domain 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 p <dig>  and p <dig> , we found that all of domains in the two proteins cooperatively interact with other domains except pf <dig>  as shown by a 3d structure from pdb in figure i .
on the other hand, it is easy to estimate the interaction relations between proteins by considering cooperative domains.
for example, proteins p <dig> and p <dig> probably have the strongest interaction because they have many cooperative-domain interactions.
by further combining our method with a protein docking procedure   <cit> , the detailed interactions at atomic level can be identified, which makes it possible to construct the stable and coherent crystal structure of a complex.
CONCLUSIONS
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.

 many proteins involved in signal transduction, gene regulation and other biological activities require interaction with other proteins or cofactors to achieve specific processes. 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 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, phylogenetic profile, protein structure, and domain information. in particular, inferring protein-protein interactions based on domain information, such as association method, probabilistic method, 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 by integrating multiple data sources has also been investigated. 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 of rna polymerase rpb and domain of rna polymerase rpb 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. in their work, the appearance frequencies of domain combinations in a set of interacting and non-interacting protein pairs are counted to construct ap matrices which provide useful information about the distribution of multi-domain interactions. for example, among the listed domain combination pairs with high appearance probability values which are counted based on the total protein interaction pairs in yeast, there are two-domain pairs, three-domain pairs and 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- 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 and an association probabilistic method with multi-domain pairs, 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. 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.  in this paper, we investigate domain cooperation in protein interactions by extending two-domain interactions to multi-domain interactions. we first define the types of domains and domain pairs, and then describe the main results. assume that there are m domains d …, dm involved in the experimental interaction data. we use to represent a two-domain pair, one domain in a protein and the other in another protein, and use to denote a generalized pair i.e. a three-domain pair, where dm and dr appear in one protein and dn in another protein. a multi-domain pair means a two-domain pair or a three-domain pair. in figure we list all the multi-domain pairs in proteins. a cooperative-domain pair implies a generalized pair in which two domains dm-dr referred as cooperative domains coexist in a protein p and cooperatively interact with dn in another protein p the cooperative-domain pair should have a stronger interaction effect than the corresponding two-domain pairs and. a strongly cooperative-domain pair is a cooperative-domain pair which satisfies that there is an interaction effect of dm or dr on dn only if the domains dm and dr appear together. in figure d and d are strongly cooperative domains interacting with d because all other domain pairs involving d or d have no interactions. a superdomain implies two'combined' domains dm-dr which are special cooperative domains and always appear together in individual proteins. note that we extend two-domain interactions only to three-domain 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. the concept of cooperative domains in our work seems to be similar to han et al.'s "domain combination". 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, only when the interaction strength of a three-domain pair is larger than those of the corresponding two-domain pairs and, 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 is considered in our method according to the rules of selecting variables, the two-domain pairs and 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. in the following text, pr represents the probability that domain dm interacts with dn. pr represents the probability that domains dm and dr cooperatively interact with dn. similarly, pr represents the probability that domains dn and dr cooperatively interact with dm. 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 dm and dr are cooperative domains if pr <pr and pr <pr 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 mips to get reliable cooperative-domain interactions. totally we found two-domain interactions, superdomains and cooperative-domain pairs, among which pairs are strongly cooperative domain interactions according to the above definition. some detected cooperative domains and superdomains in mips are respectively listed in tables and 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. 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 cooperative-domain interaction work cooperatively to facilitate specific functions. for instance, two domains in superdomains pf05000-pf pf02775-pf pf02800-pf or pf00488–pf 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 pf08033-pf pf03953-pf or pf08544-pf for cooperative domains, some of them have similar go annotations of functions, such as pf00806-pf where pf is a pumilio-family rna binding repeat and pf 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–pf both pf and pf belong to the skyp family. it is interesting that three domains in the strongly cooperative-domain interaction are found to have same functions, and they are all rna polymerase domains. as another example, we identified cooperative domains pf00036–pf and the pfam description also supports the combination of pf with pf. 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 i-iii 2-1-2-5-11-27-1 1-1-2-12-1-8 1-1-3-16-18-6 1-1-3-39-16-3-16 2-1-2-5-11-1-4-9-1-5-1 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 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 protein pairs with crystal structures that contain cooperative-domain pairs identified by our approach. 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, and such multi-domain cooperation leads to the complex formed by protein q and p. 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, 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. the performance of each method in terms of rmse and elapsed training time for fivefold cross-validation is summarized in table in order to check the effect of cooperative domains on the accuracy, here we computed rmse only on those protein pairs containing cooperative-domain pairs. rmse comparison results on all protein pairs are given in table iv and table v. from table 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 two-domain pairs. table 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 multi-domain 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 cross-validation is krogan's confidence data. 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 from which we can see that for the confidence prediction, our approach employing multi-domain 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 we also made a direct comparison of our approach based on two-domain pairs and multi-domain pairs, and the results are summarized in figure we can see that lpm based on multi-domain pairs in training and testing has less prediction error in each round of fivefold cross validation than lpm based on only two-domain pairs. apmm also has such a tendency except the first round in testing. such results further confirm the benefit of considering multi-domain 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. to compare our approach with the extended em algorithm and validate the benefit of multi-domain 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. the training sets respectively consist of protein interactions from single organism and multiple organisms. based on yeast protein interaction dataset, we found two-domain interactions, superdomains, cooperative domain pairs, among which pairs are strongly cooperative-domain interactions. in the protein interaction dataset of three organisms, we detected two-domain interactions, superdomains and cooperative-domain interactions, where are strongly cooperative. among the cooperative-domain interactions in yeast and three organisms, pairs are yeast-specific. with these domain interactions, the prediction accuracy of protein-protein interactions is measured by the receiver operating characteristic curve, which is a plot of the true positive rate against the false positive rate for different thresholds. the result is plotted in figure from which we can see that apmm has a higher prediction accuracy than the extended em algorithm on multiple-organism data. the auc values of apmm, em trained on multiple-organism data and em trained on single-organism data are respectively, and. 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 multi-domain pairs and with only two-domain pairs. the result summarized in figure 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. 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 with the significance of the overlap computed by comparing with randomly predicted domain pairs. we can see that domain interactions predicted by our approach have a significant overlap with ipfam and domain interactions predicted from multiple-organism 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 with p-values, 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 high-scoring predicted domain interactions, the prediction result exploiting multiple-organism data has a much higher mean confidence score than that based on single-organism data, which is shown in figure the domain interactions in ipfam have been used as a gold standard set to evaluate the predicted domain-domain interactions. we conducted a comparison experiment to evaluate the performance of our approach and the methods in riley et al. and guimeraes et al. based on the number of high-scoring domain-domain interactions confirmed by the gold standard set. specifically, three methods were applied in a same training set and we checked the overlap of the predicted domain-domain interactions with ipfam by selecting a same number of high-scoring predicted domain interactions. the results based on high-scoring predicted domain interactions are listed in figure where pe denotes pe approach with network reliability 60% and pe denotes pe approach with network reliability 50%. apmm means apmm based on multi-domain pairs and apmm means apmm based on two-domain pairs. from figure 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 two-domain pairs, apmm based on multi-domain pairs has a slightly smaller ipfam overlap. this is because when our methods include multi-domain pairs, according to the definition of cooperative domains and the rule of selecting variables, some two-domain pairs are replaced with cooperative-domain pairs. at the same time, the current gold standard set only contains two-domain interactions. the distribution of the ipfam overlaps is shown in figure 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 two-domain interactions, our method can also infer cooperative-domain interactions. as for identifying cooperative domains, we made a rough comparison with han et al.'s domain combination approach. han et al. provided on their website a set of proteins based on which they listed predicted domain combination interacting pairs with top confidence. among these pairs, there are two-domain pairs, three-domain pairs and four and above domain pairs. we applied our approach to the same dataset and found cooperative-domain pairs among high-scoring domain interactions, among high-scoring domain interactions, and among high-scoring domain interactions. note that in high-scoring domain interactions, the number of cooperative domains is not more than han's, 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. 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, 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 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 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. 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 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. as an example, figure illustrates how to reconstruct the rna polymerase ii-tfiis complex by our approach at protein, domain and atomic levels respectively with the following five steps. in the first step, from the information of tap-ms, there are total different proteins in this complex as its subunits ). 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 ). there are domains involved in this complex, so it is infeasible to clearly explain the interaction relationships between domains and proteins only by two-domain pairs. in the third step, cooperative domain interactions are obtained by performing our approach on protein interaction data, which provide valuable information ). in the fourth step, physical interactions of those proteins in the complex can be predicted at the protein level, where thick lines denote the physical interactions realized by cooperative domain interactions and thin ones are realized by two-domain 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 p and p, we found that all of domains in the two proteins cooperatively interact with other domains except pf as shown by a 3d structure from pdb in figure i. on the other hand, it is easy to estimate the interaction relations between proteins by considering cooperative domains. for example, proteins p and p probably have the strongest interaction because they have many cooperative-domain interactions. by further combining our method with a protein docking procedure, the detailed interactions at atomic level can be identified, which makes it possible to construct the stable and coherent crystal structure of a complex.  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. 
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 and an association probabilistic method with multi-domain pairs. 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. 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. 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. 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. comparison experiments in terms of protein/domain interaction prediction justified the benefit of considering multi-domain cooperation. domains are the basic functional units of proteins.
 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 and an association probabilistic method with multi-domain pairs. 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 and. 