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Proc Natl Acad Sci U S A. Sep 20, 2005; 102(38): 13532–13537.
Published online Sep 12, 2005. doi:  10.1073/pnas.0505874102
PMCID: PMC1224643
Genetics

Statistical methods for identifying yeast cell cycle transcription factors

Abstract

Knowing transcription factors (TFs) involved in the yeast cell cycle is helpful for understanding the regulation of yeast cell cycle genes. We therefore developed two methods for predicting (i) individual cell cycle TFs and (ii) synergistic TF pairs. The essential idea is that genes regulated by a cell cycle TF should have higher (lower, if it is a repressor) expression levels than genes not regulated by it during one or more phases of the cell cycle. This idea can also be used to identify synergistic interactions of TFs. Applying our methods to chromatin immunoprecipitation data and microarray data, we predict 50 cell cycle TFs and 80 synergistic TF pairs, including most known cell cycle TFs and synergistic TF pairs. Using these and published results, we describe the behaviors of 50 known or inferred cell cycle TFs in each cell cycle phase in terms of activation/repression and potential positive/negative interactions between TFs. In addition to the cell cycle, our methods are also applicable to other functions.

Keywords: cell cycle regulators, microarray data, synergistic interactions

To understand how cell cycle genes are regulated, it is useful to identify transcription factors (TFs) that are cell cycle regulators. In the yeast Saccharomyces cerevisiae, a number of such TFs have already been identified through various approaches (1-4). A recent powerful tool is the chromatin immunoprecipitation (ChIP)-chip technique, which utilizes ChIP to isolate DNA bound by a TF and applies microarrays to precipitated DNAs to identify genes bound by the TF. Using this technique, Lee et al. (4) identified 11 cell cycle TFs. Assuming that genes coordinately bound are coordinately expressed, they also determined several TFs that might have combinatorial or synergistic regulations.

Many bioinformatic methods have been proposed to identify synergistic pairs of TFs (5-10). Some of these methods (9, 10) assume that a pair of TFs is synergistic if genes regulated by both TFs show stronger coexpression patterns than the expression patterns of genes regulated by either TF alone. This type of method requires data collected over multiple time points to calculate the degree of coexpression, and some of these methods ignore the additive effects of the two TFs (5, 8-10). Also, a pair of TFs may interact only under certain conditions, whereas these methods consider all time points, which may introduce noise.

In this study, we propose two methods to find, respectively, individual TFs and synergistic pairs of TFs that are cell cycle regulators in yeast. The essential idea is that if a TF is a cell cycle regulator, then genes regulated and not regulated by it should, on average, have significantly different expression levels during one or more phases of the cell cycle (5). The target genes of TFs are collected from four TF databases (11-14) and ChIP-chip data (15), and the expression data of yeast genes are gathered from the microarray data of Spellman et al. (16). In this study, the majority of known cell cycle-related TFs and synergistic pairs are identified. Combining our inferences with published results, we describe the regulatory behaviors of 50 TFs in terms of activation/repression and positive/negative interaction between TFs.

Materials and Methods

Data Processing. We use the data set of Spellman et al. (16) that contains expression profiles of 6,178 ORFs in the yeast genome during the cell cycle with α-factor arrest. Eighteen time points are studied. We revert the log ratios of cDNA microarray data (16) to the original values by taking the exponent of two. (We do not use the log-transformed values, because we will take the average of the expression levels of a gene at the time points studied in each cell cycle phase.) To estimate the average expression level of genes in a group at a specific phase, we first calculate the average expression level of each gene over the time points in the phase and then take the mean of the average expression levels of these genes in the same group.

Method for Identifying Cell Cycle TFs. Our first method is for detecting cell cycle TFs. The main steps are as follows:

Step 1. The known or putative target genes of each known TF are collected from four TF databases (11-14) and ChIP-chip data (15).

Step 2. A gene is said to be potentially bound or regulated by TF α if there is evidence from the four databases, or if its p value in the TF α ChIP-chip experiment (pc) is smaller than a certain low threshold (e.g., pc < 0.0001), whereas a gene is said not to be bound or regulated by TF α if its p value in the TF α ChIP-chip experiment is larger than a certain high threshold (e.g., pc > 0.8). For TF α, we generate two gene groups, Gα and G: a gene belongs to group Gα if it is potentially regulated by TF α but to group G if it is not regulated by TF α.

Step 3. TF α is said to be a cell cycle regulator if (i) there exists at least one phase of the cell cycle where the expression levels of genes in Gα are significantly different from the expression levels in one or more of the other phases, and (ii) the expression levels of genes in Gα are on average significantly higher (or lower) than those of genes in G in at least one phase of the cell cycle. We consider five cell cycle phases: G1, S, S/G2, G2/M, and M/G1.

We use the Kolmogorov-Smirnov (KS) test to examine the two statistical criteria in Step 3. The KS test is a nonparametric test to determine whether two distributions differ significantly. The KS test calculates the maximum vertical deviation (D) between the empirical distribution functions of the two groups to determine whether the two data sets are drawn from the same distribution. Let x be the average expression level of a gene over all experimental points in a cell cycle phase. Let fi(x) be the density function of x for the genes in group i and Fi(x) be the corresponding (cumulative) distribution function. For groups i and j, if the statistic D is significantly large, we infer that the two groups of genes are from two different distributions and are expressed differently.

For a given TF, we perform 10 KS tests for equation M1 possible pairs of the five phases to examine the first criterion in Step 3. If at least one test has a p value lower than 0.01, we proceed to the next test. Otherwise, the TF will not be considered further.

A similar method is applied to examine whether the expression levels of genes in Gα are on average significantly higher (or lower) than those of genes in G in at least one phase of the cell cycle. For each phase, we test equation M2 vs. equation M3 by using the two-sided KS test, where F denotes the distribution function of the expression levels of genes in a specific group. If H0 is rejected, we compare the statistics D- = supx[FGα(x) - FG(x)] and D+ = supx[FG(x) - FGα(x)] of the two distributions to determine whether FGα <st FG (i.e., D- < D+) or FGα >st FG (i.e., D- > D+). FGα <st FG means that the expression levels in group Gα are stochastically greater than their corresponding expression levels in G group. Fig. 2, which is published as supporting information on the PNAS web site, gives an example to show how the KS test works.

Method for Identifying Synergistic TF Pairs. Our second method is to test whether there is synergistic interaction between two TFs during any phase of the cell cycle. The procedure is as follows:

Step 1. Before testing whether two TFs (say α and β) interact, we study whether they are associated in the same gene more often than random expectation. That is, let N1 be the total number of genes in Gα, N2 be the total number of genes in Gβ, N12 be the number of genes in Gα,β, and N be the total number of genes in the yeast genome and calculate whether N12/N is greater than the random expectation (N1/N) × (N2/N). This test, in spirit, is similar to the χ2 test of independence. Suppose that the random variables of row and column factors are independent. Then the joint probability of N12/N should be equal to the product of the two marginal probabilities, (N1/N) × (N2/N). If there exists a positive association, then N12/N will be greater than (N1/N) × (N2/N). (This step can be skipped if one wishes to find more potential synergic pairs.)

Step 2. For each pair with significant association, we test whether there exists at least one phase of the cell cycle where the expression levels of genes in Gα,β are significantly different from the expression levels in one or more of the other phases.

Step 3. We generate four groups of genes, Gα,β, Gα,-β, G-α,β, and G-α,-β, and collect their expression data under different cell cycle phases. For most pairs, we set the threshold (pc) as >0.8 to define a gene not regulated by a specific TF. However, some pairs require a lower threshold (pc) to have a sufficient number of genes in group Gα,-β or G-α,β for performing the ANOVA test (at least five in each group).

Step 4. We test the following model using ANOVA on the expression data of four groups:

equation M4

where i = α or -α; j = β or -β; k represents gene k in group Gα,β, Gα,-β, G-α,β, or G-α,-β; Oijk is the observed average expression level of gene k in group Gα,β, Gα,-β, G-α,β, or G-α,-β; μ is the overall mean; μi is the mean in group Gα or G; μj is the mean in group Gβ or G; μij is the interaction effect to be estimated; and εijk is the random noise. If the estimate of the term μαβ is significantly positive (negative), then there is positive (negative) interaction between TFs α and β. Note that when a TF (say β) does not have a DNA-binding domain, we assume that its single effect does not exist and modify the model as

equation M5

To test a third-order interaction among TFs α, β, and γ, we may first check whether the three TFs are associated more often than expected and then analyze the following ANOVA model to test the significance of μαβγ:

equation M6

Because this test requires more data than are presently available, we will not pursue it in this study.

Results

We use the microarray data of Spellman et al. (16) for gene expression during the cell cycle. Different pc values (the p value in the ChIP-chip data) are used to define whether a gene is potentially bound or regulated and not bound or regulated by a specific TF. We performed some different thresholds for binding (ranging from 0.0001 to 0.01) and not binding (ranging from 0.2 to 0.8) to select the thresholds for a balance between the false positive and false negative rates. As shown in Fig. 3, which is published as supporting information on the PNAS web site, the proposed method is robust to the selection of binding and not binding thresholds. Because five tests for the five cell cycle phases are performed for every TF and every TF pair, it is necessary to do the correction for multiple tests. We use the false discovery rate (q value) instead of the Bonferroni correction for a balance between the numbers of true and false positives (17). From the p and q values of a test (all methods use the same definition), three confidence levels are defined: confident (p < 10-5 and q < 10-5), plausible (p < 0.001 and q <0.001), and doubtful (p < 0.01 and q < 0.01). We also use permutation tests to verify our methods. The results are shown in Fig. 4, which is published as supporting information on the PNAS web site. We find that the p value of the permutation test is close to the estimated p value, indicating the reliability of our results.

Identifying Cell Cycle TFs. Our first method identifies 30 TFs to be confident or plausible when we set pc < 0.0001 for the definition of TF binding. Table 1 shows the functions and involved phases (with literature evidence) of the 30 TFs. Among these TFs, 19 have already been experimentally verified to be cell cycle TFs; here we include MET31 and MET4, which were identified by Spellman et al. (16, 18) and Tavazoie et al. (18). Tables 3-5, which are published as supporting information on the PNAS web site, show the results of the KS test with different binding thresholds. We also use the Mann-Whitney (MW) test and find that the KS and MW tests give congruent results (Tables 3-5 and Tables 6-8, which are published as supporting information on the PNAS web site). The MW test is equivalent to the Wilcoxon rank sum test, which is designed to test the shift of locations among two distributions. However, this kind of test cannot be used to detect the change of scales and shapes between two distributions. The KS test serves as an omnibus test for this purpose (19). We can compare the results generated from the MW and KS tests to explore whether two distributions change locations, scales, and shapes significantly. In our studies, the results of the MW and KS tests are similar, indicating that the differences between the two distributions are mainly the shift of locations.

Table 1.
Thirty TFs identified as confident or plausible cell cycle TFs by the KS test with pc < 0.0001

Table 1 missed 11 of the 30 known cell cycle TFs. When the binding threshold (pc) becomes less stringent (i.e., larger), more known TFs can be predicted. For example, when we set pc < 0.01, 25 known cell cycle TFs are found, including six additional known cell cycle TFs: RCS1, RME1, XBP1, ASH1, SUM1, and NDT80. Five known TFs (HIR3, SKN7, YHP1, UME6, and IME1) cannot be inferred by our method; although their pKS are small, their qKS are not low enough to pass our criteria. Note also that although selecting a higher (less stringent) binding threshold can identify more known cell cycle TFs, it may also include more irrelevant TFs.

Table 1 also shows the predicted regulatory behaviors of the 30 confident or plausible TFs. Most TFs are differentially expressed during one or more phases of the cell cycle, suggesting that most of these TFs have a high probability to be cell cycle related. Let us consider two examples. First, FKH1 is involved in a G2 wave of transcription, and genes in GFKH1 have indeed a significantly higher expression level than genes in G-FKH1 in the G2 phase. Second, SWI5 activates transcription of genes expressed in the G1 phase, and genes in GSWI5 are expressed significantly higher than genes in G-SWI5 in the G1 phase. These inferences are consistent with evidence from the literature.

Fig. 5, which is published as supporting information on the PNAS web site, shows the average expression level of each gene group regulated by one of the 30 TFs identified to be putative cell cycle regulators during different phases. Most of the expression patterns support our inferences. For example, genes in GFKH2 are expressed at a lower level than genes in G-FKH2 in M/G1 and G1 but are expressed at a higher level than are genes in G-FKH2 in G2, and the expression level of FKH2 itself is low in M/G1 and G1 but high in G2. These observations indicate that FKH2 is a cell cycle activator for genes in GFKH2 during the G2 phase. It is known that the YOX1 transcription peaks in the late G1 phase, and this initiates repression of the early cycle box activity until the late M phase (20). The regulatory behavior of YOX1 and the expression levels of genes in GYOX1 are consistent with the above description. ACE2 and SWI5 are thought to be activators in G1, and we find that the average expression levels of genes in GACE2 and GSWI5 in the G1 phase are significantly higher than those in G-ACE2 and G-SWI5, respectively. The ACE2 and SWI5 genes are transcribed in G2 (21), and the localization of these two proteins to the nucleus occurs during G1, so that they are active in G1 instead of G2 (22, 23). Therefore, combining Table 1, Fig. 5, and, sometimes, literature survey, one can infer which TFs are activators and which are repressors.

Synergistic Pairs of Cell Cycle TFs. The second method is applied to test synergistic interaction between two TFs (Table 9, which is published as supporting information on the PNAS web site). A total of 203 TFs are used, so that there are 20,503 possible pairs of TFs. When a very stringent criterion (pc < 0.0001) is used to define TF binding, we identify 18 confident pairs, which include eight known (experimentally verified) synergistic pairs. A total of 30 pairs are identified as confident, plausible, or doubtful, and this set includes 9 of the 12 known synergistic pairs. For the other three known pairs (ACE2-SWI5, HIR1-HIR2, and HIR2-HIR3), the numbers of genes in groups Gα,-β and G-α,β are too small to perform the ANOVA analysis. These three known pairs can be identified when the TF-binding criterion is relaxed to be 0.001. Combining the results using pc < 0.0001 and pc < 0.001, we identify 103 pairs, which is much smaller than the 20,503 possible pairs from 203 TFs and provides a reasonably small number of TF pairs to be tested experimentally. Interestingly, this set includes all of the 12 known synergistic pairs: ACE2-SWI5 (21), DIG1-STE12 (24), FKH1-NDD1 (25), FKH1-MCM1 (26), FKH2-MCM1 (26), FKH2-NDD1 (26), HIR1-HIR2 (27), HIR2-HIR3 (11), HIR1-HIR3 (11), MCM1-NDD1 (25), SWI4-SWI6 (SBF) (28), and MBP1-SWI6 (MBF) (2). Furthermore, our predictions for the activation function of all these pairs are consistent with literature evidence. For example, ACE2-SWI5, MBP1-SWI6, and SWI4-SWI6 activate genes at the G1 phase.

Table 2 shows the results of an ANOVA analysis with pc < 0.0001; for pc < 0.001, see Table 10, which is published as supporting information on the PNAS web site. Our results provide some interesting insights. Let us consider some examples. First, DIG1 and TEC1 are involved in the MAP kinase (MAPK) signaling pathway, and both regulate TEC1, FUS1, PCL2, MSB2, STE12, and PRM1 (TEC1 is self-regulated). All these genes have a higher expression level at the M/G1 phase than at other phases and are either pheromone-related or involved in the MAPK pathway. Our results suggest that DIG1 and TEC1 cooperatively activate these genes at the M/G1 phase. Second, RLM1 is responsible for cell wall organization and biogenesis, whereas SWI5 activates transcription of genes in the G1 phase and the M/G1 boundary. The target genes of the pair RLM1-SWI5, including CRH1, HSP150, PIR3, PIR1, and YLR194C, are required for cell wall architecture and stability (11) and are considered to be cell cycle genes at the M/G1 phase (16). Third, NDD1-YOX1 regulates cell cycle genes (16) KIN3, DBF2, SPO12, UTH1, and MFA2, which function as part of a network in exit from mitosis or mating pheromone α-factor.

Table 2.
Putative cell cycle synergistic pairs of TFs identified by the ANOVA model with pc < 0.0001

In Tables 2 (pc < 0.0001) and 10 (pc < 0.001), 80 synergistic pairs from 39 TFs are considered as confident or plausible in the analysis. Fig. 6, which is published as supporting information on the PNAS web site, shows the synergy relations for these TF pairs. Many TFs form a group in which TFs are synergistic with each other and coregulate genes at the same time. For example, HIR1, HIR2, and HIR3 help control the cell cycle transcription of histone genes (29) and in our results, these three genes form a synergistic group at the S and G2 phases. As another example, MCM1, NDD1, and FKH1/FKH2 are the critical activators of a group of M phase-specific transcripts (20), and we find that these three genes form a synergistic group at the M phase. Similarly, MCM1-NDD1-REB1 and DAT1-HAP1-MSN4 function at M and G1, respectively.

Discussion

Several published methods use similar data (e.g., ChIP-chip data, motif information, and expression data) and/or similar analysis approaches (e.g., group genes by presence/absence of binding in ChIP-chip experiments; compare the correlation of expression levels of genes with the same motifs and assess whether the reduction in variance is significant) to identify synergistic TF pairs (5, 6, 9, 10, 30). In particular, Banerjee and Zhang (9) used Lee et al.'s (4) ChIP-chip data and Cho et al.'s (31) expression data and identified 31 TF pairs with a significant level of cooperativity. They considered 10 of these TF pairs to be cell cycle related, including eight literature-supported TF pairs. Our method has identified all of these synergistic pairs and identified four other synergistic pairs with literature support (HIR1-HIR3, HIR2-HIR3, FKH1-MCM1, and DIG1-STE12). Four pairs considered as uncharacterized functional pairs by Banerjee and Zhang (9) (GAT3-PDR1, FHL1-GAT3, GAT3-MSN4, and MSN4-YAP5) are also identified by our method. In addition, our results are consistent with those of Kato et al. (30), who integrated sequence, expression, and localization data to identify combinatorial regulation of TFs and binding motifs.

Das et al. (5) applied the method of multivariate adaptive regression splines (MARS) to study the correlation of the occurrences of TFs and the expression levels of genes bound by TFs. This is a nonparametric adaptive regression method. With spline basis functions in the MARS model, it is more flexible to model the correlation of TFs and expression levels of genes from observations. However, a large number of observations are required to estimate the coefficients and knots for the spline basis functions in MARS. In existing studies of yeast cell cycle TFs, only a few observations (microarray data) are available for a phase. Therefore, we propose the ANOVA-type approach in this study.

In comparison with current methods, our method has the following advantages: (i) it can detect more synergistic pairs, (ii) it can infer the activation (repression) phase, and (iii) it does not require multiple time points.

In the analysis of individual TFs (Tables 3 and 4) and of synergistic pairs (Tables (Tables22 and 9), 50 TFs are considered confident or plausible as individual cell cycle TFs or as synergistic TF pairs. Twenty-four of these 50 regulators are indeed known cell cycle regulators. In addition, for some TFs such as GAT3, HAA1, MET18, and RLM1, half of their target genes are cell cycle genes according to Spellman et al. (16). Some other TFs have been identified to be regulators in other pathways, such as BAS1 in biosynthesis pathway, FHL1 in rRNA processing, GAL4 in galactose-induction, MIG1 and MIG2 in glucose repression, and MSN2 and MSN4 in stress conditions. Whether these TFs are really cell cycle TFs needs to be investigated in the future.

Combining the present and published results, we propose a model to describe the regulatory behaviors of the 50 known or putative cell cycle regulators (Fig. 1); there are 37, 23, 34, 25, and 22 TFs involved in phases M/G1,G1,S,G2, and M, respectively. In the G1 phase, SKN7 (4, 32) and STB1 (4, 33) contribute directly to G1-specific transcription. ASH1 serves to repress the late G1-specific transcription of HO and prevents mating-type switching (34, 35). RME1 acts as an activator of at least one late G1-specific transcript, CLN2 (20, 36). ACE2 and SWI5 are thought to be cooperative activators at the G1 phase (22, 23). SWI4, SWI6, and MBP1 are involved at the G1 phase, and SWI4-SWI6 (SBF) (28) and MBP1-SWI6 (MBF) (2) activate late G1 and early S genes. All these verified cell cycle TFs are predicted to function at the G1 phase by our methods (ASH1 can be identified when we relax the binding threshold to 0.01; see Table 5).

Fig. 1.
The regulatory behaviors of 50 known or putative yeast cell cycle TFs. The descriptions are from Tables Tables1,1, ,2,2, 3, 4 and 9 and the literature. TF α in red (blue) means that genes in Gα are expressed significantly ...

In the S phase, YOX1 transcription peaks in the late G1 (31) and represses the early cell cycle box (bound by MCM1) activity until the M phase (37). For HIR1-HIR2 (or HIR1-HIR3 or HIR2-HIR3), they function as transcriptional corepressors to regulate histone gene transcription in the yeast cell cycle, but they must be transiently inactivated at the G1/S phase boundary for the transcription of histone genes to be derepressed (27). Therefore, HIR1, HIR2, and HIR3 are indeed corepressors, but genes regulated by them are derepressed in the S and G2 phases (16, 30, 38). Further, some studies suggest that FKH1 and FKH2 are also involved in the S phase (1, 4, 30, 39). All these verified cell cycle TFs and synergistic pairs are predicted to function in the S phase by our methods.

Transcriptional control in the G2 and M phases is less well characterized. The present understanding is that NDD1 is the critical activator of a group of M phase-specific transcripts (13, 20, 25, 40). This M phase-specific transcription requires FKH1/FKH2 as well as MCM1 and NDD1. Our methods indicate that FKH2, NDD1, MCM1, FKH1-MCM1, FKH2-MCM1, and MCM1-NDD1 function in the M phase. Other studies (1, 4) suggested that MCM1, together with FKH1 or FKH2, recruits the NDD1 protein in late G2, and that FKH1, NDD1, and FKH2-MCM1 function in the G2 phase.

In the M/G1 phase, the known TFs include YOX1, DIG1, TEC1, and STE12 (24, 37). DIG1-STE12 is involved in the regulation of mating-specific genes (24). Kato et al. (30) suggested that SWI4, YOX1, SWI5, DIG1, and STE12 function during this phase. Our methods indicate that SWI4, SWI5, YOX1, TEC1, DIG1, and STE12 (the synergistic pair DIG1-STE12) function at this phase.

Some TFs are present at many phases in the cell cycle. For example, let us consider FKH2. Genes in GFKH2 have a higher expression level than those in G-FKH2 in the S, G2, and M phases but have a lower expression level than those in G-FKH2 in the M/G1 and G1 phases. Genes in GFKH2 are expressed in the G1 phase in two patterns: genes in GFKH2,NDD1 have a lower expression level than genes in G-FKH2,-NDD1, whereas genes in GFKH2,SWI6 have a higher expression level than genes in G-FKH2,-SWI6. A TF can act as both a repressor and an activator of gene expression by cooperating with different TFs, making it difficult to confirm in individual analysis. Such phenomenon is common in Fig. 1; for example, TEC1 in the M/G1 phase; PDR1, MET18, and HAP1 in the G1 phase; SWI6 and MBP1 in the S phase; and HIR3 and YOX1 in the G2 phase.

Conclusion

Our approach has the following features: (i) It can find both individual TFs and synergistic pairs of TFs that act under a specific condition; (ii) it can describe the regulatory behaviors of identified TFs and synergistic TF pairs; (iii) it can be applied to expression data with few arrays or even for a single time point; (iv) for synergistic pair analysis, our model takes the additive effects into account via the ANOVA model; and (v) a TF can be an activator or a repressor in different phases. These features make it simple to apply our methods to detect TFs in other functions or processes, such as stress response, metabolism, drug treatments, etc.

However, our approach has some limitations. First, the target genes of TFs are not simple to obtain. We collect the information from four TF databases and ChIP-chip data, which may not have been generated specifically for the cell cycle. The p value threshold of ChIP-chip experiments should be defined carefully to obtain correct target genes, and the conditions of ChIP-chip experiments have to be consistent with microarray data (such as the cell cycle condition in this study). In addition, there may exist some combinatorial rules, such as the order and distance between two TF-binding sites, of the binding-site motifs of two synergistic TFs. Lack of such information can reduce the sensitivity and accuracy of our inference. In the future, these limitations might be overcome when more data become available.

Supplementary Material

Supporting Information:

Acknowledgments

We thank Michael Zhang, Geoff Morris, and Josh Rest for suggestions. This study was supported by Academia Sinica and National Science Council) grants in Taiwan.

Notes

Abbreviations: TF, transcription factor; ChIP, chromatin immunoprecipitation; KS, Kolmogorov-Smirnov; MW, Mann-Whitney.

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