BACKGROUND
transcription factor activities  rather than levels of transcription factor expression mediate transcriptional regulations.
various post-transcriptional and post-translational modifications abolish significant correlations between tfas and the level of transcription factor expression.
therefore, a strategy to determine the physiological functions and interactions of transcription factors based on the analysis of tfa profiles would be more fundamentally sound than one based on transcript levels per se.
however, owing to post-translational modifications, tfas are difficult to measure experimentally and therefore, many analyses infer tfas by computational analysis of target gene expression levels either from single regulatory factors alone or in combination  <cit> .
among these, network component analysis   <cit>  and generalized nca   <cit>  provide a robust framework for deducing tfas based on dna microarray data, promoter connectivity, and genetic regulatory constraints imposed by regulatory knock-out experiments.
using tfa profiles deduced by nca and gnca, we are now in a position to assign transcription factor functions and reconstruct functional interactions between transcription factors.
the goal of this work is to demonstrate how we analyze tfa profiles to determine physiologically relevant characteristics of transcription factors.
specifically, by analyzing tfa profiles of the s. cerevisiae cell cycle we identify cell cycle regulators and putative interaction partners of two forkhead transcription factors  that are responsible for expression of a gene cluster within the m/g <dig> interval and involved in mitotic exit  <cit> .
once tfa profiles are determined, the transcription factor regulators and interactions are deduced based on the following hypotheses: 1) transcription factors with similar activity patterns function together; 2) transcription factors involved in cell cycle regulation exhibit oscillatory activity patterns, 3) activities of transcription factors which functionally interact with each other will be disturbed if one of the interacting partners is deleted.
these hypotheses are in spirit similar to the traditional analysis of gene expression.
in contrast to traditional analysis of gene expression, our analyses are constructed and applied directly to tfa profiles.
RESULTS
overall strategy
a flow diagram demonstrating the relationships between each component of the methodology is presented in figure  <dig>  given the gene expression data and connectivity network between transcription factors and gene expression, we first deduced tfas from gene expression by using gnca.
the deduced tfas were then analyzed by two complementary methods.
first, we used cluster analysis  <cit>  to group tfas that behave in a similar manner.
second, a statistical analysis  <cit>  was used to determine if the signal from each of the tfas was periodic.
the results from these two analyses were integrated to deduce putative cell cycle regulators.
we hypothesized that putative cell cycle regulators should exhibit periodic activity profiles and cluster closely with known cell cycle regulators.
then tfa profiles from wild type and the fkh <dig> fkh <dig> mutant strain under the same experimental conditions were statistically analyzed to deduce transcription factors whose profiles were significantly perturbed, thus identifying putative functional interaction partners of the fork-head transcription factors.
application of gnca to the combined wild-type and mutant data set
we used gnca to analyze both the wild-type  <cit>  and the fkh <dig> fkh <dig> mutant data  <cit> .
the wild-type data and the tf-knockout data were organized in different columns of the e matrix .
the elements in p  corresponding to the specific knockout strain were kept at zero, in addition to the zero constraints placed in a  according to the transcription factor-gene connectivity information.
the first step in gnca was to select sub-networks based on available transcription factor-gene connectivity  <cit> .
each sub-network was constructed to satisfy the gnca criteria.
gnca requires that the number of transcription factors  in each sub-network be less than that of data points  in the data matrix.
in the combined cell cycle microarray data set, m =  <dig>  and thus the number of transcription factor in gnca in each analysis cannot exceed  <dig>  thus, subsets of the  <dig> transcription factors included in the genome-wide location analysis  <cit>  were selected to form sub-networks for gnca.
overlapping random sub-networks were generated and screened using the gnca criteria.
among them, four that satisfy the gnca criteria were selected in order to show that using multiple sub-networks makes it possible to determine tfas more than the number of data points .
each sub-network contained  <dig> transcription factors, but together, a total of  <dig> transcription factors were analyzed.
the transcription factors involved in each of the  <dig> sub-networks are shown in figure  <dig>  only  <dig> transcription factors among  <dig> transcription factors were fully overlapped among all  <dig> sub-networks.
after applying gnca independently to the  <dig> sub-networks,  <dig> tfas were determined.
figure  <dig> shows the tfas of the  <dig> known cell cycle factors from  <dig> different sub-networks.
qualitatively, these tfas appear to show expected oscillatory behavior for  <dig>   <dig>  and  <dig> cycles according to the method of synchronization .
the dynamics of overlapping tfa profiles between the four different sub-networks are very similar.
this indicates that the deduced tfas were insensitive to the sub-network selection.
in addition, combining the fkh <dig> fkh <dig> mutant data with the wild-type data yields similar tfas predicted from wild-type data alone  <cit> , suggesting the consistency between the two data sets.
it is recognized that most transcription factors are regulated in post-transcriptional processes.
thus, their activity may deviate significantly from the expression level as noted previously  <cit> .
for  <dig> transcription factors with both gene expression level and tfa available, the correlation coefficients ranged from -  <dig>  to  <dig> .
the wide range difference in the correlation coefficients confirms that tfas and expression levels exhibit very different dynamic profiles and therefore tfas cannot be substituted by expression levels in analysis.
sensitivity analysis
to assess the effect of connectivity errors on our results, we altered up to 10% of the connectivity graph for every subnetwork, by randomly deleting and inserting connections between transcription factors and genes.
this effectively simulates the presence of false negatives and false positives in chip-chip assays.
subsequently, we ran gnca on our randomly perturbed graphs and compared the deduced tfas to our reported results via the correlation coefficient.
the procedure was performed  <dig> times and the tfas deduced from each run were compared with the tfas computed with unaltered connectivity using pearson correlation coefficients .
transcription factors with high correlation coefficients suggest robustness of the results against connectivity errors.
determination of cell cycle-dependent regulators based on tfa dynamics
we hypothesized that transcription factors with similar activity patterns are involved in related processes.
thus, clustering of tfas would allow identification of transcription factors related to cell cycle regulation.
after hierarchical clustering ,  <dig> transcriptional factors  were found to cluster closely with the  <dig> known cell cycle regulators.
in addition to cluster analysis, we performed a statistical test to identify the set of tfas with a periodic profile.
figure 5a shows the power spectra of the  <dig> known cell cycle regulator.
a power spectrum is a representation of a signal in the frequency domain.
a dominant peak in the power spectrum corresponds to the fact that the underlying process has a principal oscillation frequency.
most of the power spectra to identify periodic patterns exhibit a single strong peak at low frequency.
this suggests that the dynamic profiles appear to be periodic.
to classify whether a signal is periodic or not, we employed a statistical criterion  <cit>  of rejecting the null hypothesis of purely random process.
the result suggests that  <dig> out of  <dig> known cell cycle regulators exhibit periodic behavior.
this confirms that the activity profiles of cell cycle regulators are periodic.
we then applied the same periodicity test to the rest of  <dig> transcription factors and found that about  <dig> of the deduced tfas from elutriation and α-factor arrest were statistically periodic and  <dig> of the deduced tfas from cdc <dig> were statistically periodic.
combining the results of the periodicity test and cluster analysis, we found that  <dig>  out of the  <dig> transcription factors closely clustered with the known cell cycle factors were statistically periodic and were regarded as putative cell cycle-related regulators.
the power spectra of these  <dig> putative cell cycle regulators are shown in figure 5b, and the tfa profiles of these regulators are illustrated in figure  <dig>  the clustered tfa pattern of all cell cycle-related transcription factors  shows that the peak activities of these transcription factors gradually change from one phase to another through the cell cycle.
among the  <dig> putative cell cycle-related regulators, hir <dig> is a regulator of histones  <cit> , and it is therefore reasonable to expect it to have cell cycle related functions.
it is not clear how the other  <dig> transcription factors are related to cell cycle regulation.
lee et al.
<cit>  categorized dal <dig> and mss <dig> as metabolism regulators, hir <dig> as a dna/rna/protein biosynthesis regulator, and rlm <dig> as environmental response regulators.
these results suggested that transcription factors related to many other cellular processes may be involved in or dependent on cell cycle regulation to coordinate cellular processes  <cit> .
functional interaction of fkh <dig> fkh <dig> with other transcription factors
comparing the tfas derived from the wild-type strain and the fkh <dig> fkh <dig> mutant under the same experimental conditions allows the determination of functional interactions between fkh <dig> fkh <dig> with other transcription factors.
if such interaction exists, the activities of the interaction partners will change in the fkh <dig> fkh <dig> mutant.
in general the fkh <dig> fkh <dig> mutant showed reduced oscillation amplitude as compared to the wild type .
in particular, ace <dig>  swi <dig>  and ndd <dig> showed significantly reduced oscillation in the fkh <dig> fkh <dig> mutant, suggesting potential interactions between these transcription factors and the two fork-head transcription factors.
indeed, it was found that fkh <dig> forms a complex with mcm <dig> and ndd <dig>  <cit>  which controls g2/m genes and also binds the promoters of ace <dig> and swi <dig> to activate genes at the following m/g <dig> phase.
the reduced amplitude in tfas of ace <dig> and swi <dig> in the fkh <dig> fkh <dig> mutant support that there is a cascade interaction between the two forkhead transcription factors and ace <dig> and swi <dig>  <cit> .
tfa profiles of the wild-type strain  show that ace <dig> and swi <dig> were most active around m/g <dig> phase while fkh <dig>  fkh <dig>  mcm <dig>  and ndd <dig> were most active at g2/m, g <dig>  m/g <dig>  and g2/m phase, respectively.
these results are well consistent with previous results that mcm <dig>  ace <dig>  and swi <dig> are m/g <dig> transcriptional regulators while the complex of mcm <dig>  fkh <dig> and ndd <dig> is a g2/m activator.
therefore, this result shows that tfa in a regulator knockout strain can be used to determine functional interactions.
by utilizing the pearson correlation coefficient and deviation coefficient defined in the methods section, figure  <dig> shows that most transcription factors were aggregated in one cluster.
outside of this cluster are transcription factors which potentially were affected by the fkh <dig> fkh <dig> mutation and thus are functional interaction partners of the forkhead transcription factors.
these interaction partners include ace <dig>  ndd <dig>  and swi <dig>  which are known to interact with fkh <dig>  and hap <dig>  rts <dig>  cha <dig>  and fhl <dig>  which were not known to interact with the forkhead transcription factors.
in particular, hap <dig> was also identified in the above analysis as a putative cell cycle-related regulator, supporting their functional interaction with the forkhead transcription factors.
cha <dig> and hap <dig> were classified as metabolism-related factors, fhl <dig> dna/rna/protein synthesis, and rts <dig> cell cycle and data processing  <cit> .
their modes of interaction with the forkhead transcription factors remain unknown.
discussion
transcriptional regulators are commonly modified at the post-transcriptional level, and consequently their biological activities do not correlate significantly with expression levels.
previous work infer tfas from expression levels of genes regulated by single factors or in combination  <cit> .
in general, the major difference between previous work and that of nca is that the former require an explicit quantification of the control strengths  a priori.
bussemaker et al.
<cit>  defined the control strength as the motif copy number in corresponding promoters and found that there was no statistical benefit to model expression with more than single factors and thus deduced single tfas.
wang et al.
<cit>  considered an expression-weighted motif to find potential target genes of single transcription factors.
gao et al.
<cit>  used chip-chip log occupancy ratios as a surrogate for transcription factor binding affinity.
in contrast, nca explicitly models combinatorial regulation of gene expression, and allows both the control strengths and the tfas to be deduced simultaneously with given network connectivity.
in this approach, the lack of connectivity in specific pairs of transcription factor and promoter is used to provide constraints for data decomposition in order to obtain unique solutions when specific criteria are satisfied  <cit> .
gnca expands these capabilities by allowing incorporation of constraints onto the deduced tfas, such as transcription factor knockout experiments, which offer a rich source of data and biochemical information.
development of these methodologies significantly expands the capabilities of transcriptional regulation analysis.
with gnca, we analyzed the combined wild-type and fkh <dig> fkh <dig> mutant data set and showed that gnca can be used to identify tfas which are consistent with cell physiology, transcription factors with potential cell cycle dependent roles, as well as interactions between transcription factors.
on the basis that transcription factors exhibiting similar activity patterns function together, we identified  <dig> transcription factors that clustered closely with the known cell cycle regulators.
we performed a periodicity test to determine the tfa profiles that exhibit periodic behavior, and by combining the sets of transcription factors collected by these two methods, we identified  <dig> putative cell cycle-related regulators: dal <dig>  hap <dig>  hir <dig>  mss <dig>  and rlm <dig>  these transcription factors may participate in functions driven by cell cycles, or may regulate cell cycle directly or indirectly.
our comparison between the wild-type tfas and the mutant tfas confirmed that the forkhead transcription factors interact with ace <dig>  ndd <dig>  and swi <dig>  this result is consistent with previous reports  <cit> .
using this approach, we identified  <dig> additional transcription factors that may functionally interact with fkh <dig> fkh <dig> directly or indirectly: hap <dig>  rts <dig>  cha <dig>  and fhl <dig>  most of these transcription factors are not known to be related to cell cycle, suggesting that cell cycle regulation interacts with other physiological functions.
it is worth noting that our analysis can be sensitive to errors in the connectivity graph.
through a sensitivity analysis we determined that all the known cell cycle regulators and all the known forkhead interaction partners have tfas that exhibit low sensitivity to the connectivity network when using  <dig>  as a correlation coefficient threshold.
these results suggest that our analysis is robust to errors in connectivity.
with the same sensitivity criterion,  <dig>  of the  <dig> putative cell cycle-related regulators and  <dig>  of the  <dig> putative forkhead interaction partners were determined to be robust to connectivity errors.
the lack of sensitivity to error increases confidence in these predictions.
a total of  <dig>  genes and  <dig>  transcription factors were analyzed from  <dig> microarray experiments.
both limited connectivity information from chip-chip and missing data points in dna microarray expression attribute to the limited number of genes and tfs that can be studied in the current investigation.
on the other hand, the results suggest that our analysis on this limited set of genes and tfs appears to be sufficient: our analysis strategy recovers nearly 90% of the known cell cycle regulators.
on the basis of the tfa profiles, the time series of the key cell cycle regulators are summarized in figure  <dig>  a dominant feature in this map is the overlapping tfas among known cell cycle regulators.
this is common among some transcription factor complexes, including sbf  and mbf , as well as transcription factors known to regulate the same phase in the cell cycle including ace <dig>  swi <dig> and mcm <dig> .
in addition, overlapping tfas were also observed among different phases of cell cycle: transcription factors during one stage regulate transcription factors that function in the next stage.
it is well known that serial regulation among transcription factors forms a connected regulatory network  <cit> .
from the tfa profiles, we also observe the intrinsic property of the connected regulatory network among cell cycle factors in cell cycle regulation .
among the putative cell cycle-related transcription factors , dal <dig> is phosphorylated by cdk <dig>  <cit>  which is considered to be involved in g2/m transition  <cit> .
the activity of dal <dig> peaked over the g2/m phase is also in agreement with its regulatory role .
hir <dig> functions as a transcriptional repressor of histone gene expression during the cell cycle  <cit> .
histone synthesis is triggered at the beginning of the s phase.
so hir <dig> is expected to have the lowest tfa around s phase.
as such, tfa of hir <dig> from nca showed that it indeed has the lowest tfa around s phase .
most well characterized transcription factors showed biologically relevant activity profiles at specific cell cycle phases, suggesting that tfas deduced from gnca are biologically meaningful and a good predictor of transcription factor function and interaction.
CONCLUSIONS
protein function and interaction are often deduced computationally through analysis of genomic sequence, protein sequence, domain architecture, phylogenic profile, or gene expression level.
gene expression analysis represents the only current technique that takes into account dynamic behavior to assign interaction and function.
however, it has been shown that for proteins significantly regulated post-transcriptionally  their gene expression levels do not correlate well with their activity.
here a method for screening the physiological roles of transcription factors and their functional interactions based on their dynamic activity profiles was introduced.
our method first determines tfas, which were then further analyzed with cluster and periodicity analysis to determine transcription factor function.
by combining the results from both cluster analysis and periodicity analysis, we recovered more than 90% of transcription factors that are proposed to be involved in cell cycle regulation.
in addition, we discovered  <dig> putative transcription factors that may be related to cell cycle regulation.
functional interactions between transcription factors were determined by isolating statistically significant perturbations in tfa patterns between mutant Δfkh1Δfkh <dig> and wild-type experiments carried out under the same experimental conditions.
this method allowed for the identification of  <dig> novel and  <dig> previously verified fork-head transcription factor interaction partners.
we recognize that the chip-chip data may be condition-dependent and noisy.
however, together with microarray data, they provide useful information for functional deduction of transcription regulators.

 transcription factor activities rather than levels of transcription factor expression mediate transcriptional regulations. various post-transcriptional and post-translational modifications abolish significant correlations between tfas and the level of transcription factor expression. therefore, a strategy to determine the physiological functions and interactions of transcription factors based on the analysis of tfa profiles would be more fundamentally sound than one based on transcript levels per se. however, owing to post-translational modifications, tfas are difficult to measure experimentally and therefore, many analyses infer tfas by computational analysis of target gene expression levels either from single regulatory factors alone or in combination. among these, network component analysis and generalized nca provide a robust framework for deducing tfas based on dna microarray data, promoter connectivity, and genetic regulatory constraints imposed by regulatory knock-out experiments. using tfa profiles deduced by nca and gnca, we are now in a position to assign transcription factor functions and reconstruct functional interactions between transcription factors. the goal of this work is to demonstrate how we analyze tfa profiles to determine physiologically relevant characteristics of transcription factors. specifically, by analyzing tfa profiles of the s. cerevisiae cell cycle we identify cell cycle regulators and putative interaction partners of two forkhead transcription factors that are responsible for expression of a gene cluster within the m/g interval and involved in mitotic exit. once tfa profiles are determined, the transcription factor regulators and interactions are deduced based on the following hypotheses: 1) transcription factors with similar activity patterns function together; 2) transcription factors involved in cell cycle regulation exhibit oscillatory activity patterns, 3) activities of transcription factors which functionally interact with each other will be disturbed if one of the interacting partners is deleted. these hypotheses are in spirit similar to the traditional analysis of gene expression. in contrast to traditional analysis of gene expression, our analyses are constructed and applied directly to tfa profiles.  overall strategy a flow diagram demonstrating the relationships between each component of the methodology is presented in figure given the gene expression data and connectivity network between transcription factors and gene expression, we first deduced tfas from gene expression by using gnca. the deduced tfas were then analyzed by two complementary methods. first, we used cluster analysis to group tfas that behave in a similar manner. second, a statistical analysis was used to determine if the signal from each of the tfas was periodic. the results from these two analyses were integrated to deduce putative cell cycle regulators. we hypothesized that putative cell cycle regulators should exhibit periodic activity profiles and cluster closely with known cell cycle regulators. then tfa profiles from wild type and the fkh fkh mutant strain under the same experimental conditions were statistically analyzed to deduce transcription factors whose profiles were significantly perturbed, thus identifying putative functional interaction partners of the fork-head transcription factors. application of gnca to the combined wild-type and mutant data set we used gnca to analyze both the wild-type and the fkh fkh mutant data. the wild-type data and the tf-knockout data were organized in different columns of the e matrix. the elements in p corresponding to the specific knockout strain were kept at zero, in addition to the zero constraints placed in a according to the transcription factor-gene connectivity information. the first step in gnca was to select sub-networks based on available transcription factor-gene connectivity. each sub-network was constructed to satisfy the gnca criteria. gnca requires that the number of transcription factors in each sub-network be less than that of data points in the data matrix. in the combined cell cycle microarray data set, m = and thus the number of transcription factor in gnca in each analysis cannot exceed thus, subsets of the transcription factors included in the genome-wide location analysis were selected to form sub-networks for gnca. overlapping random sub-networks were generated and screened using the gnca criteria. among them, four that satisfy the gnca criteria were selected in order to show that using multiple sub-networks makes it possible to determine tfas more than the number of data points. each sub-network contained transcription factors, but together, a total of transcription factors were analyzed. the transcription factors involved in each of the sub-networks are shown in figure only transcription factors among transcription factors were fully overlapped among all sub-networks. after applying gnca independently to the sub-networks, tfas were determined. figure shows the tfas of the known cell cycle factors from different sub-networks. qualitatively, these tfas appear to show expected oscillatory behavior for and cycles according to the method of synchronization. the dynamics of overlapping tfa profiles between the four different sub-networks are very similar. this indicates that the deduced tfas were insensitive to the sub-network selection. in addition, combining the fkh fkh mutant data with the wild-type data yields similar tfas predicted from wild-type data alone, suggesting the consistency between the two data sets. it is recognized that most transcription factors are regulated in post-transcriptional processes. thus, their activity may deviate significantly from the expression level as noted previously. for transcription factors with both gene expression level and tfa available, the correlation coefficients ranged from - to. the wide range difference in the correlation coefficients confirms that tfas and expression levels exhibit very different dynamic profiles and therefore tfas cannot be substituted by expression levels in analysis. sensitivity analysis to assess the effect of connectivity errors on our results, we altered up to 10% of the connectivity graph for every subnetwork, by randomly deleting and inserting connections between transcription factors and genes. this effectively simulates the presence of false negatives and false positives in chip-chip assays. subsequently, we ran gnca on our randomly perturbed graphs and compared the deduced tfas to our reported results via the correlation coefficient. the procedure was performed times and the tfas deduced from each run were compared with the tfas computed with unaltered connectivity using pearson correlation coefficients. transcription factors with high correlation coefficients suggest robustness of the results against connectivity errors. determination of cell cycle-dependent regulators based on tfa dynamics we hypothesized that transcription factors with similar activity patterns are involved in related processes. thus, clustering of tfas would allow identification of transcription factors related to cell cycle regulation. after hierarchical clustering, transcriptional factors were found to cluster closely with the known cell cycle regulators. in addition to cluster analysis, we performed a statistical test to identify the set of tfas with a periodic profile. figure 5a shows the power spectra of the known cell cycle regulator. a power spectrum is a representation of a signal in the frequency domain. a dominant peak in the power spectrum corresponds to the fact that the underlying process has a principal oscillation frequency. most of the power spectra to identify periodic patterns exhibit a single strong peak at low frequency. this suggests that the dynamic profiles appear to be periodic. to classify whether a signal is periodic or not, we employed a statistical criterion of rejecting the null hypothesis of purely random process. the result suggests that out of known cell cycle regulators exhibit periodic behavior. this confirms that the activity profiles of cell cycle regulators are periodic. we then applied the same periodicity test to the rest of transcription factors and found that about of the deduced tfas from elutriation and α-factor arrest were statistically periodic and of the deduced tfas from cdc were statistically periodic. combining the results of the periodicity test and cluster analysis, we found that out of the transcription factors closely clustered with the known cell cycle factors were statistically periodic and were regarded as putative cell cycle-related regulators. the power spectra of these putative cell cycle regulators are shown in figure 5b, and the tfa profiles of these regulators are illustrated in figure the clustered tfa pattern of all cell cycle-related transcription factors shows that the peak activities of these transcription factors gradually change from one phase to another through the cell cycle. among the putative cell cycle-related regulators, hir is a regulator of histones, and it is therefore reasonable to expect it to have cell cycle related functions. it is not clear how the other transcription factors are related to cell cycle regulation. lee et al. categorized dal and mss as metabolism regulators, hir as a dna/rna/protein biosynthesis regulator, and rlm as environmental response regulators. these results suggested that transcription factors related to many other cellular processes may be involved in or dependent on cell cycle regulation to coordinate cellular processes. functional interaction of fkh fkh with other transcription factors comparing the tfas derived from the wild-type strain and the fkh fkh mutant under the same experimental conditions allows the determination of functional interactions between fkh fkh with other transcription factors. if such interaction exists, the activities of the interaction partners will change in the fkh fkh mutant. in general the fkh fkh mutant showed reduced oscillation amplitude as compared to the wild type. in particular, ace swi and ndd showed significantly reduced oscillation in the fkh fkh mutant, suggesting potential interactions between these transcription factors and the two fork-head transcription factors. indeed, it was found that fkh forms a complex with mcm and ndd which controls g2/m genes and also binds the promoters of ace and swi to activate genes at the following m/g phase. the reduced amplitude in tfas of ace and swi in the fkh fkh mutant support that there is a cascade interaction between the two forkhead transcription factors and ace and swi. tfa profiles of the wild-type strain show that ace and swi were most active around m/g phase while fkh fkh mcm and ndd were most active at g2/m, g m/g and g2/m phase, respectively. these results are well consistent with previous results that mcm ace and swi are m/g transcriptional regulators while the complex of mcm fkh and ndd is a g2/m activator. therefore, this result shows that tfa in a regulator knockout strain can be used to determine functional interactions. by utilizing the pearson correlation coefficient and deviation coefficient defined in the methods section, figure shows that most transcription factors were aggregated in one cluster. outside of this cluster are transcription factors which potentially were affected by the fkh fkh mutation and thus are functional interaction partners of the forkhead transcription factors. these interaction partners include ace ndd and swi which are known to interact with fkh and hap rts cha and fhl which were not known to interact with the forkhead transcription factors. in particular, hap was also identified in the above analysis as a putative cell cycle-related regulator, supporting their functional interaction with the forkhead transcription factors. cha and hap were classified as metabolism-related factors, fhl dna/rna/protein synthesis, and rts cell cycle and data processing. their modes of interaction with the forkhead transcription factors remain unknown. discussion transcriptional regulators are commonly modified at the post-transcriptional level, and consequently their biological activities do not correlate significantly with expression levels. previous work infer tfas from expression levels of genes regulated by single factors or in combination. in general, the major difference between previous work and that of nca is that the former require an explicit quantification of the control strengths a priori. bussemaker et al. defined the control strength as the motif copy number in corresponding promoters and found that there was no statistical benefit to model expression with more than single factors and thus deduced single tfas. wang et al. considered an expression-weighted motif to find potential target genes of single transcription factors. gao et al. used chip-chip log occupancy ratios as a surrogate for transcription factor binding affinity. in contrast, nca explicitly models combinatorial regulation of gene expression, and allows both the control strengths and the tfas to be deduced simultaneously with given network connectivity. in this approach, the lack of connectivity in specific pairs of transcription factor and promoter is used to provide constraints for data decomposition in order to obtain unique solutions when specific criteria are satisfied. gnca expands these capabilities by allowing incorporation of constraints onto the deduced tfas, such as transcription factor knockout experiments, which offer a rich source of data and biochemical information. development of these methodologies significantly expands the capabilities of transcriptional regulation analysis. with gnca, we analyzed the combined wild-type and fkh fkh mutant data set and showed that gnca can be used to identify tfas which are consistent with cell physiology, transcription factors with potential cell cycle dependent roles, as well as interactions between transcription factors. on the basis that transcription factors exhibiting similar activity patterns function together, we identified transcription factors that clustered closely with the known cell cycle regulators. we performed a periodicity test to determine the tfa profiles that exhibit periodic behavior, and by combining the sets of transcription factors collected by these two methods, we identified putative cell cycle-related regulators: dal hap hir mss and rlm these transcription factors may participate in functions driven by cell cycles, or may regulate cell cycle directly or indirectly. our comparison between the wild-type tfas and the mutant tfas confirmed that the forkhead transcription factors interact with ace ndd and swi this result is consistent with previous reports. using this approach, we identified additional transcription factors that may functionally interact with fkh fkh directly or indirectly: hap rts cha and fhl most of these transcription factors are not known to be related to cell cycle, suggesting that cell cycle regulation interacts with other physiological functions. it is worth noting that our analysis can be sensitive to errors in the connectivity graph. through a sensitivity analysis we determined that all the known cell cycle regulators and all the known forkhead interaction partners have tfas that exhibit low sensitivity to the connectivity network when using as a correlation coefficient threshold. these results suggest that our analysis is robust to errors in connectivity. with the same sensitivity criterion, of the putative cell cycle-related regulators and of the putative forkhead interaction partners were determined to be robust to connectivity errors. the lack of sensitivity to error increases confidence in these predictions. a total of genes and transcription factors were analyzed from microarray experiments. both limited connectivity information from chip-chip and missing data points in dna microarray expression attribute to the limited number of genes and tfs that can be studied in the current investigation. on the other hand, the results suggest that our analysis on this limited set of genes and tfs appears to be sufficient: our analysis strategy recovers nearly 90% of the known cell cycle regulators. on the basis of the tfa profiles, the time series of the key cell cycle regulators are summarized in figure a dominant feature in this map is the overlapping tfas among known cell cycle regulators. this is common among some transcription factor complexes, including sbf and mbf, as well as transcription factors known to regulate the same phase in the cell cycle including ace swi and mcm. in addition, overlapping tfas were also observed among different phases of cell cycle: transcription factors during one stage regulate transcription factors that function in the next stage. it is well known that serial regulation among transcription factors forms a connected regulatory network. from the tfa profiles, we also observe the intrinsic property of the connected regulatory network among cell cycle factors in cell cycle regulation. among the putative cell cycle-related transcription factors, dal is phosphorylated by cdk which is considered to be involved in g2/m transition. the activity of dal peaked over the g2/m phase is also in agreement with its regulatory role. hir functions as a transcriptional repressor of histone gene expression during the cell cycle. histone synthesis is triggered at the beginning of the s phase. so hir is expected to have the lowest tfa around s phase. as such, tfa of hir from nca showed that it indeed has the lowest tfa around s phase. most well characterized transcription factors showed biologically relevant activity profiles at specific cell cycle phases, suggesting that tfas deduced from gnca are biologically meaningful and a good predictor of transcription factor function and interaction.  protein function and interaction are often deduced computationally through analysis of genomic sequence, protein sequence, domain architecture, phylogenic profile, or gene expression level. gene expression analysis represents the only current technique that takes into account dynamic behavior to assign interaction and function. however, it has been shown that for proteins significantly regulated post-transcriptionally their gene expression levels do not correlate well with their activity. here a method for screening the physiological roles of transcription factors and their functional interactions based on their dynamic activity profiles was introduced. our method first determines tfas, which were then further analyzed with cluster and periodicity analysis to determine transcription factor function. by combining the results from both cluster analysis and periodicity analysis, we recovered more than 90% of transcription factors that are proposed to be involved in cell cycle regulation. in addition, we discovered putative transcription factors that may be related to cell cycle regulation. functional interactions between transcription factors were determined by isolating statistically significant perturbations in tfa patterns between mutant Δfkh1Δfkh and wild-type experiments carried out under the same experimental conditions. this method allowed for the identification of novel and previously verified fork-head transcription factor interaction partners. we recognize that the chip-chip data may be condition-dependent and noisy. however, together with microarray data, they provide useful information for functional deduction of transcription regulators. 
the recently developed network component analysis and its generalized form provide a robust framework for deducing the transcription factor activities from various types of dna microarray data and transcription factor-gene connectivity. by subjecting tfa profiles to analyses based upon physiological signatures we were able to identify cell cycle related transcription factors consistent with current literature, transcription factors with potential cell cycle dependent roles, and interactions between transcription factors. by combining the results from both cluster analysis and periodicity analysis, we recovered nearly 90% of the known cell cycle regulators, and identified putative cell cycle-related transcription factors. using gnca, we determined tfas from both wild type and fkh fkh deletion mutant microarray data encompassing orfs. this hypothesis was supported by the tfa profiles of known cell cycle factors and was used as a basis to uncover other potential cell cycle factors. the goal of this work is to demonstrate the utility of tfas in inferring transcription factor functions and interactions in saccharomyces cerevisiae cell cycle regulation. in addition, by analyzing expression data from transcription factor knockout strains, we determined verified and putative interaction partners of the forkhead transcription factors. sensitivity of tfas to connectivity errors was determined to provide confidence level of these predictions. since transcription factors are often regulated at the post-transcriptional level, their activities, rather than expression levels may provide valuable information for investigating functions and their interactions. we hypothesized that transcription factors participating in the cell cycle regulation exhibit cyclic activity profiles.
 since transcription factors are often regulated at the post-transcriptional level, their activities, rather than expression levels may provide valuable information for investigating functions and their interactions. the recently developed network component analysis and its generalized form provide a robust framework for deducing the transcription factor activities from various types of dna microarray data and transcription factor-gene connectivity. the goal of this work is to demonstrate the utility of tfas in inferring transcription factor functions and interactions in saccharomyces cerevisiae cell cycle regulation.  using gnca, we determined tfas from both wild type and fkh fkh deletion mutant microarray data encompassing orfs. we hypothesized that transcription factors participating in the cell cycle regulation exhibit cyclic activity profiles. this hypothesis was supported by the tfa profiles of known cell cycle factors and was used as a basis to uncover other potential cell cycle factors. by combining the results from both cluster analysis and periodicity analysis, we recovered nearly 90% of the known cell cycle regulators, and identified putative cell cycle-related transcription factors. in addition, by analyzing expression data from transcription factor knockout strains, we determined verified and putative interaction partners of the forkhead transcription factors. sensitivity of tfas to connectivity errors was determined to provide confidence level of these predictions.  by subjecting tfa profiles to analyses based upon physiological signatures we were able to identify cell cycle related transcription factors consistent with current literature, transcription factors with potential cell cycle dependent roles, and interactions between transcription factors. 