Chapter
GENOME SCALE ANALYSIS OF
REGULATORY NETWORK
DYNAMICS
5.1 INTRODUCTION ................................................................................................. 5-1
5.2 MATERIALS AND METHODS ........................................................................... 5-2
5.2.1 DATASETS ...................................................................................................... 5-2
5.2.2 BACK-TRACKING ALGORITHM ........................................................................... 5-3
5.2.3 INTERCHANGE INDEX ....................................................................................... 5-4
5.2.4 TOPOLOGICAL MEASURES ................................................................................ 5-4
5.2.5 NORMALIZATION FOR REGULATORY HUBS ......................................................... 5-5
5.2.6 REGULATORY MOTIFS ...................................................................................... 5-5
5.2.7 RANDOM NETWORKS ....................................................................................... 5-6
5.2.8 SENSITIVITY ANALYSIS ..................................................................................... 5-6
5.3 RESULTS AND DISCUSSION ........................................................................... 5-6
5.3.1 REGULATORY NETWORK IN YEAST .................................................................... 5-6
5.3.2 DIFFERENTIAL USE OF THE REGULATORY NETWORK .......................................... 5-9
5.3.3 DYNAMICS OF REGULATORY INTERACTIONS ...................................................... 5-9
5.3.4 REGULATORY SPECIFICITY THROUGH TF COMBINATIONS ................................. 5-14
5.3.5 LARGE-SCALE TOPOLOGICAL CHANGES .......................................................... 5-15
5.3.6 TF HUBS IN THE REGULATORY NETWORK ........................................................ 5-18
5.3.7 PREFERENTIAL USE OF NETWORK MOTIFS ....................................................... 5-21
5.3.8 INTER-REGULATION OF TFS IN THE CELL CYCLE AND SPORULATION .................. 5-23
5.4 CONCLUSIONS ................................................................................................ 5-28
5.5 REFERENCES .................................................................................................. 5-28
5
5.1 Introduction
GENOME SCALE ANALYSIS OF
REGULATORY NETWORK
DYNAMICS
5
Parts of this chapter appeared in:
1. Luscombe, N.1*, Madan Babu, M.1*, Yu, H., Snyder, M., Teichmann, S. A.* and Gerstein, M.*
(2004). Genomic analysis of regulatory network dynamics reveals large topological changes,
Nature, in press
5.1 Introduction
Living cells respond to a variety of endogenous and exogenous stimuli by altering the
expression of specific sets of genes. Transcriptional regulation plays a central role in directing
the appropriate expression of these genes at the right time and much experimental data have
been published that describe individual transcription factor to target gene interactions (Horak et
al., 2002; Iyer et al., 2001; Lee et al., 2002; Lieb et al., 2001; Matys et al., 2003; Ren et al.,
2000; Svetlov and Cooper, 1995).
From a theoretical point of view, the collection of all these interactions on a genomic scale can
be conceptualised as a directed network. Several studies have examined the properties of
these biological networks as static entities in which all the observed and putative molecular
interactions co-exist (Bader and Hogue, 2002; Guelzim et al., 2002; Jeong et al., 2001; Jeong et
al., 2000; Milo et al., 2002; Ravasz et al., 2002; Rzhetsky and Gomez, 2001; Schlitt et al., 2003;
Segal et al., 2003; Shen-Orr et al., 2002; von Mering et al., 2002; Wuchty et al., 2003).
However useful the picture coming out of these studies is, it does not correspond to what
actually happens in the cell, which is a highly dynamic system, with interactions selectively
5-1
5.2 Materials and Methods
occurring at different times. That's why the exploration of network dynamics under different
cellular conditions has been repetitively mentioned as a key factor in furthering our
understanding of how the regulatory system is used in living cells (Barabasi and Oltvai, 2004;
de Menezes and Barabasi, 2004; Fell, 1997; Lee et al., 2002; Savageau, 1976; Strogatz, 2001).
So far, no research group explored the dynamics of the complete transcriptional regulatory
network of an organism. In this chapter, we investigate for the first time the yeast network under
different cellular conditions. We do so by decomposing the static network along five dimensions
that correspond to different cell cycles: sporulation, diauxic shift, DNA damage, and stress
response, and by integrating the network with the results of 240 microarray experiments that
characterize gene expression changes during these different cell conditions.
We demonstrate that, contrary to prior expectations, differentially active sub-networks are
distinct in terms of their global and local network topologies, occurrence of regulatory hubs, and
system of inter-regulation between transcription factors. These differences can be interpreted in
biological terms once the five cellular processes are further classified into two broad categories:
endogenous and exogenous. The former includes the cell cycle and sporulation, which are
progressive processes with an internal program of transcriptional regulation. The latter
comprises diauxic shift, DNA damage, and stress response, which respond to environmental
changes with a rapid, large-scale turnover in the repertoire of expressed genes.
Our results shows that the transcriptional regulatory network has evolved to accommodate
diverse biological demands, and that this has implied major structural changes in the network's
architecture at both the global and local level to suit different purposes.
5.2 Materials and Methods
5.2.1 Datasets
The yeast transcriptional regulatory dataset was compiled from the results of genetic,
biochemical and ChIp-chip experiments (Horak et al., 2002; Iyer et al., 2001; Lee et al., 2002;
Lieb et al., 2001; Matys et al., 2003; Ren et al., 2000; Svetlov and Cooper, 1995). The initial
dataset contained 7,419 TF-target interactions between 180 TFs and 3,474 target genes (Yu et
al., 2003). From this, we removed non-DNA-binding factors such as histone deacetylases that
are not involved in direct transcriptional regulation through promoter binding. This was done by
a sequence search of 156 known DNA-binding motifs from Pfam (Bateman et al., 2004) against
the amino acid sequences of the 180 TFs; those without a significant match were removed from
the dataset, including their regulatory interactions. The final dataset contained 7,074 regulatory
interactions comprising 142 TFs, and 3,420 target genes (supplementary materials). The major
5-2
5.2 Materials and Methods
results of this study remain unchanged when a smaller dataset excluding ChIp-chip data is
used.
The gene expression data was compiled from a total of 240 published microarray experiments
for five cellular conditions: cell cycle (Cho et al., 1998), sporulation (Chu et al., 1998), diauxic
shift (DeRisi et al., 1997), DNA damage (Gasch et al., 2001), and stress response (Gasch et al.,
2000). The conditions were classified as endogenous and exogenous by whether they have an
internal or external program of transcriptional regulation of genes. We obtained the lists of
genes that experience significant gene expression changes during each condition from the
original publications; a total of 455, 477, 1,823, 1,718, and 866 genes are defined as
differentially expressed in the respective conditions. For the endogenous conditions, we used
information regarding expression levels through a time-course. We obtained lists of genes that
are differentially expressed during a particular phase from the respective publications (Cho et
al., 1998; Chu et al., 1998), and we used these data to observe the changes in regulatory
system usage during successive phases of the cellular conditions. The cell cycle was divided
into the early G1 (75 genes), late G1 (143), S (97), G2 (69), and M phases (105). Sporulation
was divided into the metabolic (52), early I (61), early II (45), early-mid (95), middle (158), midlate (61), and late phases (5).
5.2.2 Back-tracking algorithm
We used a back-tracking algorithm to define the sections of the transcriptional regulatory
network that are actively employed in each cellular condition (Cormen et al., 2001). The method
assumes that genes undergoing differential expression are regulated by TFs that are linked to
them in the regulatory network.
There are three steps: (i) defining sets of differentially expressed genes in each condition, (ii)
identifying TFs that are present in the cell for each condition, and (iii) identifying sections of the
regulatory network that are actively used to control each condition.
(i) Section 5.2.1 above, describes how differentially expressed genes were identified. (ii) To
identify the present TFs, we used a reference dataset for yeast protein and mRNA abundance –
calibrated from scaling many mRNA and protein measurements over the cell cycle to define the
starting expression levels of TFs (Jansen et al., 2002). TFs were grouped into high (17 TFs),
medium (62 TFs) or low abundance (63 TFs) relative to all yeast proteins. For each condition
we then assessed the expression level changes of all TFs relative to the start point. This is
possible because the experiments for all cellular conditions were conducted with the cell cycle
as the reference state. TFs were considered present in a condition if: (a) they have high
abundance at the start point, (b) have medium abundance and the expression level goes up or
stays level during the condition, or (c) have low abundance and the expression level goes up.
The numbers of present TFs in each condition are: cell cycle (88 TFs), sporulation (85 TFs),
5-3
5.2 Materials and Methods
diauxic shift (76 TFs), DNA damage (75 TFs), and stress response (85 TFs). (iii) To identify the
active sections of the regulatory network, we started with the list of differentially expressed
genes in a condition. We detected the present TFs that are connected to these genes by a
regulatory interaction, and we flagged them. We then identified further present TFs that are
connected to the already flagged TFs, and we flagged these also. The process is repeated
iteratively until no further TFs are detected.
For serial and parallel inter-regulation, we defined the active sub-networks during the cell cycle
and sporulation time-courses by repeating the back-tracking procedure on genes that are
differentially expressed in a particular phase. We tested alternative back-tracking models in
which we apply different stringencies for present TFs. We made similar observations for all
models.
5.2.3 Interchange index
We calculated an interchange index (Ii) for each TF, i, in a particular condition, j, that measures
the fraction of regulatory interactions that are unique to a particular condition. It is calculated as
n
ij
Ii 
j
Ni
where nij is the number of regulatory interactions unique to condition j and Ni is the
total number of regulatory interactions active in all conditions. Values range from 0 to 1. Low
values indicate that most interactions are maintained across multiple conditions. High values
indicate that most interactions are replaced and so are unique to particular conditions.
5.2.4 Topological measures
Connectivity statistics were calculated individually for the static and active sub-networks (Albert
and Barabasi, 2002). The average degree (<k>) measures the mean number of regulatory
interactions to and from nodes in a network. The average incoming degree (<kin>) is the mean
number of interactions entering TFs and target genes, and the average outgoing degree (<kout>)
is the mean number of interactions leaving TFs. We determined the most suitable distributions
for the incoming and outgoing degrees by calculating best-fitting exponential (Pk = Cie-k) and
power-law (Pk = Cok-) distributions to the data for each network (where Pk is the probability that
a randomly picked node has k interactions). Exponents were calculated by optimising the sum
of the squared errors between the actual and fitted data. The average path length (<l>) is the
mean distance, in number of nodes, between pairs of nodes in each network. Here we
considered only the distance between TFs and all terminating target genes connected to them.
The diameter (d) is the maximum path length in the network. The average clustering coefficient
(<c>) is the mean ratio of the number of regulatory interactions between a node’s neighbours
and the maximum number of possible interactions. The clustering coefficient for a node i is
5-4
5.2 Materials and Methods
calculated as ci 
2 Ei
, where Ei is the existing number of regulatory interactions between
ki (ki  1)
k nodes connected to it. In calculating the coefficients, we ignored the directionality of the
regulatory interactions.
5.2.5 Normalization for regulatory hubs
Hubs were defined as the TFs in the top 30%, by number of targets, in at least one of the five
cellular
conditions.
using pij 
normalized
n
 n
the
number
of
target
genes
for
each
TF
ij
nij
n
ij
i
We
j
, where pij is the propensity that TF i regulates nij genes in
ij
i
j
condition j. This provides a measure of the relative influence of a TF as a regulatory hub in a
particular cellular condition. Hubs were clustered according to their propensity values using a kmeans clustering algorithm (Tavazoie et al., 1999) with k = 6, where k is the pre-defined number
of clusters. The value of k was chosen so as to group the five cellular conditions separately, and
also provide an additional cluster for condition-independent hubs. Tests using k = 4-8 resulted in
similar clusters with a few outlying TFs. The clusters were then separated into those containing
TFs that are condition-dependent and independent.
We used an equivalent procedure to cluster TFs used during the cell cycle time-course. We
calculated propensity values for all TFs active in the cell cycle, and clustered them using k = 6
(a cluster for each phase, plus one for the ubiquitous TFs). Clusters were separated into those
containing TFs that are phase-specific and ubiquitous.
5.2.6 Regulatory motifs
We identified three of the most commonly used regulatory motifs using methods described by
Shen-Orr et al. (Shen-Orr et al., 2002) and Lee et al. (Lee et al., 2002). In order to identify the
motifs, we constructed a pair of adjacency matrices A and B. Matrix A contained binary entries
Aij, where a 1 indicated a regulatory interaction from TF j to target gene i. Matrix B was a submatrix of A, containing only the rows corresponding to target genes that are TFs themselves.
For single input motifs, we identified the subset of rows in B, such that the sum of each row was
1. For each TF column, we then found non-zero entries. For multiple input motifs, we identified
the subset of rows in A so that the sum of each row was greater than 1. Then for each row, we
identified other rows regulated by the same set of TFs. The collection of rows represented a
motif. Finally with feed forward motifs, for each primary TF we identified non-zero entries in B,
which correspond to regulated secondary TFs. For each primary and secondary TF pair, we
then identified all rows in A regulated by both TFs.
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5.3 Results and Discussion
5.2.7 Random networks
We generated 1,000 random networks for each cellular condition as a control. For each random
network, we: (i) sampled the same number of differentially expressed genes out of all yeast
genes for a given condition, (ii) sampled the same number of present TFs from the list of all
TFs, and (iii) used the back-tracking algorithm through the static network. We applied the
calculations described in the methods section to calculate the architecture of each random
network.
5.2.8 Sensitivity analysis
We tested the sensitivity of our results to random errors in the data. We generated 1,000 static
networks with error rates of 30% by introducing additions, deletions, and rearrangements of
regulatory interactions at random. For each condition, we then back-tracked through these
erroneous networks using the original differentially expressed genes and present TFs.
5.3 Results and Discussion
5.3.1 Regulatory network in yeast
The known transcriptional regulatory interactions in yeast come from a variety of sources. To
obtain as complete a regulatory network as possible, we have compiled a dataset of direct
regulatory interactions between TFs and their target genes from the results of genetic,
biochemical, and ChIp-chip experiments (see Methods) (Horak et al., 2002; Iyer et al., 2001;
Lee et al., 2002; Lieb et al., 2001; Matys et al., 2003; Ren et al., 2000; Svetlov and Cooper,
1995). This dataset contains 7,074 interactions involving 142 TFs, and 3,420 non-TF target
genes. We display this static network in Figure 5.1, with the TFs in an arc around the upper half
of the circle and target genes in a larger arc in the lower half. There are regulatory interactions
between TFs themselves and also from TFs to the target genes. In a table in Figure 5.1 (inset),
we list topological measures that describe the gross features of the network (Albert and
Barabasi, 2002; Barabasi and Oltvai, 2004).
With this network, we integrate the results of 240 microarray experiments that characterize gene
expression changes during five cellular conditions: cell cycle (Cho et al., 1998), sporulation
(Chu et al., 1998), diauxic shift (DeRisi et al., 1997), DNA damage (Gasch et al., 2001), and
stress response (Gasch et al., 2000). Genes that undergo significant changes in expression
levels are considered to experience transcriptional regulation in the respective conditions. We
classify the cellular processes into two broad categories: endogenous and exogenous. The
former includes the cell cycle and sporulation, which are progressive processes with an internal
program of transcriptional regulation that drives the sequential turnover of genes through
subsequent stages (eg G1, S, etc in cell cycle). The latter comprises diauxic shift, DNA damage
and stress response, which respond to environmental changes with a rapid, global turnover in
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5.3 Results and Discussion
the repertoire of expressed genes. Though sporulation is initiated by an environmental change,
such as nitrogen depletion (Chu et al., 1998), we have placed it in the endogenous category as
it progresses through multiple cellular phases via internal regulation.
Employing a back-tracking algorithm (see Methods), we use the expression data to trace the
paths in the regulatory network that are actively used in particular cellular conditions, and at
different time-points during the multi-stage, endogenous processes. In the following sections,
we demonstrate that the different active sub-networks are distinct in terms of their global and
local network topologies, occurrence of regulatory hubs, and system of inter-regulation between
transcription factors.
5-7
5.3 Results and Discussion
Figure 5.1: The transcriptional regulatory network in yeast
Figure 5.1: The nodes in the arc are the 113 transcription factors, and the 1,362 target genes
that are active in one of the five cellular conditions. The connecting edges depict the 2,479
active regulatory interactions. The nodes are ordered by the number of cellular conditions in
which they are active; nodes and edges are colour-coded by the number of cellular conditions
under which they are active, from light blue (one condition) to green (five conditions). The
number of regulators and target genes active in a given number of conditions is provided. *The
table below the main figure summarizes the topological measures calculated for the whole
regulatory network (including inactive sections); please refer to the main text for explanations of
the measures.
5-8
5.3 Results and Discussion
5.3.2 Differential use of the regulatory network
Different subsets of TFs, target genes and regulatory interactions are active in each of the five
cellular conditions. Starting with the target genes (defined as “active genes”), a total of 1,906
are differentially expressed in at least one of the cellular conditions (Figure 5.1, lower arc). The
smallest numbers of targets are found in the cell cycle (280 genes that have regulatory data),
and sporulation (257 genes), and the largest numbers are in diauxic shift (748 genes) and DNA
damage (678 genes). Half of all active targets (803 genes that have regulatory data) are
uniquely expressed in one of the five conditions, and the remainder (559 genes) is common to
two or more. There is a large difference in their functional classes (Mewes et al., 2002): for
example cell cycle and sporulation are enriched for genes involved in cell growth, division and
DNA synthesis, and diauxic shift is enriched for metabolism and energy related functions.
In contrast to the target genes, most TFs are used in more than one condition (defined as
“active TFs”), and 31 are used in all five (Figure 5.1, upper arc). This is because in a given
condition, though only a minor proportion (4-12%) of yeast genes is differentially expressed,
about half of the TFs are used to regulate them. For example during the cell cycle, 70 TFs are
used to regulate just 280 target genes. It is surprising that regulatory specificity can be achieved
with such great overlap in TF usages between the five processes, and we discuss this issue
below.
5.3.3 Dynamics of regulatory interactions
A topical but little studied issue is the dynamic nature of the regulatory interactions between TFs
and their targets. Two recent studies addressed this for a small number of TFs, and reported
that distinct regulatory interactions are indeed made according to the cellular state (Odom et al.,
2004; Zeitlinger et al., 2003). However, the full extent and character of this phenomenon across
all TFs is currently unknown. Here we examine this on a genomic scale.
In Figure 5.2, we present the sub-networks – including the TFs, target genes and regulatory
interactions – that are active under different cellular states. The dynamics of the regulatory
network are strikingly clear: distinct sections of the entire system are used to control each
condition. The sizes of the active sub-networks vary according to the number of target genes
requiring regulation; thus much larger sub-networks are used during diauxic shift and DNA
damage compared with the other conditions.
The figure also highlights how regulatory interactions are maintained or rewired across the subnetworks, by displaying partially overlapping subsets of edges. Out of a total 2,479 active
regulatory interactions, 1,476 are unique to a particular condition, and the remainder is common
to two or more. Thus, over half of the interactions are completely replaced with new ones
between conditions, resulting in specific regulation of the respective cellular states.
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5.3 Results and Discussion
Just 66 interactions are retained across four or more conditions. We can consider these to be
“hot links” (de Menezes and Barabasi, 2004; Goh et al., 2002), regulatory interactions that are
most actively used relative to the rest of the network. Many of these interactions originate from
two types of TFs: metabolic regulators such as Mig1 and Mig2, and general transcriptional
regulators such as Abf1 and Reb1. We therefore associate these hot links with the continual
regulation of house-keeping functions in the cell. As will be shown later, many of the TFs
making these links also comprise condition-independent hubs.
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Figure 5.2: Dynamic representation of the transcriptional regulatory network and standard statistics
4
31
TF
s
1
Gs
3T
80
Figure 5.2: (a) Schematics and summary of properties for the endogenous and exogenous sub-networks. (b) Graphs of the static and condition-specific
networks. TFs and target genes are shown as nodes in the upper and lower sections of each graph respectively, and regulatory interactions are drawn as
edges; they are coloured by the number of conditions in which they are active. Different conditions use distinct sections of the network. (c) Standard
statistics (global topological measures and local network motifs) describing network structures. These vary between endogenous and exogenous
conditions; those that are high compared with other conditions are shaded. (Note, the graph for the static state displays only sections that are active in at
least one condition, but the table provides statistics for the entire network including inactive regions).
5.3 Results and Discussion
As most TFs are actively used across multiple conditions, we now explore how they maintain or
replace regulatory interactions (Figure 5.3). We quantify this for each TF with an index (Ii) that
measures the percentage of interactions that are unique to a single condition (see Methods).
The index ranges from 0 to 1, with higher values signifying a larger proportion of replaced
interactions. A histogram of the indices reveals a tri-modal distribution: 42 TFs interchange most
of their interactions between conditions (Ii  0.7), 16 preserve most of their interactions (Ii 
0.3), and 55 exchange only part of their interactions (0.3 < Ii < 0.7). This divide demonstrates
how some TFs exert their regulatory influence via radically altered sets of interactions
depending on the condition, whereas others retain similar sets of interactions. An important
observation highlighted by the TFs of high indices is the shift in regulatory functions as they
target alternative sets of genes.
We now focus on three example TFs (Figure 5.3): Yox1, whose interactions are highly variable,
Rcs1, whose interactions are invariant, and Abf1 which is between these extremes.
First, Yox1 makes a total of 120 regulatory interactions. It has a high exchange index (Ii = 0.84)
and as shown in Figure 5.3, there is little overlap of interactions across cellular conditions. The
TF has so far been implicated in control of the cell cycle, and DNA synthesis and repair, but
information about its full range of regulatory functions is currently limited (Kaufmann, 1993;
Pramila et al., 2002). Consistent with its role in DNA synthesis, it makes 21 regulatory
interactions during the cell cycle and 30 during sporulation. Surprisingly, it produces the most
interactions – 91 – during diauxic shift, which suggests a previously unreported role in this
process. The exchange of regulatory interactions brings about a dramatic shift in the function of
Yox1; it is focused on controlling cell growth during the cell cycle and sporulation, whereas it
redirects its attention to protein synthesis during diauxic shift.
Second, Rcs1 makes a total of 25 interactions. It has a low exchange index (Ii = 0.28) and as
shown in Figure 5.3, most of its interactions are used across multiple conditions. Therefore, in
contrast to Yox1, it retains similar regulatory functions in the different cellular states. Consistent
with its activity during sporulation and stress response, it is involved in several processes
including regulation of metal ion metabolism (Blaiseau et al., 2001; Yamaguchi-Iwai et al., 1995)
and cell size control (Gil et al., 1991; Jorgensen et al., 2002).
Finally, Abf1 makes a total of 160 regulatory interactions. It has an intermediate exchange index
(Ii = 0.51), and among its many cited functions as general transcriptional activator are the
regulation of meiosis (Gailus-Durner et al., 1996), metabolic activities (Nebohacova et al.,
1996), translation (Della Seta et al., 1990; Mager and Planta, 1990) and gene silencing (Diffley
and Stillman, 1989). It preserves 79 interactions across multiple conditions (Figure 5.3),
corresponding to the consistent regulation of a core set of cellular functions such as glycolytic
pathways, translation and cell biogenesis. The other half of interactions – 81 – is exchanged,
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5.3 Results and Discussion
and this results in a shift of regulatory focus on top of its core functions. In the cell cycle and
sporulation Abf1 regulates cell growth, whereas in stress response it controls intracellular
transport.
Figure 5.3: Interchange of regulatory interactions
Figure 5.3: The histogram plots the distribution of interchange index (Ii) values for all active
transcription factors. Index values range from 0 for TFs that maintain the same regulatory
interactions across multiple conditions to 1 for TFs that replace all regulatory interactions.
Above the plot are network diagrams showing the regulatory interactions made by three
representative transcription factors: Rcs1, Abf1 and Yox1. Regulatory interactions are black if
retained across two or more conditions, or coloured if they are unique to a single condition. The
conditions are labelled in the figure, along with a brief description of the major regulatory
function of the transcription factor in that state.
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5.3 Results and Discussion
5.3.4 Regulatory specificity through TF combinations
95 TFs are used in multiple conditions. In Figure 5.4a, we show that for the endogenous
conditions, 53 out of a total 92 TFs overlap between the cell cycle and sporulation. A similar
pattern emerges for the exogenous conditions, in which 44 out of 100 TFs are used in all three
states. Therefore the key to regulatory specificity cannot lie in the activity of individual TFs.
Figure 5.4: Overlap in TF and TF combination usages
Figure 5.4: (a) Overlap in transcription factor usage. There is large overlap in the usage of
transcription factors between conditions, as similar sets of regulators are used across all five
cellular conditions. (b) Overlap in pair-wise transcription factor combination usage. Unlike the
individual transcription factors, there is very little overlap in the use of pair-wise transcription
factor combinations between conditions. Thus, regulatory specificity is achieved through
combinatorial use of regulatory partners.
Instead combinatorial use of TFs provides a clue to the expression of particular target genes
(Pilpel et al., 2001). In the static network, a gene has an average of 2.1 incoming interactions,
which means that in general, about two TFs regulate each gene. We consider a pair of TFs to
combine if they both target the same gene in a given cellular condition.
360 different pair-wise combinations are used across the five cellular conditions, and in contrast
to individual TFs, there is very little overlap in the use of TF pairs (Figure 5.4b). For example, in
the endogenous conditions, just 3 out of 149 pairs overlap between the cell cycle and
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5.3 Results and Discussion
sporulation, and we make similar observations for the exogenous conditions. Overall, 309 TF
pairs are unique to a single condition, indicating that much of the regulatory specificity is
achieved through combinatorial TF use.
An example of combinatorial TF specificity is illustrated by Abf1, the general transcriptional
activator which we cited earlier. During sporulation, it combines with Ime1 to regulate Hop1,
which is involved in chromosomal segregation. During diauxic shift, it acts in conjunction with
the Hap2-Hap4 heteromeric complex to regulate the Aac2 major mitochondrial ADP/ATP carrier.
5.3.5 Large-scale topological changes
We have shown that the regulatory sub-networks for the five cellular conditions differ in terms of
the target genes that are expressed, the TF combinations that are used, and the regulatory
interactions that are made. The complex topology of these sub-networks can be captured by
assessing graph-theoretic measures that describe their structures on a global scale. Using
these methods, recent studies have shown that molecular biological networks, including the
regulatory system, are remarkably consistent in their architectural features (Agrawal, 2002;
Albert and Barabasi, 2002; Barabasi and Oltvai, 2004; Featherstone and Broadie, 2002; Jeong
et al., 2001; Oltvai and Barabasi, 2002; Tong et al., 2004; Wagner, 2001; Watts and Strogatz,
1998). For instance, cross-species comparisons of metabolic pathways demonstrated that the
reduced networks of parasitic bacterium and the highly developed networks of large multicellular organisms preserve the same scale-free topology with similar degree exponents (Jeong
et al., 2000; Wagner and Fell, 2001). In addition, the average path lengths and clustering
coefficients remain constant irrespective of network size, indicating that all retain their small
world-ness and high level of clustering (Jeong et al., 2000; Ravasz et al., 2002).
We use five graph-theoretic measures to compare the topology of the networks in the five
cellular conditions. We list the values of these measures for the complete network in Figure 5.1,
and we describe how we calculate them in the Methods section. The first measure is the mean
number of incoming interactions per target gene (<kin>). In the static network this is 2.1 and
indicates that on average each gene is regulated by two TFs. The distribution of incoming
connections per target gene follows an exponential behaviour of exponent  = 0.8, with the
probability that a given gene to be regulated by k TFs decreasing as Pk = Cie-k. The behaviour
indicates a sharp decay in the distribution, and presumably reflects the molecular constraints on
the number of TFs that can co-regulate at the same promoter. The second measure is the
average number of target genes per TF (<kout>). In the static network this is 49.8, and the
distribution of outgoing connectivities follows a power-law, where the probability that a given TF
regulates k genes decreases as Pk = Cok- with the exponent  = 0.6. This behaviour signifies a
broader decay profile, and it is indicative of a hub-containing network structure, where selected
TF nodes have a disproportionately large number of targets. The exponent is smaller than
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5.3 Results and Discussion
observed for other molecular biological networks, signifying that the distribution is not as
polarized between hub and non-hub nodes.
We also assess the interactions between TFs. The third measure is the path length (l) which
quantifies the shortest distance between two nodes in a network. Here we define it as the
distance – in number of intermediate TFs – between any given TF and a terminating target
gene. The average path length (<l>) over the static network is 4.7, indicating that there are
nearly five intermediate TFs in an average regulatory path. The fourth measure is the diameter
(d), and it measures the maximal path length between any two nodes in the network. This is 12
in the static network, showing that the longest path has 12 intermediate TFs.
Finally, the fifth measure is the average clustering coefficient (<c>), which measures the level of
interconnection between TFs. This coefficient is defined as the ratio of existing links between a
node’s neighbours compared with the maximum possible links between them, and can vary
between 0 for a totally dispersed node to 1 for a fully clustered one. The average coefficient
(<c>) is 0.11 for the static network.
Given the results from previous studies of diverse networks, the expectation is for the
topological measures to remain constant between the condition-specific sub-networks. We
simulate random sub-networks corresponding to each cellular condition by sampling a given
number of genes from the set of all targets, and back-tracking from these randomly picked
genes (see Methods). Despite large variations in the sizes (232 < n < 746) and sampled regions
of the simulated networks, most of the measures are invariant as expected. Average incoming
degrees are 1.6-1.7 (<kin>), average path lengths (<l>) are 2.5-2.8 diameters (d) are 10-12 and
average clustering coefficients (<c>) are 0.8-0.9. The differences in values are not statistically
significant (p > 0.96). Only the average outgoing degree (<kout>) changes – ranging from 4.8 in
the smallest sub-network to 18.8 in the largest – but this is unsurprising as outgoing edges must
be shared from a limited pool of TF nodes.
Given the prior results and the observations in the simulated networks, the expectation is for the
topological measures to remain constant. In fact, the situation is very different for the real subnetworks and their architectural features vary considerably between conditions (Figure 5.2).
The average outgoing degree (<kout>) doubles from endogenous (<kout> = 6.5-7.9) to
exogenous conditions (<kout> = 9.0-17.1). The difference is statistically significant (p < 210-3),
and values are larger than in the random networks for the exogenous conditions (p < 0.07 for
diauxic shift). Power-law behaviour is maintained for all sub-networks, however the exponents
() double from 0.8 to 1.5 between the exogenous and endogenous conditions.
5-16
5.3 Results and Discussion
The changes in outgoing degrees have biological implications. Exogenous conditions can be
thought to represent two-fold states in which large numbers of genes need to be up- or downregulated quickly in response to often drastic environmental changes. The most efficient way to
achieve this is by having TFs regulate a large number of genes simultaneously. Endogenous
conditions, on the other hand, correspond to states in which expression regulation is
coordinated through multiple stages, and each TF targets fewer genes so as to fine-tune this
process. The larger degree exponents in the exogenous conditions signify greater polarisation
in the outgoing distribution, and indicate a network structure in which a few hubs are more
dominant.
The average incoming degree (<kin>) increases by a fifth from the exogenous (<kin> = 1.6) to
the endogenous conditions (<kin> = 1.9-2.0). Again the change is statistically significant (p <
310-4); values are larger for the endogenous conditions (p < 0.01 for cell cycle), and smaller for
the exogenous conditions (p < 0.05 for stress) when compared with the random controls.
Though exponential behaviour is maintained throughout, the change in exponents signifies a
faster drop-off for the exogenous conditions (exo = 1.1-1.3 compared with endo = 0.7-0.8).
These observations suggest that TF combination usage is simpler in the exogenous conditions
reflecting the more direct-acting nature of these cellular states.
Average path lengths (<l>) double between exogenous (<l> = 2.0-2.2) and endogenous
conditions (<l> = 3.4-4.5). Again this difference is statistically significant (p < 10-10), and values
are larger than expected at random for endogenous conditions (p < 0.02 for cell cycle) and
smaller for exogenous conditions (p < 510-3 for DNA damage). Further, the diameter (d)
doubles from diauxic shift and DNA damage (d = 6) to the cell cycle (d = 12). As the path length
and diameter measure the distance between a TF and its final target, they gauge the immediacy
of a regulatory signal. The short distances in the exogenous sub-networks suggest that
perturbations in the environment would reach the necessary targets very quickly. We speculate
that the longer path lengths in the endogenous sub-networks are due to the use of regulatory
chains; as the cell cycle and sporulation are multi-stage processes, they require the sequential
regulation of genes in a time-dependent manner (Lee et al., 2002; Simon et al., 2001). This
effectively forms a chain of regulatory events that correspond to the intermediate TFs in the long
paths.
Average clustering coefficients (<c>) are small, indicating that the sub-networks do contain
many cliques of highly interconnected TFs. However, values nearly double from the
endogenous (<c> = 0.08-0.09) to exogenous conditions (<c> = 0.14-0.15). Again the difference
is significant (p < 0.01) and coefficients are larger than expected in the endogenous conditions
(p < 510-3 for cell cycle). This means that there is more inter-regulation between TFs in the cell
cycle and sporulation, which reflects the multi-stage nature of these processes.
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5.3 Results and Discussion
We performed a sensitivity analysis of our results by adding, deleting or rearranging 30% of the
regulatory interactions at random. All of the observations that we make in this study are
unaffected, suggesting that our findings are robust against addition of noise to the data.
5.3.6 TF hubs in the regulatory network
Above we showed that the outgoing degree distribution approximates to a power-law, and that
this was indicative of a network containing regulatory hubs. These hubs have been of great
general interest as they are the most influential components of networks and dictate the overall
structures of graphs (Barabasi and Albert, 1999; Barabasi and Oltvai, 2004). However, there
has so far been some ambiguity in the precise definition of hubs (Guelzim et al., 2002; Madan
Babu and Teichmann, 2003; Martinez-Antonio and Collado-Vides, 2003; Shen-Orr et al., 2002).
More importantly, their regulatory role in the network has been the subject of much discussion.
On the one hand, hubs are portrayed as general regulators that target genes across a wide
spectrum of functions and conditions (Barabasi and Oltvai, 2004; Lee et al., 2002; Madan Babu
and Teichmann, 2003; Martinez-Antonio and Collado-Vides, 2003). Topologically they are
located upstream in the network and so they can amplify their range of control over multiple
functions by regulating other TFs (Madan Babu and Teichmann, 2003). An example is the Abf1
general transcriptional activator which has 291 targets in the static network. On the other hand,
this view must be reconciled with the modular nature of the regulatory network (Alon, 2003;
Barabasi and Oltvai, 2004; Guelzim et al., 2002; Hartwell et al., 1999; Oltvai and Barabasi,
2002; Wall et al., 2004). Numerous studies have identified functionally distinct modules within
the regulatory network (Ihmels et al., 2002; Tavazoie et al., 1999), and have shown that many of
them centre about their own hubs (Bar-Joseph et al., 2003; Segal et al., 2003). Furthermore, it
has been argued that hubs are topologically isolated from each other in order to decrease the
likelihood of cross talk between modules (Maslov and Sneppen, 2002). These observations
imply that hubs are generally associated with a specific cellular function and an example is the
Swi4 cell cycle regulator that has 138 targets.
We address this debate by examining the dynamic usage of hubs, and assessing whether key
regulators in the static network remain important under different cellular conditions. As with the
topological measures, we can establish a prior expectation by considering the occurrence of
hubs in the random sub-networks. We define hubs in a given network as the top 30% of TFs by
numbers of target genes. The randomised sub-graphs have 77-96% overlap in the TFs that are
classified as hubs; thus they clearly converge on very similar sets of TFs despite their very
different sizes and back-tracking from distinct sets of genes.
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5.3 Results and Discussion
Figure 5.5 shows the data for the real sub-networks. It is a two-dimensional matrix in which the
columns correspond to the cellular states and the rows represent the composite set of all TF
hubs for the five conditions.
Figure 5.5: Condition specific transient hubs and permanent hubs
Y MR 0 1 6 C
YL R1 8 3 C
YI L 1 3 1 C
S WI 4
YDR4 5 1 C
S WI 6
STE1 2
MB P 1
MC M1
YDR1 4 6 C
YL R1 3 1 C
U ME 6
I ME 1
YNL 2 1 6 W
SI N3
YI R0 2 3 W
YPL 0 3 8 W
YNL 1 0 3 W
Y MR 0 2 1 C
CBF 1
YBL 0 2 1 C
YI L 1 2 2 W
HAP4
HAP2
YHR2 0 6 W
YAP1
HSF 1
YPL 0 8 9 C
YCR0 6 5 W
CI N5
YDR3 1 0 C
YDR2 5 9 C
MS N 2
YDR5 0 1 W
MS N 4
Y GL 0 9 6 W
PDR1
YL R4 0 3 W
Y GL 0 7 1 W
YI R0 1 8 W
YKL 0 4 3 W
YL R0 1 3 W
Y GL 2 0 9 W
Y ML 0 2 7 W
YF R0 3 4 C
YEL 0 0 9 C
YBR0 4 9 C
Y GL 0 3 5 C
YKL 1 1 2 W
YDR0 4 3 C
YPR0 6 5 W
Figure 5.5: A cluster diagram depicts the use of regulatory hubs in different cellular conditions.
The five cellular conditions are shown as columns, and the top 30% of transcription factors (by
number of target genes) are displayed as rows. The intersecting cell is coloured according to
the normalized number of target genes a transcription factor regulates in each condition, and
transcription factors are clustered using the k-means clustering algorithm. Therefore, distinct
sets of transcription factors act as regulatory hubs during different conditions, as highlighted by
the coloured boxes; most factors act as condition-specific hubs, and a minor proportion act as
condition-independent hubs throughout all cellular states. Gene names are coloured in blue if
the transcription factor has an obvious regulatory role in the specific condition. Gene names are
coloured red for transcription factors whose regulatory roles were previously unclear according
to the Saccharomyces Genome Database.
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5.3 Results and Discussion
In order to identify patterns of hub usage, we cluster the TFs according to the normalized
number of their target genes. Strikingly evident are two main groups of TFs: conditionindependent hubs that are important regardless of the cellular condition, and condition-specific
hubs that are influential in one condition, but are much less significant in others. The conditionindependent cluster contains the general, multi-functional regulators discussed above. It
comprises multi-functional regulators such as the Abf1 general transcriptional activator, and
house-keeping TFs such as Mig1 and Mig2 (Klein et al., 1999; Lutfiyya et al., 1998) that are
required regardless of the cellular condition.
Most of the TFs are condition-dependent and this reflects the dynamic nature of the regulatory
network as different sets of TFs assume varying importance during the lifetime of the cell. It is
also emphasized by the smaller overlap in TF hub usage compared with the random subnetworks (36-74% depending on cellular conditions).
The condition-specific hubs group into distinct clusters for each of the five cellular states.
Clusters are smaller for the exogenous conditions, highlighting the more polarised nature of
their sub-networks. About half of the TFs are known to be important for the particular condition
(Figure 5.5: blue labels) (Christie et al., 2004; Mewes et al., 2002). For example, in the first
cluster, 5 out of 11 TFs are known cell cycle regulators and include the Swi4 and Mbp1 G1/S
factors (Andrews and Herskowitz, 1989; Breeden and Mikesell, 1991; Koch et al., 1993). In
sporulation, we find Ime1, a key inducer of early meiotic genes (Kassir et al., 2003; Kassir et al.,
1988; Vershon and Pierce, 2000), and Ume6, a co-activator (Bowdish et al., 1995; Kassir et al.,
2003; Strich et al., 1994; Vershon and Pierce, 2000). Ndt80, an important regulator of the
middle stages of sporulation (Kassir et al., 2003; Vershon and Pierce, 2000; Xu et al., 1995) is
absent as it currently has only one assigned target gene in the dataset. During diauxic shift we
find the Hap2 and Hap4 global regulators of respiratory gene expression and activator of
cytochrome C (Forsburg and Guarente, 1989; Hahn and Guarente, 1988; Olesen et al., 1987).
For the remaining TFs, it is harder to make direct functional associations with their respective
cellular conditions. These are of great interest. As hubs, they are clearly important in the cellular
process under consideration and we can tentatively add to their functional annotations. Such
functional predictions are not trivial to do, and it is only by integrating gene expression data with
the regulatory network that we are able to do this.
Many TFs have functions that appear unrelated to the condition (Figure 5.5: black labels). For
example in sporulation, there are three regulators of nitrogen utilization (YIR023W, YPL038W,
YNL103W). These may appear to be surprising inclusions, but as sporulation is often initiated
through nitrogen depletion, their appearance is biologically meaningful. Other unexpected
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5.3 Results and Discussion
examples include the YBL021C regulator of respiratory functions and we anticipate an equally
important regulatory role during sporulation.
Of particular interest are four TFs that were previously unannotated (Figure 5.5: red labels). For
these we predict key regulatory functions in their respective conditions. Thus, we associate
YDR451C with a role in cell cycle, YIL122W with sporulation, and YIR018W with stress
response. YLR013W acts as a condition-independent hub, and we envisage a general
regulatory function as seen for Abf1 or a house-keeping task as for Reb1. These regulatory
predictions should provide a useful starting point for further experimental characterization.
Additionally, we also find that temporary and permanent hubs regulate themselves (Figure 5.6).
We find that there is much more inter-regulation of temporary hubs within cell cycle and
sporulation than for stress, DNA damage and Diauxic shift. This will be discussed in detail in a
separate section.
Figure 5.6: Inter-regulation within and among regulatory hubs
sporulation
cell
cycle
permanent
hubs
stress
diauxic
shift
DNA
damage
Figure 5.6: The inter-regulation of temporary and permanent hubs portrays a network that shifts
its weight between different hubs to bring about distinct cellular states.
5.3.7 Preferential use of network motifs
So far, we have studied the networks from a global perspective; however, we can also examine
them at a local level. Analyses of regulatory network structures have revealed the occurrence of
motifs, which represent compact units that build up the whole network (Lee et al., 2002; Milo et
al., 2002; Shen-Orr et al., 2002). These motifs display specific patterns of inter-regulation
between the TFs and their targets, and we calculate the occurrence of three that are most
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5.3 Results and Discussion
prevalent in the regulatory network (Table 5.1): single input, multiple input, and feed forward
motifs. Single input motifs consist of units in which a lone TF regulates its targets and multiple
input motifs comprise units where two or more TFs are involved. Feed forward motifs are
composed of two TFs, where the primary TF targets the secondary TF, and both regulate a final
target. Thus the single and multiple input motifs can be considered as direct-acting units,
whereas the feed forward motif can be thought of as an indirect-acting motif requiring an interregulatory link between TFs.
Table 5.1: Network motif usage in five cellular conditions
network motifs
endogenous conditions
cell cycle
sporulation
130 (32.0%)
117 (38.9%)
96 (23.7%)
50 (16.6%)
feed-forward loop
180 (44.3%)
Total
406 (100%)
single input motif
multiple input motif
exogenous conditions
diauxic shift
DNA damage
stress response
438 (57.4%)
462 (55.7%)
228 (59.1%)
180 (23.6.0%)
226 (27.3%)
78 (20.2%)
134 (44.5%)
145 (19.0%)
141 (17.0%)
80 (20.7%)
301 (100%)
763 (100%)
829 (100%)
386 (100%)
Table 5.1: The table summarizes the number of regulatory interactions that are used in singleinput, multiple input, and feed forward motifs during the five cellular conditions. In parentheses
we calculate the percentage of regulatory interactions used in the given motif with respect to the
total number of regulatory interactions used in all motifs for a condition. Single input motifs are
favoured in exogenous conditions, whereas feed forward motifs are favoured in endogenous
conditions. Motif occurrences that are high with respect to other conditions are shaded green,
and those that are low are shaded dark pink.
Recent work has shown that the usage pattern of motifs is highly conserved across related
networks, including the regulatory systems of diverse organisms such as B. subtilis, E. coli, and
yeast (Milo et al., 2004). Furthermore, the relative occurrence of motifs does not change when
smaller sub-networks of various sizes are considered (Milo et al., 2002). Therefore, as for the
topological measures, we expect motif usage to remain invariant between conditions. Indeed,
for the random controls, we show that motif occurrence stays comparable to the static network
regardless of the number of target genes that are sampled for back-tracking (p > 0.12).
Contrary to this expectation, there is a conspicuous difference in motif usage between
conditions (Table 5.1; p < 10-9). Exogenous conditions prefer to use the direct-acting units,
particularly the single input motif. These comprise over 4/5 of the regulatory interactions,
whereas the proportion drops to roughly 1/2 in the endogenous conditions. The motif is over
represented in DNA damage and stress response when compared with the random sub-graphs
(p < 10-3). The indirect-acting feed forward motif, on the other hand, is extensively used in the
cell cycle and sporulation and comprises over 2/5 of the regulatory interactions. It is used much
5-22
5.3 Results and Discussion
more than expected at random in these conditions (p < 10-4). We discussed earlier that the
clustering coefficients are larger in these conditions, indicating a higher degree of interregulation between the TFs. The use of feed forward motifs accentuates this observation. In
fact, the regulatory neighbourhood with the highest clustering coefficient in the cell cycle subnetwork (c = 0.3) contains five inter-connected motifs, with Mbp1 as the primary TF and Swi4 as
the final target gene. Though the motif is used sparingly in the exogenous conditions (the
relative share drops to about 2/5 during stress response) they may still play an important role in
filtering spurious signals from the environment (Mangan and Alon, 2003; Mangan et al., 2003).
Previous studies have ascribed specific information processing tasks to motifs. It has been
suggested that feed forward motifs can act as regulatory buffers; it acts as a circuit that
responds only to persistent regulatory signals from the primary TF, and allows for a rapid
shutdown of the signal (Mangan and Alon, 2003; Mangan et al., 2003). It would therefore
appear suited to endogenous processes that require a controlled replacement of genes through
multiple phases. With the use of feed forward motifs, the cell will only enter the next phase of
the condition once the regulatory signal from the previous phase has stabilized. Furthermore,
this signal can be quickly terminated once the cell has entered a new phase. The regulation of
Ime2 during sporulation is an illustrative example. The gene is regulated by two early phase TFs
– Rim1 as the primary and Ime1 as the secondary TFs – and it encodes for an important kinase
that stimulates 20 further TFs during the middle and late phases. Subsequent phosphorylation
of Ime1 by Ime2 ensures a quick shutdown of the transcriptional cascade during the latter
stages of sporulation.
Single input and multiple input motifs are designed for the simultaneous regulation of many
genes, and are thus suited for controlling the large-scale turnover of genes seen in exogenous
conditions. Single input motifs have previously been implicated in regulating systems of genes
that function as a unit to form a complex or a pathway (Shen-Orr et al., 2002). Multiple input
motifs can be thought of as an extension of this, but with stricter control because of the use of
several TFs. An example is the regulation of three proteosomal subunits (Rpt2, Rpt4, Rpt6) by a
lone TF, Rpn2, during DNA damage.
5.3.8 Inter-regulation of TFs in the cell cycle and sporulation
Earlier we showed that the sub-networks of the endogenous conditions have larger clustering
coefficients and longer path lengths compared with the exogenous conditions. We suggested
that this results from a greater degree of inter-regulation between TFs, and the formation of
regulatory chains. To study these observations in detail, we examined the temporal nature of
the endogenous sub-networks as the cell progresses through successive phases, and observed
how TFs regulate each other to bring about the sequential regulation of genes in a timedependent manner. Young and colleagues previously coined the term “serial inter-regulation” to
describe the connectivity between the main cell cycle regulators (Simon et al., 2001). Here for
5-23
5.3 Results and Discussion
the first, time we report the full scope of inter-regulation between all TFs used present during
both endogenous conditions.
The expression data for the cell cycle and sporulation provide measurements of gene
expression levels at numerous time-points through the course of the cellular conditions. Genes
were classified as being expressed at a particular cellular phase by the nature of the expression
changes during these time-courses (Cho et al., 1998). Thus for the cell cycle, which we
consider in detail now, genes were assigned to one of the five phases pre-defined by Cho et al.
(Cho et al., 1998): early G1, late G1, S, G2, and M. To identify the active sub-networks during
each phase, we then repeated the back-tracking procedure using these classified genes. The
results of our analysis are presented in Figure 5.7.
In Figure 5.7a, we show a cluster diagram of the TFs that are used during the cell cycle. The
columns represent the 70 active TFs, and the rows correspond to the five cellular phases. We
shaded the intersecting cell by the normalized number of genes targeted during a given phase.
It is immediately obvious that most TFs operate during a particular phase, which is highlighted
by their phase-specific targeting of genes. The activity of the major cell cycle regulators is in line
with previous observations, emphasizing the validity of the methods we used in this paper
(Futcher, 2002): Swi4 and Mbp1 are clustered in the late G1 phase (Koch et al., 1993), Fkh1 is
found in G2 (Koranda et al., 2000; Kumar et al., 2000; Pic et al., 2000; Zhu et al., 2000), Mcm1
is in M (Koranda et al., 2000; Kumar et al., 2000; Pic et al., 2000; Zhu et al., 2000), and Ace2
and Swi5 are in the early G1 phase (McBride et al., 1999; McInerny et al., 1997). Of note is the
residual activity of many TFs in additional phases; so for example, Swi4 and Mbp1 also target
genes during the S phase as well as late G1. This is because many cell cycle regulators are
often active during the transition between phases. It also underlines the somewhat arbitrary
nature of the definition of phases in the expression data and the clustering method we used to
group the TFs. Despite these limitations, it is clear that TFs are predominantly active during their
assigned phases.
In addition to the phase-specific TFs, we had a sizeable minority of TFs that are ubiquitously
active throughout the cell cycle. These TFs regulate genes indiscriminately of the cellular
phase. Interestingly, about a third of these TFs comprises the condition-independent hubs
defined in Figure 5.5, and includes examples such as the Abf1 general transcriptional activator.
5-24
5.3 Results and Discussion
Figure 5.7: Inter-regulation between TFs through the phases of the cell cycle
Figure 5.7: (a) Cluster diagram depicting the activity of 70 transcription factors during the cell
cycle. The five phases of the cell cycle are shown as rows, and the transcription factors are
shown as columns. Names of transcription factors discussed in the main text are highlighted in
red. The intersecting cell is coloured according to the normalized number of target genes a
transcription factor regulates in each phase, and factors are clustered using the k-means
algorithm. Distinct sets of transcription factors regulate genes during the different phases, as
highlighted by the different colours. Phase-specific transcription factors are mainly active during
a particular phase (early G1 – light blue, late G1 – green, S – orange, G2 – red, and M –
magenta), and ubiquitous factors are active throughout the whole cell cycle (ubiquitous – dark
blue). (b) Serial inter-regulation of transcription factors. A series of network diagrams depict the
regulatory interactions between phase-specific transcription factors. Factors active in one phase
regulate further factors in subsequent phases of the cell cycle; thus factors in early and late G1
regulate those in G2 and M, which in turn regulate factors in the G1 phase of the next cycle. (c)
Parallel inter-regulation of transcription factors. A network diagram depicts a two-tier system of
regulatory interactions from the ubiquitous factors that are active throughout the cell cycle to the
phase-specific factors. The serial and parallel inter-regulatory processes act in tandem to drive
the cell cycle forward.
5-25
5.3 Results and Discussion
Of importance is the pattern of inter-regulation between TFs. Figures 5.7b,c depicts the two
main methods of inter-regulation: serial and parallel. In serial inter-regulation (Figure 5.7b), TFs
in one phase regulate further TFs in subsequent phases to drive the cell cycle forward (Simon
et al., 2001). Among the complex circuitry, we can identify complete loops of regulatory
interactions. Swi4 and Mbp1 in late G1 target TFs in the G2 and M phases. Fkh1 and Mcm1 in
these phases in turn regulate Swi5 and Ace2 in early G1 of the next cell cycle. Finally Mcm1
loops back to regulate Swi4, the original TF. These types of regulatory chains contribute to the
long path lengths observed in the endogenous conditions.
In addition to serial inter-regulation, here we introduce the concept of parallel inter-regulation
(Figure 5.7c), in which the ubiquitously active TFs regulate the temporal activity of the phasespecific TFs. Parallel inter-regulation effectively provides a two-tier system, in which the
ubiquitous TFs provide a stable and prolonged signal for the phase-specific TFs. An example is
the general regulator Abf1 that is active throughout the cell cycle. It regulates four TFs in the
early G1 to M phases. Specificity is achieved by exchanging regulatory partners. Thus in early
G1, Abf1 combines with Sin3 to regulate Ume6, which acts as a mitotic repressor (Kadosh and
Struhl, 1997). In the M phase the same factor acts alone to regulate Pho2, a co-regulator of
Swi5 for homothallic switching (Bhoite et al., 2002). In this way, a single TF can be involved in
regulating several cellular functions, so ensuring a smooth transition between phases.
Furthermore, as many of the ubiquitous TFs are also condition-independent hubs involved in
housekeeping functions, they provide a channel of communication through which to coordinate
the basic cellular processes and the progression of the cell cycle. There is also some reciprocal
regulation from the phase-specific to ubiquitous TFs – shown in pale colours in Figure 5.7c –
though these are much less frequent.
We made similar observations for sporulation (Figure 5.8). The phase-specific TFs include
known meiosis regulators Ime1, Ume6 and Ndt80, and many of the ubiquitous TFs comprise the
condition-independent hubs. Again, the serial and parallel methods of inter-regulation operate in
tandem to guide the cellular process through its time-course.
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5.3 Results and Discussion
Figure 5.8: Inter-regulation between TFs through the phases of the sporulation
Figure 5.8: (a) Cluster diagram depicting the activity of transcription factors during the different
stages in sporulation. The seven phases of sporulation are shown as rows, and the transcription
factors are shown as columns. The intersecting cell is coloured according to the normalized
number of target genes a transcription factor regulates in each phase, and factors are clustered
using the k-means algorithm. Distinct sets of transcription factors regulate genes during the
different phases, as highlighted by the different colours. Phase-specific transcription factors are
mainly active during a particular phase (metabolic – light blue, early I and II – green, earlymiddle – orange, middle – red, mid-late – magenta and late - brown), and ubiquitous factors are
active throughout the whole process of sporulation (ubiquitous – dark blue). (b) Serial interregulation of transcription factors. A series of network diagrams depict the regulatory
interactions between phase-specific transcription factors. Factors active in one phase regulate
further factors in subsequent phases of sporulation; thus factors in metabolic regulate those in
early, which in turn regulate factors in the early-middle phase of sporulation. (c) Parallel interregulation of transcription factors. A network diagram depicts a two-tier system of regulatory
interactions from the ubiquitous factors that are active throughout sporulation to the phasespecific factors. The serial and parallel inter-regulatory processes act in tandem to drive the
whole process of sporulation forward.
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5.5 References
5.4 Conclusions
We examined the dynamics of the regulatory system in yeast under different cellular conditions
and obtained unexpected results. By studying the dynamic interchange of regulatory
interactions, we found that some transcription factors maintain the same interactions regardless
of the cellular state, whereas others replace most interactions to provide alternative regulatory
roles depending on the condition.
Contrary to prior expectations, the dynamics of the regulatory system usage is accompanied by
large structural changes in the network architecture. These changes include shortening of path
length in environmental response conditions, and increased clustering of transcription factors
with consequent refinement of control in internally driven multi-stage conditions. There are also
major changes at the local level, in which specific network motifs appear to be favoured.
We also investigated interactions between transcription factors in the context of the cell cycle,
and we introduced the concept of serial and parallel inter-regulation acting in tandem to drive
the cell through multi-stage conditions.
We found that the role of the regulatory hubs in the network changes too. Although there is a
small number of transcription factors that act as hubs throughout all cellular conditions, most of
them behave like hubs in specific conditions only. The resulting picture is of a network that shifts
its weight between different foci to coordinate distinct cellular processes. As highly connected
transcription factors have a tendency to be lethal when removed from the system, this unveiled
transient nature of the hubs has implications for their possibly condition-dependent lethality.
Finally, our defined sets of regulatory hubs that are collectively active can be used in a bottomup approach for the classification of cellular conditions. One could even think of engineering
entirely new cellular conditions by activating alternative combinations of regulatory hubs.
5.5 References
Agrawal, H. (2002). Extreme self-organization in networks constructed from gene expression
data. Phys Rev Lett 89, 268702.
Albert, R. and Barabasi, A. L. (2002). Statistical mechanics of complex networks. Reviews of
Modern Physics 74, 47-111.
Alon, U. (2003). Biological networks: the tinkerer as an engineer. Science 301, 1866-7.
Andrews, B. J. and Herskowitz, I. (1989). Identification of a DNA binding factor involved in
cell-cycle control of the yeast HO gene. Cell 57, 21-9.
5-28
5.5 References
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