BACKGROUND
transcriptional regulation plays a crucial role in the regulation of gene expression.
as well known, it is accomplished by the binding of transcription factors  to the tf binding sites  in the promoters of genes.
in eukaryotic cells, transcriptional regulation is usually achieved by the cooperation between multiple tfs to regulate the expression of genes.
therefore, knowing the precise cooperative interactions among tfs is helpful for uncovering the mechanisms of transcriptional regulation.
with advances in high-throughput microarray technologies and diverse data sources, it is now possible to investigate the cooperative interactions among tfs.
many computational methods have been developed to identify cooperative tf pairs by using one or several kinds of experimental data.
some methods only used chip-chip data  <cit> .
several other methods integrated chip-chip and gene expression data  <cit> .
another two methods integrated chip-chip data with other data sources such as protein-protein interaction data  <cit>  and tf knockout data  <cit> .
on the contrary, pilpel et al.
's method did not use chip-chip data but integrated tfbs and gene expression data  <cit> .
wang et al.
's and hu et al.
's methods both integrated multiple data sources by using a bayesian approach  <cit> .
chip-chip, gene expression, tfbs, tf knockout and protein-protein interaction data were used to investigate the cooperative interactions among tfs in the above mentioned methods.
however, the nucleosome occupancy data was not used even though several researches have revealed the association between nucleosomes and tfbss  <cit> .
because nucleosome occupancy has been demonstrated as an important strategy to regulate gene expression by affecting the accessibility of tfbss to tfs, this biological knowledge motivates us to consider the effect of nucleosome occupancy on the cooperativity between tfs and adopt the nucleosome occupancy data for our research.
our method is developed based on the following two rationales.
first, if two tfs cooperate, they should have a significantly higher number of common target genes than random expectation.
second, the tfbss of these two cooperative tfs  should tend to be co-depleted of nucleosomes in order to make themselves simultaneously accessible to tf binding.
methods
data sources
we used three data sources in this study.
first, the genome-wide nucleosome occupancy data of saccharomyces cerevisiae was downloaded from mavrich et al.
's study  <cit> .
they established a genome-wide map of nucleosome locations and the map shows which region in the genome is occupied by nucleosomes.
second, the tf-gene documented regulation data was downloaded from yeastract database  <cit> , which deposited the documented regulation evidence  between tfs and their target genes.
third, the tfbs data was downloaded from swissregulon database  <cit> .
each tfbs has its predicted genomic location and a posterior probability to indicate the confidence of this putative tfbs.
in this study, a threshold  <dig>  of the posterior probability was applied to select putative tfbss.
the total number of distinct tfs from the above two databases was  <dig>  and therefore  <dig>  tf pairs were considered in this study.
the proposed method
the proposed method is developed based on the following two biologically plausible assumptions.
first, two cooperative tfs should share a significantly larger set of target genes than random expectation.
this assumption has also been used in existing methods  <cit> .
second, the tfbss of two cooperative tfs  should be co-depleted of nucleosomes to make themselves simultaneously accessible to tf binding.
this assumption is biologically plausible since it has been shown that functionally cooperative tf pairs are associated with nucleosome-depleted promoters  <cit> .
therefore, given a tf pair, we calculate the significance of the overlap of their target genes and the significance of being co-depleted of nucleosomes on their tfbss.
our method assigns a cooperativity score to each of the  <dig> tf pairs.
finally,  <dig> tf pairs whose cooperativity scores larger than  <dig> are predicted as cooperative tf pairs.
the flow chart of our method is shown in figure  <dig> and described as follows.
step1-define the target genes of each of the  <dig> tfs
a tf's target genes are defined as those genes  that are known to be regulated by the tf from the tf-gene documented regulation evidence  or  whose promoters contain the binding sites of the tf .
step2-calculate the significance of the target gene overlap
given a tf pair, the significance of the overlap between the target genes of these two tfs is calculated using the hyper-geometric test  <cit> :
poverlap=∑i=mminn1in-n1n2-inn <dig>
where n <dig> is the number of target genes of the first tf, n <dig> is the number of target genes of the second tf, n =  <dig> is the number of total genes in the yeast genome, and m is the number of common target genes.
the smaller the poverlap, the more significant the target gene overlap.
step3-calculate the significance of being co-depleted of nucleosomes on the tfbss
from the common target genes of the given tf pair, we extract the genes which have both tfs' binding sites in their promoters, and denote it as set a. if multiple tfbss of the same tf are found, only the most confident tfbs  is considered.
therefore, the promoter of each gene in set a contains one tfbs of the first tf and one tfbs of the second tf.
for each gene in set a, the state of nucleosome occupancy of each of the two tfbss can be specified to one of the two categories:
occupied,ifanypositioninthetfbsisoccupiedbyanucleosome.depleted,ifnopositioninthe tfbsisoccupiedbyanucleosome.
then the state of nucleosome occupancy can be converted to a binary value and denoted as s:
stfbsj= <dig> occupied <dig> depleted
where j =  <dig> for the first tf and j =  <dig> for the second tf.
according to the values of s and s, each gene in set a can be assigned to a cell in a  <dig> ×  <dig> contingency table  and the number of genes in each of the four cells in the contingency table can be obtained.
then the fisher exact test  <cit>  is used to calculate the significance of tfbs <dig> and tfbs <dig> to be co-depleted of nucleosomes.
the p-value is denoted as
pnu= ∑i=amina+b,a+ca+bic+da+c-ia+b+c+da+c
where a is the number of genes whose promoters contain both tfbs <dig> and tfbs <dig> depleted of nuclesomes, b is the number of genes whose promoters contain tfbs <dig> occupied by nucleosomes and tfbs <dig> depleted of nuclesomes, c is the number of genes whose promoters contain tfbs <dig> depleted of nucleosomes and tfbs <dig> occupied by nuclesomes, and d is the number of genes whose promoters contain both tfbs <dig> and tfbs <dig> occupied by nuclesomes.
the smaller the pnu, the more significant the tfbs <dig> and tfbs <dig> to be co-depleted of nucleosomes.
step4-calculate the cooperativity score
the cooperativity score is defined as −logpoverlap +.
the higher the score is, the more likely a tf pair has cooperativity.
there are two situations that can have a high score.
one is a small poverlap, i.e.
the tf pair has a significant overlap between their target genes.
the other situation is a small pnu, i.e.
the two tfs show a high tendency of being co-depleted of nucleosomes on their tfbss to make them simultaneously accessible to tf binding.
RESULTS
according to the cooperativity score,  <dig> tf pairs can be sorted decreasingly, and then constitute a ranked prediction of cooperative tf pairs.
finally,  <dig> tf pairs whose cooperativity scores larger than  <dig> are predicted as cooperative tf pairs.
detailed investigation of the  <dig> predicted cooperative tf pairs
in table  <dig>  we list these  <dig> predicted cooperative tf pairs.
all of them have at least one of the following three lines of evidence:  being predicted by existing methods,  the existence of protein-protein interactions, and  the co-annotation in the same mips functional categories.
more precisely, 63%  of the pairs have all three lines of evidence, 26%  of the pairs have two lines of evidence, and 11%  of the pairs have only one line of evidence.
note that among these  <dig> predicted cooperative tf pairs,  <dig> pairs are also predicted by existing methods.
the other  <dig> pairs are novel cooperative tf pairs predicted by our method.
the biological relevance of these  <dig> novel cooperative tf pairs is justified by the existence of protein-protein interactions and co-annotation in the same mips functional categories.
more precisely, 75%  of the novel pairs
are highly biologically plausible since they have protein-protein interactions and are co-annotated in the same mips functional categories, and the other 25%  of the novel pairs  are moderately biologically plausible since they are co-annotated in the same mips functional categories but do not have protein-protein interactions.
performance comparison with  <dig> existing methods
in this study, we adopted three performance indices to compare our predictions with  <dig> existing methods' predictions .
depending on the threshold value used, different methods obtained different number of predicted cooperative tf pairs .
the three performance indices are introduced in following subsections, and the comparison results are also shown.
the table shows the information of  <dig> existing methods adopted for comparison.
the data sources used, a brief description of the method, the p-value threshold and the number of predicted cooperative tf pairs of each method are described in columns  <dig>   <dig>   <dig> and  <dig>
performance index 1: the similarity of protein-protein interaction partners between the two tfs of each pctfp
following previous studies in the literature  <cit> , we evaluated cooperativity between two tfs in a pctfp based on the rationale: the similarity of protein-protein interactions  partners between two tfs suggests that they contribute to the same biological processes and participate in the same regulatory mechanism.
the physical ppi data were downloaded from the biogrid database  <cit> .
given a list of pctfps from a method, we measured the similarity of ppi partners between the two tfs of each pctfp by calculating a score −logp , which represents the significance of their ppi partners overlap.
note that p is the p-value calculated by the hypergeometric distribution shown in the formula , n <dig> is the number of genes whose proteins have physical ppi with the first tf, n <dig> is the number the genes whose proteins have physical ppi with the second tf, n =  <dig> is the number of total genes in the yeast genome, and m is the number of genes whose proteins have physical ppi with both tfs.
the greater the −logp is, the more significant the cooperativity of a pctfp is.
to evaluate the performance of a list of pctfps from a method, where each pctfp has been given a score −logp , we took the mean of these scores as the final score of this performance index.
figure 2a shows that our method outperforms  <dig> existing methods in this score.
performance index 2: functional similarity between the two tfs of each pctfp
we evaluated cooperativity between two tfs in a pctfp based on the rationale: if two tfs have similar biological functions, then they tend to participate in the same regulatory mechanism  <cit> .
the functional similarity score of a pctfp is adopted from yang et al.
's study  <cit> , which proposed an improving go semantic similarity measures using download random walks.
the greater the functional similarity score is, the more significant the cooperativity of a pctfp is.
to evaluate the performance of a list of pctfps from a method, where each pctfp has been given a functional similarity score, we took the mean of these scores as the final score of this performance index.
figure 2b shows that our method outperforms  <dig> existing methods in this score.
performance index 3: the significance of the overlap between a list of pctfps from a method and a benchmark set of  <dig> known cooperative tf pairs
yang et al.
<cit>  proposed a performance index to test the prediction accuracy of different methods by comparing the significance of the overlap of different lists of pctfps with a benchmark set of known cooperative tf pairs.
the benchmark set  has  <dig> tf pairs, which is complied from the mips transcription complex catalog  <cit> .
as far as we know, this is the only high-quality dataset of tf cooperativity currently available  <cit> .
then given a list of predicted cooperative tf pairs from a method, we calculated the significance of the overlap of this list with the benchmark set using yang et al.
's index.
for the given list, a score which represents the significance of the overlap is defined as the −logp , where p is the p-value computed using fisher exact test.
the higher the score, the better the performance.
figure 2c shows that our method outperforms  <dig> existing methods in this score.
<dig> .
<dig>
met4/met28/met <dig> complex
the list of  <dig> known cooperative tf pairs are derived from biochemically well-defined transcriptional complexes within the mips complex catalogue.
discussion
our method is robust against different thresholds of the cooperativity score
in this study, we set a threshold of cooperativity score to be  <dig> and reported  <dig> pctfps whose cooperativity scores are larger than the threshold.
the number of pctfps reported by our method is similar to those of five previous methods  <cit> .
to check the robustness of our method against different thresholds of the cooperativity score, we tested four different thresholds .
figure  <dig> shows that no matter which threshold is used, the performance of our method is always the same  on the performance index  <dig>  this suggests that our method is robust against different thresholds of the cooperativity score.
our method is robust against different qualities of tfbs data
the quality of tfbs data retrieved from swissregulon database depends on the posterior probability threshold being used.
in this study, a threshold  <dig>  of the posterior probability was applied to select putative tfbss.
to check the robustness of our method against different qualities of tfbs data, we tested four different posterior probability thresholds .
figure  <dig> shows that no matter which threshold is used, the performance of our method is always the same  on the performance index  <dig>  this suggests that our method is robust against different thresholds of posterior probability to control the quality of tfbs data.
our method outperforms existing methods in the precision and recall when using a benchmark set of  <dig> known cooperative tf pairs
in the performance index  <dig>  the significance of the overlap of the list of pctfps from a method with the benchmark set of  <dig> known cooperative tf pairs is used to evaluate the performance of a method.
here, we use the precision and recall to evaluate the performance of a method.
as shown in figure  <dig>  our method outperforms  <dig> existing methods in the precision and outperforms  <dig> existing methods in the recall.
the nucleosome occupancy data contributes to the overall improved prediction
to demonstrate that the nucleosome occupancy data contributes to the overall improved prediction, we tested our method when nucleosome data are used  and when nucleosome data are not used  on the performance index  <dig>  as shown in figure  <dig>  the −logp of t w/ nucleosome is higher than that of t w/o nucleosome by  <dig> , meaning that the p-value of t w/ nucleosome is less than that of t w/o nucleosome by more than  <dig> folds.
this suggests that nucleosome occupancy data do contribute to the overall improved prediction of our method.
issue of applying our method to other model organisms
our method is used to infer the cooperativity between two yeast tfs by integrating the tf-gene documented regulation, tfbs and nucleosome occupancy data.
theoretically, it can be applied to other model organisms which also have these three kinds of genome-wide data.
there are two reasons why we used yeast as the model organism to test our method.
first, yeast is the only organism which has more than  <dig> tf-gene documented regulation data available.
the useful tf-gene documented regulation data  <cit> , which provide the experimentally validated regulatory relationships between tfs and genes, are collected from more than  <dig> published papers by the team of the yeastract database  <cit> .
second, yeast is the only organism that is tested by more than  <dig> existing algorithms.
therefore, using yeast as the model organism makes it possible to compare our predictions with the predictions of many existing methods.
a cooperative tf network
cell cycle
since cell cycle process has been well investigated in the literature, let us discuss it in more details.
cell cycle is a complex process and it consists of four main phases: g <dig>  s, g <dig> and m.
g1/s phase
the g <dig> to s phase transition of the eukaryotic cell cycle is crucial to the coordination of cell cycle progression with cellular growth.
during the g1/s transition of the cell cycle in yeast, sbf and mbf are known to activate gene expression  <cit> .
sbf is a protein complex composed of swi <dig> and swi <dig>  and mbf is a protein complex composed of mbp <dig> and swi <dig>  <cit> .
our method successfully predicted the cooperativity between swi <dig> and swi <dig>  and the cooperativity between mbp <dig> and swi <dig> .
moreover, mbp <dig> is known to related to swi <dig> because the mbp <dig> swi <dig> double knockout strain were inviable.
the cooperativity between mbp <dig> and swi <dig> is successfully captured by our method .
in addition, a study suggests that stb <dig> may affect mbf-dependent transcription  <cit> .
stb <dig> is a protein which regulates the timing of start transcription in the absence of the g <dig> regulator cln <dig>  the cooperativity between stb <dig> and swi <dig>  is successfully identified by our method .
g2/m phase
in the g2/m phase, fkh <dig> and fkh <dig> play essential roles in the activation of the clb <dig> cluster genes and they share 72% identical dna binding domain.
moreover, the double mutant of fkh <dig> and fkh <dig> displays obvious morphological change  <cit> .
our method successfully predicts the cooperativity between fkh <dig> and fkh <dig> .
m/g <dig> phase
in m/g <dig> phase, ace <dig> and swi <dig> co-regulate the expression of many cell cycle genes in yeast  <cit> .
moreover, ace <dig> and swi <dig> proteins show similarity at the amino acid level and bind to the same dna sequence with 82% identical dna binding domains.
our method successfully identifies the cooperativity between ace <dig> and swi <dig> .
CONCLUSIONS
in this paper, we developed a method to infer the cooperativity between two tfs by integrating the tf-gene documented regulation, tfbs and nucleosome occupancy data.
two tfs are predicted as cooperative if  they have a significantly higher number of common target genes than random expectation and  their binding sites  tend to be co-depleted of nucleosomes in order to make these binding sites simultaneously accessible to tf binding.
a list of  <dig> cooperative tf pairs has been predicted by our method.
among these  <dig> predicted cooperative tf pairs,  <dig> pairs are also predicted by existing methods.
the other  <dig> pairs are novel cooperative tf pairs.
the biological relevance of these  <dig> novel cooperative tf pairs is justified by the existence of protein-protein interactions and co-annotation in the same mips functional categories.
moreover, our method is shown to outperform the  <dig> existing methods based on the three performance indices:  the similarity of protein-protein interaction partners between two tfs,  the functional similarity between two tfs, and  the overlap between a method's prediction result and the benchmark set of  <dig> known cooperative tf pairs.
finally, the cooperative tf network constructed from the  <dig> predicted pairs demonstrates that our method has the power to find cooperative tf pairs of different biological processes.
we believe that our prediction will help biologists to understand the mechanism of transcriptional regulation in eukaryotic cells.
competing interests
the authors declare that they have no competing interests.
authors' contributions
wsw conceived the research topic and provided essential guidance.
wsw, fjl and mhj developed the algorithm and wrote the manuscript.
fjl, mhj and ccc performed all the simulations.
ymh provided advices on the manuscript writing.
all authors have read and approved the final manuscript.
declarations
the publication charges of this article were funded by ministry of science and technology of taiwan most-103-2221-e-006-174-my <dig>

 transcriptional regulation plays a crucial role in the regulation of gene expression. as well known, it is accomplished by the binding of transcription factors to the tf binding sites in the promoters of genes. in eukaryotic cells, transcriptional regulation is usually achieved by the cooperation between multiple tfs to regulate the expression of genes. therefore, knowing the precise cooperative interactions among tfs is helpful for uncovering the mechanisms of transcriptional regulation. with advances in high-throughput microarray technologies and diverse data sources, it is now possible to investigate the cooperative interactions among tfs. many computational methods have been developed to identify cooperative tf pairs by using one or several kinds of experimental data. some methods only used chip-chip data. several other methods integrated chip-chip and gene expression data. another two methods integrated chip-chip data with other data sources such as protein-protein interaction data and tf knockout data. on the contrary, pilpel et al.'s method did not use chip-chip data but integrated tfbs and gene expression data. wang et al.'s and hu et al.'s methods both integrated multiple data sources by using a bayesian approach. chip-chip, gene expression, tfbs, tf knockout and protein-protein interaction data were used to investigate the cooperative interactions among tfs in the above mentioned methods. however, the nucleosome occupancy data was not used even though several researches have revealed the association between nucleosomes and tfbss. because nucleosome occupancy has been demonstrated as an important strategy to regulate gene expression by affecting the accessibility of tfbss to tfs, this biological knowledge motivates us to consider the effect of nucleosome occupancy on the cooperativity between tfs and adopt the nucleosome occupancy data for our research. our method is developed based on the following two rationales. first, if two tfs cooperate, they should have a significantly higher number of common target genes than random expectation. second, the tfbss of these two cooperative tfs should tend to be co-depleted of nucleosomes in order to make themselves simultaneously accessible to tf binding. methods data sources we used three data sources in this study. first, the genome-wide nucleosome occupancy data of saccharomyces cerevisiae was downloaded from mavrich et al.'s study. they established a genome-wide map of nucleosome locations and the map shows which region in the genome is occupied by nucleosomes. second, the tf-gene documented regulation data was downloaded from yeastract database, which deposited the documented regulation evidence between tfs and their target genes. third, the tfbs data was downloaded from swissregulon database. each tfbs has its predicted genomic location and a posterior probability to indicate the confidence of this putative tfbs. in this study, a threshold of the posterior probability was applied to select putative tfbss. the total number of distinct tfs from the above two databases was and therefore tf pairs were considered in this study. the proposed method the proposed method is developed based on the following two biologically plausible assumptions. first, two cooperative tfs should share a significantly larger set of target genes than random expectation. this assumption has also been used in existing methods. second, the tfbss of two cooperative tfs should be co-depleted of nucleosomes to make themselves simultaneously accessible to tf binding. this assumption is biologically plausible since it has been shown that functionally cooperative tf pairs are associated with nucleosome-depleted promoters. therefore, given a tf pair, we calculate the significance of the overlap of their target genes and the significance of being co-depleted of nucleosomes on their tfbss. our method assigns a cooperativity score to each of the tf pairs. finally, tf pairs whose cooperativity scores larger than are predicted as cooperative tf pairs. the flow chart of our method is shown in figure and described as follows. step1-define the target genes of each of the tfs a tf's target genes are defined as those genes that are known to be regulated by the tf from the tf-gene documented regulation evidence or whose promoters contain the binding sites of the tf. step2-calculate the significance of the target gene overlap given a tf pair, the significance of the overlap between the target genes of these two tfs is calculated using the hyper-geometric test: poverlap=∑i=mminn1in-n1n2-inn where n is the number of target genes of the first tf, n is the number of target genes of the second tf, n = is the number of total genes in the yeast genome, and m is the number of common target genes. the smaller the poverlap, the more significant the target gene overlap. step3-calculate the significance of being co-depleted of nucleosomes on the tfbss from the common target genes of the given tf pair, we extract the genes which have both tfs' binding sites in their promoters, and denote it as set a. if multiple tfbss of the same tf are found, only the most confident tfbs is considered. therefore, the promoter of each gene in set a contains one tfbs of the first tf and one tfbs of the second tf. for each gene in set a, the state of nucleosome occupancy of each of the two tfbss can be specified to one of the two categories: occupied,ifanypositioninthetfbsisoccupiedbyanucleosome.depleted,ifnopositioninthe tfbsisoccupiedbyanucleosome. then the state of nucleosome occupancy can be converted to a binary value and denoted as s: stfbsj= occupied depleted where j = for the first tf and j = for the second tf. according to the values of s and s, each gene in set a can be assigned to a cell in a × contingency table and the number of genes in each of the four cells in the contingency table can be obtained. then the fisher exact test is used to calculate the significance of tfbs and tfbs to be co-depleted of nucleosomes. the p-value is denoted as pnu= ∑i=amina+b,a+ca+bic+da+c-ia+b+c+da+c where a is the number of genes whose promoters contain both tfbs and tfbs depleted of nuclesomes, b is the number of genes whose promoters contain tfbs occupied by nucleosomes and tfbs depleted of nuclesomes, c is the number of genes whose promoters contain tfbs depleted of nucleosomes and tfbs occupied by nuclesomes, and d is the number of genes whose promoters contain both tfbs and tfbs occupied by nuclesomes. the smaller the pnu, the more significant the tfbs and tfbs to be co-depleted of nucleosomes. step4-calculate the cooperativity score the cooperativity score is defined as −logpoverlap +. the higher the score is, the more likely a tf pair has cooperativity. there are two situations that can have a high score. one is a small poverlap, i.e. the tf pair has a significant overlap between their target genes. the other situation is a small pnu, i.e. the two tfs show a high tendency of being co-depleted of nucleosomes on their tfbss to make them simultaneously accessible to tf binding.  according to the cooperativity score, tf pairs can be sorted decreasingly, and then constitute a ranked prediction of cooperative tf pairs. finally, tf pairs whose cooperativity scores larger than are predicted as cooperative tf pairs. detailed investigation of the predicted cooperative tf pairs in table we list these predicted cooperative tf pairs. all of them have at least one of the following three lines of evidence: being predicted by existing methods, the existence of protein-protein interactions, and the co-annotation in the same mips functional categories. more precisely, 63% of the pairs have all three lines of evidence, 26% of the pairs have two lines of evidence, and 11% of the pairs have only one line of evidence. note that among these predicted cooperative tf pairs, pairs are also predicted by existing methods. the other pairs are novel cooperative tf pairs predicted by our method. the biological relevance of these novel cooperative tf pairs is justified by the existence of protein-protein interactions and co-annotation in the same mips functional categories. more precisely, 75% of the novel pairs are highly biologically plausible since they have protein-protein interactions and are co-annotated in the same mips functional categories, and the other 25% of the novel pairs are moderately biologically plausible since they are co-annotated in the same mips functional categories but do not have protein-protein interactions. performance comparison with existing methods in this study, we adopted three performance indices to compare our predictions with existing methods' predictions. depending on the threshold value used, different methods obtained different number of predicted cooperative tf pairs. the three performance indices are introduced in following subsections, and the comparison results are also shown. the table shows the information of existing methods adopted for comparison. the data sources used, a brief description of the method, the p-value threshold and the number of predicted cooperative tf pairs of each method are described in columns and performance index 1: the similarity of protein-protein interaction partners between the two tfs of each pctfp following previous studies in the literature, we evaluated cooperativity between two tfs in a pctfp based on the rationale: the similarity of protein-protein interactions partners between two tfs suggests that they contribute to the same biological processes and participate in the same regulatory mechanism. the physical ppi data were downloaded from the biogrid database. given a list of pctfps from a method, we measured the similarity of ppi partners between the two tfs of each pctfp by calculating a score −logp, which represents the significance of their ppi partners overlap. note that p is the p-value calculated by the hypergeometric distribution shown in the formula, n is the number of genes whose proteins have physical ppi with the first tf, n is the number the genes whose proteins have physical ppi with the second tf, n = is the number of total genes in the yeast genome, and m is the number of genes whose proteins have physical ppi with both tfs. the greater the −logp is, the more significant the cooperativity of a pctfp is. to evaluate the performance of a list of pctfps from a method, where each pctfp has been given a score −logp, we took the mean of these scores as the final score of this performance index. figure 2a shows that our method outperforms existing methods in this score. performance index 2: functional similarity between the two tfs of each pctfp we evaluated cooperativity between two tfs in a pctfp based on the rationale: if two tfs have similar biological functions, then they tend to participate in the same regulatory mechanism. the functional similarity score of a pctfp is adopted from yang et al.'s study, which proposed an improving go semantic similarity measures using download random walks. the greater the functional similarity score is, the more significant the cooperativity of a pctfp is. to evaluate the performance of a list of pctfps from a method, where each pctfp has been given a functional similarity score, we took the mean of these scores as the final score of this performance index. figure 2b shows that our method outperforms existing methods in this score. performance index 3: the significance of the overlap between a list of pctfps from a method and a benchmark set of known cooperative tf pairs yang et al. proposed a performance index to test the prediction accuracy of different methods by comparing the significance of the overlap of different lists of pctfps with a benchmark set of known cooperative tf pairs. the benchmark set has tf pairs, which is complied from the mips transcription complex catalog. as far as we know, this is the only high-quality dataset of tf cooperativity currently available. then given a list of predicted cooperative tf pairs from a method, we calculated the significance of the overlap of this list with the benchmark set using yang et al.'s index. for the given list, a score which represents the significance of the overlap is defined as the −logp, where p is the p-value computed using fisher exact test. the higher the score, the better the performance. figure 2c shows that our method outperforms existing methods in this score.. met4/met28/met complex the list of known cooperative tf pairs are derived from biochemically well-defined transcriptional complexes within the mips complex catalogue. discussion our method is robust against different thresholds of the cooperativity score in this study, we set a threshold of cooperativity score to be and reported pctfps whose cooperativity scores are larger than the threshold. the number of pctfps reported by our method is similar to those of five previous methods. to check the robustness of our method against different thresholds of the cooperativity score, we tested four different thresholds. figure shows that no matter which threshold is used, the performance of our method is always the same on the performance index this suggests that our method is robust against different thresholds of the cooperativity score. our method is robust against different qualities of tfbs data the quality of tfbs data retrieved from swissregulon database depends on the posterior probability threshold being used. in this study, a threshold of the posterior probability was applied to select putative tfbss. to check the robustness of our method against different qualities of tfbs data, we tested four different posterior probability thresholds. figure shows that no matter which threshold is used, the performance of our method is always the same on the performance index this suggests that our method is robust against different thresholds of posterior probability to control the quality of tfbs data. our method outperforms existing methods in the precision and recall when using a benchmark set of known cooperative tf pairs in the performance index the significance of the overlap of the list of pctfps from a method with the benchmark set of known cooperative tf pairs is used to evaluate the performance of a method. here, we use the precision and recall to evaluate the performance of a method. as shown in figure our method outperforms existing methods in the precision and outperforms existing methods in the recall. the nucleosome occupancy data contributes to the overall improved prediction to demonstrate that the nucleosome occupancy data contributes to the overall improved prediction, we tested our method when nucleosome data are used and when nucleosome data are not used on the performance index as shown in figure the −logp of t w/ nucleosome is higher than that of t w/o nucleosome by, meaning that the p-value of t w/ nucleosome is less than that of t w/o nucleosome by more than folds. this suggests that nucleosome occupancy data do contribute to the overall improved prediction of our method. issue of applying our method to other model organisms our method is used to infer the cooperativity between two yeast tfs by integrating the tf-gene documented regulation, tfbs and nucleosome occupancy data. theoretically, it can be applied to other model organisms which also have these three kinds of genome-wide data. there are two reasons why we used yeast as the model organism to test our method. first, yeast is the only organism which has more than tf-gene documented regulation data available. the useful tf-gene documented regulation data, which provide the experimentally validated regulatory relationships between tfs and genes, are collected from more than published papers by the team of the yeastract database. second, yeast is the only organism that is tested by more than existing algorithms. therefore, using yeast as the model organism makes it possible to compare our predictions with the predictions of many existing methods. a cooperative tf network cell cycle since cell cycle process has been well investigated in the literature, let us discuss it in more details. cell cycle is a complex process and it consists of four main phases: g s, g and m. g1/s phase the g to s phase transition of the eukaryotic cell cycle is crucial to the coordination of cell cycle progression with cellular growth. during the g1/s transition of the cell cycle in yeast, sbf and mbf are known to activate gene expression. sbf is a protein complex composed of swi and swi and mbf is a protein complex composed of mbp and swi. our method successfully predicted the cooperativity between swi and swi and the cooperativity between mbp and swi. moreover, mbp is known to related to swi because the mbp swi double knockout strain were inviable. the cooperativity between mbp and swi is successfully captured by our method. in addition, a study suggests that stb may affect mbf-dependent transcription. stb is a protein which regulates the timing of start transcription in the absence of the g regulator cln the cooperativity between stb and swi is successfully identified by our method. g2/m phase in the g2/m phase, fkh and fkh play essential roles in the activation of the clb cluster genes and they share 72% identical dna binding domain. moreover, the double mutant of fkh and fkh displays obvious morphological change. our method successfully predicts the cooperativity between fkh and fkh. m/g phase in m/g phase, ace and swi co-regulate the expression of many cell cycle genes in yeast. moreover, ace and swi proteins show similarity at the amino acid level and bind to the same dna sequence with 82% identical dna binding domains. our method successfully identifies the cooperativity between ace and swi.  in this paper, we developed a method to infer the cooperativity between two tfs by integrating the tf-gene documented regulation, tfbs and nucleosome occupancy data. two tfs are predicted as cooperative if they have a significantly higher number of common target genes than random expectation and their binding sites tend to be co-depleted of nucleosomes in order to make these binding sites simultaneously accessible to tf binding. a list of cooperative tf pairs has been predicted by our method. among these predicted cooperative tf pairs, pairs are also predicted by existing methods. the other pairs are novel cooperative tf pairs. the biological relevance of these novel cooperative tf pairs is justified by the existence of protein-protein interactions and co-annotation in the same mips functional categories. moreover, our method is shown to outperform the existing methods based on the three performance indices: the similarity of protein-protein interaction partners between two tfs, the functional similarity between two tfs, and the overlap between a method's prediction result and the benchmark set of known cooperative tf pairs. finally, the cooperative tf network constructed from the predicted pairs demonstrates that our method has the power to find cooperative tf pairs of different biological processes. we believe that our prediction will help biologists to understand the mechanism of transcriptional regulation in eukaryotic cells. competing interests the authors declare that they have no competing interests. authors' contributions wsw conceived the research topic and provided essential guidance. wsw, fjl and mhj developed the algorithm and wrote the manuscript. fjl, mhj and ccc performed all the simulations. ymh provided advices on the manuscript writing. all authors have read and approved the final manuscript. declarations the publication charges of this article were funded by ministry of science and technology of taiwan most-103-2221-e-006-174-my 
therefore, it is crucial to understand the precise cooperative interactions among tfs. the nucleosome occupancy data is not yet used for this research topic despite that several researches have revealed the association between nucleosomes and tfbss. in this study, we developed a novel method to infer the cooperativity between two tfs by integrating the tf-gene documented regulation, tfbs and nucleosome occupancy data. tf-gene documented regulation and tfbs data were used to determine the target genes of a tf, and the genome-wide nucleosome occupancy data was used to assess the nucleosome occupancy on tfbss. our method identifies cooperative tf pairs based on two biologically plausible assumptions. various kinds of experimental data including chip-chip, tf binding site, gene expression, tf knockout and protein-protein interaction data have been used to identify cooperative tf pairs in existing methods. finally, a list of cooperative tf pairs has been predicted by our method. the other pairs are novel cooperative tf pairs predicted by our method. the biological relevance of these novel cooperative tf pairs is justified by the existence of protein-protein interactions and co-annotation in the same mips functional categories. we show that our method performs better than these existing methods in identifying cooperative tf pairs in yeast. finally, the cooperative tf network constructed from the predicted cooperative tf pairs shows that our method has the power to find cooperative tf pairs of different biological processes. our method is effective in identifying cooperative tf pairs in yeast. each tf pair is given a cooperativity score by our method. we believe that our study will help biologists to understand the mechanisms of transcriptional regulation in eukaryotic cells. if two tfs cooperate, then they should have a significantly higher number of common target genes than random expectation and their binding sites should tend to be co-depleted of nucleosomes in order to make these binding sites simultaneously accessible to tf binding. transcriptional regulation of gene expression is usually accomplished by multiple interactive transcription factors. moreover, we adopted three performance indices to compare our predictions with existing methods' predictions. the higher the score is, the more likely a tf pair has cooperativity. among these tf pairs, pairs are also predicted by existing methods.
 transcriptional regulation of gene expression is usually accomplished by multiple interactive transcription factors. therefore, it is crucial to understand the precise cooperative interactions among tfs. various kinds of experimental data including chip-chip, tf binding site, gene expression, tf knockout and protein-protein interaction data have been used to identify cooperative tf pairs in existing methods. the nucleosome occupancy data is not yet used for this research topic despite that several researches have revealed the association between nucleosomes and tfbss.  in this study, we developed a novel method to infer the cooperativity between two tfs by integrating the tf-gene documented regulation, tfbs and nucleosome occupancy data. tf-gene documented regulation and tfbs data were used to determine the target genes of a tf, and the genome-wide nucleosome occupancy data was used to assess the nucleosome occupancy on tfbss. our method identifies cooperative tf pairs based on two biologically plausible assumptions. if two tfs cooperate, then they should have a significantly higher number of common target genes than random expectation and their binding sites should tend to be co-depleted of nucleosomes in order to make these binding sites simultaneously accessible to tf binding. each tf pair is given a cooperativity score by our method. the higher the score is, the more likely a tf pair has cooperativity. finally, a list of cooperative tf pairs has been predicted by our method. among these tf pairs, pairs are also predicted by existing methods. the other pairs are novel cooperative tf pairs predicted by our method. the biological relevance of these novel cooperative tf pairs is justified by the existence of protein-protein interactions and co-annotation in the same mips functional categories. moreover, we adopted three performance indices to compare our predictions with existing methods' predictions. we show that our method performs better than these existing methods in identifying cooperative tf pairs in yeast. finally, the cooperative tf network constructed from the predicted cooperative tf pairs shows that our method has the power to find cooperative tf pairs of different biological processes.  our method is effective in identifying cooperative tf pairs in yeast. many of our predictions are validated by the literature, and our method outperforms existing methods. we believe that our study will help biologists to understand the mechanisms of transcriptional regulation in eukaryotic cells. transcription factor cooperativitynucleosometranscription factor binding siteyeast15- december the 25th international conference on genome informatics tokyo, japan 