BACKGROUND
despite the major role of regulatory networks in orchestrating complex cellular functions, the architecture and function of most networks is largely unknown.
several methods were previously suggested for reconstructing the structure of regulatory networks from expression data.
most methods learn simplified models  <cit>  based on abstract regulator-target relations rather than a biochemical model of the binding of a transcription factor  to a promoter.
furthermore, since they rely on the mrna levels of both target and tf, they fail when the tf is not itself regulated at the transcription level .
complementary approaches learn a regulation program by integrating gene expression data with additional data sources, such as genome-wide tf binding data  <cit>  or promoter sequence information  <cit> , into a single coherent model.
each of these approaches has some limitations.
tf-binding data are still scarce, can suffer from high false positive rates, and even true binding of a tf does not necessarily imply regulation.
analyzing promoter sequences is limited by the relatively small number of known cis-regulatory motifs, the difficulty to detect significant novel binding motifs, and the high false positive rate when scanning for motif occurrences in promoters.
nevertheless, by requiring consistency between several heterogeneous data types, integrative models are typically more robust and accurate.
here, we present a novel integrated approach to analyze transcriptional regulatory programs.
we use a gene expression data set to decompose genes into coherent modules of co-regulated genes, based on a biochemically-motivated model.
our model uses realistic constraints, suggesting a mechanistic explanation for their expression patterns using combinations of a small number of unknown putative regulators.
we employ two novel strategies to increase model robustness.
first, we use gene modules – sets of targets controlled by the same biochemical regulatory functions – to learn a global network model which is simpler and biologically meaningful.
furthermore, we devise an algorithm that learns a robust model based on an ensemble learning approach.
although the biochemical constraints are insufficient to build a fully realistic model with current datasets, they provide a principled way to extract a biologically coherent modular structure for the data.
we then use this modular decomposition to search for novel binding motifs in sets of genes defined by the network structure, and test for enrichment for those motifs in all the learned modules.
the motif combinations present in the target genes define a second, sequence-based regulation program.
in particular, it allows us to explore the regulation of transcription factors.
we apply our approach to the transcriptional program of the fission yeast cell cycle, a system which is only partially characterized  <cit> .
in particular, a large portion of the cell cycle , and the transition from g <dig> to m are not explained by any known transcriptional regulator  in fission yeast.
this is in contrast to the regulatory program of the cell cycle of the budding yeast, saccharomyces cerevisiae, where a closed loop of transcriptional regulators is known  <cit> .
previous studies show that one cannot project the regulatory program from budding yeast to fission yeast: the set of regulators is only partially overlapping between these two divergent species, as are their target gene set and binding site sequences .
this is consistent with the functional differences between the cell cycle of these two species .
several studies measuring genome-wide expression profiles in s. pombe throughout the cell cycle were recently published  <cit> , but their initial analysis only partly filled up the gaps in understanding.
our analysis discovered  <dig> coherent modules spanning different phases of the cell cycle and covering diverse processes from metabolism to cell division.
the resulting learned motif library is composed of  <dig> regulatory elements, including both known cell-cycle regulatory elements and novel ones.
finally, we analyze how specific regulatory topologies underlie distinct dynamics behaviour of gene expression in the fission yeast cell cycle.
RESULTS
we developed an integrated approach to analyze the regulatory program controlling gene expression during a dynamical process from expression and sequence data .
we illustrate and test the steps of our approach based on the fission yeast cell cycle dataset.
our approach consists of six steps:  we derived an input set of transcription rate profiles for  <dig> cell-cycle regulated genes from a gene expression time series data set spanning  <dig> cell cycles  <cit>  and sampled  <dig> datasets from this input set, each containing  <dig> genes.
we learned a regulation model for each of the  <dig> data sets.
each such model identifies a set of modules, co-regulated target gene sets, and describes their transcription rate profiles using a set of learned regulator activity profiles and a set of regulator-to-gene affinity parameters.
we generated a unified model from the resulting ensemble of  <dig> models, capturing the variance and significance of different elements in the individual models.
we used the structure of the unified model to guide a search for novel cis-regulatory motifs, resulting in a library of  <dig> motifs.
we identified the motif composition of each promoter by scanning the promoters of all s. pombe genes against our library and identified motifs enriched in core gene modules in our unified model.
we contrasted the expression- and sequence-based regulatory relations, highlighting key elements of transcriptional regulation in the s. pombe cell cycle.
below we describe each step of our approach.
biochemical regulatory networks: an expression-based biochemical model of modular gene regulation
we developed a novel algorithm, biochemical regulatory network inference , which takes expression levels for a set of genes, converts them to transcription rates  and learns a biochemical model of gene regulation.
in our modular regulatory model, inferred regulators are connected to modules of co-regulated genes , and control their dynamic behaviour based on biochemical principles .
brni is based on our method to infer biochemical models of single gene regulation  <cit> .
this method infers a set of regulators needed to explain the observed expression levels, and for each such regulator it learns a temporal activity profile rj, representing its activity levels over time.
the connections between  regulators and  target genes follow biochemical rules that describe how the regulator controls the expression of the gene, based on affinity parameters .
the model accounts for the biochemical processes of binding and dissociation, thus allowing for different non-linear combinations of regulators, both as activators and as repressors.
specifically, for each gene the learned biochemical model includes the set of regulators controlling it , the affinity parameter γji between the gene and each of its regulators, and the gene-specific activity levels of each binding state {αi}.
the set of affinity and activity parameters {γji, αi} uniquely defines the target gene transcription rates as a function of the regulator behaviour rj.
a multiplicative noise model is used to account for deviations between observed transcription rates and those predicted by the regulation functions.
such a detailed biochemical model contains, however, many parameters .
given the limited amount of data, the learned model might represent over-fitting of this data.
in particular, it can be strongly biased by data points or genes suffering from high measurement errors.
to overcome this, we developed here two novel and complementary approaches:  modifying the model to include modules of target genes; and  using a bootstrap approach, where we learn an ensemble of models from which we derive a high-confidence unified model.
first, we modified our model to introduce target gene modules.
each module consists of genes with similar expression patterns, the same set of inferred regulators and the same affinity and activity parameters .
this greatly reduces the number of parameters in the learned models and lowers the dimensionality of the search space, thus increasing the model's robustness and speeding up the search.
we devised an iterative search algorithm that learns this modular model by alternating between refinement of the module regulation model  and optimal assignment of genes to modules .
second, we devised a bootstrap procedure for learning a model: rather than learning a single model, we learn an ensemble of models each based on a different sampled subset of target genes .
the speedup gained by the model's modularity allows us to learn an entire ensemble of models in reasonable time.
finally, we integrate the ensemble of models into a unified consensus model .
we first map the regulators between different runs based on their time profile similarities.
next, we define core gene modules based on sets of genes that frequently co-occur in the same module.
in the resulting integrated network each regulatory connection is assigned a confidence score, and each affinity parameter is associated with an error bar.
learning regulatory modules in the fission yeast cell cycle
we applied our algorithm to expression profiles of  <dig> cycling genes measured during the fission yeast cell cycle  <cit>  and derived a unified model with  <dig> regulators controlling  <dig> core modules .
our analysis shows that both the initial structure learning, as well as the bootstrap step improve the coherence of the resulting modules .
the modules consisted of  <dig> to  <dig> genes with correlated expression profiles and a distinct phase .
five modules  peak at m/g1; two modules  peak at g1; two modules  at g1/s, two modules  at s/g <dig> and four modules  at g <dig>  several of the distinct modules represent coherent biological processes, as reflected by their members' known functions .
the modules cover both classical cell cycle processes  as well as general growth processes .
each of the four regulators, denoted r <dig> through r <dig>  has a distinct cell cycle phase .
r <dig> peaks at g2/m and is the dominant regulator in the model.
r <dig> peaks at g <dig>  r <dig> peaks at g1/s and r <dig> has a wide peak at g <dig>
the  <dig> gene modules in the unified model.
for each enriched function, the number of genes in the module having that function is shown in parentheses.
*transcription rates, as predicted by our pre-processing .
learning a motif-based model of gene regulation
a complementary view of the transcriptional program is driven by the promoter sequences of the target genes.
assuming a transcription factor binds a specific motif, the full motif set in the promoters of the target genes induces a connectivity model between tfs and target genes.
the structure of our expression based learned network therefore provides two key clues to finding cis-regulatory motifs.
first, we can search for motifs enriched in a module, as the co-expression of module genes may indicate a shared regulatory mechanism.
second, we can also search for motifs shared by the targets of the same regulator across modules.
if that regulator corresponds to a dna binding factor, or even to an indirect regulatory activity, we expect its targets to share a regulatory element .
importantly, these targets can be distributed across multiple modules with distinct expression patterns due to combinatorial regulation.
thus, such related motifs may not be identified by the former, module-based approach.
notably, a comparative analysis of different partial models shows that different components of the regulatory model  improve the resulting modules in terms of their correspondence with known binding motifs .
this suggests that the same model can also improve the discovery of novel motifs.
we used an automated approach , to systematically learn a non-redundant library of motifs in this manner.
the resulting library consists of  <dig> motifs,  <dig> of which were derived from modules and  <dig> from regulators.
these motifs match the known cell cycle regulatory elements mcb , ace <dig>  fkh <dig> , pcb and the histone accct box, as well as include several novel motifs .
we next scanned the whole genome against this library and tested each motif for enrichment in the promoters of gene module members.
we found  <dig> significant motif-module pairs.
seven of the modules are significantly enriched for at least one motif .
notably, we found no enrichment when we performed a similar scan of s. pombe modules with five additional known cell-cycle motifs from s. cerevisiae that do not have a known counterpart in s. pombe .
this is in contrast to the above mentioned elements mcb, fkh <dig> and ace <dig>  which are similar or identical to their s. cerevisiae counterparts.
cis-regulation of expression modules in the fission yeast cell cycle
the motif analysis resulted in several interesting insights on the regulatory mechanisms controlling each module some of them recapitulate known facts, indicating the validity of our results, while others are novel, and suggest new testable hypotheses.
for example, the histone module  consists of all seven histone genes in the input set .
the transcription rates of the module's genes are predicted to peak at m/g <dig>  while their measured expression levels peak at s phase.
the genes in this module are associated with only four promoters, since eight of the nine s. pombe histone genes are arranged in divergently-transcribed pairs.
we found that all histone promoters contain a previously described histone specific motif .
recent studies show that this site is bound and activated by the ams <dig> transcription factor  <cit> .
our analysis also shows that ams <dig> itself is a member of module  <dig>  and has an mcb motif in its promoter, and another novel motif, a.gcg.c.
interestingly, two of the histone promoters contain an mcb site as well, and three of them contain the a.gcg.c motif.
this suggests a possible feed forward loop involving the mbf complex , ams <dig>  and the histone genes , as we discuss below.
the regulation of histones by mbf may be a conserved feature of the yeast cell cycle transcriptional network.
in s. cerevisiae the promoters of histone genes contain mostly swi <dig>  swi <dig> and mbp <dig> motifs, raising the possibility of their activation by mbf and/or sbf  <cit> .
finally, we discovered a third novel motif  that appears in three of the four promoters.
this motif might serve as the  binding site for the repressor hip <dig>  further experiments are needed to validate the proposed regulatory role of mbf and the novel sites in s. pombe histone genes.
the cell division module  consists of  <dig> genes, encoding mostly cell wall proteins and glycoproteins whose expression peaks at m/g <dig>  the module genes' promoters are enriched for the ace <dig> motif , the fkh1/ <dig> motif , and for two novel motifs .
regulation of the module by ace <dig> is consistent with the module's function , the down-regulation of nine module genes in an ace <dig> deletion strain  <cit> , and the phase of ace <dig> transcription which slightly precedes that of the module's genes, consistent with a positive regulatory role.
further experiments are needed to explore the additional role of fkh <dig> and the factors binding the novel motifs in modulating the expression pattern of the module's genes.
the two cell wall biogenesis and cell division modules  include the ace <dig> and fkh <dig> genes.
the modules' genes are associated with a putative pcb motif  and a fkh <dig> motif .
although the phase of these modules is similar to that of module  <dig>  their genes do not contain any ace <dig> sites, supporting their separation to distinct modules.
notably, the fkh <dig> sites in module  <dig> are concentrated further upstream of the gene start than in module  <dig> , supporting their further separation.
the hypothesis that fkh <dig> and sep <dig>  are joint regulators in these modules is supported by the effect of sep <dig> deletion on several of the modules' genes  <cit>  and by the similarity of the peak phase of rate of transcription of the modules' genes and fkh <dig> .
these results are consistent with a recent study  <cit>  demonstrating that in three promoters containing both sites, both fkh <dig> and sep <dig> bind and play opposing roles in repression and activation of their joint targets, respectively.
notably,  <dig> of the  <dig> modules' genes have only fkh <dig> sites in their promoters, suggesting that fkh <dig> can regulate expression in promoters that lack pcb.
since only a repressive role has been demonstrated for fkh <dig> in s. pombe, these promoters may be regulated solely by de-repression or by a novel unknown mechanism.
the translation module  consists of  <dig> genes, mostly related to translation regulation and ribosome biogenesis that peak in early g <dig> phase, the major growth phase for s. pombe.
the module contains two prominent yet unknown motifs – agagcg  and tttggttcg .
each of these motifs appears in approximately 5% of all s. pombe genes, and is enriched in genes that perform metabolic functions.
since the expression of genes encoding the translation and ribosome biogenesis machineries is also modulated in response to environmental stresses, the discovered motifs could be responsible for their regulation either under stress or in normal cell cycle conditions.
in the latter case, they could provide a novel mechanistic explanation for cell cycle regulation during the g <dig> phase.
overall, the analysis led to several testable hypotheses on the fission yeast cell cycle:  mbf and ams <dig> form a feed-forward loop to control histone gene expression;  histone gene expression is controlled through the novel motif gattgactga, which may be a hir <dig> target site;  fkh <dig> may control the cell division module;  fkh <dig> may control distinct modules involved in cell wall biogenesis and cell division, both in combination with sep <dig>  and alone, possibly solely though a de-repression mechanism; and  growth related functions, such as ribosome biogenesis, are under cell cycle control through two novel cis-elements, agagcg and tttggttcg.
the power and limitation of an expression based regulatory model
we next compared the expression- and cis-regulatory networks we learned.
in particular, we examined whether learned regulator profiles correspond to specific transcription factors.
if this is the case, we expect each regulator to be mapped to a specific regulatory element from our library.
when considering each of the regulators, however, we do not find such matching.
for example, the regulator r <dig>  peaks at g2/m and captures a "centralized" activity around the narrow time interval covering m/g <dig>  g <dig> and g1/s, and is thus associated with the regulatory elements and activity of several transcription factors active during those phases .
similarly, r <dig> peaks at m/g <dig>  and is connected to the many histone sites through module  <dig> genes, but also to ace <dig> motif .
its combination with r <dig> explains the delayed activity of this module's members.
overall, we find that the learning algorithm avoids the need for additional regulators to explain the expression of different modules in those phases by using either r <dig> alone or in different combinations with the other learned regulators, thus achieving more delayed or early expression peaks.
although the individual learned regulators do not correspond to specific transcription factors, the network induced by their combinations is meaningful.
first, as discussed above, the network consists of modules with coherent biological functions.
second, the network topology allowed us to discover most known cell cycle binding sites and several novel ones.
third, the modules display distinct binding site compositions.
in particular, in several cases  genes with very similar expression profiles were partitioned into separate modules.
our analysis showed that each of these modules was characterized by a distinct promoter configuration, supporting the partition.
this strength of the regulatory model is due to its non-linear nature.
future work can incorporate motif finding and scoring as an integral part of the learning algorithm, thus using cis-regulatory distinctions to identify concrete regulators.
reconstructing a network of transcriptional regulation
to further associate the inferred regulatory networks with concrete regulatory functions, we examined whether the relation between the timing of expression of cell-cycle related transcription factors and the timing of expression of gene modules that are associated with their binding sites.
naively, we would expect to find an activator's binding site in promoters of genes which are induced in a subsequent phase.
conversely, we expect to find the binding sites for repressors in promoters of genes that are repressed in the subsequent phase.
this simple prediction may be distorted by a delay between the regulator's gene transcription and the binding of its protein to target promoters.
such a delay could result from slowed dynamics or active regulation in any of the intermediate steps between transcription and binding .
we examined each of the four cell-cycle transcription factors which have both a cyclic transcriptional profile and a known binding motif: ace <dig>  cdc <dig> and rep <dig> , fkh <dig>  and ams <dig> .
we found that each is associated with a distinct mechanism resulting in different dynamic behaviour of its targets, together forming an integrated network with a cyclic behaviour .
first, ace2's expression slightly precedes that of its targets in module  <dig>  supporting a simple activatory model .
other targets  exhibit a longer delay, but their regulation mechanism might be different since they do not respond to an ace <dig> deletion  <cit> .
second, mbf and ams <dig> target genes display a narrow spectrum of peak times, from in-phase with their respective regulator up to a slight delay from that regulator .
these spectra may be achieved by interactions of these transcription factors with other regulators.
for example, genes whose promoters harbour both ams <dig> sites  and mbf sites  exhibit a delayed  expression phase compared to the effect of each one of these regulators alone .
upon closer inspection, we find that ams <dig> is in fact part of a feed-forward activatory chain: it contains an mbf site in its promoter, its expression is slightly preceded by cdc <dig> and rep <dig>  and it precedes the histones' expression profiles .
finally, there is no delay between the peak expression of fkh <dig> and the genes in its target modules .
this may be explained by its repressive role and a delay between its transcription and its binding to target promoters, as recently reported in  <cit> .
this work showed that while sep <dig> is likely an activator and binds concurrently with the expression of its target genes, fkh <dig> is likely a repressor and binds when the expression of the same target genes is low.
since fkh <dig> itself is regulated in this fashion  it might close a negative feedback loop, suggesting a mechanism for regulating the g2/m part of the cell cycle: fkh <dig> is transcribed during m/g <dig>  and following translation and localization to the nucleus binds to these promoters for the length of g <dig>  inhibiting their activation by sep <dig>  as it degrades gradually during g <dig>  by the end of this phase it no longer prevents sep <dig> binding and activation during m/g <dig> .
in conclusion, we propose the following model for the transcriptional regulatory circuit governing the cell cycle, as it emerges from our integrated analysis .
as explained above, fkh <dig> is the only component that could by itself close a loop of transcriptional regulation around the cell cycle.
along with the sep1/mbx <dig> pbf complex, it regulates several other regulators, including the mbf subunit rep <dig>  ace <dig> and ams <dig>  finally, the motif ga.gcg.c, which is similar to mcb and could be an alternative variant of it, plays a dominant role both in cell cycle regulated genes as well as in the promoters of some of the regulators themselves .
thus, our integrated analysis discovered novel players, interactions and dynamics in the s. pombe cell cycle, in particular suggesting how combinatorial regulation can lead to a full cyclic circuit of transcriptional regulation.
CONCLUSIONS
we have presented an integrated approach for the analysis of transcriptional programs.
our analysis comprised of two components: a biochemically motivated model of gene regulation based on the expression data, inducing a division to expression modules; and a binding motif analysis based on the division to those modules and regulatory relations.
we have applied our approach to the analysis of the fission yeast cell cycle program.
this approach is generally applicable to expression profiles measured along time courses.
the regulation program we learned allowed us to derive important biological insights.
first, it induced an informative division to coherent regulatory modules.
in particular, it was able to separate between modules with similar expression peak phases but with clearly distinct binding site compositions, based on more subtle differences in expression profiles.
this division resulted in identification of several novel binding sites  in the second part of the analysis, allowing us to detect the structural features underlying distinct dynamic behaviour.
our analysis suggests several novel potential mechanisms for differential regulation of genes along the cell cycle.
these include a feed-forward chain of mbf with ams <dig> leading to delayed expression of histone genes, a putative binding site for the histone gene repressor hip <dig>  combinatorial regulation of specific cell division genes by ace <dig> and fkh <dig> , putative sites acting during the g <dig> phase to regulate cell growth modules, and a negative feedback loop involving fkh <dig> and sep <dig> that may control expression dynamics in the g2/m phase of the fission yeast cell cycle.
despite these successes, our analysis also showed certain limitations of learning biochemically motivated models from expression data alone.
in particular, the learned regulators cannot be interpreted as transcription factors, but rather reflect more abstract regulatory functions, potentially carried out by multiple transcription factors.
several factors may contribute to this result, including the assumption of our regulation model that factor binding indicates direct activity, and the score used by the learning algorithm which favours the most parsimonious model that can explain the data, resulting in regulation schemes with a small number of "abstract" regulators.
thus, the model can fail to correctly separate between regulators when their activities are highly correlated , or when their peak activities are concentrated in a narrow part of the cell cycle .
by integrating promoter sequences explicitly into the regulation model  <cit>   we can overcome some of the limitations of the current approach.
such an integration can incorporate promoter composition as hard or soft constraints to the regulatory network structure, or it can iterate between learning of these two phases  <cit> .
such approaches may be able to achieve better integration of these different sources of data, leading to a more accurate and interpretable model of the regulatory network.

 despite the major role of regulatory networks in orchestrating complex cellular functions, the architecture and function of most networks is largely unknown. several methods were previously suggested for reconstructing the structure of regulatory networks from expression data. most methods learn simplified models based on abstract regulator-target relations rather than a biochemical model of the binding of a transcription factor to a promoter. furthermore, since they rely on the mrna levels of both target and tf, they fail when the tf is not itself regulated at the transcription level. complementary approaches learn a regulation program by integrating gene expression data with additional data sources, such as genome-wide tf binding data or promoter sequence information, into a single coherent model. each of these approaches has some limitations. tf-binding data are still scarce, can suffer from high false positive rates, and even true binding of a tf does not necessarily imply regulation. analyzing promoter sequences is limited by the relatively small number of known cis-regulatory motifs, the difficulty to detect significant novel binding motifs, and the high false positive rate when scanning for motif occurrences in promoters. nevertheless, by requiring consistency between several heterogeneous data types, integrative models are typically more robust and accurate. here, we present a novel integrated approach to analyze transcriptional regulatory programs. we use a gene expression data set to decompose genes into coherent modules of co-regulated genes, based on a biochemically-motivated model. our model uses realistic constraints, suggesting a mechanistic explanation for their expression patterns using combinations of a small number of unknown putative regulators. we employ two novel strategies to increase model robustness. first, we use gene modules – sets of targets controlled by the same biochemical regulatory functions – to learn a global network model which is simpler and biologically meaningful. furthermore, we devise an algorithm that learns a robust model based on an ensemble learning approach. although the biochemical constraints are insufficient to build a fully realistic model with current datasets, they provide a principled way to extract a biologically coherent modular structure for the data. we then use this modular decomposition to search for novel binding motifs in sets of genes defined by the network structure, and test for enrichment for those motifs in all the learned modules. the motif combinations present in the target genes define a second, sequence-based regulation program. in particular, it allows us to explore the regulation of transcription factors. we apply our approach to the transcriptional program of the fission yeast cell cycle, a system which is only partially characterized. in particular, a large portion of the cell cycle, and the transition from g to m are not explained by any known transcriptional regulator in fission yeast. this is in contrast to the regulatory program of the cell cycle of the budding yeast, saccharomyces cerevisiae, where a closed loop of transcriptional regulators is known. previous studies show that one cannot project the regulatory program from budding yeast to fission yeast: the set of regulators is only partially overlapping between these two divergent species, as are their target gene set and binding site sequences. this is consistent with the functional differences between the cell cycle of these two species. several studies measuring genome-wide expression profiles in s. pombe throughout the cell cycle were recently published, but their initial analysis only partly filled up the gaps in understanding. our analysis discovered coherent modules spanning different phases of the cell cycle and covering diverse processes from metabolism to cell division. the resulting learned motif library is composed of regulatory elements, including both known cell-cycle regulatory elements and novel ones. finally, we analyze how specific regulatory topologies underlie distinct dynamics behaviour of gene expression in the fission yeast cell cycle.  we developed an integrated approach to analyze the regulatory program controlling gene expression during a dynamical process from expression and sequence data. we illustrate and test the steps of our approach based on the fission yeast cell cycle dataset. our approach consists of six steps: we derived an input set of transcription rate profiles for cell-cycle regulated genes from a gene expression time series data set spanning cell cycles and sampled datasets from this input set, each containing genes. we learned a regulation model for each of the data sets. each such model identifies a set of modules, co-regulated target gene sets, and describes their transcription rate profiles using a set of learned regulator activity profiles and a set of regulator-to-gene affinity parameters. we generated a unified model from the resulting ensemble of models, capturing the variance and significance of different elements in the individual models. we used the structure of the unified model to guide a search for novel cis-regulatory motifs, resulting in a library of motifs. we identified the motif composition of each promoter by scanning the promoters of all s. pombe genes against our library and identified motifs enriched in core gene modules in our unified model. we contrasted the expression- and sequence-based regulatory relations, highlighting key elements of transcriptional regulation in the s. pombe cell cycle. below we describe each step of our approach. biochemical regulatory networks: an expression-based biochemical model of modular gene regulation we developed a novel algorithm, biochemical regulatory network inference, which takes expression levels for a set of genes, converts them to transcription rates and learns a biochemical model of gene regulation. in our modular regulatory model, inferred regulators are connected to modules of co-regulated genes, and control their dynamic behaviour based on biochemical principles. brni is based on our method to infer biochemical models of single gene regulation. this method infers a set of regulators needed to explain the observed expression levels, and for each such regulator it learns a temporal activity profile rj, representing its activity levels over time. the connections between regulators and target genes follow biochemical rules that describe how the regulator controls the expression of the gene, based on affinity parameters. the model accounts for the biochemical processes of binding and dissociation, thus allowing for different non-linear combinations of regulators, both as activators and as repressors. specifically, for each gene the learned biochemical model includes the set of regulators controlling it, the affinity parameter γji between the gene and each of its regulators, and the gene-specific activity levels of each binding state {αi}. the set of affinity and activity parameters {γji, αi} uniquely defines the target gene transcription rates as a function of the regulator behaviour rj. a multiplicative noise model is used to account for deviations between observed transcription rates and those predicted by the regulation functions. such a detailed biochemical model contains, however, many parameters. given the limited amount of data, the learned model might represent over-fitting of this data. in particular, it can be strongly biased by data points or genes suffering from high measurement errors. to overcome this, we developed here two novel and complementary approaches: modifying the model to include modules of target genes; and using a bootstrap approach, where we learn an ensemble of models from which we derive a high-confidence unified model. first, we modified our model to introduce target gene modules. each module consists of genes with similar expression patterns, the same set of inferred regulators and the same affinity and activity parameters. this greatly reduces the number of parameters in the learned models and lowers the dimensionality of the search space, thus increasing the model's robustness and speeding up the search. we devised an iterative search algorithm that learns this modular model by alternating between refinement of the module regulation model and optimal assignment of genes to modules. second, we devised a bootstrap procedure for learning a model: rather than learning a single model, we learn an ensemble of models each based on a different sampled subset of target genes. the speedup gained by the model's modularity allows us to learn an entire ensemble of models in reasonable time. finally, we integrate the ensemble of models into a unified consensus model. we first map the regulators between different runs based on their time profile similarities. next, we define core gene modules based on sets of genes that frequently co-occur in the same module. in the resulting integrated network each regulatory connection is assigned a confidence score, and each affinity parameter is associated with an error bar. learning regulatory modules in the fission yeast cell cycle we applied our algorithm to expression profiles of cycling genes measured during the fission yeast cell cycle and derived a unified model with regulators controlling core modules. our analysis shows that both the initial structure learning, as well as the bootstrap step improve the coherence of the resulting modules. the modules consisted of to genes with correlated expression profiles and a distinct phase. five modules peak at m/g1; two modules peak at g1; two modules at g1/s, two modules at s/g and four modules at g several of the distinct modules represent coherent biological processes, as reflected by their members' known functions. the modules cover both classical cell cycle processes as well as general growth processes. each of the four regulators, denoted r through r has a distinct cell cycle phase. r peaks at g2/m and is the dominant regulator in the model. r peaks at g r peaks at g1/s and r has a wide peak at g the gene modules in the unified model. for each enriched function, the number of genes in the module having that function is shown in parentheses. *transcription rates, as predicted by our pre-processing. learning a motif-based model of gene regulation a complementary view of the transcriptional program is driven by the promoter sequences of the target genes. assuming a transcription factor binds a specific motif, the full motif set in the promoters of the target genes induces a connectivity model between tfs and target genes. the structure of our expression based learned network therefore provides two key clues to finding cis-regulatory motifs. first, we can search for motifs enriched in a module, as the co-expression of module genes may indicate a shared regulatory mechanism. second, we can also search for motifs shared by the targets of the same regulator across modules. if that regulator corresponds to a dna binding factor, or even to an indirect regulatory activity, we expect its targets to share a regulatory element. importantly, these targets can be distributed across multiple modules with distinct expression patterns due to combinatorial regulation. thus, such related motifs may not be identified by the former, module-based approach. notably, a comparative analysis of different partial models shows that different components of the regulatory model improve the resulting modules in terms of their correspondence with known binding motifs. this suggests that the same model can also improve the discovery of novel motifs. we used an automated approach, to systematically learn a non-redundant library of motifs in this manner. the resulting library consists of motifs, of which were derived from modules and from regulators. these motifs match the known cell cycle regulatory elements mcb, ace fkh, pcb and the histone accct box, as well as include several novel motifs. we next scanned the whole genome against this library and tested each motif for enrichment in the promoters of gene module members. we found significant motif-module pairs. seven of the modules are significantly enriched for at least one motif. notably, we found no enrichment when we performed a similar scan of s. pombe modules with five additional known cell-cycle motifs from s. cerevisiae that do not have a known counterpart in s. pombe. this is in contrast to the above mentioned elements mcb, fkh and ace which are similar or identical to their s. cerevisiae counterparts. cis-regulation of expression modules in the fission yeast cell cycle the motif analysis resulted in several interesting insights on the regulatory mechanisms controlling each module some of them recapitulate known facts, indicating the validity of our results, while others are novel, and suggest new testable hypotheses. for example, the histone module consists of all seven histone genes in the input set. the transcription rates of the module's genes are predicted to peak at m/g while their measured expression levels peak at s phase. the genes in this module are associated with only four promoters, since eight of the nine s. pombe histone genes are arranged in divergently-transcribed pairs. we found that all histone promoters contain a previously described histone specific motif. recent studies show that this site is bound and activated by the ams transcription factor. our analysis also shows that ams itself is a member of module and has an mcb motif in its promoter, and another novel motif, a.gcg.c. interestingly, two of the histone promoters contain an mcb site as well, and three of them contain the a.gcg.c motif. this suggests a possible feed forward loop involving the mbf complex, ams and the histone genes, as we discuss below. the regulation of histones by mbf may be a conserved feature of the yeast cell cycle transcriptional network. in s. cerevisiae the promoters of histone genes contain mostly swi swi and mbp motifs, raising the possibility of their activation by mbf and/or sbf. finally, we discovered a third novel motif that appears in three of the four promoters. this motif might serve as the binding site for the repressor hip further experiments are needed to validate the proposed regulatory role of mbf and the novel sites in s. pombe histone genes. the cell division module consists of genes, encoding mostly cell wall proteins and glycoproteins whose expression peaks at m/g the module genes' promoters are enriched for the ace motif, the fkh1/ motif, and for two novel motifs. regulation of the module by ace is consistent with the module's function, the down-regulation of nine module genes in an ace deletion strain, and the phase of ace transcription which slightly precedes that of the module's genes, consistent with a positive regulatory role. further experiments are needed to explore the additional role of fkh and the factors binding the novel motifs in modulating the expression pattern of the module's genes. the two cell wall biogenesis and cell division modules include the ace and fkh genes. the modules' genes are associated with a putative pcb motif and a fkh motif. although the phase of these modules is similar to that of module their genes do not contain any ace sites, supporting their separation to distinct modules. notably, the fkh sites in module are concentrated further upstream of the gene start than in module, supporting their further separation. the hypothesis that fkh and sep are joint regulators in these modules is supported by the effect of sep deletion on several of the modules' genes and by the similarity of the peak phase of rate of transcription of the modules' genes and fkh. these results are consistent with a recent study demonstrating that in three promoters containing both sites, both fkh and sep bind and play opposing roles in repression and activation of their joint targets, respectively. notably, of the modules' genes have only fkh sites in their promoters, suggesting that fkh can regulate expression in promoters that lack pcb. since only a repressive role has been demonstrated for fkh in s. pombe, these promoters may be regulated solely by de-repression or by a novel unknown mechanism. the translation module consists of genes, mostly related to translation regulation and ribosome biogenesis that peak in early g phase, the major growth phase for s. pombe. the module contains two prominent yet unknown motifs – agagcg and tttggttcg. each of these motifs appears in approximately 5% of all s. pombe genes, and is enriched in genes that perform metabolic functions. since the expression of genes encoding the translation and ribosome biogenesis machineries is also modulated in response to environmental stresses, the discovered motifs could be responsible for their regulation either under stress or in normal cell cycle conditions. in the latter case, they could provide a novel mechanistic explanation for cell cycle regulation during the g phase. overall, the analysis led to several testable hypotheses on the fission yeast cell cycle: mbf and ams form a feed-forward loop to control histone gene expression; histone gene expression is controlled through the novel motif gattgactga, which may be a hir target site; fkh may control the cell division module; fkh may control distinct modules involved in cell wall biogenesis and cell division, both in combination with sep and alone, possibly solely though a de-repression mechanism; and growth related functions, such as ribosome biogenesis, are under cell cycle control through two novel cis-elements, agagcg and tttggttcg. the power and limitation of an expression based regulatory model we next compared the expression- and cis-regulatory networks we learned. in particular, we examined whether learned regulator profiles correspond to specific transcription factors. if this is the case, we expect each regulator to be mapped to a specific regulatory element from our library. when considering each of the regulators, however, we do not find such matching. for example, the regulator r peaks at g2/m and captures a "centralized" activity around the narrow time interval covering m/g g and g1/s, and is thus associated with the regulatory elements and activity of several transcription factors active during those phases. similarly, r peaks at m/g and is connected to the many histone sites through module genes, but also to ace motif. its combination with r explains the delayed activity of this module's members. overall, we find that the learning algorithm avoids the need for additional regulators to explain the expression of different modules in those phases by using either r alone or in different combinations with the other learned regulators, thus achieving more delayed or early expression peaks. although the individual learned regulators do not correspond to specific transcription factors, the network induced by their combinations is meaningful. first, as discussed above, the network consists of modules with coherent biological functions. second, the network topology allowed us to discover most known cell cycle binding sites and several novel ones. third, the modules display distinct binding site compositions. in particular, in several cases genes with very similar expression profiles were partitioned into separate modules. our analysis showed that each of these modules was characterized by a distinct promoter configuration, supporting the partition. this strength of the regulatory model is due to its non-linear nature. future work can incorporate motif finding and scoring as an integral part of the learning algorithm, thus using cis-regulatory distinctions to identify concrete regulators. reconstructing a network of transcriptional regulation to further associate the inferred regulatory networks with concrete regulatory functions, we examined whether the relation between the timing of expression of cell-cycle related transcription factors and the timing of expression of gene modules that are associated with their binding sites. naively, we would expect to find an activator's binding site in promoters of genes which are induced in a subsequent phase. conversely, we expect to find the binding sites for repressors in promoters of genes that are repressed in the subsequent phase. this simple prediction may be distorted by a delay between the regulator's gene transcription and the binding of its protein to target promoters. such a delay could result from slowed dynamics or active regulation in any of the intermediate steps between transcription and binding. we examined each of the four cell-cycle transcription factors which have both a cyclic transcriptional profile and a known binding motif: ace cdc and rep, fkh and ams. we found that each is associated with a distinct mechanism resulting in different dynamic behaviour of its targets, together forming an integrated network with a cyclic behaviour. first, ace2's expression slightly precedes that of its targets in module supporting a simple activatory model. other targets exhibit a longer delay, but their regulation mechanism might be different since they do not respond to an ace deletion. second, mbf and ams target genes display a narrow spectrum of peak times, from in-phase with their respective regulator up to a slight delay from that regulator. these spectra may be achieved by interactions of these transcription factors with other regulators. for example, genes whose promoters harbour both ams sites and mbf sites exhibit a delayed expression phase compared to the effect of each one of these regulators alone. upon closer inspection, we find that ams is in fact part of a feed-forward activatory chain: it contains an mbf site in its promoter, its expression is slightly preceded by cdc and rep and it precedes the histones' expression profiles. finally, there is no delay between the peak expression of fkh and the genes in its target modules. this may be explained by its repressive role and a delay between its transcription and its binding to target promoters, as recently reported in. this work showed that while sep is likely an activator and binds concurrently with the expression of its target genes, fkh is likely a repressor and binds when the expression of the same target genes is low. since fkh itself is regulated in this fashion it might close a negative feedback loop, suggesting a mechanism for regulating the g2/m part of the cell cycle: fkh is transcribed during m/g and following translation and localization to the nucleus binds to these promoters for the length of g inhibiting their activation by sep as it degrades gradually during g by the end of this phase it no longer prevents sep binding and activation during m/g. in conclusion, we propose the following model for the transcriptional regulatory circuit governing the cell cycle, as it emerges from our integrated analysis. as explained above, fkh is the only component that could by itself close a loop of transcriptional regulation around the cell cycle. along with the sep1/mbx pbf complex, it regulates several other regulators, including the mbf subunit rep ace and ams finally, the motif ga.gcg.c, which is similar to mcb and could be an alternative variant of it, plays a dominant role both in cell cycle regulated genes as well as in the promoters of some of the regulators themselves. thus, our integrated analysis discovered novel players, interactions and dynamics in the s. pombe cell cycle, in particular suggesting how combinatorial regulation can lead to a full cyclic circuit of transcriptional regulation.  we have presented an integrated approach for the analysis of transcriptional programs. our analysis comprised of two components: a biochemically motivated model of gene regulation based on the expression data, inducing a division to expression modules; and a binding motif analysis based on the division to those modules and regulatory relations. we have applied our approach to the analysis of the fission yeast cell cycle program. this approach is generally applicable to expression profiles measured along time courses. the regulation program we learned allowed us to derive important biological insights. first, it induced an informative division to coherent regulatory modules. in particular, it was able to separate between modules with similar expression peak phases but with clearly distinct binding site compositions, based on more subtle differences in expression profiles. this division resulted in identification of several novel binding sites in the second part of the analysis, allowing us to detect the structural features underlying distinct dynamic behaviour. our analysis suggests several novel potential mechanisms for differential regulation of genes along the cell cycle. these include a feed-forward chain of mbf with ams leading to delayed expression of histone genes, a putative binding site for the histone gene repressor hip combinatorial regulation of specific cell division genes by ace and fkh, putative sites acting during the g phase to regulate cell growth modules, and a negative feedback loop involving fkh and sep that may control expression dynamics in the g2/m phase of the fission yeast cell cycle. despite these successes, our analysis also showed certain limitations of learning biochemically motivated models from expression data alone. in particular, the learned regulators cannot be interpreted as transcription factors, but rather reflect more abstract regulatory functions, potentially carried out by multiple transcription factors. several factors may contribute to this result, including the assumption of our regulation model that factor binding indicates direct activity, and the score used by the learning algorithm which favours the most parsimonious model that can explain the data, resulting in regulation schemes with a small number of "abstract" regulators. thus, the model can fail to correctly separate between regulators when their activities are highly correlated, or when their peak activities are concentrated in a narrow part of the cell cycle. by integrating promoter sequences explicitly into the regulation model we can overcome some of the limitations of the current approach. such an integration can incorporate promoter composition as hard or soft constraints to the regulatory network structure, or it can iterate between learning of these two phases. such approaches may be able to achieve better integration of these different sources of data, leading to a more accurate and interpretable model of the regulatory network. 
we discovered coherent modules, covering diverse processes from cell division to metabolism and associated them with learned regulatory elements, including both known cell-cycle regulatory elements and novel ones, some of which are associated with g modules. it describes the expression profiles of gene modules consisting of hundreds of genes using a small number of regulators and affinity parameters. in cases where physical protein-dna data are lacking, such methods are essential for the analysis of the underlying regulatory program. here, we present a novel approach for the analysis of modular regulatory programs. our method – biochemical regulatory network inference – is based on an algorithm that learns from expression data a biochemically-motivated regulatory program. we then use the topology of the learned regulatory program to guide the discovery of a library of cis-regulatory motifs, and determined the motif compositions associated with each module. we test our method on the cell cycle regulatory program of the fission yeast. our approach provides a biologically-driven, principled way for deconstructing a set of genes into meaningful transcriptional modules and identifying their associated cis-regulatory programs. previous methods allow dissecting regulatory modules from genomics data, such as expression profiles, protein-dna binding, and promoter sequences. our analysis sheds light on the architecture and function of the regulatory network controlling the fission yeast cell cycle, and a similar approach can be applied to the regulatory underpinnings of other modular transcriptional responses. we integrate the regulatory relations from the expression- and motif-based models into a single network, highlighting specific topologies that result in distinct dynamics of gene expression in the fission yeast cell cycle. transcriptional responses often consist of regulatory modules – sets of genes with a shared expression pattern that are controlled by the same regulatory mechanisms.
 transcriptional responses often consist of regulatory modules – sets of genes with a shared expression pattern that are controlled by the same regulatory mechanisms. previous methods allow dissecting regulatory modules from genomics data, such as expression profiles, protein-dna binding, and promoter sequences. in cases where physical protein-dna data are lacking, such methods are essential for the analysis of the underlying regulatory program.  here, we present a novel approach for the analysis of modular regulatory programs. our method – biochemical regulatory network inference – is based on an algorithm that learns from expression data a biochemically-motivated regulatory program. it describes the expression profiles of gene modules consisting of hundreds of genes using a small number of regulators and affinity parameters. we developed an ensemble learning algorithm that ensures the robustness of the learned model. we then use the topology of the learned regulatory program to guide the discovery of a library of cis-regulatory motifs, and determined the motif compositions associated with each module. we test our method on the cell cycle regulatory program of the fission yeast. we discovered coherent modules, covering diverse processes from cell division to metabolism and associated them with learned regulatory elements, including both known cell-cycle regulatory elements and novel ones, some of which are associated with g modules. we integrate the regulatory relations from the expression- and motif-based models into a single network, highlighting specific topologies that result in distinct dynamics of gene expression in the fission yeast cell cycle.  our approach provides a biologically-driven, principled way for deconstructing a set of genes into meaningful transcriptional modules and identifying their associated cis-regulatory programs. our analysis sheds light on the architecture and function of the regulatory network controlling the fission yeast cell cycle, and a similar approach can be applied to the regulatory underpinnings of other modular transcriptional responses. 