BACKGROUND
advanced high-throughput microarray technologies have facilitated the investigation of gene expression in a genome-wide manner  <cit> .
because of the complex nature and large volume of data, whole-genome expression profiles often require appropriate and comprehensive analytic methods.
gene clustering according to the expression similarity has been popularly used in this perspective, often as the first step of analysis  <cit> .
in addition, functional enrichment analysis or pathway analysis was proposed to explain the global gene expression changes in the context of available knowledge, such as functional annotation of genes  <cit> .
a classical enrichment analysis uses functionally annotated gene sets a priori defined from external gene databases  and cross-references them with over- or under-expressed genes  <cit> .
the use of enrichment analysis can be extended for different kinds of biological insights.
for example, co-expressed genes grouped by clustering algorithm are likely to be regulated by common transcriptional control  <cit> .
by using another type of gene set classified by the presence or absence of known transcription factor binding sites  in promoter regions , it can identify overrepresented tfbs with the corresponding putative transcriptional regulators  <cit> .
in spite of promising utility, the conventional enrichment analysis dealing with individual gene clusters has several limitations.
first, the size of gene clusters or gene sets is often so small that the statistical evaluation is prone to ascertainment bias, i.e.
the significance of enrichment for small gene sets are frequently over- or underestimated.
the advanced type of enrichment analysis, gene set enrichment analysis  overcame this limitation by dealing with the entire genes represented by array as ranked gene list ordered by phenotypic correlation  <cit> .
however, gsea is suited for the comparison of two dichotomous phenotypic classes such as tumor versus normal, limiting its general use with gene clustering.
second, the accumulating biological knowledge on genes substantially increased the number of available gene sets to be used in enrichment analysis.
although recently proposed enrichment analysis tools can generate rich descriptions with the help of extended gene sets  <cit> , they often produce unmanageably large lists for candidate gene sets to be considered especially when dealing with a large number of clusters.
rigorous statistical evaluation with the correction for multiple tests adjustment might be helpful to some extent, however, the development of integrative method is highly challenging to make the results more comprehensive.
in this study, we propose a method of gene set expression coherence analysis  to provide a more advanced solution than the mere combining of gene clustering and enrichment analysis.
the algorithm first selects functional gene sets with significantly high expression coherence as biologically relevant candidates for the corresponding expression profiles.
then, gene set clustering further reduces them into a number of functionally related gene sets, or functional clusters.
on each functional cluster, putative transcriptional regulators are further identified using modified gsea algorithm and regulatory motif gene sets.
to demonstrate the applicability of our algorithm, we used two publicly available time-series gene expression profiles of the murine myogenesis and erythropoiesis.
for respective profiles, our algorithm identified a number of functional themes and putative transcriptional regulators largely consistent with previous reports.
as comprehensive and integrative method, gseca algorithm has extended applicability for the analysis of multiple microarray expression datasets.
RESULTS
the overview of gseca
the primary goal of gseca algorithm is the discovery of molecular functions along with the elucidation of transcriptional regulatory logics for the interpretation of microarray datasets.
for this purpose, two kinds of gene information – functional annotations in public gene database and the presence of regulatory motif sequences, or tfbs in the promoter regions – are used in terms of functional and regulatory motif gene sets, respectively.
gseca is composed of three major steps: selection of gene sets with significantly high expression coherence, clustering of functional gene sets into functional clusters and the identification of regulatory motifs associated with individual functional clusters.
first, gseca determines whether gene members belonging to a predefined functional gene set are correlated with each other across the gene expression profiles .
to do this, gseca calculates the mean of pearson correlation coefficient  for all pairs of gene members.
the average pcc measure is used as the expression coherence of the corresponding gene set and it indicates how closely gene members are correlated with each other.
the significance level for expression coherence level is then determined by gene permutation tests with adjustment for multiple tests.
the functional gene sets with significantly high expression coherence are selected and the identified functional annotations are assumed to indicate the putative functionalities for which genes have coordinated expression changes across the different time points or experimental conditions.
some of the candidate functional gene sets showed similar expression changes, making it possible to group them into a number of clusters.
thus, gseca further categorizes those gene sets into several clusters using conventional clustering methods such as hierarchical or k-means clustering algorithm.
the mean expression values of gene sets are used for the clustering and the gene sets with similar expression patterns are assigned into respective functional clusters.
the functional annotations of gene sets assigned into a single functional cluster are also likely to represent similar molecular functions or pathways.
thus, this clustering reduces a collection of functional gene sets into more comprehensive set of functional clusters, and we refer collectively to these procedures as "functional clustering".
for each functional cluster, gseca further identifies putative transcriptional regulators responsible for the expression patterns of the individual functional clusters.
for this, gseca exploits modified gsea algorithm with regulatory motif gene sets predefined according to the presence of known tfbs in their promoter regions .
to apply the gsea algorithm, seed expression values of a functional cluster are first calculated for each time point by averaging the expression values of all genes belonging to the functional cluster.
the entire genes in the array are then ordered according to the expression similarity or pcc with the seed values to make a ranked gene list.
in the list, genes whose expression changes are similar to the seed values become top-positioned.
the gene members of a regulatory motif set are then matched to the ordered rank list and measured for the enrichment using gsea algorithm  <cit> .
the significance level of enrichment is determined by gene permutation tests.
the use of pcc as gene ordering metric is one of distinguishing features in gseca algorithm and also extends the applicability of the conventional gsea algorithm for the analysis of time-series expression profiles.
application of gseca to murine myogenesis and erythropoiesis expression profiles
cellular differentiation represent a series of intricate and complex cellular events the majority of which are under the control of transcriptional regulation.
therefore, time-series gene expression profiles derived from an in vitro cell differentiation model are good candidates for the application of gseca algorithm.
for test sets, we selected two kinds of publicly available time-series expression profiles representing the differentiation of murine myocytes  <cit>  and erythrocytes  <cit> .
first, we selected  <dig>  functional gene sets including  <dig> –  <dig> genes and calculated expression coherence for each functional gene set.
significance level of expression coherence was determined by gene permutation tests and adjusted for multiple tests.
as a result,  <dig> and  <dig> functional gene sets with significantly high expression coherence  were identified in myogenesis and erythropoiesis expression profiles, respectively.
we further used hierarchical clustering to classify functional gene sets with similar expression patterns into individual functional clusters.
the  <dig> myogenesis-related functional gene sets were assigned into  <dig> functional clusters.
among the clusters,  <dig> functional gene sets with muscle-related functional annotations showed active transcriptional up-regulation after the induction of myogenesis and they were assigned into functional cluster  <dig> .
it is not surprising that muscle-related functional gene sets are captured as one of key clusters in myogenesis-related expression profiles.
however, it proves that our algorithm is able to identify the primary functional theme of interests, which would be beneficial in searching for perturbation-related molecular functions.
in addition, the expression patterns observed for functional cluster  <dig> and  <dig> were distinguished from those of functional cluster  <dig>  two kinds of functional annotations – cholesterol biosynthesis and enzymatic activities of nadh dehydrogenase – were identified for functional cluster  <dig> and  <dig>  respectively.
these functions are likely to propose the additional functionalities associated with myogenesis in terms of cellular components and energy metabolism.
it has been known that genes with general housekeeping functions such as ribosomal genes, tend to be strongly correlated in expression profiles without direct evidence for their phenotypic association  <cit> .
this is also the case of myogenesis dataset and the majority of functional gene sets identified with significantly high expression coherence  were indicative of general housekeeping functions such as nucleotide or protein metabolism.
our study shows that the genes with housekeeping functions have correlated expression patterns not only at the individual gene level but also at the gene set level.
thus, it is reasonable to collectively treat them as a single functional cluster representing general housekeeping function .
among the  <dig> erythropoiesis-related functional gene sets , two gene sets with characteristic functions of red blood cells – oxygen binding and hemoglobin complex – were assigned into functional cluster  <dig>  higher expression coherence of the two gene sets suggests that the genes with red blood cell function have coordinated and marked transcriptional up-regulation across the process of erythropoiesis.
in addition, three gene sets with heterogeneous molecular functions such as cell adhesion and neurotransmitter receptor activity, were assigned into another functional cluster  <dig>  although speculative, those functions might present the potential functionalities with collaborative roles in erythropoiesis or hematopoiesis.
likewise the case of myogenesis,  <dig> functional gene sets representing the housekeeping functions showed similar expression changes throughout the erythropoiesis and they were collectively grouped into functional cluster  <dig>
identification of putative transcriptional regulators with modified gsea algorithm and regulatory motif gene sets
the next step of gseca is to identify the regulatory motif gene sets associated with individual functional clusters, which might propose the putative transcriptional regulators of the corresponding functional cluster.
in case of myogenesis-related functional clusters, the cluster  <dig> with key annotations of muscle functions, showed significant enrichment  for regulatory motif gene sets representing six transcription factors of arnt, srebp- <dig>  sp- <dig>  myod, e2a, and usf .
among them, myod is a well known transcription factor whose role in myogenic differentiation has been previously established  <cit> .
this finding is consistent with that functional cluster  <dig> is composed of a set of muscle-related functional gene sets.
the other transcription factors with significance enrichment might propose putative transcription regulators with regulatory roles in myogenesis, i.e.
sp- <dig> have some evidences on their co-activator role with myod factors in muscle-specific gene expressions  <cit> .
for erythropoiesis-related functional cluster  <dig>  three regulatory motifs such as srebp- <dig>  usf and gata- <dig> were significantly enriched.
in this case, gata- <dig> was notable because the expression profile was derived from experiments in which gata-1-null cell lines  are restored for their gata- <dig> activity  <cit> , supporting the biological relevance of regulatory motifs identified by gseca algorithm.
asignificantly enriched  regulatory motif gene sets are shown for the corresponding transcription factors.
when more than one regulatory motif sets corresponding to a single transcription factor were identified, the most significant one was listed taking the redundancy of regulatory motif gene sets into consideration.
the listing order of transcription factors is according to the significance level of enrichment in individual functional clusters.
in addition, the functional cluster  <dig> of myogenesis profile representing the housekeeping functions showed enrichment for multiple ubiquitous transcription factors such as nrf- <dig>  e2f, creb, nf-y, and zf <dig>  this is also the case of functional cluster  <dig> of erythropoiesis-related expression profile.
the enrichment of multiple transcription factors might indicate the ubiquitous nature of the corresponding factors associated with general housekeeping functions  <cit> .
however, the heterogeneity of functional gene sets might have also caused the enrichment of multiple regulatory motifs because the gene sets with housekeeping functions are manually assigned into a single cluster.
synergistic motif pairs in murine myogenesis and erythropoiesis
transcription regulation among higher eukaryotes is likely to be mediated by multiple transcription factors in combinatorial modes rather than by a single agent  <cit> .
in this perspective, the transcription factors that showed significant enrichment with functional clusters are good candidates for such potential synergism.
thus, we further investigated the synergistic relationship between regulatory motifs identified in previous step, i.e.
<dig> regulatory motifs enriched in functional  <dig>  and  <dig> motifs in functional cluster  <dig> .
motif synergy was called when genes belonging to both regulatory motif gene sets have significantly high expression coherence .
in case of myogenesis, three motif pairs  involving five transcription factors were observed to have potential synergistic relationships .
considering the evidences on the synergistic action between sp- <dig> and myod  <cit> , these motif pair sets might have possible combinatorial roles for the cellular process of myogenesis.
in case of erythropoiesis, srebp- <dig> and usf were observed to have putative synergistic relationship.
such relationship provides good candidate for the further transcription analysis associated with the erythropoiesis, given the previous evidences for their relationship in the transcriptional control of genes involved in lipid metabolism  <cit> .
it must be noted that in silico analysis-yielded putative candidates cannot be assigned directly to functionality; however, it suggests the putative synergism between transcription factors and provides a testable set of hypotheses: transcription factors x <dig> and x <dig> might play a synergistic role for function y under cellular condition z.
atwo regulatory motif gene sets are demonstrated as motif  <dig> and motif  <dig> with the gene numbers and expression coherence  of the corresponding gene set.
for motifs pairs, genes occurred both in two regulatory motif gene sets are separately measured for gene numberb and expression coherence.
the significance levelc determined by permutation tests is also demonstrated.
only the motif pairs with significant expression coherence  are shown in the list.
comparison of gseca results with conventional enrichment analysis
to demonstrate the advantages of gseca, we performed the conventional strategy in which gene clustering and enrichment analysis are separately performed.
for two test expression datasets, gene clustering was first performed using two commonly used gene partitioning algorithm of k-means and self-organizing maps .
clustering was done with diverse setting for the gene numbers to be clustered  as well as the number of clusters , which fits in the conventionally used setting.
for test, we selected  <dig> and  <dig> functional gene sets representing the characteristic functions of myogenesis- and erythropoiesis-expression profiles, respectively.
the comparison results are demonstrated in figure  <dig>
in case of myogenesis-related  <dig> functional gene sets, enrichment analyses combined with k-means or som clustering both yielded low level of significance which did not reach the threshold level of gseca .
this is also the case of erythropoiesis-related two functional gene sets.
one plausible explanation for this low level of significance is the small size of functional gene sets in that functional gene sets containing less than  <dig> genes  showed the lowest level of significance.
in case of  <dig> gene sets in erythropoiesis, they both have less than  <dig> genes and showed variable level of significance across the different settings or used clustering methods.
this is consistent with our initial assumption that conventional enrichment analysis dealing with small gene cluster or gene sets might be prone to over- or under-estimation of the significance.
the significance for enrichment of regulatory motif gene sets were also improved in gseca analysis as shown for  <dig> and  <dig> gene sets for myogenesis and erythropoiesis expression profiles, respectively.
the significance of enrichment for biologically relevant regulatory motifs such as myod and gata- <dig> is two to three folds higher in gseca results.
the improved statistical power in detecting the regulatory motifs of interest might be due to the modified gsea algorithm used in our method  <cit> .
the adoption of modified gsea algorithm is likely to provide the robustness and sensitivity of the advanced gsea algorithm as possible explanation for improved statistical power over the conventional methods.
considerations on gseca methodology
the initial assumption of gseca is that functional gene sets with significantly high expression coherence suggest putative functionality.
it must be noted that annotated functions of gene sets with higher expression coherences do not always correspond directly with the actual biological functions  <cit> .
nonetheless, many physiological cellular responses require the simultaneous participation of gene products and genes with central roles are likely to have similar regulatory control and expression patterns  <cit> .
comparative analysis also showed that co-expression patterns of many functionally-related genes are conserved across diverse species  <cit> .
thus, gene sets with significantly high expression coherence might, if not all, represent the key molecular functions of the corresponding expression profiles.
our algorithm also concerns how the functionality represented by functional clusters can be linked to regulatory motifs to elucidate the putative transcriptional regulators.
cares must be taken in that genes collected from the functional gene sets assigned to a functional cluster might not fully represent the putative transcriptional targets considering that the current functional gene annotation is not complete.
to compensate for this, gseca implements a modified gsea algorithm to exploit the entire gene expression profiles in terms of correlation with seed values of functional clusters.
similarity-based gene ordering along with the enrichment algorithm is likely to ensure the robustness and sensitivity of gsea algorithm as demonstrated by the comparison with conventional strategy.
the use of gsea algorithm also facilitates the adoption of the extended application for gsea algorithm recently proposed to increase the statistical power or for improved biological insights.
for example, by using absolute correlation as ordering parameter, gsea can detects unique functional categories whose gene members have both extreme transcriptional up- and down-regulation  <cit> .
if such strategy can be applied in gseca algorithm, it can detect putative regulatory motifs with dual roles of transcriptional enhancers and inhibitors in the cellular contexts.
however, one distinguishing feature of gseca, the use of distance metric such as pcc also limits the use of gseca algorithm only for time- or condition-series expression profiles as compared with conventional gsea which is oriented for the comparison of two phenotypic classes.
we also provide an additional method to identify putative synergistic motif pairs among multiple transcription factors.
the method has been previously introduced and used to identify the synergistic combination between transcription factors in yeast  <cit>  and human  <cit> .
however, due to the large number of regulatory motif gene sets in pairwise combination and permutation tests to be considered, the method is often not feasible for general application.
thus, it would be beneficial to select a subset of putative regulatory motifs to reduce the computational work load and gseca can provide such plausible candidates for the in-depth analyses of combinatorial actions between transcription factors.
expression coherence-based identification of motif synergy would provide clues on the complex structure of regulatory modules and substrates for further experimental validation  <cit> .
however, recent studies on the elucidation of transcription regulatory networks use more sophisticated network assumptions and detailed parameters on the motif sequences and their relationships  <cit> .
moreover, in silico analysis-based results and significances must be interpreted with care because they do not always represent the actual functionality or causality.
in addition, there have been efforts to incorporate the biological knowledge into the gene clustering to maximize the statistical efficiency and reliability of the analysis results.
for example, functional gene annotations can be directly incorporated in the distance metric  <cit> , or used to guide the clustering procedures  <cit> .
however, most methods in this perspective use the functional go categories as additional information for fine-tuning of distance metrics to optimize the clustering, or to evaluate the results of conventional clustering algorithms  <cit> .
by contrast, gseca algorithm directly calculates the expression coherences of predefined gene sets then, categorizes into a number of functional clusters by gene set clustering.
gene set-based clustering used in gseca provides an additional advantage over the conventional strategy in which gene clusters are individually measured for enrichment with functional or regulatory motif gene sets, i.e.
improved statistical power and comprehensive interpretation of the results.
CONCLUSIONS
in this study, we address an integrative method for the interpretation of multiple expression profiles in terms of two kinds of gene information; function gene annotation and sequence information of tfbs in the regulatory regions.
it measures two kinds of parameters, expression coherence and the extent of enrichment in similarity-based ranked gene list to identify the putative functionality and transcription regulators, respectively.
our method successfully identified the key molecular functions and putative transcriptional regulators for two test expression profiles, which were largely consistent with the literature-based knowledge.
with improved statistical power over the conventional strategy, our algorithm has extended applicability for rich descriptions of high-throughput microarray expression data.

 advanced high-throughput microarray technologies have facilitated the investigation of gene expression in a genome-wide manner. because of the complex nature and large volume of data, whole-genome expression profiles often require appropriate and comprehensive analytic methods. gene clustering according to the expression similarity has been popularly used in this perspective, often as the first step of analysis. in addition, functional enrichment analysis or pathway analysis was proposed to explain the global gene expression changes in the context of available knowledge, such as functional annotation of genes. a classical enrichment analysis uses functionally annotated gene sets a priori defined from external gene databases and cross-references them with over- or under-expressed genes. the use of enrichment analysis can be extended for different kinds of biological insights. for example, co-expressed genes grouped by clustering algorithm are likely to be regulated by common transcriptional control. by using another type of gene set classified by the presence or absence of known transcription factor binding sites in promoter regions, it can identify overrepresented tfbs with the corresponding putative transcriptional regulators. in spite of promising utility, the conventional enrichment analysis dealing with individual gene clusters has several limitations. first, the size of gene clusters or gene sets is often so small that the statistical evaluation is prone to ascertainment bias, i.e. the significance of enrichment for small gene sets are frequently over- or underestimated. the advanced type of enrichment analysis, gene set enrichment analysis overcame this limitation by dealing with the entire genes represented by array as ranked gene list ordered by phenotypic correlation. however, gsea is suited for the comparison of two dichotomous phenotypic classes such as tumor versus normal, limiting its general use with gene clustering. second, the accumulating biological knowledge on genes substantially increased the number of available gene sets to be used in enrichment analysis. although recently proposed enrichment analysis tools can generate rich descriptions with the help of extended gene sets, they often produce unmanageably large lists for candidate gene sets to be considered especially when dealing with a large number of clusters. rigorous statistical evaluation with the correction for multiple tests adjustment might be helpful to some extent, however, the development of integrative method is highly challenging to make the results more comprehensive. in this study, we propose a method of gene set expression coherence analysis to provide a more advanced solution than the mere combining of gene clustering and enrichment analysis. the algorithm first selects functional gene sets with significantly high expression coherence as biologically relevant candidates for the corresponding expression profiles. then, gene set clustering further reduces them into a number of functionally related gene sets, or functional clusters. on each functional cluster, putative transcriptional regulators are further identified using modified gsea algorithm and regulatory motif gene sets. to demonstrate the applicability of our algorithm, we used two publicly available time-series gene expression profiles of the murine myogenesis and erythropoiesis. for respective profiles, our algorithm identified a number of functional themes and putative transcriptional regulators largely consistent with previous reports. as comprehensive and integrative method, gseca algorithm has extended applicability for the analysis of multiple microarray expression datasets.  the overview of gseca the primary goal of gseca algorithm is the discovery of molecular functions along with the elucidation of transcriptional regulatory logics for the interpretation of microarray datasets. for this purpose, two kinds of gene information – functional annotations in public gene database and the presence of regulatory motif sequences, or tfbs in the promoter regions – are used in terms of functional and regulatory motif gene sets, respectively. gseca is composed of three major steps: selection of gene sets with significantly high expression coherence, clustering of functional gene sets into functional clusters and the identification of regulatory motifs associated with individual functional clusters. first, gseca determines whether gene members belonging to a predefined functional gene set are correlated with each other across the gene expression profiles. to do this, gseca calculates the mean of pearson correlation coefficient for all pairs of gene members. the average pcc measure is used as the expression coherence of the corresponding gene set and it indicates how closely gene members are correlated with each other. the significance level for expression coherence level is then determined by gene permutation tests with adjustment for multiple tests. the functional gene sets with significantly high expression coherence are selected and the identified functional annotations are assumed to indicate the putative functionalities for which genes have coordinated expression changes across the different time points or experimental conditions. some of the candidate functional gene sets showed similar expression changes, making it possible to group them into a number of clusters. thus, gseca further categorizes those gene sets into several clusters using conventional clustering methods such as hierarchical or k-means clustering algorithm. the mean expression values of gene sets are used for the clustering and the gene sets with similar expression patterns are assigned into respective functional clusters. the functional annotations of gene sets assigned into a single functional cluster are also likely to represent similar molecular functions or pathways. thus, this clustering reduces a collection of functional gene sets into more comprehensive set of functional clusters, and we refer collectively to these procedures as "functional clustering". for each functional cluster, gseca further identifies putative transcriptional regulators responsible for the expression patterns of the individual functional clusters. for this, gseca exploits modified gsea algorithm with regulatory motif gene sets predefined according to the presence of known tfbs in their promoter regions. to apply the gsea algorithm, seed expression values of a functional cluster are first calculated for each time point by averaging the expression values of all genes belonging to the functional cluster. the entire genes in the array are then ordered according to the expression similarity or pcc with the seed values to make a ranked gene list. in the list, genes whose expression changes are similar to the seed values become top-positioned. the gene members of a regulatory motif set are then matched to the ordered rank list and measured for the enrichment using gsea algorithm. the significance level of enrichment is determined by gene permutation tests. the use of pcc as gene ordering metric is one of distinguishing features in gseca algorithm and also extends the applicability of the conventional gsea algorithm for the analysis of time-series expression profiles. application of gseca to murine myogenesis and erythropoiesis expression profiles cellular differentiation represent a series of intricate and complex cellular events the majority of which are under the control of transcriptional regulation. therefore, time-series gene expression profiles derived from an in vitro cell differentiation model are good candidates for the application of gseca algorithm. for test sets, we selected two kinds of publicly available time-series expression profiles representing the differentiation of murine myocytes and erythrocytes. first, we selected functional gene sets including – genes and calculated expression coherence for each functional gene set. significance level of expression coherence was determined by gene permutation tests and adjusted for multiple tests. as a result, and functional gene sets with significantly high expression coherence were identified in myogenesis and erythropoiesis expression profiles, respectively. we further used hierarchical clustering to classify functional gene sets with similar expression patterns into individual functional clusters. the myogenesis-related functional gene sets were assigned into functional clusters. among the clusters, functional gene sets with muscle-related functional annotations showed active transcriptional up-regulation after the induction of myogenesis and they were assigned into functional cluster. it is not surprising that muscle-related functional gene sets are captured as one of key clusters in myogenesis-related expression profiles. however, it proves that our algorithm is able to identify the primary functional theme of interests, which would be beneficial in searching for perturbation-related molecular functions. in addition, the expression patterns observed for functional cluster and were distinguished from those of functional cluster two kinds of functional annotations – cholesterol biosynthesis and enzymatic activities of nadh dehydrogenase – were identified for functional cluster and respectively. these functions are likely to propose the additional functionalities associated with myogenesis in terms of cellular components and energy metabolism. it has been known that genes with general housekeeping functions such as ribosomal genes, tend to be strongly correlated in expression profiles without direct evidence for their phenotypic association. this is also the case of myogenesis dataset and the majority of functional gene sets identified with significantly high expression coherence were indicative of general housekeeping functions such as nucleotide or protein metabolism. our study shows that the genes with housekeeping functions have correlated expression patterns not only at the individual gene level but also at the gene set level. thus, it is reasonable to collectively treat them as a single functional cluster representing general housekeeping function. among the erythropoiesis-related functional gene sets, two gene sets with characteristic functions of red blood cells – oxygen binding and hemoglobin complex – were assigned into functional cluster higher expression coherence of the two gene sets suggests that the genes with red blood cell function have coordinated and marked transcriptional up-regulation across the process of erythropoiesis. in addition, three gene sets with heterogeneous molecular functions such as cell adhesion and neurotransmitter receptor activity, were assigned into another functional cluster although speculative, those functions might present the potential functionalities with collaborative roles in erythropoiesis or hematopoiesis. likewise the case of myogenesis, functional gene sets representing the housekeeping functions showed similar expression changes throughout the erythropoiesis and they were collectively grouped into functional cluster identification of putative transcriptional regulators with modified gsea algorithm and regulatory motif gene sets the next step of gseca is to identify the regulatory motif gene sets associated with individual functional clusters, which might propose the putative transcriptional regulators of the corresponding functional cluster. in case of myogenesis-related functional clusters, the cluster with key annotations of muscle functions, showed significant enrichment for regulatory motif gene sets representing six transcription factors of arnt, srebp- sp- myod, e2a, and usf. among them, myod is a well known transcription factor whose role in myogenic differentiation has been previously established. this finding is consistent with that functional cluster is composed of a set of muscle-related functional gene sets. the other transcription factors with significance enrichment might propose putative transcription regulators with regulatory roles in myogenesis, i.e. sp- have some evidences on their co-activator role with myod factors in muscle-specific gene expressions. for erythropoiesis-related functional cluster three regulatory motifs such as srebp- usf and gata- were significantly enriched. in this case, gata- was notable because the expression profile was derived from experiments in which gata-1-null cell lines are restored for their gata- activity, supporting the biological relevance of regulatory motifs identified by gseca algorithm. asignificantly enriched regulatory motif gene sets are shown for the corresponding transcription factors. when more than one regulatory motif sets corresponding to a single transcription factor were identified, the most significant one was listed taking the redundancy of regulatory motif gene sets into consideration. the listing order of transcription factors is according to the significance level of enrichment in individual functional clusters. in addition, the functional cluster of myogenesis profile representing the housekeeping functions showed enrichment for multiple ubiquitous transcription factors such as nrf- e2f, creb, nf-y, and zf this is also the case of functional cluster of erythropoiesis-related expression profile. the enrichment of multiple transcription factors might indicate the ubiquitous nature of the corresponding factors associated with general housekeeping functions. however, the heterogeneity of functional gene sets might have also caused the enrichment of multiple regulatory motifs because the gene sets with housekeeping functions are manually assigned into a single cluster. synergistic motif pairs in murine myogenesis and erythropoiesis transcription regulation among higher eukaryotes is likely to be mediated by multiple transcription factors in combinatorial modes rather than by a single agent. in this perspective, the transcription factors that showed significant enrichment with functional clusters are good candidates for such potential synergism. thus, we further investigated the synergistic relationship between regulatory motifs identified in previous step, i.e. regulatory motifs enriched in functional and motifs in functional cluster. motif synergy was called when genes belonging to both regulatory motif gene sets have significantly high expression coherence. in case of myogenesis, three motif pairs involving five transcription factors were observed to have potential synergistic relationships. considering the evidences on the synergistic action between sp- and myod, these motif pair sets might have possible combinatorial roles for the cellular process of myogenesis. in case of erythropoiesis, srebp- and usf were observed to have putative synergistic relationship. such relationship provides good candidate for the further transcription analysis associated with the erythropoiesis, given the previous evidences for their relationship in the transcriptional control of genes involved in lipid metabolism. it must be noted that in silico analysis-yielded putative candidates cannot be assigned directly to functionality; however, it suggests the putative synergism between transcription factors and provides a testable set of hypotheses: transcription factors x and x might play a synergistic role for function y under cellular condition z. atwo regulatory motif gene sets are demonstrated as motif and motif with the gene numbers and expression coherence of the corresponding gene set. for motifs pairs, genes occurred both in two regulatory motif gene sets are separately measured for gene numberb and expression coherence. the significance levelc determined by permutation tests is also demonstrated. only the motif pairs with significant expression coherence are shown in the list. comparison of gseca results with conventional enrichment analysis to demonstrate the advantages of gseca, we performed the conventional strategy in which gene clustering and enrichment analysis are separately performed. for two test expression datasets, gene clustering was first performed using two commonly used gene partitioning algorithm of k-means and self-organizing maps. clustering was done with diverse setting for the gene numbers to be clustered as well as the number of clusters, which fits in the conventionally used setting. for test, we selected and functional gene sets representing the characteristic functions of myogenesis- and erythropoiesis-expression profiles, respectively. the comparison results are demonstrated in figure in case of myogenesis-related functional gene sets, enrichment analyses combined with k-means or som clustering both yielded low level of significance which did not reach the threshold level of gseca. this is also the case of erythropoiesis-related two functional gene sets. one plausible explanation for this low level of significance is the small size of functional gene sets in that functional gene sets containing less than genes showed the lowest level of significance. in case of gene sets in erythropoiesis, they both have less than genes and showed variable level of significance across the different settings or used clustering methods. this is consistent with our initial assumption that conventional enrichment analysis dealing with small gene cluster or gene sets might be prone to over- or under-estimation of the significance. the significance for enrichment of regulatory motif gene sets were also improved in gseca analysis as shown for and gene sets for myogenesis and erythropoiesis expression profiles, respectively. the significance of enrichment for biologically relevant regulatory motifs such as myod and gata- is two to three folds higher in gseca results. the improved statistical power in detecting the regulatory motifs of interest might be due to the modified gsea algorithm used in our method. the adoption of modified gsea algorithm is likely to provide the robustness and sensitivity of the advanced gsea algorithm as possible explanation for improved statistical power over the conventional methods. considerations on gseca methodology the initial assumption of gseca is that functional gene sets with significantly high expression coherence suggest putative functionality. it must be noted that annotated functions of gene sets with higher expression coherences do not always correspond directly with the actual biological functions. nonetheless, many physiological cellular responses require the simultaneous participation of gene products and genes with central roles are likely to have similar regulatory control and expression patterns. comparative analysis also showed that co-expression patterns of many functionally-related genes are conserved across diverse species. thus, gene sets with significantly high expression coherence might, if not all, represent the key molecular functions of the corresponding expression profiles. our algorithm also concerns how the functionality represented by functional clusters can be linked to regulatory motifs to elucidate the putative transcriptional regulators. cares must be taken in that genes collected from the functional gene sets assigned to a functional cluster might not fully represent the putative transcriptional targets considering that the current functional gene annotation is not complete. to compensate for this, gseca implements a modified gsea algorithm to exploit the entire gene expression profiles in terms of correlation with seed values of functional clusters. similarity-based gene ordering along with the enrichment algorithm is likely to ensure the robustness and sensitivity of gsea algorithm as demonstrated by the comparison with conventional strategy. the use of gsea algorithm also facilitates the adoption of the extended application for gsea algorithm recently proposed to increase the statistical power or for improved biological insights. for example, by using absolute correlation as ordering parameter, gsea can detects unique functional categories whose gene members have both extreme transcriptional up- and down-regulation. if such strategy can be applied in gseca algorithm, it can detect putative regulatory motifs with dual roles of transcriptional enhancers and inhibitors in the cellular contexts. however, one distinguishing feature of gseca, the use of distance metric such as pcc also limits the use of gseca algorithm only for time- or condition-series expression profiles as compared with conventional gsea which is oriented for the comparison of two phenotypic classes. we also provide an additional method to identify putative synergistic motif pairs among multiple transcription factors. the method has been previously introduced and used to identify the synergistic combination between transcription factors in yeast and human. however, due to the large number of regulatory motif gene sets in pairwise combination and permutation tests to be considered, the method is often not feasible for general application. thus, it would be beneficial to select a subset of putative regulatory motifs to reduce the computational work load and gseca can provide such plausible candidates for the in-depth analyses of combinatorial actions between transcription factors. expression coherence-based identification of motif synergy would provide clues on the complex structure of regulatory modules and substrates for further experimental validation. however, recent studies on the elucidation of transcription regulatory networks use more sophisticated network assumptions and detailed parameters on the motif sequences and their relationships. moreover, in silico analysis-based results and significances must be interpreted with care because they do not always represent the actual functionality or causality. in addition, there have been efforts to incorporate the biological knowledge into the gene clustering to maximize the statistical efficiency and reliability of the analysis results. for example, functional gene annotations can be directly incorporated in the distance metric, or used to guide the clustering procedures. however, most methods in this perspective use the functional go categories as additional information for fine-tuning of distance metrics to optimize the clustering, or to evaluate the results of conventional clustering algorithms. by contrast, gseca algorithm directly calculates the expression coherences of predefined gene sets then, categorizes into a number of functional clusters by gene set clustering. gene set-based clustering used in gseca provides an additional advantage over the conventional strategy in which gene clusters are individually measured for enrichment with functional or regulatory motif gene sets, i.e. improved statistical power and comprehensive interpretation of the results.  in this study, we address an integrative method for the interpretation of multiple expression profiles in terms of two kinds of gene information; function gene annotation and sequence information of tfbs in the regulatory regions. it measures two kinds of parameters, expression coherence and the extent of enrichment in similarity-based ranked gene list to identify the putative functionality and transcription regulators, respectively. our method successfully identified the key molecular functions and putative transcriptional regulators for two test expression profiles, which were largely consistent with the literature-based knowledge. with improved statistical power over the conventional strategy, our algorithm has extended applicability for rich descriptions of high-throughput microarray expression data. 
for respective profiles, our algorithm identified myocyte- and erythrocyte-related molecular functions, along with the putative transcriptional regulators for the corresponding molecular functions. subsequent enrichment analysis using predefined gene sets can provide clues on which functional themes or regulatory sequence motifs are associated with individual gene clusters. in spite of the potential utility, gene clustering and enrichment analysis have been used in separate platforms, thus, the development of integrative algorithm linking both methods is highly challenging. each functional cluster is then, investigated for the enrichment of transcriptional regulatory motifs using modified gene set enrichment analysis and regulatory motif gene sets. the method was tested for two publicly available expression profiles representing murine myogenesis and erythropoiesis. in this study, we propose an algorithm for discovery of molecular functions and elucidation of transcriptional logics using two kinds of gene information, functional and regulatory motif gene sets. those candidate gene sets are further processed into a number of functionally related themes or functional clusters according to the expression similarities. the algorithm, termed gene set expression coherence analysis first selects functional gene sets with significantly high expression coherences. as an integrative and comprehensive method for the analysis of large-scaled gene expression profiles, our method is able to generate a set of testable hypotheses: the transcriptional regulator x regulates function y under cellular condition z. gseca algorithm is implemented into freely available software package.
 gene clustering has been widely used to group genes with similar expression pattern in microarray data analysis. subsequent enrichment analysis using predefined gene sets can provide clues on which functional themes or regulatory sequence motifs are associated with individual gene clusters. in spite of the potential utility, gene clustering and enrichment analysis have been used in separate platforms, thus, the development of integrative algorithm linking both methods is highly challenging.  in this study, we propose an algorithm for discovery of molecular functions and elucidation of transcriptional logics using two kinds of gene information, functional and regulatory motif gene sets. the algorithm, termed gene set expression coherence analysis first selects functional gene sets with significantly high expression coherences. those candidate gene sets are further processed into a number of functionally related themes or functional clusters according to the expression similarities. each functional cluster is then, investigated for the enrichment of transcriptional regulatory motifs using modified gene set enrichment analysis and regulatory motif gene sets. the method was tested for two publicly available expression profiles representing murine myogenesis and erythropoiesis. for respective profiles, our algorithm identified myocyte- and erythrocyte-related molecular functions, along with the putative transcriptional regulators for the corresponding molecular functions.  as an integrative and comprehensive method for the analysis of large-scaled gene expression profiles, our method is able to generate a set of testable hypotheses: the transcriptional regulator x regulates function y under cellular condition z. gseca algorithm is implemented into freely available software package. 