Identifying Responsive Modules by Mathematical Programming: An Application to Budding Yeast Cell Cycle

High-throughput biological data offer an unprecedented opportunity to fully characterize biological processes. However, how to extract meaningful biological information from these datasets is a significant challenge. Recently, pathway-based analysis has gained much progress in identifying biomarkers for some phenotypes. Nevertheless, these so-called pathway-based methods are mainly individual-gene-based or molecule-complex-based analyses. In this paper, we developed a novel module-based method to reveal causal or dependent relations between network modules and biological phenotypes by integrating both gene expression data and protein-protein interaction network. Specifically, we first formulated the identification problem of the responsive modules underlying biological phenotypes as a mathematical programming model by exploiting phenotype difference, which can also be viewed as a multi-classification problem. Then, we applied it to study cell-cycle process of budding yeast from microarray data based on our biological experiments, and identified important phenotype- and transition-based responsive modules for different stages of cell-cycle process. The resulting responsive modules provide new insight into the regulation mechanisms of cell-cycle process from a network viewpoint. Moreover, the identification of transition modules provides a new way to study dynamical processes at a functional module level. In particular, we found that the dysfunction of a well-known module and two new modules may directly result in cell cycle arresting at S phase. In addition to our biological experiments, the identified responsive modules were also validated by two independent datasets on budding yeast cell cycle.


Introduction
High-throughput biological technologies allow the simultaneous measurement of the expression of thousands of genes or proteins, which offers an unprecedented opportunity to fully characterize biological processes [1]. Nevertheless, extracting a comprehensive overview from the huge amount of information is a significant challenge [2]. During the last decade, high-throughput analysis mainly focused on dissecting the individual genes responsible for specific phenotypes, and some biomarkers for human diseases have successfully been identified through analysis of genome-wide expression profiles [3,4,5,6]. However, it is well accepted that genes or proteins within a cell do not function alone, and they interact with each other to form networks or pathways so as to carry out biological functions [7,8,9,10,11]. Therefore, it is crucial to reveal the essential biological mechanisms from a system perspective, and pathway-based analysis is becoming a popular method of analyzing high-throughput data. Several approaches have been proposed to score known pathways by the coherency of expression changes among their member genes [12,13,14,15,16]. Generally, a known pathway is drawn from sources such as the Gene Ontology (GO) [17] and KEGG [18] databases. In contrast to the documented pathways, however, it is a more difficult task to identify novel sub-networks or pathways responsive to phenotypes from biomolecular networks. Recently, gene-set-based or pathway-based analysis has been extended to perform classification of microarray data by exploiting the phenotype difference [19,20,21] and a number of approaches have been demonstrated for not scoring known pathways but extracting relevant sub-networks based on coherent expression patterns of the corresponding genes in the protein-protein interaction (PPI) networks [22,23,24,25]. However, these approaches are mainly molecule-complex-based [23,25] or individual-gene-based analysis, such as [19], in which the authors indicated that candidate sub-networks are seeded with a single protein and iteratively expanded to add other proteins into the sub-networks. Note that, in biology, a complex is a cluster of genes or proteins so closely related that they intergrade [26], while a pathway is a group of genes or proteins that are interacted (or related) [1].
In contrast to existing works, in this paper we first developed a novel module-based method to identify phenotype-based responsive modules by integrating gene expression data and high-quality PPI networks, which are able to reveal the potential causal or dependent relations between network modules and biological phenotypes. Specifically, we formulated the problem to identify phenotype-based responsive modules as a multi-classification problem of modules on phenotypes by a mathematical programming model, rather than identifying individual genes and gene sets, where the modules are resulted from the topological structure of the PPI networks. Then, the proposed method was applied to the cell-cycle process of budding yeast Saccharomyces cerevisiae (S. cerevisiae) to identify phenotype-based responsive modules and further examine their regulation roles in the phase transition process based on the microarray data of our biological experiments.
The cell cycle process, by which one cell grows and divides into two daughter cells, is a vital biological process, the regulation of which is highly conserved among the eukaryotes [27,28]. Although extensive studies have been conducted on the cell cycle process [29,30], in particular by modeling the budding yeast [31,32,33], many detail regulations still remain unclear from network viewpoint. Generally, there are mainly two ways to perturb a biological system, that is, external stimulus, such as exposure to DNA-damaging agents, methyl methanesulfonate (MMS) [34,35,36], and internal stimulus, such as knocking out some genes [34,37]. To functionally relate network modules to different phenotypes, we designed biological experiments by combining these two types of stimuli so as to create various phenotypes for the cell cycle process. In our biological experiments, when adding MMS at 15 min (G1 phase) or knocking out elg1 at the beginning of the cell cycle process, the cell cycle continues, nevertheless, when adding MMS at 15 min (G1 phase) to elg1 mutant strains, the cell cycle arrests at S phase.
By the proposed module-based method with exploiting highthroughput data of various phenotypes resulted from our biological experiments, we identified phenotype-based responsive modules and dynamical transition modules of budding yeast cell cycle. A responsive module means that the module potentially plays an important role in some phenotypes, while a transition module indicates that the module is potentially responsible for the transition from one phenotype to another from a dynamical perspective. After the identification of phenotype-based and transition-based responsive modules for the cell cycle phases and their transitions, the identified responsive modules were also validated by classifying the cell cycle phases of two independent datasets on budding yeast cell cycle.
Based on the computational and experimental results, the main contributions of this work can be summarized as follows. First, our method is able to identify phenotype-based and transition-based responsive network modules, drawn from the topological structure of a biomolecular network, instead of dissecting complexes or individual gene-based pathways. Second, the identified modules lead to new insights into the cell cycle process and provide biological interpretations on the functional roles of network modules. In particular, according to the validation on the other two independent datasets and also the functional validation, the phenotype-based responsive modules are potentially signatures or network biomarkers of the cell cycle process. We revealed the reason of arresting cell cycle at S phase under both internal and external stimuli from a network viewpoint, that is, we identified one well-known module ''CLN1 CLN2 CLN3 BUD2'' involved in cell cycle process and two new modules ''PKC1 TOS2 KEL2 PPZ2 SKN7'' and ''SSD1 LST8 TOR1 KOG1 TOR2'', whose dysfunction results in cell cycle arresting. Third, our method is also a new theoretical model for multi-classification analysis, which was used to study the cell cycle process by relating network modules to different phenotypes and even phase transitions from a dynamical perspective. In addition, we showed that the identified responsive modules can also be directly used to annotate functions of genes or proteins.

Microarray Experiment
The biological experiment was performed on S. cerevisiae. SH521 strain was used as the wild-type source (WT). Since elg1 involves in DNA replication and genome integrity, we knocked out elg1 gene of SH521 using PCR based one-step gene replacement [38,39]. WT and elg1 mutant were cultured in rich YPD medium (1% yeast extract, 2% peptone, and 2% glucose) at 30uC as described [40]. Cells were synchronized to early G1 phase by adding 20 ng/ml alpha factor (US Biology) as described [41], and exposed to 0.01% DNA-damage reagent methyl methanesulfate (MMS, Sigma) after being released into pre-warmed YPD medium. Cells at the indicated time points shown in Figure 1 were harvested for flow cytometry analysis [42] and total RNA isolation [43]. RNA samples were subjected to gene-microarray analysis with Affymetrix GeneChipH Yeast Genome S98 arrays and Scanner GeneChipH 3000. Two biological replicates have done for each condition. The microarray data are available at http://www. aporc.org/doc/wiki/CellCycle.

Data Preprocessing
The microarray data of our experiment contains 5714 genes and 20 samples. The CEL files were preprocessed by RMA algorithm in R bioconductor package (www.bioconductor.org). Probe sets were mapped to NCBI Entrez gene symbols using the Affymetrix annotation. If there are multiple probe sets corresponding to the same gene, we average them individually. First, because of the fact that many genes of microarray data were irrelevant or redundant [44], we applied ANOVA method to identify genes that were differentially expressed on one or more of the ten groups relative to the others (p-value ,0.05). As a result, 4443 genes from microarray data were finally retained for further analysis. Second, we downloaded a curated PPI network of S. cerevisiae from MIPS [45], and we only considered those PPIs, of which both interacted proteins are contained in our microarray data. Figure 2 illustrates the schematic flowchart of our method. On the one hand, given the microarray data with m genes and n samples, gene expression values g ij were normalized to z-transformed scores z ij , which for each gene i has mean m~0 and deviation s~1 over all samples j. On the other hand, we decomposed the PPI network into l modules by the Markov Clustering (MCL) algorithm [46]. To integrate the gene microarray data and PPI modules, we mapped the normalized expression values of each gene on its corresponding protein in the modules, and then we defined the module responsive value as a combined z-score [19] for k~1, Á Á Á , l and j~1, Á Á Á , n,

Identifying Responsive Modules by a Mathematical Programming Model
where DN M k D is the number of proteins in the module M k . In this way, we obtained the responsive matrix with element M kj representing the responsive value of module M k in the case of sample s j . To identify responsive modules under different phenotypes or conditions, we defined r kj~Mkj : x k , where x k is 1 if module M k is selected, otherwise 0. Therefore, nonzero r kj means that module M k is selected, while we do not select module M k if r kj is zero. Assume that there are K phenotypes among n samples, to relate n samples to K phenotypes, we aimed to classify the n samples into K clusters. Meanwhile, we intended to identify the minimum number of responsive modules in this multi-classification process. In this study, we exploited the idea of K-means clustering to formulate such a multi-classification problem as a mathematical programming model, which aims to minimize the within-cluster error sum of squares, that is, where m q is the mean of sample points s j in the sample cluster S q . Based on this framework, we calculated the values of P K q~1 P s j [Sq s j {m q 2 for all possible classifications, and denoted these values as T 1 ,T 2 , Á Á Á ,T a , respectively (Note that a in T a corresponds to all the classifications). On the other hand, for the targeted classification, the value is written as have successfully classified the samples, where superscript t means the transpose of a vector or a matrix. By expanding T Ã {T r , which is the function of M kj and x k , we can further express the conditions as (see Supporting Information S1 for more details), where Cis a matrix function of M kj with element C(r,k) representing the k-th module's contribution to the r-th condition. From the above analysis, we formulated the module-identification problem as the following binary integer programming:

Algorithm of Solving Binary Integer Programming Problem
Clearly, the formulated integer programming problem is NPhard. Therefore, we have to adopt other techniques to obtain an approximate solution due to the computational complexity of this problem.
In the integer programming problem, we aimed to identify the number of modules as small as possible but with high accuracy of the classification. Therefore, we defined an index to evaluate the effect of classification, that is, the average power of classification of modules. For the purpose, an approximate algorithm is designed as follows: Step 1). Rank the modules according to their scores, max k C( : ,k), increasingly, which evaluate the power of classification of the k-th module individually, where C( : ,k) means the kth column of matrix C.
Step 2). Add the module one by one to compute the average power of classification of modules, where I is the set of chosen modules and card(I) is the cardinality of set I, according to the ranking in Step 1). When the minimum value of max P k[I C( : ,k)=card(I) is achieved, we select the ahead card(I) number of modules in the ranking in Step 1) as the responsive modules.

Sample Clustering
The microarray data of our biological experiment totally contains 5714 genes and 20 samples. The first batch of 10 samples are composed of 5 control samples and 5 elg1 mutant samples (see Figure 1), and the other batch of 10 samples are biological replicate of the first batch. There are totally ten phenotypes in our experiment and we will identify responsive modules to these phenotypes as well as their transitions. We extracted 4443 genes with differential information underlying these phenotypes by ANOVA (see Methods). To group these samples from a global respective, we implemented the hierarchical clustering on these genes and the results are shown in Supporting Information S2. We found that the 20 samples are almost successfully classified into ten classes of phenotypes, that is, the biological replicates and three time points of cell cycle phases are clustered together. The various phenotypes of our experiment are correlated with the genomewide gene expression profiles. Therefore, we focus our subsequent analyses on these 4443 genes for identifying responsive and transition modules corresponding to these phenotypes. First, gene expression values were normalized over all samples, and PPI network was decomposed into modules by clustering algorithm. Then a responsive value can be defined for each module by combining the z-scores of genes in the corresponding module, i.e., the responsive matrix is formed. To select responsive modules for different phenotypes, we defined a variable x k representing whether a module is selected, and further formulated this problem by an integer programming model. Finally, we identified the responsive modules by solving the integer programming problem to classify the phenotypes. doi:10.1371/journal.pone.0041854.g002

Responsive Modules of Cell Cycle Phases for Each Group of Conditions
For our experiments, we categorized the 20 samples into four groups, i.e., control group, MMS group, elg1 mutant group, and elg1 mutant MMS group. By implementing our method, we identified 14, 17, 8 and 23 responsive modules for the control group, MMS group, elg1 mutant group and elg1 mutant MMS group, respectively (see Supporting Information S2). In the control group, we arranged the responsive modules on the corresponding cell cycle phases, at which the maximum responsive values of the modules are achieved. The results of 14 responsive modules of three cell cycle phases are shown in Figure 3. The three cell cycle phases can be discriminated by these responsive modules according to our method. In our integer programming model, they are the minimal number of modules with the maximum average discrimination power for distinguishing the different phenotypes. The discrimination power underlying these modules indicates that they are subnetwork biomarkers of reflecting the progression status during the cell cycle process.
In Figure 3, for instance, as a network-based biomarker for S phase, in which the DNA is synthesized and chromosomes replicated, the identified responsive module ''POL2 DPB11 DPB2 SLD2 OYE2'' contains the genes performing these kinds of functions, which are consistent with the biological functions of S phase. Specifically, POL2 is a catalytic subunit of DNA polymerase (II) epsilon, a chromosomal DNA replication polymerase that exhibits processivity and proofreading exonuclease activity, and also involved in DNA synthesis during DNA repair [47]. DPB11 is a replication initiation protein that loads DNA pol epsilon onto prereplication complexes at origins and a checkpoint sensor recruited to stalled replication forks by the checkpoint clamp complex where it activates Mec1p [48]. DPB2 is the second largest subunit of DNA polymerase (II) epsilon, and is required for normal yeast chromosomal replication, whose expression peaks at the G1/S phase boundary [49]. SLD2 is a protein required for DNA replication, and is phosphorylated at S phase by S-phase cyclin-dependent kinases (CDKs) [50]. As a member of the module, it implicates that OYE2 may be also involved in the S phase. Moreover, the identified module ''NUF2 NNF2 SMC4 BRE1 YEL043W'' possesses the consistent function in G2/M phase, in which the chromosomes are separated and the cell is divided into two daughters. NUF2 is involved in chromosome segregation, spindle checkpoint activity and kinetochore clustering [51]. NNF2 plays a role in chromosome segregation [52]. SMC4 reorganizes chromosomes during cell division [53]. BRE1 is found to be required for double-strand break repair (DSBR), transcription, silencing, and checkpoint control [54].
Furthermore, as an illustration for other groups, the module ''SIF2 PIB2 HOS4'' in elg1 mutant MMS group is involved in the negative regulation of meiosis [55], which is consistent with the phenotype of elg1 mutant MMS group. In this module, SIF2 is a WD40 repeat-containing subunit of the SET3C histone deacetylase complex, which represses early/middle sporulation genes and antagonizes telomeric silencing [56], PIB2 is a protein binding phosphatidylinositol 3-phosphate, involved in telomere-proximal repression of gene expression [57], and HOS4 is a subunit of the SET3 complex, which is a meiotic-specific repressor of sporulation specific genes that contains deacetylase activity [56].
From the above analyses, we concluded that the identified responsive modules indeed characterize the corresponding phenotypes, which confirms the effectivenss of our method. Each module can be regarded as a network-based biomarker for the cell cycle process, which is not individual-gene-based or moleculecomplex-based, but rather a functional-module-based signature decomposed from the PPI network. This feature is quite different from conventional pathway-based analysis, which is still based on individual genes, and then extended to subnetworks. To some extent, the identified discriminative phenotype-based responsive modules reflect the endogenous dynamics of the cell cycle, which also indicate that the different responses and similar drivers correspond to various phenotypes in the progression of development phases.

Transition Modules between Different Phases of Cell Cycle
The transition modules refer to those modules that are potentially responsible for the dynamical transition of phases in the cell-cycle process. We identified these modules by our method based on the classification of the dynamics and these phenotypes. Compared to the control condition, we identified these transition modules from G1 phase to S phase and from S phase to G2/M phase under internal stimulus, external stimulus and both, respectively. The procedure of identifying the transition modules from G1 phase to S phase under external stimulus is performed by classifying the samples of G1 phase and S phase under external stimulus and the control condition. The similar procedures were also implemented for other phase transitions in other groups. The identified transition modules between these phases are shown in Figure 4. The significant differences between these modules in these phases indicate that they are biological signatures and changeover markers for the cell-cycle phase transition.
In the module ''PKC1 TOS2 KEL2 PPZ2 SKN7'', PKC1 is a protein serine/threonine kinase essential for cell wall remodeling during growth [58], TOS2 is a protein involved in localization of CDC24p to the site of bud growth [59], KEL2 is a protein that functions in a complex with KEL1p to negatively regulate mitotic exit [60], PPZ2 is a serine/threonine protein phosphatase Z, and is involved in regulation of potassium transport, which affects cell cycle progression [61]. The analysis on the functional module of marking the transition concludes that the cooperation of these genes in the subnetwork plays an important role for the dynamical transition from S phase to G2/M phase.
Furthermore, identification of the transition modules provides more evidence of the differences of cell-cycle-phase phenotypes and indicates the causal units for the cell development, especially in the phase-transition points. In our experiment, we paid a special attention to the identified transition modules shown in Figure 4C, which correspond to the transition from S phase (30 min) to S phase (45 min). With the aim of identifying the functional modules of critical transition and development of these phases, our experiment generated various phenotypes by stimuli. When we implemented the internal stimulus of gene mutant and external stimulus of DNA damage, the cell cycle would arrest at the S phase. With this in mind, the identified modules potentially play essential roles in the process of cell cycle arresting at S phase caused by the double stimuli. In the modules, ''CLN1 CLN2 CLN3 BUD2'' and ''SSD1 LST8 TOR1 KOG1 TOR2'', CLN1, CLN2 and CLN3 are well-known cyclins involved in regulation of the cell cycle [62], and BUD2 is a GTPase activating factor for RSR1p/ BUD1p required for both axial and bipolar budding patterns [63]. Moreover, TOR1 and TOR2 are two PIK-related protein kinases and constitute a complex, which is involved in meiosis, SSD1 is a translational repressor and cooperates with Tor complex to maintain cellular integrity, and LST8 and KOG1 are known to play roles in TOR signaling pathway [64].
From the above analysis of these transition modules (Table 1), we concluded that it is the dysfunctions of these modules that possibly contribute to cell cycle arresting at S phase responsive to gene mutant of elg1and DNA damage of MMS. The details of the transition modules under different stimuli are shown in Supporting Information S1 and S2.

Functional Analysis of Responsive Modules
We detected various responsive modules for the multiple phenotypes of cell cycles individually. A part of these functional distinct modules are identified among a series of processes contributing to cell cycle, development and DNA integrity in budding yeast. The enriched functions of these identified modules include DNA replication, DNA repair, checkpoint signaling, chromosome segregation and cell division (see Table 2). The results of GO functional enrichment analysis are shown in Supporting Information S2.
For instance, as a responsive module in both MMS group and elg1 mutant MMS group, module ''MSH5 SWE1 HSL7 AIM10'' is involved in mitotic cell cycle process [55], where MSH5 is a protein of the MUTS family which forms a dimer with MSH4p that facilitates crossovers between homologs during meiosis [65]. SWE1 is a protein kinase that regulates the G2/M transition by inhibition of CDC28p kinase activity [66]. And HSL7 is a protein arginine Nmethyltransferase that exhibits septin and HSL1p-dependent bud neck localization as well as periodic HSL1p-dependent phosphor-ylation. It is required along with HSL1p for bud neck recruitment, phosphorylation, and degradation of SWE1p [67,68]. AIM10, whose biological process is still unclear (http://www.yeastgenome. org/), is a protein with similarity to tRNA synthetases [69]. From the functional analysis of this module, we concluded that AIM10 is related to the cell cycle process.
The functional analysis of these modules indicates that they are the biomarkers for the phenotypes. Specially, the identified transition modules clearly offer a potential clue to explain why the cell cycle arrests at S phase. It is the dysfunction of the modules ''PKC1 TOS2 KEL2 PPZ2 SKN7'', ''CLN1 CLN2 CLN3 BUD2'' and ''SSD1 LST8 TOR1 KOG1 TOR2'' that result in cell cycle arresting. On the other hand, because the functions of components of a module are believed to be related [2], we can attribute some functions of components in one module to those not well known genes, i.e., annotate the functions of those genes. Based on this idea, we concluded that the component AIM10 of the module ''MSH5 SWE1 HSL7 AIM10'' may be related with mitotic cell cycle, although its biological process is still not known, and the component OYE2 of the module ''POL2 DPB11 DPB2 SLD2 OYE2'' may be involved in one or more of the processes of DNA replication, DNA repair, and mismatch repair. In addition, we found that the identified modules contain dynamical complexes, such as the module ''CLN1 CLN2 CLN3 BUD2'', which is consistent with the idea of [23] to some extent, however, the results of our method are more specific and extended in some sense.

Responsive Modules are Informative of Classifying Cell Cycle Phases
To validate that the identified responsive modules of various cell-cycle phenotypes are informative and general, we conducted the classification of cell cycle phases by these modules based on two independent datasets. Specifically, we tested the samples of the first cell cycle in the first dataset GSE3635 [29]. And we chose the samples of the first cell cycle in WildType_rep1 in the second dataset GSE8799 [30]. In addition, we also tested the samples of the second cell cycle. The results are shown in Figures 5 and 6, respectively, and we successfully classified the three cell-cycle phases of the two independent datasets. Therefore, we concluded that these responsive modules are capable of correctly identifying their expression features in various cell-cycle phenotypes, and are important clue of marking cell development stages. The validation not only provides evidence on the effectiveness and advantage of our method, but also verifies that the identified modules functionally correspond to the phenotypes of the cell cycle process.

Discussion
In this paper, by integrating high-throughput gene expression data and PPI network, we developed a novel method to identify responsive modules and dynamical transition modules for various phenotypes and phase transitions under internal and external stimulus of yeast cell cycle process. In this work, to alleviate the problem of noisy data of protein-protein interactions, we chose a widely-used gold standard [70,71] PPI database for S. cerevisiae, i.e., MIPS [45] as our source network for analysis. However, the noise inside may also have influence on the results. Additionally, for yeast PPI, we have checked other databases, such as IntAct [72] and BioGRID [73]. We found that, compared to MIPS, although these two databases contain more interactions, the overlap between MIPS and IntAct (or BioGRID) is relatively small. Therefore, we chose the high-quality PPIs documented in MIPS as our reference network. Our method is network-based or functional module-based analysis, different from the existing works, which are mainly individual-gene-based or molecule-complex-based study [19,23,25]. In addition, although we adopted the phenotype difference to identify responsive modules, our method is quite different from those exploited the similar tasks [19,20,21]. For instance, in [21], the authors obtained gene sets by classifying biological functions of genes and then identified the gene sets according to their significant difference between two phenotypes, while our method focused on functional modules and formulated the module identification as an integer programming problem.
Our method is based on the ideas of K-means clustering and exploits the supervised clustering to identify responsive and transition modules. In other words, our work focuses on identifying the functional modules (or subnetworks from the network perspective), rather than identifying genes (or gene sets) with similar expression values or patterns under multi-conditions (e.g., biclustering methods [16]). Therefore, the biclustering method and our method are quite different approaches which are designed from two different perspectives.
Based on the experiment, we identified responsive modules for the groups of conditions and transition modules for the dynamical phase transitions in yeast cell-cycle process. As biological signatures or network biomarkers for the cell cycle, functional analyses show that some identified modules are involved in a series of processes such as DNA replication, DNA repair, checkpoint signaling, chromosome segregation, and cell division, which contribute to cell cycle and DNA integrity in yeast. The transition modules characterize a dynamical process from one phenotype to another, and therefore our method offers a new alternative to study dynamical processes of biological systems from the viewpoint of network modules, which leads to new biological insights. In particular, from a dynamical perspective, we showed that modules ''PKC1 TOS2 KEL2 PPZ2 SKN7'', ''CLN1 CLN2 CLN3 BUD2'' and ''SSD1 LST8 TOR1 KOG1 TOR2'' potentially play an essential role in phase arresting. This explains why the cell cycle arrests at the S phase when adding MMS to elg1 mutant strains at 15 min. As validation of generality, we tested these identified responsive modules in two independent datasets of the cell cycle process. The results in Figures 5 and 6 indicate that we not only presented the expression change of modules, but also gave the corresponding cell cycle stages from our biological experiments of internal and external stimuli, i.e., phenotypes, thereby verifying the effective-ness of our findings. Further biological experiment to validate the results is our future topic. Although we restricted our work on integrating microarray gene expression data and PPI network, the method can be straightforwardly extended to other areas, such as multi-classification problem (e.g., disease classification), other type of high-throughput data and biomolecular network analysis. Due to the small sample size, we adopted with-cluster error sum of squares as an  optimization function (see Methods), but other simpler classifiers can also be used in a similar manner to identify the responsive modules when the sample size is reasonably large.
In summary, by formulating the identification of phenotypebased responsive modules as a mathematical programming problem, we proposed a general method to identify phenotypebased responsive modules and further revealed possible causal or dependent relations between network modules and biological phenotypes of budding yeast cell cycle. The resulting responsive modules provide new insight into the regulation mechanisms of cell-cycle process from a network viewpoint. Clearly, the identification of transition modules offers a new way to study dynamical processes at a functional module level. In this paper, we have considered that the changes of the module activity under different biological conditions. However, the composition of the modules may also vary under different conditions. Therefore, it is also an interesting research topic for identifying the composition variations in these modules in addition to their activities.

Supporting Information
Supporting Information S1