BACKGROUND
an achievement that would have a major impact on our understanding of transcriptional regulatory networks would be to map out the coordinated dynamic responses of signaling proteins, transcription factors and target genes over time.
the primary challenges to such an effort are development of high-throughput technologies to measure transcription factor activities at the genome-scale, and computational tools to interpret the data and predict the structure and dynamics of the underlying networks.
recent development of high-throughput technologies has enabled large-scale measurements of biological signals related to transcription, such as the expression of target genes and the activities of transcription factors.
for target gene expression, microarrays measure the expression levels of thousands of genes simultaneously  <cit> .
however, efforts to broadly assess transcription factor activities on a genome wide scale are much more limited.
technologies such as chromatin immunoprecipitation-on-a-chip can identify all of the dna binding sites occupied by a single transcription factor for a given condition  <cit> .
flow cytometry can also be used to determine transcription factor activities by labeling active factors with fluorescently labeled antibodies  <cit> , but throughput is limited by the number of available antibodies and colors.
as yet, there is no transcription factor-focused equivalent of the gene expression array, which would enable monitoring of all transcription factor activities at a time.
such technology would be critical to generating a complete dynamic network of transcription empirically.
to compensate for this inability to assay transcription factor activity at the large scale, there have been several efforts to infer regulatory networks computationally  <cit> .
one of these approaches, called network component analysis , is a method for determining both activities and regulatory influence for a set of transcription factors with known target genes  <cit> .
nca has been successfully applied in several areas.
it was used to identify previously unnoticed oscillatory activity patterns in the yeast cell cycle  <cit> , as well as to generate a predicted activation time course of catabolite repressor protein in escherichia coli, which was verified experimentally  <cit> .
more recently, nca was used to predict activities of important transcription factors like sterol regulatory element-binding proteins and peroxisome proliferative-activated receptors in a mouse knockout model of human glycerol kinase deficiency  <cit> .
in parallel, several studies have expanded and strengthened nca as a computational tool  <cit> .
in eukaryotic systems, inflammation and activation of innate immunity are fundamental host responses to microbial invasion and endogenous danger signals.
blood leukocytes contribute to this inflammatory response, and exposure to a prototypical stimulus such as lps leads first to changes in gene expression, then production of cytokines which are secreted and cause secondary transcriptional and other responses  <cit> .
in previous work, we and others generated a set of gene expression profiles from human subjects over  <dig> hours following the intravenous administration of bacterial endotoxin lps  <cit> .
experimental endotoxicosis produces in the previously healthy individual a transient but significant systemic inflammatory response, characterized by fever, tachycardia, malaise, and a hepatic acute phase response.
administration of endotoxin is presumed to model the early inflammatory changes associated with a microbial invasion, sepsis and the systemic inflammatory response syndrome  <cit> .
we used this data to determine important clusters of genes involved in the early inflammatory response, as well as to depict the temporal changes in gene expression as inflammation resolved over the first twenty-four hours.
in this study, we calculated transcription factor activities and regulatory influences in the above dataset using nca, and interpreted the results to develop a dynamic network of transcription events following experimental endotoxicosis in humans.
RESULTS
our approach follows the schematic in figure  <dig>  nca requires two inputs: a set of gene expression profiles and a pre-defined regulatory network, which is a matrix that contains initial estimates of the influence each transcription factor on the target genes.
the original gene expression data set is obtained from calvano et al  <cit> , in which peripheral blood leukocytes were obtained from four different individuals prior to and at five time points after injection with endotoxin,  <dig> profiles in total.
to define a regulatory network which could account for a significant percentage of the gene expression response, we identified a set of key transcription factors previously known to be involved in the lps response, together with a set of known target genes for these factors.
ten transcription factors were chosen for our study .
nfkb <dig> , rela  and irf <dig> were chosen as factors involved in the primary response to endotoxin.
endotoxin binding to toll-like receptors  leads to activation of nf-κb dimers, among which p65:p <dig> is common  <cit> .
lps stimulation also induces irf <dig> activation through tlr <dig>  <cit> .
these transcription factors induce expression of several cytokines which can further activate a secondary transcription response through factors such as stat <dig>   <dig> and  <dig>  <cit> .
creb <dig> is activated by lps through the p <dig> kinase-sapk <dig> pathway  <cit> .
it is known that lps activates ap- <dig> complexes consisting of fos, jun, junb and jund  <cit> .
among these factors, jun and fos were chosen for our model.
the role of myc in inflammation response is poorly understood  <cit> ; however, many genes connected to myc showed significant changes in their expression levels in the original study and so we included it as well  <cit> .
to identify established regulatory interactions between these transcription factors and target genes, we relied largely on the primary literature  <cit>  .
however, two knowledge-bases were also used: ingenuity systems  and pathway studio  <cit> .
both the ingenuity and pathway studio knowledge-bases consist of regulatory relationships parsed from medline abstracts; the ingenuity knowledge-base also includes information from manually-curated peer-reviewed publications.
for our ten transcription factors, this strategy resulted in a list of  <dig>  target genes, with  <dig>  interactions between transcription factors and target genes.
to reconcile differences in these different sources of regulatory network information , we only included an interaction in our network if it could be identified in two out of the three resources.
this filtering process reduced our list to  <dig> target genes regulated by  <dig> interactions with the ten transcription factors.
to focus on the most useful expression information, we only considered target genes for which expression changed significantly over time .
the network for the inflammatory response finally included  <dig> transcription factors,  <dig> target genes and  <dig> regulatory relations.
this network can be represented in matrix form, with a density of ~15%, or  <dig> relations/.
in contrast, the expected density of a genome-wide regulatory relationship matrix, given our current state of knowledge about human transcriptional regulation would be about  <dig> % .
our network density is therefore relatively high, reflecting the comparatively high level of research interest in this system.
we estimated the activation of the transcription factors in our network over time using nca .
nca decomposes a matrix containing gene expression values  into a matrix which represents the influence of a transcription factor on a target gene  and a matrix which contains the transcription factor activities   <cit> .
we found that both outputs of nca – predicted factor activities a and regulatory influences s – have added additional insights to gene expression data where the underlying regulatory network structure is partially known.
transcription factor activities
transcription factor activities are sometimes, but not always, correlated with the gene expression of the factor.
we compared the calculated transcription factor activities with the gene expression data for each factor .
nfkb <dig>  rela, stat <dig>  stat <dig> and myc showed strong positive correlation between activities and expression , possibly due to auto- or cross-regulation.
for example, nfkb <dig> activity and expression are tightly correlated , possibly because the nf-κb p65:p <dig> complex can regulate nfkb <dig>  <cit> .
stat <dig> activity and expression are also strongly correlated , which might relate to the transcriptional effect of stat <dig> on stat <dig> expression  <cit> , particularly given that stat <dig> and stat <dig> have highly correlated activities .
on the other hand, the activities and expression show lower or no correlation for irf <dig>  jun, fos and creb .
the linear model of gene expression upon which nca rests does not account for the interactions between transcription factors.
however, we wondered if the nca-predicted correlation in transcription factor activities could be due to the combined action of two transcription factors, either as a complex or otherwise.
we therefore checked transcription factor pairs with significant activity correlation to published protein-protein interactions catalogued in the biomolecular interaction network database   <cit> .
interestingly, transcription factors known to act together showed high correlation in their activity profiles .
for example, highly correlated transcription factors nfkb <dig> and rela regulate their target genes as a p65: <dig> heterodimer form  <cit> , and stat <dig> and stat <dig> are also known to act as a dimer  <cit> , as are jun and fos  <cit> .
additionally, some transcription factors  showed a positive correlation in their activity even though they are not known to form a complex with other transcription factors.
transcription factors can have similar – and even coordinated – activities without direct interaction, so it may be that these latter predictions reflect an indirect interaction.
on the other hand, it is possible that some of the correlated transcription factor activities may be based on incorrect nca predictions.
the largest possible source of error for nca decomposition is the initial connectivity matrix, which is based on the current, generally incomplete or erroneous, understanding of the human transcriptional regulatory network.
the effect of missing or false data in the connectivity matrix is hard to predict in advance.
however, the sensitivity of nca to the connectivity matrix can be estimated by adding or removing connections randomly from the original matrix, and repeating the nca calculation multiple times  <cit> .
using this approach, we found that transcription factor activities predicted by nca and our original connectivity matrix were robust, even if 10–15% of the connectivity matrix contained inaccurate connections .
given that our matrix was limited to only high-confidence interactions, this level of sensitivity was assumed to be tolerable.
nca simulation was performed based on the original network model with 1~20% of random noisy connections.
a pair of a transcription factor and a target gene was randomly selected; a random connection was added if the original connection did not exist, or removed otherwise.
for each percentage of random connections, the simulation was repeated by  <dig> times.
mean and standard deviation of activity correlations with the original noise-free network model were calculated.
regulatory influence matrix and gene expression clustering
we thought that the adjusted strength matrix might be used to enhance typical gene expression clustering techniques.
signed quantitative values of the adjusted strengths were able to form more biological meaningful clusters beyond the prior binary regulatory connections.
in figure 3a, target genes were hierarchically clustered with the adjusted strengths of transcription factors and shown with gene expression.
we identified seven major clusters, which correlate to the coordinated action of transcription factors to regulate gene expression.
cluster a highlights the influence of nfkb <dig> and rela on a set of eighteen genes.
interestingly, some genes are linked to p <dig> only, suggesting that these genes may be under the specific control of the p65:p <dig> homodimer, rather than the p65:p <dig> heterodimer.
for example, the cluster suggests that cxcl <dig> expression depends on both p <dig> and p <dig>  which has been demonstrated experimentally in nfkb1-/- and rela-/- knockout mice  <cit> .
clusters b and c contain the genes regulated by stats  <dig> and  <dig>  while cluster d genes are regulated by jun and fos.
clusters e and g are primarily regulated by myc, but with repression in e and induction in g. cluster f genes are regulated by stat <dig>  all of the transcription factors known to act in dimers  <cit>  – the nf-κb complex of nfkb1-rela, as well as stat1-stat <dig> and jun-fos – were either in the same cluster or closely adjoining clusters, and had correlated activation profiles.
however, although stat <dig> and myc had correlating activation profiles, the genes under their influence  did not cluster closely.
therefore, when studied together, activation profiles and regulatory influences may provide insight on the coordination between transcription factors.
although our clustering was based on the matrix of regulatory influence, the clusters also provided a strong basis for interpreting gene expression.
pair-wise correlation tests on expression between genes within a cluster showed significantly higher average correlation than random clusters .
furthermore, the resulting gene expression clusters can be immediately linked to the specific transcription factors whose action created the expression profile.
importantly, clustering by transcription strength can identify new clusters unobtainable by clustering the expression data alone.
for example, cluster f and g could not be distinguished when the same clustering method was applied to the gene expression data alone .
however, they formed unmistakable clusters from the regulatory strength matrix, being linked to the regulatory influence of either stat <dig> or myc.
furthermore, our clusters required the nca-processed strength matrix, and could not be obtained from the initial connectivity matrix, the clustering of which led to groups of genes that did not show common expression patterns .
we conclude that the estimated transcription factor regulatory strengths can provide unique insights with regard to the regulation underlying gene expression, even between genes with similar expression.
for n genes in a cluster, n/ <dig> pair-wise pearson's correlations on expression were measured and their average was calculated.
next, n genes were randomly selected from a set of ~ <dig>  human genes and the average pair-wise correlation was calculated from the random gene set.
the distribution of the average pair-wise correlation of random genes was re-estimated  <dig>  times to generate a null distribution of the average pair-wise correlations.
a p-value for each cluster was estimated by counting the number of random gene sets for which the average correlation is larger than the cluster correlation.
*no random gene set that exceeded the cluster was found in  <dig>  repeats.
correlation test and prediction over extended regulatory sets
the clusters shown in figure 3a suggested that we might be able to use our cluster information to discover new regulatory relationships.
we first determined the average normalized expression pattern of the genes in each cluster .
the expression vector for each gene was normalized to have zero mean and a standard deviation of  <dig>  and then normalized gene expression sets were averaged for each cluster .
we then divided all human genes measured on the expression array into three groups: those for which we had high-confidence regulatory information linking the dominant transcription factors in the cluster to the gene ; genes for which we had lower-confidence regulatory information , but could still be valid to extend our model ; and genes where we found no evidence of regulation by the cluster transcription factors .
if a cluster had more than two dominant transcription factors, only genes which had established regulatory interactions with all factors were collected for the extended gene group.
we first wanted to see if a gene in the extended gene group had similar expression to a cluster .
first, pearson's correlations were calculated between each gene in the extended gene group and the average normalized gene expression of each cluster.
we then also randomly selected one thousand genes from the no-evidence gene group, and calculated correlations between expression of these genes and the clusters.
to obtain standard deviations, we performed this step one hundred times.
the fraction of genes with a pearson's correlation >  <dig>  was then compared between both groups using fisher's exact test .
we found that average gene expression in each cluster was more highly correlated with genes in the corresponding extended gene set than in the no-evidence gene set, particularly for clusters a, b and g.
based on an earlier report involving p <dig> targets  <cit> , we decided to use the average normalized expression pattern of each cluster to predict new target genes for dominant transcription factors, first, we identified the genes with significant changes in gene expression in each gene group .
we then identified the subset of genes whose expression best matched each cluster using pearson's correlations, and determined the relationship between the fraction of accepted genes  that was contained in the extended gene set versus the "no evidence" gene set for each cluster .
as expected, all extended gene sets had higher accepted rates than the "no evidence" gene sets.
however, as can be seen in figure 4d, genes in the extended set for clusters a and b were many times more likely to be matched the cluster aggregate expression profile than "no evidence" genes.
this indicates that cluster a and b expression profiles are better able to distinguish true member genes than the profiles for cluster d or g. we identified  <dig> genes in the extended gene set for cluster a and  <dig> for cluster b that were highly correlated  to the cluster aggregate expression profile .
genes that showed high correlation to the average expression profile of a cluster  were accepted as part of the cluster.
we also focused on clusters a and b for predicting new target genes from the "no evidence" group.
some of the predicted new member genes for these clusters are listed in table  <dig> <cit> .
although there was no evidence for including these genes in our model initially, we were able to partially validate certain target gene predictions based on evidence beyond the original knowledge-bases that we used to define our sets.
notable among this evidence was the use of genome-scale location analysis  <cit> , as well as bioinformatics techniques  <cit>  to detect nf-κb binding to the promoters of several predicted target sites.
we conclude that such clustering may be useful for identifying new target genes, particularly in combination with other methods.
the ten most correlated target genes, as well as genes related to innate immunity  and genes which were supported by other evidence, are shown.
*predicted as a target gene from the motif sequence analysis.
**dna-protein binding detected in lps stimulation.
***up-regulated by a mutant of stat <dig> which can activate expression in the absence of tyrosine phosphorylation.
overall regulatory dynamics in response to lps
finally, we were able to address our original goal of building an integrated temporal model of the human blood leukocyte response to lps .
this required the integration of our calculated transcription factor activities, transcription factor regulatory influences on each gene, clustering on the adjusted strength, and the gene expression data.
endotoxin was administered to the subjects at  <dig> hours.
during the next two-hour period, irf <dig>  p <dig> and p <dig> were activated and interacted to regulate gene expression, as were jun and fos as well as creb <dig>  by two hours, these transcription factors had already affected gene expression, including the genes in clusters a and d as well as the additional genes we predicted to belong in cluster a. between  <dig> and  <dig> hours after endotoxin administration, cytokines such as the interleukins  and tumor necrosis factor  whose genes were expressed at  <dig> hours were produced and secreted.
these secreted proteins then and maintained or initiated the activity of several transcription factors in the blood leukocytes.
presumably, tnf then reactivated the nf-κb complex and some of ils stimulated ap- <dig> complex  <cit> .
in contrast, irf <dig> activation rapidly returned the base level of activity.
the ils could have activated the stats to initiate a secondary response, inducing expression of the genes in clusters b and c together with the additional genes predicted to belong to cluster b. after  <dig> hours, the transcription factors began to return to their basal level of activity, leading to a near-complete return to initial values of gene expression by  <dig> hours.
the temporal model therefore provided a global view of activation, transcription and resolution of the blood leukocyte response to lipopolysaccharide in humans.
CONCLUSIONS
the overall goal of this work was to build a dynamic network of transcription events following endotoxin administration from the time course response by global gene expression in peripheral blood leukocytes.
from the expression profiles, we were able to predict the activities of ten transcription factors over time, as well as the regulatory strength a given transcription factor exerted on its target genes using nca.
taken together, the activities often exhibited a high degree of correlation, both between factors and also between a factor's activity and its gene expression profile.
we also found that the regulatory strength matrix can be clustered to determine groups of genes which are not only co-expressed, but also co-regulated.
importantly, new and biologically relevant clusters were determined, suggesting that clustering by this approach is potentially more meaningful than methods which do not incorporate regulatory network information.
identification of these clusters also led us to identify many additional putative interactions between transcription factors and target genes not included in the known network, and most importantly, enabled us to describe and visualize the activation of regulatory proteins and target genes over time.
certain limitations in both the available expression data as well as nca itself could be addressed to make this approach more powerful.
gene expression analyses obtained from whole blood leukocyte samples provide an integrated signal from different leukocyte populations which are difficult to deconvolute, and so using a single cell population would be advantageous, such as could be obtained using cell sorting or other methods.
additionally, the number of transcription factors which can be used in nca is approximately the number of expression profiles in the data set, and so a greater number of expression profiles – obtained at best shortly after the endotoxin administration – would also have been useful.
finally, nca's scaling property, which makes it difficult to predict the direction of transcription factor activity, as well as nca's current inability to incorporate time course information from the data set are important limitations to the method.
some approaches that may overcome these challenges include recent studies in which transcription factor activities were estimated using ordinary differential equation  <cit>  or probabilistic models  <cit>  of time course data.
future work might therefore focus on combining nca with such efforts.
notwithstanding these limitations, we were able to reconstruct the dynamics of endotoxin-dependent transcription in human peripheral blood leukocytes using the above results.
this included identifying the activity of ten transcription factors regulating expression of ninety-nine genes.
we also were able to identify additional genes that could be included in our model, notably  <dig> which had less initial evidence, but were substantiated by our predictions.
given that there were  <dig>  genes with significant changes in gene expression for which regulatory relations were known, we were therefore able to capture between 8%  and 11%  of the explainable response.
furthermore, we were also able to identify new target genes based on the average gene expression profile of significant clusters, which could expand the scope of our temporal network still further.
with a larger network reconstruction and data set specifically designed for use with nca, it might be possible to move toward a near-complete characterization of dynamic transcription responses.

 an achievement that would have a major impact on our understanding of transcriptional regulatory networks would be to map out the coordinated dynamic responses of signaling proteins, transcription factors and target genes over time. the primary challenges to such an effort are development of high-throughput technologies to measure transcription factor activities at the genome-scale, and computational tools to interpret the data and predict the structure and dynamics of the underlying networks. recent development of high-throughput technologies has enabled large-scale measurements of biological signals related to transcription, such as the expression of target genes and the activities of transcription factors. for target gene expression, microarrays measure the expression levels of thousands of genes simultaneously. however, efforts to broadly assess transcription factor activities on a genome wide scale are much more limited. technologies such as chromatin immunoprecipitation-on-a-chip can identify all of the dna binding sites occupied by a single transcription factor for a given condition. flow cytometry can also be used to determine transcription factor activities by labeling active factors with fluorescently labeled antibodies, but throughput is limited by the number of available antibodies and colors. as yet, there is no transcription factor-focused equivalent of the gene expression array, which would enable monitoring of all transcription factor activities at a time. such technology would be critical to generating a complete dynamic network of transcription empirically. to compensate for this inability to assay transcription factor activity at the large scale, there have been several efforts to infer regulatory networks computationally. one of these approaches, called network component analysis, is a method for determining both activities and regulatory influence for a set of transcription factors with known target genes. nca has been successfully applied in several areas. it was used to identify previously unnoticed oscillatory activity patterns in the yeast cell cycle, as well as to generate a predicted activation time course of catabolite repressor protein in escherichia coli, which was verified experimentally. more recently, nca was used to predict activities of important transcription factors like sterol regulatory element-binding proteins and peroxisome proliferative-activated receptors in a mouse knockout model of human glycerol kinase deficiency. in parallel, several studies have expanded and strengthened nca as a computational tool. in eukaryotic systems, inflammation and activation of innate immunity are fundamental host responses to microbial invasion and endogenous danger signals. blood leukocytes contribute to this inflammatory response, and exposure to a prototypical stimulus such as lps leads first to changes in gene expression, then production of cytokines which are secreted and cause secondary transcriptional and other responses. in previous work, we and others generated a set of gene expression profiles from human subjects over hours following the intravenous administration of bacterial endotoxin lps. experimental endotoxicosis produces in the previously healthy individual a transient but significant systemic inflammatory response, characterized by fever, tachycardia, malaise, and a hepatic acute phase response. administration of endotoxin is presumed to model the early inflammatory changes associated with a microbial invasion, sepsis and the systemic inflammatory response syndrome. we used this data to determine important clusters of genes involved in the early inflammatory response, as well as to depict the temporal changes in gene expression as inflammation resolved over the first twenty-four hours. in this study, we calculated transcription factor activities and regulatory influences in the above dataset using nca, and interpreted the results to develop a dynamic network of transcription events following experimental endotoxicosis in humans.  our approach follows the schematic in figure nca requires two inputs: a set of gene expression profiles and a pre-defined regulatory network, which is a matrix that contains initial estimates of the influence each transcription factor on the target genes. the original gene expression data set is obtained from calvano et al, in which peripheral blood leukocytes were obtained from four different individuals prior to and at five time points after injection with endotoxin, profiles in total. to define a regulatory network which could account for a significant percentage of the gene expression response, we identified a set of key transcription factors previously known to be involved in the lps response, together with a set of known target genes for these factors. ten transcription factors were chosen for our study. nfkb, rela and irf were chosen as factors involved in the primary response to endotoxin. endotoxin binding to toll-like receptors leads to activation of nf-κb dimers, among which p65:p is common. lps stimulation also induces irf activation through tlr. these transcription factors induce expression of several cytokines which can further activate a secondary transcription response through factors such as stat and. creb is activated by lps through the p kinase-sapk pathway. it is known that lps activates ap- complexes consisting of fos, jun, junb and jund. among these factors, jun and fos were chosen for our model. the role of myc in inflammation response is poorly understood; however, many genes connected to myc showed significant changes in their expression levels in the original study and so we included it as well. to identify established regulatory interactions between these transcription factors and target genes, we relied largely on the primary literature. however, two knowledge-bases were also used: ingenuity systems and pathway studio. both the ingenuity and pathway studio knowledge-bases consist of regulatory relationships parsed from medline abstracts; the ingenuity knowledge-base also includes information from manually-curated peer-reviewed publications. for our ten transcription factors, this strategy resulted in a list of target genes, with interactions between transcription factors and target genes. to reconcile differences in these different sources of regulatory network information, we only included an interaction in our network if it could be identified in two out of the three resources. this filtering process reduced our list to target genes regulated by interactions with the ten transcription factors. to focus on the most useful expression information, we only considered target genes for which expression changed significantly over time. the network for the inflammatory response finally included transcription factors, target genes and regulatory relations. this network can be represented in matrix form, with a density of ~15%, or relations/. in contrast, the expected density of a genome-wide regulatory relationship matrix, given our current state of knowledge about human transcriptional regulation would be about %. our network density is therefore relatively high, reflecting the comparatively high level of research interest in this system. we estimated the activation of the transcription factors in our network over time using nca. nca decomposes a matrix containing gene expression values into a matrix which represents the influence of a transcription factor on a target gene and a matrix which contains the transcription factor activities. we found that both outputs of nca – predicted factor activities a and regulatory influences s – have added additional insights to gene expression data where the underlying regulatory network structure is partially known. transcription factor activities transcription factor activities are sometimes, but not always, correlated with the gene expression of the factor. we compared the calculated transcription factor activities with the gene expression data for each factor. nfkb rela, stat stat and myc showed strong positive correlation between activities and expression, possibly due to auto- or cross-regulation. for example, nfkb activity and expression are tightly correlated, possibly because the nf-κb p65:p complex can regulate nfkb. stat activity and expression are also strongly correlated, which might relate to the transcriptional effect of stat on stat expression, particularly given that stat and stat have highly correlated activities. on the other hand, the activities and expression show lower or no correlation for irf jun, fos and creb. the linear model of gene expression upon which nca rests does not account for the interactions between transcription factors. however, we wondered if the nca-predicted correlation in transcription factor activities could be due to the combined action of two transcription factors, either as a complex or otherwise. we therefore checked transcription factor pairs with significant activity correlation to published protein-protein interactions catalogued in the biomolecular interaction network database. interestingly, transcription factors known to act together showed high correlation in their activity profiles. for example, highly correlated transcription factors nfkb and rela regulate their target genes as a p65: heterodimer form, and stat and stat are also known to act as a dimer, as are jun and fos. additionally, some transcription factors showed a positive correlation in their activity even though they are not known to form a complex with other transcription factors. transcription factors can have similar – and even coordinated – activities without direct interaction, so it may be that these latter predictions reflect an indirect interaction. on the other hand, it is possible that some of the correlated transcription factor activities may be based on incorrect nca predictions. the largest possible source of error for nca decomposition is the initial connectivity matrix, which is based on the current, generally incomplete or erroneous, understanding of the human transcriptional regulatory network. the effect of missing or false data in the connectivity matrix is hard to predict in advance. however, the sensitivity of nca to the connectivity matrix can be estimated by adding or removing connections randomly from the original matrix, and repeating the nca calculation multiple times. using this approach, we found that transcription factor activities predicted by nca and our original connectivity matrix were robust, even if 10–15% of the connectivity matrix contained inaccurate connections. given that our matrix was limited to only high-confidence interactions, this level of sensitivity was assumed to be tolerable. nca simulation was performed based on the original network model with 1~20% of random noisy connections. a pair of a transcription factor and a target gene was randomly selected; a random connection was added if the original connection did not exist, or removed otherwise. for each percentage of random connections, the simulation was repeated by times. mean and standard deviation of activity correlations with the original noise-free network model were calculated. regulatory influence matrix and gene expression clustering we thought that the adjusted strength matrix might be used to enhance typical gene expression clustering techniques. signed quantitative values of the adjusted strengths were able to form more biological meaningful clusters beyond the prior binary regulatory connections. in figure 3a, target genes were hierarchically clustered with the adjusted strengths of transcription factors and shown with gene expression. we identified seven major clusters, which correlate to the coordinated action of transcription factors to regulate gene expression. cluster a highlights the influence of nfkb and rela on a set of eighteen genes. interestingly, some genes are linked to p only, suggesting that these genes may be under the specific control of the p65:p homodimer, rather than the p65:p heterodimer. for example, the cluster suggests that cxcl expression depends on both p and p which has been demonstrated experimentally in nfkb1-/- and rela-/- knockout mice. clusters b and c contain the genes regulated by stats and while cluster d genes are regulated by jun and fos. clusters e and g are primarily regulated by myc, but with repression in e and induction in g. cluster f genes are regulated by stat all of the transcription factors known to act in dimers – the nf-κb complex of nfkb1-rela, as well as stat1-stat and jun-fos – were either in the same cluster or closely adjoining clusters, and had correlated activation profiles. however, although stat and myc had correlating activation profiles, the genes under their influence did not cluster closely. therefore, when studied together, activation profiles and regulatory influences may provide insight on the coordination between transcription factors. although our clustering was based on the matrix of regulatory influence, the clusters also provided a strong basis for interpreting gene expression. pair-wise correlation tests on expression between genes within a cluster showed significantly higher average correlation than random clusters. furthermore, the resulting gene expression clusters can be immediately linked to the specific transcription factors whose action created the expression profile. importantly, clustering by transcription strength can identify new clusters unobtainable by clustering the expression data alone. for example, cluster f and g could not be distinguished when the same clustering method was applied to the gene expression data alone. however, they formed unmistakable clusters from the regulatory strength matrix, being linked to the regulatory influence of either stat or myc. furthermore, our clusters required the nca-processed strength matrix, and could not be obtained from the initial connectivity matrix, the clustering of which led to groups of genes that did not show common expression patterns. we conclude that the estimated transcription factor regulatory strengths can provide unique insights with regard to the regulation underlying gene expression, even between genes with similar expression. for n genes in a cluster, n/ pair-wise pearson's correlations on expression were measured and their average was calculated. next, n genes were randomly selected from a set of ~ human genes and the average pair-wise correlation was calculated from the random gene set. the distribution of the average pair-wise correlation of random genes was re-estimated times to generate a null distribution of the average pair-wise correlations. a p-value for each cluster was estimated by counting the number of random gene sets for which the average correlation is larger than the cluster correlation. *no random gene set that exceeded the cluster was found in repeats. correlation test and prediction over extended regulatory sets the clusters shown in figure 3a suggested that we might be able to use our cluster information to discover new regulatory relationships. we first determined the average normalized expression pattern of the genes in each cluster. the expression vector for each gene was normalized to have zero mean and a standard deviation of and then normalized gene expression sets were averaged for each cluster. we then divided all human genes measured on the expression array into three groups: those for which we had high-confidence regulatory information linking the dominant transcription factors in the cluster to the gene; genes for which we had lower-confidence regulatory information, but could still be valid to extend our model; and genes where we found no evidence of regulation by the cluster transcription factors. if a cluster had more than two dominant transcription factors, only genes which had established regulatory interactions with all factors were collected for the extended gene group. we first wanted to see if a gene in the extended gene group had similar expression to a cluster. first, pearson's correlations were calculated between each gene in the extended gene group and the average normalized gene expression of each cluster. we then also randomly selected one thousand genes from the no-evidence gene group, and calculated correlations between expression of these genes and the clusters. to obtain standard deviations, we performed this step one hundred times. the fraction of genes with a pearson's correlation > was then compared between both groups using fisher's exact test. we found that average gene expression in each cluster was more highly correlated with genes in the corresponding extended gene set than in the no-evidence gene set, particularly for clusters a, b and g. based on an earlier report involving p targets, we decided to use the average normalized expression pattern of each cluster to predict new target genes for dominant transcription factors, first, we identified the genes with significant changes in gene expression in each gene group. we then identified the subset of genes whose expression best matched each cluster using pearson's correlations, and determined the relationship between the fraction of accepted genes that was contained in the extended gene set versus the "no evidence" gene set for each cluster. as expected, all extended gene sets had higher accepted rates than the "no evidence" gene sets. however, as can be seen in figure 4d, genes in the extended set for clusters a and b were many times more likely to be matched the cluster aggregate expression profile than "no evidence" genes. this indicates that cluster a and b expression profiles are better able to distinguish true member genes than the profiles for cluster d or g. we identified genes in the extended gene set for cluster a and for cluster b that were highly correlated to the cluster aggregate expression profile. genes that showed high correlation to the average expression profile of a cluster were accepted as part of the cluster. we also focused on clusters a and b for predicting new target genes from the "no evidence" group. some of the predicted new member genes for these clusters are listed in table. although there was no evidence for including these genes in our model initially, we were able to partially validate certain target gene predictions based on evidence beyond the original knowledge-bases that we used to define our sets. notable among this evidence was the use of genome-scale location analysis, as well as bioinformatics techniques to detect nf-κb binding to the promoters of several predicted target sites. we conclude that such clustering may be useful for identifying new target genes, particularly in combination with other methods. the ten most correlated target genes, as well as genes related to innate immunity and genes which were supported by other evidence, are shown. *predicted as a target gene from the motif sequence analysis. **dna-protein binding detected in lps stimulation. ***up-regulated by a mutant of stat which can activate expression in the absence of tyrosine phosphorylation. overall regulatory dynamics in response to lps finally, we were able to address our original goal of building an integrated temporal model of the human blood leukocyte response to lps. this required the integration of our calculated transcription factor activities, transcription factor regulatory influences on each gene, clustering on the adjusted strength, and the gene expression data. endotoxin was administered to the subjects at hours. during the next two-hour period, irf p and p were activated and interacted to regulate gene expression, as were jun and fos as well as creb by two hours, these transcription factors had already affected gene expression, including the genes in clusters a and d as well as the additional genes we predicted to belong in cluster a. between and hours after endotoxin administration, cytokines such as the interleukins and tumor necrosis factor whose genes were expressed at hours were produced and secreted. these secreted proteins then and maintained or initiated the activity of several transcription factors in the blood leukocytes. presumably, tnf then reactivated the nf-κb complex and some of ils stimulated ap- complex. in contrast, irf activation rapidly returned the base level of activity. the ils could have activated the stats to initiate a secondary response, inducing expression of the genes in clusters b and c together with the additional genes predicted to belong to cluster b. after hours, the transcription factors began to return to their basal level of activity, leading to a near-complete return to initial values of gene expression by hours. the temporal model therefore provided a global view of activation, transcription and resolution of the blood leukocyte response to lipopolysaccharide in humans.  the overall goal of this work was to build a dynamic network of transcription events following endotoxin administration from the time course response by global gene expression in peripheral blood leukocytes. from the expression profiles, we were able to predict the activities of ten transcription factors over time, as well as the regulatory strength a given transcription factor exerted on its target genes using nca. taken together, the activities often exhibited a high degree of correlation, both between factors and also between a factor's activity and its gene expression profile. we also found that the regulatory strength matrix can be clustered to determine groups of genes which are not only co-expressed, but also co-regulated. importantly, new and biologically relevant clusters were determined, suggesting that clustering by this approach is potentially more meaningful than methods which do not incorporate regulatory network information. identification of these clusters also led us to identify many additional putative interactions between transcription factors and target genes not included in the known network, and most importantly, enabled us to describe and visualize the activation of regulatory proteins and target genes over time. certain limitations in both the available expression data as well as nca itself could be addressed to make this approach more powerful. gene expression analyses obtained from whole blood leukocyte samples provide an integrated signal from different leukocyte populations which are difficult to deconvolute, and so using a single cell population would be advantageous, such as could be obtained using cell sorting or other methods. additionally, the number of transcription factors which can be used in nca is approximately the number of expression profiles in the data set, and so a greater number of expression profiles – obtained at best shortly after the endotoxin administration – would also have been useful. finally, nca's scaling property, which makes it difficult to predict the direction of transcription factor activity, as well as nca's current inability to incorporate time course information from the data set are important limitations to the method. some approaches that may overcome these challenges include recent studies in which transcription factor activities were estimated using ordinary differential equation or probabilistic models of time course data. future work might therefore focus on combining nca with such efforts. notwithstanding these limitations, we were able to reconstruct the dynamics of endotoxin-dependent transcription in human peripheral blood leukocytes using the above results. this included identifying the activity of ten transcription factors regulating expression of ninety-nine genes. we also were able to identify additional genes that could be included in our model, notably which had less initial evidence, but were substantiated by our predictions. given that there were genes with significant changes in gene expression for which regulatory relations were known, we were therefore able to capture between 8% and 11% of the explainable response. furthermore, we were also able to identify new target genes based on the average gene expression profile of significant clusters, which could expand the scope of our temporal network still further. with a larger network reconstruction and data set specifically designed for use with nca, it might be possible to move toward a near-complete characterization of dynamic transcription responses. 
the dynamic network illustrated changes of transcription factor activities and gene expressions as well as interactions of signaling proteins, transcription factors and target genes. the primary challenge is monitoring transcription factor activities over time, which is not yet available at the large scale. for example, network component analysis is an approach that can predict transcription factor activities over time as well as the relative regulatory influence of factors on each target gene. understanding the transcriptional regulatory networks that map out the coordinated dynamic responses of signaling proteins, transcription factors and target genes over time would represent a significant advance in the application of genome wide expression analysis. in this study, we analyzed a gene expression data set in blood leukocytes from human subjects administered with lipopolysaccharide, a prototypical inflammatory challenge, in the context of a reconstructed regulatory network including transcription factors, target genes and regulatory interactions. furthermore, we found that clustering the genes in the context of regulatory influences greatly facilitated interpretation of the expression data, as clusters of gene expression corresponded to the activity of specific factors or more interestingly, factor combinations which suggest coordinated regulation of gene expression. the resulting clusters were therefore more biologically meaningful, and also led to identification of additional genes under the same regulation.
 understanding the transcriptional regulatory networks that map out the coordinated dynamic responses of signaling proteins, transcription factors and target genes over time would represent a significant advance in the application of genome wide expression analysis. the primary challenge is monitoring transcription factor activities over time, which is not yet available at the large scale. instead, there have been several developments to estimate activities computationally. for example, network component analysis is an approach that can predict transcription factor activities over time as well as the relative regulatory influence of factors on each target gene.  in this study, we analyzed a gene expression data set in blood leukocytes from human subjects administered with lipopolysaccharide, a prototypical inflammatory challenge, in the context of a reconstructed regulatory network including transcription factors, target genes and regulatory interactions. we found that the computationally estimated activities were well correlated to their coordinated action. furthermore, we found that clustering the genes in the context of regulatory influences greatly facilitated interpretation of the expression data, as clusters of gene expression corresponded to the activity of specific factors or more interestingly, factor combinations which suggest coordinated regulation of gene expression. the resulting clusters were therefore more biologically meaningful, and also led to identification of additional genes under the same regulation.  using nca, we were able to build a network that accounted for between 8–11% genes in the known transcriptional response to lps in humans. the dynamic network illustrated changes of transcription factor activities and gene expressions as well as interactions of signaling proteins, transcription factors and target genes. 