BACKGROUND
high-throughput in vivo protein-dna binding experiments such as chip-chip and chip-seq are currently widely used to study gene regulation.
identification of transcription factor  binding sites is an essential step to understand tf function and gene regulatory networks  <cit> .
in such analyses, raw reads of chip-seq experiments are mapped to a human reference genome.
subsequently a peak-calling program is used to detect putative tf binding sites.
however, two problems arise by doing so.
first, the identified tf binding sites are dependent of the threshold value used by the peak-calling program.
if stringent criteria are applied, many potentially functional tf binding sites with weak binding  may be eliminated  <cit> .
if on the other hand non stringent cutoff values are chosen, many false binding sites are identified.
second, chip-seq experiment may not necessarily identify the direct tf-dna interactions due to the inherent inability of current chip-seq or chip-chip technology to distinguish direct versus indirect protein-dna interactions  <cit> .
so far, the first problem has been ignored  <cit> .
several studies have addressed the second problem only partially.
vallania et al.
<cit>  focused on identifying only functional direct tf binding sites by using a computational method based on weight matrices, comparative genomics, and gene expression profiles; gordan et al  <cit>  developed a method to separate direct tf binding from indirect tf binding in yeast chip-chip data but it has not been used to analyze human chip-seq experiments.
in addition, the method requires that both in vivo binding data and in vitro dna binding motifs are available; more recently, bailey et al  <cit>  proposed an interesting statistical method "central motif enrichment analysis"  to predict direct dna binding sites from chip-seq data.
unfortunately, the program only works with equal-length genomic sequences and does not provide information about functional indirect tf binding.
in the present work, a more comprehensive computational approach, bayespi2+, is developed for analyzing in vivo high-throughput protein-dna interaction data, where the above-mentioned problems are solved.
especially, non stringent peak calling cutoff values can be used allowing the inclusion of many weak protein binding sites in the data analysis.
the newly developed bayespi2+ is a c program that is based on a biophysical model of protein-dna interactions  <cit>  and that can be run in both a serial computation model and in a parallel ensemble learning framework.
bayespi2+ estimates protein binding energy matrix , protein concentration  in a solution  <cit> , and differential binding affinity  of protein-dna interactions, through in vivo protein-dna interaction experiments.
based on these predicted features, bayespi2+ allowed to distinguish high and low affinity protein binding sites called here for reasons of simplicity, type i and type ii tf binding  <cit> .
the novel method was first tested in both synthetic chip-seq data and several real in vivo protein-dna binding data sets.
then, gene regulatory difference between the predicted type i and type ii tf binding sites was investigated in two human chip-seq experiments, the estrogen receptor α  using the mcf <dig> breast cancer cell line and the spib tf using the hbl <dig> activated b cell-like diffuse large b-cell lymphoma  cell line.
esr <dig> is a member of the nuclear receptor family of ligand-activated tfs and is involved in the development and progression of breast cancer  <cit> .
spib belongs to ets-family of tfs and is required for the survival of abc dlbcl cells  <cit> .
putative spib type i and type ii binding sites were verified by in vitro protein-dna interaction experiments.
subsequently, we tested whether these binding sites have an effect on gene expression.
of interest, our analysis showed that the binding of tf to both type i and type ii binding sites is important for gene expression.
RESULTS
distinguishing type i versus type ii tf binding sites using synthetic chip-seq data sets
here, bayespi2+ was first used to infer the pbem and the chemical potential from a synthetic training data set  <cit> .
then the best pbem, i.e.
a pbem with the highest motif similarity score to a known consensus sequence motif, was chosen to predict protein binding sites in a data test set.
results of a serial computation, testing error rates , true negative , false positive  and false negative rates ), are displayed in figure  <dig>  the rates were estimated by comparing to known direct tf binding sites  with the predicted direct tf binding sites ).
it takes around fifteen to thirty minutes for a serial version of bayespi2+ to complete the prediction in one synthetic data set.
in additional file 1: figure s <dig>  test error rates by using a parallel ensemble bayespi2+ learning are shown.
in this analysis, both meta-pbem and meta-chemical-potential  were computed by five times random splitting training and testing  data.
these predictions were completed in five to eight minutes.
the overall prediction accuracy with this method is almost the same as what was obtained by a serial computation.
of interest, the longer the binding motif, the better the test error rates.
tp and tn of ace <dig> with a binding motif of 6bp are between 70% and 90% whereas the tp and tn of the other tfs with binding motifs between 8bp and 12bp are approximately 95%.
thus, both serial and parallel ensemble bayespi2+ learning are able to distinguish type i versus type ii tf binding sites in synthetic chip-seq datasets.
distinguishing type i versus type ii tf binding sites by using in vivo protein-dna binding data
prediction of pbem in five data sets of various sizes
encouraged by the results from synthetic chip-seq data, bayespi2+ was applied to five human chip-seq data sets  <cit> : nrsf, esr <dig>  ctcf, spib and stat <dig> with 6k, 17k, 27k, 43k and 74k called peaks, respectively.
for each tf, a parallel ensemble version of bayespi2+ was applied to randomly selected peaks constituting 5%, 10%, 25%, and 50% of called peaks, respectively.
each random selection was repeated ten times to estimate the meta-pbem.
a serial computation of bayespi2+ was used to infer the best pbem based on all called peaks, i.e.
100% of input data.
computational costs of all predictions were recorded in additional file 1: figure s <dig>  as expected, a linear increase of cpu time was observed when the input size is increased from 5% to 100% of called peaks.
sequence logo representations of predicted meta-pbems based on multiple random selections of 5% to 50% of called peaks and the best pbem from 100% called peaks for  and  are shown in figure  <dig> and additional file 1: figure s <dig>  respectively.
two observations can be drawn from the analysis as illustrated by the figures: 1) the predicted pbems from serial computation are similar to the meta-pbems, but positional trends in information content are observed across data of different input size with the exception of data for nrsf that has the fewest called peaks; 2) the positional trends in information content are near maximum when the number of input peaks used for analysis is greater than and equal to 25% of called peaks.
by considering both computational efficiency and the prediction accuracy, the present results indicate that multiple random selections of ~25% of called peaks are sufficient for a parallel ensemble version of bayespi2+.
especially, if the input data size is large  then a parallel ensemble learning of bayespi2+ will be preferred in the data analysis.
distinguishing type i versus type ii tf binding sites in human chip-seq data sets
subsequently, distinguishing type i versus type ii tf binding sites was analyzed in five human chip-seq datasets.
first, the meta-pbem and meta-chemical-potential of each tf, as estimated by random selection of 25% of called peaks ten times , were used to compute the expected p-values and dba for every binding site.
then, a fuzzy neural gas algorithm was applied to dba to classify called peaks into type i and type ii tf binding sites, where the expected p-value of type i and type ii tf binding is < <dig>  and > =  <dig> , respectively.
finally, the significance of meta-pbem for identification of tf binding sites sequences was evaluated by fitting the predicted tf binding affinities on dna sequences and the measured chip-seq tag density to a linear regression model, then transforming the regression coefficients to t-values  <cit> , which measures the dependence between the estimated meta-pbem and the observed chip-seq tag counts.
the results show that the meta-pbems of  <dig> tested human tfs are significantly correlated with the predicted type i  tf binding site sequences for  <dig> tfs, respectively .
distributions of both tag densities and dba are shown in figure  <dig> and additional file 1: figure s <dig> for the  <dig> tfs, respectively.
though there is a large overlap of chip-seq tag densities between the type i and type ii tf binding, the distribution of dba levels clearly separates the type i from the type ii tf binding, except for few sites with almost zero dba.
therefore, the estimated dba level is a good parameter to distinguish two types of tf binding sites, whereas the raw tag counts of called peaks are not suited to accomplish this.
distinguishing type i versus type ii tf binding sites in yeast chip-chip data sets
chip-seq is a high resolution experiment that identifies putative protein binding site sequences of short and equal-length, approximately  <dig> bp.
we therefore also tested whether bayespi2+ can predict type i tf binding sites by using unequal-length genomic sequences.
here, a series computation of bayespi2+ was applied to four yeast chip-chip experiments with tfs ace <dig>  swi <dig>  ino <dig>  and xbp <dig> in rich medium conditions  <cit> .
the putative protein binding sites are positioned on ~ <dig> yeast intergenic regions of unequal-length varying between  <dig> bp to ~  <dig> bp, with a median length of ~ <dig> bp.
the results indicate that only three of four yeast tfs  obtained good pbem by using bayespi2+ .
a plot of p-values, reflecting the confidence level of detecting a binding site,  <cit>  against the number of binding sites with p values below the defined p-value can be made for the four yeast chip-chip experiments .
the plot shows that there are more than  <dig> binding sites with confidence level p <  <dig>  for ace <dig>  swi <dig> and ino <dig>  respectively.
however, none of the xpb <dig> binding targets passed the same level of significance of binding.
the poor binding prediction for xbp <dig> can be explained either by true weak protein binding or poor quality of the chip-chip experimental data.
therefore, only ace <dig>  swi <dig> and ino <dig> were considered in the subsequent data analysis.
yeast intergenic regions with either low or high affinity binding sites  were considered as containing putative tf binding sites.
thus, about  <dig>   <dig>  and  <dig> yeast intergenic regions with binding sites for ace <dig>  swi <dig> and ino <dig>  respectively, were identified.
the inferred pbem from a serial computation analysis was used to calculate dba and the expected p-value.
in this analysis, each selected intergenic region was randomly shuffled  <dig> times.
then, type i and type ii tf binding targets were classified by applying the fuzzy neural gas algorithm on the calculated dba.
interestingly, for the three yeast tfs, no gene seems to be regulated by both type i and type ii tf binding sites, where the assignment of tf binding sites to putative target genes was based on a published annotation  <cit> .
to verify the predicted type i tf binding sites, the best predicted pbem of each tf was used to compute in silico tf binding affinities on dna sequences for type i, type ii tf binding sites, and the rest of intergenic regions, respectively.
a two tailed t-test was then performed to compare the tf binding affinities between type i and type ii tf binding sites, and between type i/ii tf binding sites and the rest of intergenic regions, respectively.
a bar plot of the t-values of the t-tests is displayed in figure  <dig>  the predicted best pbem of each tf is highly enriched in the type i tf binding but no enrichment was found in type ii tf binding.
similar results were obtained by using  <dig> collected yeast consensus sequence motifs   <cit> .
hence, the classification of type i and type ii tf binding sites by using the dba proves also robust when used to analyze unequal-length genomic sequences.
comparison of predicted type i tf binding sites identified by bayespi2+ and centrimo in mouse chip-seq data sets
first, position specific weight matrices  of three mouse tfs  were obtained from jaspar database.
based on the known pswm of each mouse tf, type i  tf binding sites were predicted by applying bayespi2+ and centrimo  <cit>  on all called peaks  of three mouse chip-seq data sets, respectively.
here, default parameter settings were used in both programs.
results suggest that around 83%, 88%, and 92% of centrimo predicted type i myc, stat <dig>  and oct <dig> binding sites are recovered by bayespi2+, respectively.
thus, for predicting type i  tf binding sites in in vivo protein-dna interaction experiment, there is a good agreement between the new biophysical model bayespi2+ and the published statistical method centrimo.
differences in expression of genes with type i and type ii tf binding sites for esr <dig> and spib transcription factors
functional esr <dig> target genes are regulated by both type i and type ii tf binding sites
after separating tf binding sites into type i and type ii binding sites, we investigated the gene regulatory differences between the two.
a functional study of putative esr <dig> target genes, regulated by either type i or type ii tf binding sites, was carried out in breast cancer cell line mcf- <dig> by using histone modification data  <cit> , microarray gene expression profiles  <cit> , and nucleosome density  <cit> .
great tool was used to find putative target genes regulated through either type i or type ii tf binding sites.
by this analysis,  <dig> and  <dig> putative target genes were identified for  <dig> esr <dig> type i tf binding sites and  <dig> for esr <dig> type ii tf binding sites, respectively.
of interest,  <dig> genes were regulated by both type i and type ii tf binding sites, henceforth called 'a' genes;  <dig> genes were regulated by type i tf binding sites only, called 'b' genes; and  <dig> genes were exclusively regulated by type ii tf binding sites, called 'c' genes in this manuscript.
for the above-mentioned three classes of regulated genes, an enrichment test  of gene expression activities  between one class of genes and the rest of genes was performed.
a heat-map of t-values and z-values is shown in figure  <dig>  'a' genes targeted by esr <dig> are more highly expressed than 'b' and 'c' genes.
of interest and counter intuitively, 'c' genes have a higher expression level than 'b' genes.
distributions of chip-seq tag densities across the three classes of target genes are shown in additional file 1: figure s <dig>  'a' genes show the highest tag counts, as expected, 'c' genes show the lowest tag counts, and 'b' genes reveal intermediate tag counts.
taken together, our results suggest that esr <dig> predominantly regulates 'a' genes with both type i and type ii esr <dig> binding sites.
the functional consequence of exclusive type i or type ii tf binding on gene expression seems to be less important.
to further study the functional consequence of the different types of esr <dig> binding to genes, histone modifications 5kb upstream, and  <dig> kb downstream of the genes were studied, respectively.
tag densities in e2-treated cells were normalized against control cells.
a heat map of histone modifications upon e2-treatment is shown in figure  <dig>  t-values were obtained by performing the t-test for genes that were grouped in the three classes of esr <dig> binding genes  against the rest of genes, respectively.
of interest, the results are consistent with the analysis of gene expression analysis by microarray: 1) histone modification patterns are different among the three classes of esr <dig> target genes; 2) only 'a' genes show decreasing nucleosome densities as evidenced by enriched faire levels.
accordingly, rna polymerase ii levels are increased as well as histone acetylation .
these observations are consistent with functional esr1-dna interactions predominantly through combined type i and type ii binding of the transcription factor.
robustness of the predicted esr <dig> type i and type ii tf binding site analysis
to test the robustness of the binding site prediction, a repeated analysis of gene expression profiles, chip-seq tag density, and histone modifications for the three classes of esr <dig> target genes was performed, but this time with removal of the binding sites with low affinity.
esr <dig> binding sites of which both chip-seq tag count was less than  <dig>  fold of the minimum tag count for type ii tf binding sites and of which the dba level was smaller than the maximum dba in type ii tf binding sites, were considered low affinity binding sites and removed.
after filtering,  <dig> and  <dig> esr <dig> type i and type ii tf binding sites were remaining, respectively.
compared to the results before changing the thresholds, few esr <dig> type i tf binding sites  but more than half of the type ii tf binding sites were lost.
great was then also used to find putative target genes for the new set of esr <dig> binding sites.
this time,  <dig> 'c' genes,  <dig> 'b' genes, and  <dig> 'a' genes were found.
gene expression profile analysis, chip-seq tag density enrichment, and histone modifications analysis for these classes of genes are given in additional file 1: figures s <dig>  s <dig>  and s <dig>  respectively.
all results are consistent with those for the previous analyses, with the exception of a similar tag density for 'b' and 'c' genes after removal of low binding affinity sites.
functional annotation of the new three classes of esr <dig> target genes by david tool revealed that 'a' genes are highly enriched in pathways active in cancer, including the mapk signaling pathway .
functional spib target genes are regulated by both type i and type ii tf binding sites
called spib chip-seq peaks  <cit>  were first classified into type i  and type ii  tf binding sites based on their estimated dba levels from the meta-pbem and meta-chemical-potential.
then, great tool was used to identify  <dig>   <dig> and  <dig> genes that were possibly regulated by type ii binding only , type i binding only  and by both , respectively.
subsequently, microarray gene expression analysis of the groups of genes in lenalidomide treated abc dlbcl cell lines   <cit>  was performed.
t-test and mann-whitney u tests were used to evaluate the significance of differential expression between spib target genes  and the rest of genes in genome .
results reveal that spib target 'a' genes have the highest expression and that 'b' and 'c' genes only show a slight increase or decrease of the gene expression level.
additionally, silencing of spib by rna interference in abc dlbcl cell line hbl <dig>  <cit>  results in significant repression of 'a' genes, but it does not have a strong impact on 'b' and 'c' genes as illustrated in figure  <dig>  these results strongly suggest that combined type i and type ii transcription factor binding is necessary for gene activation.
functional annotation of the three groups of spib target genes by david tool  shows that 'a' genes are enriched in the mapk signaling pathway , in cancer in general , in the t cell receptor signaling , and b cell receptor signaling pathways .
of interest, the latter pathways were not included among 'b' and 'c' genes.
thus, in analogy with what was demonstrated for esr <dig> in breast cancer, a combination of spib type i and type ii tf binding sites is needed to regulate gene expression in abc dlbcl cells.
spib is known to be up-regulated in abc dlbcl  <cit> .
our data show that spib likely contributes to the characteristic up-regulation of b cell receptor pathway genes in abc dlbcl.
robustness of the predicted spib type i and type ii tf binding site analysis
this analysis was performed following the same filtering criteria as for removing low affinity esr <dig> binding sites.
after filtering,  <dig> and  <dig> spib binding sites were remaining for type i and type ii tf binding, respectively.
'c' genes are increased almost two-fold , 'a' genes were slightly reduced , and 'b' genes were decreased by about one-forth .
further analysis of lenalidomide treated abc dlbcl microarray gene expression data and spib knockdown experiments in abc dlbcl cells show that 'a' genes have the most significant response.
these genes but not 'b' or 'c' genes, showed increased expression in lenalidomide-treated cells and decreased expression in knockdown experiments .
of interest, 'a' genes were highly enriched in the same pathways  as identified in the previous section.
the nature of type ii esr <dig> and spib binding
from the above analysis, chip-seq peaks represent either type i or type ii tf binding sites that can be distinguished via dba and expected p-values.
however, the question remains whether low affinity type ii tf binding represents indirect binding or binding to alternative binding sites  <cit> .
this question was investigated by searching for the putative tf binding motifs in the predicted type i and type ii esr <dig> and spib binding sites, respectively.
a serial version of bayespi2+ was first applied to find the best pbem in  <dig> type i and  <dig> type ii esr <dig> binding sites, respectively.
the results show that the known esr <dig> binding motif is only enriched in esr <dig> type i tf binding sites .
no esr <dig> binding motifs were discovered in esr <dig> type ii tf binding sites.
these results suggest that esr <dig> type ii binding represents indirect binding of esr <dig>  by contrast, the same analysis for spib shows that the spib core binding motif is similar for both type i and type ii tf binding sites .
however, there is a significant difference of the sequence at both 5' and 3' sides of the spib pbems.
in particular, the core spib binding motif ggaa is followed by a g nucleotide in type i binding sites whereas it is followed by a c in type ii spib binding sites.
this single nucleotide replacement in the vicinity of the core spib binding motif may contribute to differential binding of spib in human genome.
by applying the bayespi2+ parallel ensemble approach on the same datasets for esr <dig> and spib, after removal of low binding affinity sites, similar results were found .
verification of predicted type i and type ii spib binding sites by emsa
in order to verify spib binding sites, a two-step filtering procedure was applied to  <dig> putative spib target genes  with spib binding motifs.
for each putative spib target gene, a two-sample kolmogorov-smirnov goodness-of-fit hypothesis test was performed between time-series microarray gene expression profiles  and the gene expression profile  after down-regulation of spib by shrna  <cit> .
the assumptions were that genes controlled by spib are differentially expressed  in abc dlbcl cells treated as the above-mentioned two conditions, and that spib regulated genes are those genes with either a type i or a type ii spib binding sites located between  <dig> kb upstream and  <dig> kb downstream to the transcription start site.
in total,  <dig> genes fulfilled these criteria .
to test whether those genes contained spib binding sites and whether type ii binding sites represented alternative binding sites, as predicted by our analysis, emsa was performed on  <dig> randomly selected type i spib binding sites and  <dig> type ii spib binding sites .
for this analysis, 50bp dna sequences were selected of which the center sequence corresponded with the identified peak in our analysis.
of the  <dig> type i spib binding sequences,  <dig> showed very strong, one showed weak binding and one did not show binding.
of the  <dig> type ii spib binding probes,  <dig> showed weak binding and  <dig> showed not binding .
to check the binding to the spib core motif , 2bp of the core spib motif were mutated  for two selected type i spib binding sites , then the same gel shift analysis were performed for both the original and the mutated type i spib binding sites.
additional file 1: figure s <dig> showed that binding of spib is completely inhibited after mutating 2bp of the spib core motif.
the results of these in vitro experiments support that type i and type ii spib binding represents direct tf binding, with type ii being, at least in part, alternative weak spib binding sites.
discussion
a new biophysical model, named bayespi2+ was designed to analyze more extensively tf binding sites in in vivo protein-dna interaction data than hitherto achieved with existing models.
to achieve this bayespi2+ was designed to analyze a large number of called chip-seq peaks  simultaneously, including weak binding sites.
additionally, the differential binding affinity  for each called peak was computed to identify high affinity  and low affinity  tf binding sites.
in this work, the strength of type i  and type ii  binding sites is not in proportion to the number of measured chip-seq tag counts.
in other words, tf acts independently in type i  binding but it requires a co-factor to stabilize the protein-dna interaction in type ii  binding.
an initial test was performed on synthetic chip-seq datasets with success, yielding a true negative rate of >90%.
for the test, a serial version and a parallel ensemble learning of bayespi2+ was used with similar prediction accuracies.
however, in the test, the parallel version of bayespi2+ is at least three times faster than the serial one in completing the prediction.
thus, for very large input data , a parallel ensemble learning of bayespi2+ is recommended because it saves the overall waiting time considerably by splitting the job to multiple computer processors.
in a subsequent analysis of five human chip-seq datasets, the predicted pbems between a serial bayespi2+ computation and a parallel ensemble learning of bayespi2+ were compared.
though the best pbem identified by serial computation and the meta-pbem estimated by parallel ensemble learning were similar, a positional variation in information content of the predicted meta-pbems were observed across different sizes of input data .
the positional variation in information content for pbem reaches saturation point when the number of input peaks exceeds 25% of all called peaks.
this indicates that various binding positions within a pbem are important in the formation of the protein-dna complex, during in vivo protein-dna interactions  <cit> .
by analyzing all possible binding sites with our method, two types could be discerned.
particularly, the dba level of each tf, estimated by using the corresponding meta-pbem, allowed to recognize low affinity tf binding, called type ii tf binding sites .
additionally, the inferred meta-pbems from chip-chip data and the binding consensus sequence motifs from online databases  <cit>  are significantly enriched in the type i tf binding sites when analyzing yeast chip-chip experiments for tfs ace <dig>  swi <dig>  and ino <dig>  of interest, the latter analyses were performed on chip-chip data, thus on genomic sequences of unequal length.
therefore, our proposed new method to distinguish two types of tf binding sites is applicable to both equal-length and unequal-length genomic sequences.
of note, bayespi <dig> has a very good agreement  with centrimo concerning the analysis of type i  tf binding.
to test the function of predicted type i and type ii tf binding sites, we analyzed their effect on gene regulation.
this was done for two human tfs, esr <dig> and spib in breast cancer and diffuse large b cell lymphoma, respectively.
esr <dig> encodes the estrogen receptor alpha and contributes to cell growth in breast carcinoma  <cit> .
spib is a b cell transcription factor that is highly expressed in a clinically aggressive subtype of dlbcl, with activated b cell immunophenotype  <cit> .
genes with the putative tf binding sites were classified into three groups: 'a' genes, containing both type i and type ii tf binding sites; 'b' genes containing only type i tf binding sites; and 'c' genes, containing only type ii tf binding sites.
of interest, 'a' genes show the strongest expression in the breast cancer cell line mcf <dig> and the highest esr <dig> chip-seq tag density.
in addition, we found lower nucleosome density, higher rna polymerase ii expression and histone acetylation for 'a' genes than for 'b' or 'c' genes.
it is known that decreased nucleosome density and increased rna pol-ii binding indicate gene transcription  <cit>  whereas acetylation of histones  indicate functional tf binding  <cit>  and are important for activation of promoters and enhancers  <cit> .
functional annotation of the three types of esr <dig> target genes also suggests that, only 'a' genes are highly enriched in pathways of importance to breast cancer such as the mapk signaling pathway  <cit> .
analogous to what is observed for esr <dig> in breast carcinoma, spib 'a' genes show the highest gene expression in diffuse large b cell lymphoma, and the strongest response after silencing of spib by rna interference in abc dlbcl cell lines.
functional annotation of spib 'a' genes suggests that they are significantly involved in pathways of importance for dlbcl lymphoma biology, such as the b cell receptor signaling pathway.
the b cell receptor signaling pathway is activated in diffuse large b-cell lymphoma and contributes to tumor cell survival and proliferation  <cit> .
thus, our results indicate that esr <dig> and spib regulation of gene expression requires both type i and type ii binding.
a repeat analysis of genes controlled by either esr <dig> or spib binding sites, after filtering out the lowest binding affinity sites, yielded similar results: 'a' genes are the likely functional targets of these tfs.
though the effect of tf on genes requires direct protein-dna interaction, it has been well-known that additional and different interactions of the tf with the gene are needed for regulation  <cit> .
we show for the first time the scale of this effect by our genome-wide analysis  <cit> .
type ii tf binding sites for esr <dig> and spib were further investigated to find out whether these constituted indirect binding sites or alternative binding sites with different affinity.
no esr <dig> similar motif was found for type ii esr <dig> binding sites.
this indicates that type ii esr <dig> likely represents indirect binding to dna.
by contrast, a similar consensus motif was found for both type i and type ii spib binding sites, except for one nucleotide difference in the area adjacent to core spib motif ggaa .
these results indicate that the type ii spib binding site is an alternative low affinity spib binding site.
the findings were also confirmed by emsa: about 90% and 50% of tested sequences with putative type i and type ii spib binding sites, respectively, resulted in band shift in emsa .
these results also confirm that type ii tf binding is rather weak, which requires co-factors to enhance the binding to dna sequence.
notwithstanding, our analysis shows that type i and type ii binding sites act concertedly in gene regulation.
CONCLUSIONS
in summary, we developed a new program bayespi2+ to analyze all potential tf binding sites in the genome, without filtering.
by doing so, we found two types of functional tf binding sites, both indicate to be important for gene regulation.
bayespi2+ can be used in a serial computation or a parallel ensemble approach.
hitherto, other methods only used the top few hundred or thousand high affinity binding sites which we showed results in loss of valuable information.

 high-throughput in vivo protein-dna binding experiments such as chip-chip and chip-seq are currently widely used to study gene regulation. identification of transcription factor binding sites is an essential step to understand tf function and gene regulatory networks. in such analyses, raw reads of chip-seq experiments are mapped to a human reference genome. subsequently a peak-calling program is used to detect putative tf binding sites. however, two problems arise by doing so. first, the identified tf binding sites are dependent of the threshold value used by the peak-calling program. if stringent criteria are applied, many potentially functional tf binding sites with weak binding may be eliminated. if on the other hand non stringent cutoff values are chosen, many false binding sites are identified. second, chip-seq experiment may not necessarily identify the direct tf-dna interactions due to the inherent inability of current chip-seq or chip-chip technology to distinguish direct versus indirect protein-dna interactions. so far, the first problem has been ignored. several studies have addressed the second problem only partially. vallania et al. focused on identifying only functional direct tf binding sites by using a computational method based on weight matrices, comparative genomics, and gene expression profiles; gordan et al developed a method to separate direct tf binding from indirect tf binding in yeast chip-chip data but it has not been used to analyze human chip-seq experiments. in addition, the method requires that both in vivo binding data and in vitro dna binding motifs are available; more recently, bailey et al proposed an interesting statistical method "central motif enrichment analysis" to predict direct dna binding sites from chip-seq data. unfortunately, the program only works with equal-length genomic sequences and does not provide information about functional indirect tf binding. in the present work, a more comprehensive computational approach, bayespi2+, is developed for analyzing in vivo high-throughput protein-dna interaction data, where the above-mentioned problems are solved. especially, non stringent peak calling cutoff values can be used allowing the inclusion of many weak protein binding sites in the data analysis. the newly developed bayespi2+ is a c program that is based on a biophysical model of protein-dna interactions and that can be run in both a serial computation model and in a parallel ensemble learning framework. bayespi2+ estimates protein binding energy matrix, protein concentration in a solution, and differential binding affinity of protein-dna interactions, through in vivo protein-dna interaction experiments. based on these predicted features, bayespi2+ allowed to distinguish high and low affinity protein binding sites called here for reasons of simplicity, type i and type ii tf binding. the novel method was first tested in both synthetic chip-seq data and several real in vivo protein-dna binding data sets. then, gene regulatory difference between the predicted type i and type ii tf binding sites was investigated in two human chip-seq experiments, the estrogen receptor α using the mcf breast cancer cell line and the spib tf using the hbl activated b cell-like diffuse large b-cell lymphoma cell line. esr is a member of the nuclear receptor family of ligand-activated tfs and is involved in the development and progression of breast cancer. spib belongs to ets-family of tfs and is required for the survival of abc dlbcl cells. putative spib type i and type ii binding sites were verified by in vitro protein-dna interaction experiments. subsequently, we tested whether these binding sites have an effect on gene expression. of interest, our analysis showed that the binding of tf to both type i and type ii binding sites is important for gene expression.  distinguishing type i versus type ii tf binding sites using synthetic chip-seq data sets here, bayespi2+ was first used to infer the pbem and the chemical potential from a synthetic training data set. then the best pbem, i.e. a pbem with the highest motif similarity score to a known consensus sequence motif, was chosen to predict protein binding sites in a data test set. results of a serial computation, testing error rates, true negative, false positive and false negative rates ), are displayed in figure the rates were estimated by comparing to known direct tf binding sites with the predicted direct tf binding sites ). it takes around fifteen to thirty minutes for a serial version of bayespi2+ to complete the prediction in one synthetic data set. in additional file 1: figure s test error rates by using a parallel ensemble bayespi2+ learning are shown. in this analysis, both meta-pbem and meta-chemical-potential were computed by five times random splitting training and testing data. these predictions were completed in five to eight minutes. the overall prediction accuracy with this method is almost the same as what was obtained by a serial computation. of interest, the longer the binding motif, the better the test error rates. tp and tn of ace with a binding motif of 6bp are between 70% and 90% whereas the tp and tn of the other tfs with binding motifs between 8bp and 12bp are approximately 95%. thus, both serial and parallel ensemble bayespi2+ learning are able to distinguish type i versus type ii tf binding sites in synthetic chip-seq datasets. distinguishing type i versus type ii tf binding sites by using in vivo protein-dna binding data prediction of pbem in five data sets of various sizes encouraged by the results from synthetic chip-seq data, bayespi2+ was applied to five human chip-seq data sets: nrsf, esr ctcf, spib and stat with 6k, 17k, 27k, 43k and 74k called peaks, respectively. for each tf, a parallel ensemble version of bayespi2+ was applied to randomly selected peaks constituting 5%, 10%, 25%, and 50% of called peaks, respectively. each random selection was repeated ten times to estimate the meta-pbem. a serial computation of bayespi2+ was used to infer the best pbem based on all called peaks, i.e. 100% of input data. computational costs of all predictions were recorded in additional file 1: figure s as expected, a linear increase of cpu time was observed when the input size is increased from 5% to 100% of called peaks. sequence logo representations of predicted meta-pbems based on multiple random selections of 5% to 50% of called peaks and the best pbem from 100% called peaks for and are shown in figure and additional file 1: figure s respectively. two observations can be drawn from the analysis as illustrated by the figures: 1) the predicted pbems from serial computation are similar to the meta-pbems, but positional trends in information content are observed across data of different input size with the exception of data for nrsf that has the fewest called peaks; 2) the positional trends in information content are near maximum when the number of input peaks used for analysis is greater than and equal to 25% of called peaks. by considering both computational efficiency and the prediction accuracy, the present results indicate that multiple random selections of ~25% of called peaks are sufficient for a parallel ensemble version of bayespi2+. especially, if the input data size is large then a parallel ensemble learning of bayespi2+ will be preferred in the data analysis. distinguishing type i versus type ii tf binding sites in human chip-seq data sets subsequently, distinguishing type i versus type ii tf binding sites was analyzed in five human chip-seq datasets. first, the meta-pbem and meta-chemical-potential of each tf, as estimated by random selection of 25% of called peaks ten times, were used to compute the expected p-values and dba for every binding site. then, a fuzzy neural gas algorithm was applied to dba to classify called peaks into type i and type ii tf binding sites, where the expected p-value of type i and type ii tf binding is < and > =, respectively. finally, the significance of meta-pbem for identification of tf binding sites sequences was evaluated by fitting the predicted tf binding affinities on dna sequences and the measured chip-seq tag density to a linear regression model, then transforming the regression coefficients to t-values, which measures the dependence between the estimated meta-pbem and the observed chip-seq tag counts. the results show that the meta-pbems of tested human tfs are significantly correlated with the predicted type i tf binding site sequences for tfs, respectively. distributions of both tag densities and dba are shown in figure and additional file 1: figure s for the tfs, respectively. though there is a large overlap of chip-seq tag densities between the type i and type ii tf binding, the distribution of dba levels clearly separates the type i from the type ii tf binding, except for few sites with almost zero dba. therefore, the estimated dba level is a good parameter to distinguish two types of tf binding sites, whereas the raw tag counts of called peaks are not suited to accomplish this. distinguishing type i versus type ii tf binding sites in yeast chip-chip data sets chip-seq is a high resolution experiment that identifies putative protein binding site sequences of short and equal-length, approximately bp. we therefore also tested whether bayespi2+ can predict type i tf binding sites by using unequal-length genomic sequences. here, a series computation of bayespi2+ was applied to four yeast chip-chip experiments with tfs ace swi ino and xbp in rich medium conditions. the putative protein binding sites are positioned on ~ yeast intergenic regions of unequal-length varying between bp to ~ bp, with a median length of ~ bp. the results indicate that only three of four yeast tfs obtained good pbem by using bayespi2+. a plot of p-values, reflecting the confidence level of detecting a binding site, against the number of binding sites with p values below the defined p-value can be made for the four yeast chip-chip experiments. the plot shows that there are more than binding sites with confidence level p < for ace swi and ino respectively. however, none of the xpb binding targets passed the same level of significance of binding. the poor binding prediction for xbp can be explained either by true weak protein binding or poor quality of the chip-chip experimental data. therefore, only ace swi and ino were considered in the subsequent data analysis. yeast intergenic regions with either low or high affinity binding sites were considered as containing putative tf binding sites. thus, about and yeast intergenic regions with binding sites for ace swi and ino respectively, were identified. the inferred pbem from a serial computation analysis was used to calculate dba and the expected p-value. in this analysis, each selected intergenic region was randomly shuffled times. then, type i and type ii tf binding targets were classified by applying the fuzzy neural gas algorithm on the calculated dba. interestingly, for the three yeast tfs, no gene seems to be regulated by both type i and type ii tf binding sites, where the assignment of tf binding sites to putative target genes was based on a published annotation. to verify the predicted type i tf binding sites, the best predicted pbem of each tf was used to compute in silico tf binding affinities on dna sequences for type i, type ii tf binding sites, and the rest of intergenic regions, respectively. a two tailed t-test was then performed to compare the tf binding affinities between type i and type ii tf binding sites, and between type i/ii tf binding sites and the rest of intergenic regions, respectively. a bar plot of the t-values of the t-tests is displayed in figure the predicted best pbem of each tf is highly enriched in the type i tf binding but no enrichment was found in type ii tf binding. similar results were obtained by using collected yeast consensus sequence motifs. hence, the classification of type i and type ii tf binding sites by using the dba proves also robust when used to analyze unequal-length genomic sequences. comparison of predicted type i tf binding sites identified by bayespi2+ and centrimo in mouse chip-seq data sets first, position specific weight matrices of three mouse tfs were obtained from jaspar database. based on the known pswm of each mouse tf, type i tf binding sites were predicted by applying bayespi2+ and centrimo on all called peaks of three mouse chip-seq data sets, respectively. here, default parameter settings were used in both programs. results suggest that around 83%, 88%, and 92% of centrimo predicted type i myc, stat and oct binding sites are recovered by bayespi2+, respectively. thus, for predicting type i tf binding sites in in vivo protein-dna interaction experiment, there is a good agreement between the new biophysical model bayespi2+ and the published statistical method centrimo. differences in expression of genes with type i and type ii tf binding sites for esr and spib transcription factors functional esr target genes are regulated by both type i and type ii tf binding sites after separating tf binding sites into type i and type ii binding sites, we investigated the gene regulatory differences between the two. a functional study of putative esr target genes, regulated by either type i or type ii tf binding sites, was carried out in breast cancer cell line mcf- by using histone modification data, microarray gene expression profiles, and nucleosome density. great tool was used to find putative target genes regulated through either type i or type ii tf binding sites. by this analysis, and putative target genes were identified for esr type i tf binding sites and for esr type ii tf binding sites, respectively. of interest, genes were regulated by both type i and type ii tf binding sites, henceforth called'a' genes; genes were regulated by type i tf binding sites only, called'b' genes; and genes were exclusively regulated by type ii tf binding sites, called'c' genes in this manuscript. for the above-mentioned three classes of regulated genes, an enrichment test of gene expression activities between one class of genes and the rest of genes was performed. a heat-map of t-values and z-values is shown in figure'a' genes targeted by esr are more highly expressed than'b' and'c' genes. of interest and counter intuitively,'c' genes have a higher expression level than'b' genes. distributions of chip-seq tag densities across the three classes of target genes are shown in additional file 1: figure s'a' genes show the highest tag counts, as expected,'c' genes show the lowest tag counts, and'b' genes reveal intermediate tag counts. taken together, our results suggest that esr predominantly regulates'a' genes with both type i and type ii esr binding sites. the functional consequence of exclusive type i or type ii tf binding on gene expression seems to be less important. to further study the functional consequence of the different types of esr binding to genes, histone modifications 5kb upstream, and kb downstream of the genes were studied, respectively. tag densities in e2-treated cells were normalized against control cells. a heat map of histone modifications upon e2-treatment is shown in figure t-values were obtained by performing the t-test for genes that were grouped in the three classes of esr binding genes against the rest of genes, respectively. of interest, the results are consistent with the analysis of gene expression analysis by microarray: 1) histone modification patterns are different among the three classes of esr target genes; 2) only'a' genes show decreasing nucleosome densities as evidenced by enriched faire levels. accordingly, rna polymerase ii levels are increased as well as histone acetylation. these observations are consistent with functional esr1-dna interactions predominantly through combined type i and type ii binding of the transcription factor. robustness of the predicted esr type i and type ii tf binding site analysis to test the robustness of the binding site prediction, a repeated analysis of gene expression profiles, chip-seq tag density, and histone modifications for the three classes of esr target genes was performed, but this time with removal of the binding sites with low affinity. esr binding sites of which both chip-seq tag count was less than fold of the minimum tag count for type ii tf binding sites and of which the dba level was smaller than the maximum dba in type ii tf binding sites, were considered low affinity binding sites and removed. after filtering, and esr type i and type ii tf binding sites were remaining, respectively. compared to the results before changing the thresholds, few esr type i tf binding sites but more than half of the type ii tf binding sites were lost. great was then also used to find putative target genes for the new set of esr binding sites. this time,'c' genes,'b' genes, and'a' genes were found. gene expression profile analysis, chip-seq tag density enrichment, and histone modifications analysis for these classes of genes are given in additional file 1: figures s s and s respectively. all results are consistent with those for the previous analyses, with the exception of a similar tag density for'b' and'c' genes after removal of low binding affinity sites. functional annotation of the new three classes of esr target genes by david tool revealed that'a' genes are highly enriched in pathways active in cancer, including the mapk signaling pathway. functional spib target genes are regulated by both type i and type ii tf binding sites called spib chip-seq peaks were first classified into type i and type ii tf binding sites based on their estimated dba levels from the meta-pbem and meta-chemical-potential. then, great tool was used to identify and genes that were possibly regulated by type ii binding only, type i binding only and by both, respectively. subsequently, microarray gene expression analysis of the groups of genes in lenalidomide treated abc dlbcl cell lines was performed. t-test and mann-whitney u tests were used to evaluate the significance of differential expression between spib target genes and the rest of genes in genome. results reveal that spib target'a' genes have the highest expression and that'b' and'c' genes only show a slight increase or decrease of the gene expression level. additionally, silencing of spib by rna interference in abc dlbcl cell line hbl results in significant repression of'a' genes, but it does not have a strong impact on'b' and'c' genes as illustrated in figure these results strongly suggest that combined type i and type ii transcription factor binding is necessary for gene activation. functional annotation of the three groups of spib target genes by david tool shows that'a' genes are enriched in the mapk signaling pathway, in cancer in general, in the t cell receptor signaling, and b cell receptor signaling pathways. of interest, the latter pathways were not included among'b' and'c' genes. thus, in analogy with what was demonstrated for esr in breast cancer, a combination of spib type i and type ii tf binding sites is needed to regulate gene expression in abc dlbcl cells. spib is known to be up-regulated in abc dlbcl. our data show that spib likely contributes to the characteristic up-regulation of b cell receptor pathway genes in abc dlbcl. robustness of the predicted spib type i and type ii tf binding site analysis this analysis was performed following the same filtering criteria as for removing low affinity esr binding sites. after filtering, and spib binding sites were remaining for type i and type ii tf binding, respectively.'c' genes are increased almost two-fold,'a' genes were slightly reduced, and'b' genes were decreased by about one-forth. further analysis of lenalidomide treated abc dlbcl microarray gene expression data and spib knockdown experiments in abc dlbcl cells show that'a' genes have the most significant response. these genes but not'b' or'c' genes, showed increased expression in lenalidomide-treated cells and decreased expression in knockdown experiments. of interest,'a' genes were highly enriched in the same pathways as identified in the previous section. the nature of type ii esr and spib binding from the above analysis, chip-seq peaks represent either type i or type ii tf binding sites that can be distinguished via dba and expected p-values. however, the question remains whether low affinity type ii tf binding represents indirect binding or binding to alternative binding sites. this question was investigated by searching for the putative tf binding motifs in the predicted type i and type ii esr and spib binding sites, respectively. a serial version of bayespi2+ was first applied to find the best pbem in type i and type ii esr binding sites, respectively. the results show that the known esr binding motif is only enriched in esr type i tf binding sites. no esr binding motifs were discovered in esr type ii tf binding sites. these results suggest that esr type ii binding represents indirect binding of esr by contrast, the same analysis for spib shows that the spib core binding motif is similar for both type i and type ii tf binding sites. however, there is a significant difference of the sequence at both 5' and 3' sides of the spib pbems. in particular, the core spib binding motif ggaa is followed by a g nucleotide in type i binding sites whereas it is followed by a c in type ii spib binding sites. this single nucleotide replacement in the vicinity of the core spib binding motif may contribute to differential binding of spib in human genome. by applying the bayespi2+ parallel ensemble approach on the same datasets for esr and spib, after removal of low binding affinity sites, similar results were found. verification of predicted type i and type ii spib binding sites by emsa in order to verify spib binding sites, a two-step filtering procedure was applied to putative spib target genes with spib binding motifs. for each putative spib target gene, a two-sample kolmogorov-smirnov goodness-of-fit hypothesis test was performed between time-series microarray gene expression profiles and the gene expression profile after down-regulation of spib by shrna. the assumptions were that genes controlled by spib are differentially expressed in abc dlbcl cells treated as the above-mentioned two conditions, and that spib regulated genes are those genes with either a type i or a type ii spib binding sites located between kb upstream and kb downstream to the transcription start site. in total, genes fulfilled these criteria. to test whether those genes contained spib binding sites and whether type ii binding sites represented alternative binding sites, as predicted by our analysis, emsa was performed on randomly selected type i spib binding sites and type ii spib binding sites. for this analysis, 50bp dna sequences were selected of which the center sequence corresponded with the identified peak in our analysis. of the type i spib binding sequences, showed very strong, one showed weak binding and one did not show binding. of the type ii spib binding probes, showed weak binding and showed not binding. to check the binding to the spib core motif, 2bp of the core spib motif were mutated for two selected type i spib binding sites, then the same gel shift analysis were performed for both the original and the mutated type i spib binding sites. additional file 1: figure s showed that binding of spib is completely inhibited after mutating 2bp of the spib core motif. the results of these in vitro experiments support that type i and type ii spib binding represents direct tf binding, with type ii being, at least in part, alternative weak spib binding sites. discussion a new biophysical model, named bayespi2+ was designed to analyze more extensively tf binding sites in in vivo protein-dna interaction data than hitherto achieved with existing models. to achieve this bayespi2+ was designed to analyze a large number of called chip-seq peaks simultaneously, including weak binding sites. additionally, the differential binding affinity for each called peak was computed to identify high affinity and low affinity tf binding sites. in this work, the strength of type i and type ii binding sites is not in proportion to the number of measured chip-seq tag counts. in other words, tf acts independently in type i binding but it requires a co-factor to stabilize the protein-dna interaction in type ii binding. an initial test was performed on synthetic chip-seq datasets with success, yielding a true negative rate of >90%. for the test, a serial version and a parallel ensemble learning of bayespi2+ was used with similar prediction accuracies. however, in the test, the parallel version of bayespi2+ is at least three times faster than the serial one in completing the prediction. thus, for very large input data, a parallel ensemble learning of bayespi2+ is recommended because it saves the overall waiting time considerably by splitting the job to multiple computer processors. in a subsequent analysis of five human chip-seq datasets, the predicted pbems between a serial bayespi2+ computation and a parallel ensemble learning of bayespi2+ were compared. though the best pbem identified by serial computation and the meta-pbem estimated by parallel ensemble learning were similar, a positional variation in information content of the predicted meta-pbems were observed across different sizes of input data. the positional variation in information content for pbem reaches saturation point when the number of input peaks exceeds 25% of all called peaks. this indicates that various binding positions within a pbem are important in the formation of the protein-dna complex, during in vivo protein-dna interactions. by analyzing all possible binding sites with our method, two types could be discerned. particularly, the dba level of each tf, estimated by using the corresponding meta-pbem, allowed to recognize low affinity tf binding, called type ii tf binding sites. additionally, the inferred meta-pbems from chip-chip data and the binding consensus sequence motifs from online databases are significantly enriched in the type i tf binding sites when analyzing yeast chip-chip experiments for tfs ace swi and ino of interest, the latter analyses were performed on chip-chip data, thus on genomic sequences of unequal length. therefore, our proposed new method to distinguish two types of tf binding sites is applicable to both equal-length and unequal-length genomic sequences. of note, bayespi has a very good agreement with centrimo concerning the analysis of type i tf binding. to test the function of predicted type i and type ii tf binding sites, we analyzed their effect on gene regulation. this was done for two human tfs, esr and spib in breast cancer and diffuse large b cell lymphoma, respectively. esr encodes the estrogen receptor alpha and contributes to cell growth in breast carcinoma. spib is a b cell transcription factor that is highly expressed in a clinically aggressive subtype of dlbcl, with activated b cell immunophenotype. genes with the putative tf binding sites were classified into three groups:'a' genes, containing both type i and type ii tf binding sites;'b' genes containing only type i tf binding sites; and'c' genes, containing only type ii tf binding sites. of interest,'a' genes show the strongest expression in the breast cancer cell line mcf and the highest esr chip-seq tag density. in addition, we found lower nucleosome density, higher rna polymerase ii expression and histone acetylation for'a' genes than for'b' or'c' genes. it is known that decreased nucleosome density and increased rna pol-ii binding indicate gene transcription whereas acetylation of histones indicate functional tf binding and are important for activation of promoters and enhancers. functional annotation of the three types of esr target genes also suggests that, only'a' genes are highly enriched in pathways of importance to breast cancer such as the mapk signaling pathway. analogous to what is observed for esr in breast carcinoma, spib'a' genes show the highest gene expression in diffuse large b cell lymphoma, and the strongest response after silencing of spib by rna interference in abc dlbcl cell lines. functional annotation of spib'a' genes suggests that they are significantly involved in pathways of importance for dlbcl lymphoma biology, such as the b cell receptor signaling pathway. the b cell receptor signaling pathway is activated in diffuse large b-cell lymphoma and contributes to tumor cell survival and proliferation. thus, our results indicate that esr and spib regulation of gene expression requires both type i and type ii binding. a repeat analysis of genes controlled by either esr or spib binding sites, after filtering out the lowest binding affinity sites, yielded similar results:'a' genes are the likely functional targets of these tfs. though the effect of tf on genes requires direct protein-dna interaction, it has been well-known that additional and different interactions of the tf with the gene are needed for regulation. we show for the first time the scale of this effect by our genome-wide analysis. type ii tf binding sites for esr and spib were further investigated to find out whether these constituted indirect binding sites or alternative binding sites with different affinity. no esr similar motif was found for type ii esr binding sites. this indicates that type ii esr likely represents indirect binding to dna. by contrast, a similar consensus motif was found for both type i and type ii spib binding sites, except for one nucleotide difference in the area adjacent to core spib motif ggaa. these results indicate that the type ii spib binding site is an alternative low affinity spib binding site. the findings were also confirmed by emsa: about 90% and 50% of tested sequences with putative type i and type ii spib binding sites, respectively, resulted in band shift in emsa. these results also confirm that type ii tf binding is rather weak, which requires co-factors to enhance the binding to dna sequence. notwithstanding, our analysis shows that type i and type ii binding sites act concertedly in gene regulation.  in summary, we developed a new program bayespi2+ to analyze all potential tf binding sites in the genome, without filtering. by doing so, we found two types of functional tf binding sites, both indicate to be important for gene regulation. bayespi2+ can be used in a serial computation or a parallel ensemble approach. hitherto, other methods only used the top few hundred or thousand high affinity binding sites which we showed results in loss of valuable information. 
bayespi2+ can be run in either a serial computation model or a parallel ensemble learning framework. analysing esr and spib in breast carcinoma and activated b cell-like diffuse large b-cell lymphoma cell lines, respectively, revealed that the concerted binding to high and low affinity sites correlates best with gene expression. a new biophysical model of protein-dna interactions, bayespi2+, was developed to address the above-mentioned challenges. high-throughput in vivo protein-dna interaction experiments are currently widely used in gene regulation studies. it is evaluated in both synthetic and real in vivo protein-dna binding experiments. the program and output results are publicly available at: http://folk.uio.no/junbaiw/bayespi2plus.
 high-throughput in vivo protein-dna interaction experiments are currently widely used in gene regulation studies. hitherto, comprehensive data analysis remains a challenge and for that reason most computational methods only consider the top few hundred or thousand strongest protein binding sites whereas weak protein binding sites are completely ignored.  a new biophysical model of protein-dna interactions, bayespi2+, was developed to address the above-mentioned challenges. bayespi2+ can be run in either a serial computation model or a parallel ensemble learning framework. bayespi2+ allowed us to analyze all binding sites of the transcription factors, including weak binding that cannot be analyzed by other models. it is evaluated in both synthetic and real in vivo protein-dna binding experiments. analysing esr and spib in breast carcinoma and activated b cell-like diffuse large b-cell lymphoma cell lines, respectively, revealed that the concerted binding to high and low affinity sites correlates best with gene expression.  bayespi2+ allows us to analyze transcription factor binding on a larger scale than hitherto achieved. by this analysis, we were able to demonstrate that genes are regulated by concerted binding to high and low affinity binding sites. the program and output results are publicly available at: http://folk.uio.no/junbaiw/bayespi2plus. 4- december the international conference on intelligent biology and medicine san antonio, tx, usa 