Bioinformatics Interdepartmental Program, University of California, Los Angeles, USA

Department of Molecular, Cell, and Developmental Biology, University of California, Los Angeles, USA

Abstract

Background

When growing budding yeast under continuous, nutrient-limited conditions, over half of yeast genes exhibit periodic expression patterns. Periodicity can also be observed in respiration, in the timing of cell division, as well as in various metabolite levels. Knowing the transcription factors involved in the yeast metabolic cycle is helpful for determining the cascade of regulatory events that cause these patterns.

Results

Transcription factor activities were estimated by linear regression using time series and genome-wide transcription factor binding data. Time-translation matrices were estimated using least squares and were used to model the interactions between the most significant transcription factors. The top transcription factors have functions involving respiration, cell cycle events, amino acid metabolism and glycolysis. Key regulators of transitions between phases of the yeast metabolic cycle appear to be Hap1, Hap4, Gcn4, Msn4, Swi6 and Adr1.

Conclusions

Analysis of the phases at which transcription factor activities peak supports previous findings suggesting that the various cellular functions occur during specific phases of the yeast metabolic cycle.

Background

Budding yeast cells (

Analysis of the regulatory network of transcription factors involved in the genomewide oscillations may shed light on the underlying causes of the yeast metabolic cycle. A previous study suggests that the Cbf1-Met4-Met28-Met31-Met32 transcription regulatory complex and Gcn4p are important in regulating the short-period metabolic cycle, although it is not likely that there is a single pathway responsible for the observed oscillation. Rather, there are several coupled subsystems involved, with no hierarchical control

The long-period yeast metabolic cycle consists of three phases: Ox (oxidative, respiratory), R/B (reductive, building) and R/C (reductive, charging). Each phase is associated with a characteristic change in dissolved oxygen levels in the yeast culture. During the Ox phase, oxygen levels drop drastically. In the R/B phase, oxygen levels increase, while in the R/C phase, the longest of the three, oxygen levels stay relatively constant. During the course of the experiment, the yeast culture is continuously infused with low levels of glucose, however glucose levels in the media are almost zero at all phases of the cycle; cells appear to adsorb and metabolize available glucose immediately. Analyses of microarray time series expression data revealed that ~57% of yeast genes exhibit periodic expression during the course of a metabolic cycle and cluster into one the three superclusters, corresponding to the three phases of the yeast metabolic cycle. Gene expression in different clusters peaks at different phases, and many common metabolites also oscillate, indicating that there is a clear temporal separation between various cellular events

In the oxidative phase, oxygen is rapidly consumed in a burst of respiration. Genes whose expression peaks during this phase are highly expressed during a very narrow window of the yeast metabolic cycle. Functional and metabolome analysis indicates that in the Ox phase, oxidative phosphorylation is using up previously accumulated acetyl-CoA while ATP is being rapidly produced. The oxidative cluster is enriched for genes involving amino acid synthesis and ribosomes, indicating that cells are preparing for cell division. Genes involved in sulfur metabolism and RNA metabolism also show increased expression. During the Ox phase, ATP is abundant, and this is what enables the assembly of translation machinery for the next phase: the reductive/building phase

In the R/B phase, 40-50% of cells enter the cell cycle during each cycle of the yeast metabolic cycle

Finally, in the R/C phase, cells become dependent on non-respiratory modes of metabolism, and acetyl-CoA accumulates, which is a precursor to the upcoming respiratory Ox phase. The R/C cluster is enriched for genes involving fatty acid oxidation, glycolysis, stress-associated response and protein degradation, and this also includes genes involved in peroxisomal function, vacuoles and ubiquination machinery. Little oxygen is being consumed, and dissolved oxygen levels continue to rise. Altogether, cycles in metabolism, respiration and mitochondrial function are all important components of the yeast metabolic cycle

Analysis of intracellular concentrations of metabolites shows that many metabolites show periodic oscillations during the yeast metabolic cycle, and some may be important in the establishment and regulation of cycles

Time-series microarray data may be analyzed to determine the transcription factors that are most likely regulating the periodic genes. Other studies searched the promoters of periodic genes to find the most frequently occurring motifs and deduce the most significant transcription factors

Transcription factor

In order to determine the connections between the transcription factors themselves, Cokus

The amplitudes and phases of the

We analyzed time-series microarray data from a previous study

The advantage of the linear regression based method for estimating transcription factor activities is that calculations use existing high-throughput data to provide an elegant, purely computational solution for finding not only the most periodic and most robustly oscillating transcription factors, but also the network of relationships between them. The goal of this study is to identify the key transcription factors regulating the yeast metabolic cycle and to construct a dynamical model of the activities of these transcription factors. The hypothesis is that the most significant transcription factors encompass cellular functions corresponding to the known phases of the yeast metabolic cycle as previously defined in

Results

Transcription factors with highly periodic

We selected transcription factors that had significant

List of top 13 transcription factors

**TF**

**Periodicity**

**Phase**

**Amplitude**

**Function**

**ACE2**

0.520

45°

0.048

Cell cycle (early G1 specific transcription).

**ADR1**

0.518

48°

0.047

Glucose repression.

**ARO80**

0.544

44°

0.066

Aromatic AA degradation

**BAS1**

0.562

293°

0.082

Recombination. Purine and histidine synthesis.

**GAL3**

0.452

215°

0.036

Galactose metabolism.

**GCN4**

0.548

2°

0.085

Main regulator of general AA control.

**HAP1**

0.449

80°

0.049

Respiration. Heme-responsive. Growth potential.

**HAP3**

0.503

255°

0.048

Respiration. Subunit of heme-activ'd Hap2/3/4/5.

**HAP4**

0.620

227°

0.124

Respiration. Subunit of heme-activ'd Hap2/3/4/5.

**MSN4**

0.595

0°

0.062

Cell cycle. Stress-responsive gene expression.

**RLR1**

0.515

42°

0.063

Recombination. Transcriptional elongation.

**SPT2**

0.497

302°

0.108

Cell cycle (interacts w/histones, SWI-SNF).

**SWI6**

0.631

225°

0.058

Cell cycle (progression from G1 to S phase).

Shown are the transcription factors that remain after iterative filtering for the highest periodicity scores of their α-coefficients. Phase and amplitude were calculated from the best-fit sine waves.

Ordering transcription factors according to phase reveals a clear temporal separation between peaks in their

α-coefficients of transcription factors regulating yeast metabolic cycle

**α-coefficients of transcription factors regulating yeast metabolic cycle**. A heat map of the α-coefficients of the top transcription factors, at each time point in the dataset. Factors have been ordered by peak α-coefficient values. Oxygen levels from Tu

Cluster analysis reveals that the transcription factors exhibiting sharp spikes belong to the same cluster (Figure

Clustering results using absolute values of α-coefficients

**Clustering results using absolute values of α-coefficients**. Many transcription factors cluster closely with factors that have α-coefficient curves that are approximately negatives of each other (Figure 1).

α-coefficients of transcription factors regulating yeast metabolic cycle

**α-coefficients of transcription factors regulating yeast metabolic cycle**. A) shows all transcription factors. The 8 transcription factors in the largest cluster are represented as a single curve equal to the average of the absolute values of their α-coefficients. B) separates the transcription factor α-coefficients contributing to the averaged curve.

The phases and amplitudes of the best-fit sine waves for the

Amplitudes and phases of transcription factor α-coefficients, with phases of the best-fit-sine wave

**Amplitudes and phases of transcription factor α-coefficients, with phases of the best-fit-sine wave**. Amplitudes are those of the best-fit sine waves.

The three phases of the metabolic cycle are defined by the changes in oxygen levels

Amplitudes and phases of transcription factor α-coefficients, according to the maximum α-coefficient value

**Amplitudes and phases of transcription factor α-coefficients, according to the maximum α-coefficient value**. The peaks were calculated from average α-coefficient curves, averaged over three metabolic cycles. Amplitudes are the same as in Figure 4, those of the best-fit sine waves.

Regulatory network among transcription factors

A transition matrix was calculated to model the network of relationships between transcription factors. A previous study used a transition matrix with entries constrained to be positive

**Time-translation matrix with no constraints**. Shaded entries show significant interactions between transcription factors, with a significance threshold of 0.5. Entries shaded darker are positive values, lighter are negative values. Italics indicate that the interaction was not included in the graphical representation of the transition matrix (Figure 7), because an interaction with a greater magnitude exists in the opposite direction.

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**Time-translation matrix with constraint to produce non-negative entries**. Shaded entries show significant interactions between transcription factors, with a significance threshold of 0.5.

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**Model residuals for two phases of the yeast metabolic cycle**. Residuals were calculated from A) the transition matrix constrained for non-negative entries and B) the non-constrained transition matrix.

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Network of transcription factors regulating the yeast metabolic cycle

**Network of transcription factors regulating the yeast metabolic cycle**. The time-translation matrix is illustrated as a dynamical model of the α-coefficients of the 13 most significant transcription factors, in which the matrix entries of highest absolute values represent couplings between transcription factors. A line from factor

Discussion

The transcription factors that we identify as regulators of the yeast metabolic cycle peak can be classified into the three phases described by Tu

Hap4

This transcription factor has been previously suggested to have an important role in regulating the yeast metabolic cycle

Hap1

Another key regulator of respiration in yeast, Hap1, is directly regulated by heme, an intermediate in the signaling mechanism for oxygen levels in yeast

Swi6

The transcription factor with the most periodic activity during the yeast metabolic cycle is Swi6, a known regulator of the yeast cell cycle

Msn4

The third most periodic transcription factor that peaks at the end of the R/C phase--just before the Ox phase--is Msn4, which is known to be involved in the diauxic transition and general stress response

Possible connection to the diauxic shift

The previously discussed transcription factors are, coincidentally, some of the transcription factors known to be involved in the diauxic shift, the metabolic shift from fermentation to respiration. Hap1, Hap2/3/4/5, Msn2/4 and Yap1 are the transcription factors that mediate the activation of genes encoding antioxidant defenses during this transition

Cluster of transcription factors with sharply peaked profiles

Other transcription factors may also be important in regulating the yeast metabolic cycle, based on their periodicity scores, known function, and connectivity in the regulatory network diagram. We will discuss the additional five transcription factors Ace2, Adr1, Bas1, Gcn4 and Spt2 in detail. All five belong to the larger of the two clusters based on cluster analysis and have characteristic spikes in their

Bas1 and Gcn4

The transcription factors Bas1 and Gcn4 are involved in amino acid and nucleotide metabolism, and they peak in the Ox phase, which is known to be enriched for genes encoding amino acid metabolism, among other functions

Adr1

Glucose repression is regulated in part by Adr1. This transcription factor is required for the expression of the glucose-repressed gene Adh2, peroxisomal protein genes, and genes required for ethanol, glycerol, and fatty acid utilization

Ace2

Ace2, a transcription factor that activates genes in the G1 phase of the cell cycle

Spt2

The transcription factor Spt2 peaks in the Ox phase of the yeast metabolic cycle and is a negative transcriptional regulator associated with transcription elongation, chromatin dynamics, and genome stability

Sulfur metabolism and comparison with the short-period metabolic cycle

A previous study on the short-period metabolic cycle

Accounting for repressor or activator function of transcription factors

The fact that many transcription factors have opposite

Conclusions

Low rates of glucose induce oscillations in yeast metabolism because cells may be maintaining a balance between different pathways of energy production, while most effectively using accumulated resources in each phase. Yeast is unique because it prefers fermentation over respiration, even under aerobic conditions. Under normal aerobic growth conditions and high glucose concentrations, the high rate of fermentation inhibits the synthesis of enzymes involved in respiration; this effect is known as the Crabtree effect

Among the transcription factors regulating the yeast metabolic cycle, Hap1 and Hap4 are directly involved in respiration and are regulated primarily by levels of heme and carbon source, respectively. Therefore, it is likely that these are indeed the main regulators of mitochondrial function in the cycle, as Lelandais

In the early Ox phase, we propose that low intracellular glucose concentrations cause cells to progress through the diauxic shift, and oxidative respiration is switched on by the transcription factor Hap1. The oxidative stress induces Msn4, which activates other genes involved in the diauxic shift, as well. Gcn4 activity, which increases during periods of glucose starvation, peaks during the Ox phase, which seems analogous to conditions of glucose starvation regarding cellular function. The peak in Gcn4 indirectly promotes sulfur metabolism by activating the transcription factor Met4

After oxygen and acetyl-CoA are depleted, respiration ceases, and yeast cells enter the reductive phase of the yeast metabolic cycle. In the R/B phase, Swi6 initiates cell division, possibly due to the burst of sulfur metabolism during the previous phase. In this phase, cell undergo highly glycolytic metabolism to protect DNA from oxidative damage during replication

The R/C phase of the yeast metabolic cycle is associated with the transcription factor Adr1. It is involved in glucose repression, and its role is to activate glucose-repressed genes as intracellular glucose levels decrease. This results in the activation of pathways involving fatty acid oxidation, and ethanol and glycerol utilization during the R/C phase.

Further studies should analyze the microarray data set from studies on the short-period oscillations using the methods from this study. Depending on the similarity of the lists of transcription factors regulating the short- and long-period cycles, it would reveal whether the two types of metabolic cycles are fundamentally different or not. It may also be helpful to include other oscillating metabolites, such as glucose, acetyl-CoA, and NADP(H), in the dynamical model.

Wolf _{2}S is added to the glycolysis model. This model supports the importance of the sulfur metabolic pathway for establishing oscillations in the short-period yeast metabolic cycle. A further study could create a mathematical model that includes pathways involving heme synthesis to determine whether the Hap2/3/4/5 complex and regulation of heme biosynthesis are sufficient for inducing oscillations in the long-period yeast metabolic cycle.

Determining how the yeast metabolic cycle is regulated may have implications on other biological cycles and studies on transcription factors, as well. For example, as a function of the mammalian circadian cycle, heme concentrations oscillate

Methods

Estimation of transcription factor

The method for calculating transcription factor

where _{
i
}is the relative expression level of gene _{
ij
}is the degree to which transcription factor _{
j
}is the

which can be solved using multiple linear regression, as implemented in the MATLAB function robustfit. This function accounts for a constant term in the model by default. For the current problem, the inputs passed to the function are the logarithm of the matrix containing the binding coefficients, and the logarithm of the vector of gene expression data for the time point. The function returns a vector of

**Goodness of fit for multiple linear regression**. Estimates of the square root of residual variance, _{
OLS
}), and a robust estimate of sigma _{
robust
}
_{
robust
}and a weighted average of _{
OLS
}and _{
robust
}. Note that

Click here for file

The MATLAB function robustfit also returns estimates of the standard error for each

Identification of periodic transcription factors

Transcription factors were given a periodicity score based on autocorrelation, which is the cross-correlation of a signal with itself at various time shifts. We first calculated the raw, unscaled cross-correlation sequence of the ^{-4}).

**Autocorrelation function**. MATLAB code for calculating the autocorrelation function of transcription factor α-coefficients.

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Computation of amplitudes and phases of

Sine waves were fitted to the time-dependent

The phase of the peaks of

Further analysis of transcription factor

Transcription factors were clustered based on their time-dependent

Temporal data for levels of dissolved oxygen in the yeast culture were obtained from

Determination of time-translation matrices

Computing a transition matrix enables the prediction of transcription factor

The set of equations can be solved for

where

The two time-translation matrices were verified for correctness in modeling the dynamical system by multiplying them with the

To illustrate the network of transcription factors visually, the transition matrix was converted into a diagram such that the nodes represent transcription factors and edges correspond to the most significant entries in the translation matrix. If connections existed in both directions, only the more significant connection was considered.

Computational Tools

Algorithms for computing transcription factor

Authors' contributions

The calculations described in this manuscript were performed by AR. MP provided essential comments and guidance. The manuscript was written by AR and edited by MP. Network layouts, figures and tables were by AR. All authors read and approved the final manuscript.

Acknowledgements

We would like to thank Ferenc Raksi for stimulating discussions and feedback, and for his continuous support, encouragement, and help.