healthmedicinet

Analysis of gene expression and dynamical modeling of the PKA-RN was performed during
exponential growth. Measurements were taken under optimal temperature and after a
heat shock at 39 °C (see Methods). The regulation of stress gene expression depends
on complex transcriptional mechanisms. For example, in S. cerevisiae Msn2, Msn4, Hsf1, Yap1, and eight additional transcription factors contribute to
the transcription of heat shock genes 95]. The PKA-RN also controls stress gene expression by inhibiting the activity of Msn2,
Msn4, Hsf1, Yap1, and Skn7 10], 20], 37], 75]. Because of this complexity, we decided to focus on the transcription factors Hsf1
and Skn7 in WT and PKA-RN deletion mutants by measuring the activity of an HSE-CYC1-lacZ reporter gene construct to test their in vivo activity (see Methods), as reported before 4], 47], 50], 58]. In our hands, this reporter showed no activity in the absence of the HSE and its
activity did not correlate with the plasmid copy number in the different strains analyzed
(see Methods). Because the effect on HSE-dependent expression by deletions in PKA-RN
genes is dependent on the genetic background (17], 56], and our unpublished data), all mutants used in this work were derivatives of the
same laboratory strain (W303). Previous studies have shown that in W303, the expression
of several stress genes such as HSP104, TPS1, CTT1, GPD1, HSP12, and HSP26 are inhibited by PKA 20], 23] and, in the case of HSP12 and HSP26, their inhibition by PKA is mediated through Hsf1 20].

Cdc25 positively regulates HSE-dependent gene expression

CDC25 deletion caused strong alterations in two well-known PKA-regulated processes: growth
rate (decreased) and basal thermotolerance (increased) (Additional file 1: Table S1). HSE-driven ?-galactosidase activity at 25 °C was 3.7-fold higher in cdc25? cells than in the WT strain (Fig. 2b). After heat shock, the WT strain increased the reporter activity 2.3-fold relative
to the 25 °C condition. In cdc25? cells, ?-galactosidase activity remained unchanged at both temperatures; noteworthy
these levels were significantly higher than in the WT at 39 °C. These results indicate
that CDC25 down-regulates HSE-dependent gene expression in WT cells and they are consistent
with previous findings showing that PKA inhibits Hsf1 activity 20].

Fig. 2. De-repression of HSE-dependent gene expression in cdc25? cells is dependent on both Hsf1 and Skn7 activities. Strains transformed with reporter
plasmid pRY016 (2 ?) were grown in SD medium at 25 °C until mid-exponential phase
and treated at different temperatures as described in Methods section. Values are
reported as ?-galactosidase specific activity (nmol of hydrolyzed ONPG min
^?1
 mg
^?1
protein) and are the average and standard deviation of at least three independent
experiments. Bars that do not share at least a common letter differ significantly
(P??0.05). Strains assayed were: a WT (W303-6B), hsf1-?CTA (LM020), cdc25? (SL5001), and hsf1-?CTA cdc25? (SL6001). b WT (W303-6B), skn7? (SE1000), cdc25? (SL5001), and cdc25? skn7? (SL4001)

Hsf1 and Skn7 mediate the high basal thermotolerance and constitutive HSE-dependent
gene expression in cdc25? cells

Both Hsf1 and Skn7 transcription factors recognize HSEs 66], 76]. Therefore, we separately evaluated their contributions to the constitutively-elevated
HSE-dependent expression in cdc25? cells. An Hsf1 lacking 250 residues at the C-terminal domain (hsf1-?CTA) was used instead of a full deletion of the ORF, because the function of HSF1 is essential 60], 76]. At 25 °C the ?-galactosidase activity in the hsf1-?CTA strain equated that of the WT but, unlike the WT, after a heat shock at 39 °C its
?-galactosidase activity did not increase (Fig. 2a). This confirms that the C-terminal activation domain is required to elevate Hsf1
transcriptional activity in response to heat shock 60]. Furthermore, ?-galactosidase levels in the double mutant hsf1-?CTA cdc25? decreased significantly compared to the single cdc25? mutant, both at 25 °C and after heat shock, supporting the idea that Cdc25 regulates
Hsf1 (Fig. 2a). Accordingly, the basal thermotolerance (15 %) of hsf1-?CTA cdc25? cells decreased relative to the cdc25? single mutant (70 %) (Additional file 1: Table S2). Although basal thermotolerance of hsf1-?CTA mutant was similar to the WT strain, its duplication time at 25 °C increased slightly
(Additional file 1: Table S2). We also found that deletion of the C-terminal domain of Hsf1 suppressed
the lack of growth of cdc25? cells in acetate or galactose at 25 °C. We suggest that the C-terminal domain of
Hsf1 plays a negative role in the control of growth in non-fermentable media under
conditions of low PKA activity. In yeast, humans and in Arabidopsis, Hsp70 interacts
with the C-terminal activation domain of Hsf1 inhibiting its transcriptional activity
4], 45], 73]. We predict that the transcriptional activity and the growth-promoting potential
of the full-length Hsf1, when the cell is under under low PKA conditions, could be
re-established by deletion of genes encoding Hsp70.

In WT cells, HSE-dependent expression increased at the beginning of the post-diauxic
phase (Fig. 3). This observation agrees with the decline of PKA activity at this stage 84]. A similar pattern was observed in cdc25? cells, although their initial activity was already very high. Interestingly, the
?-galactosidase activity in the double mutant hsf1-?CTA cdc25? was smaller than the activity in cdc25? cells, remaining constant during the exponential and postdiauxic phases. This indicates
that the CTA domain of Hsf1 is required for maximal activity in low PKA cells. Unexpectedly,
?-galactosidase levels in the hsf1-?CTA strain declined steadily as the culture advanced from exponential to the post-diauxic
phase (Fig. 3). These observations reinforce the idea that Hsf1 activity is essential to enter
the post-diauxic phase at optimal temperatures. Thus, the C-terminal domain of Hsf1
plays four novel functional roles at 25 °C when PKA activity is low: i) increases
basal thermotolerance (Additional file 1: Table S3), ii) increases HSE-dependent gene expression (Figs. 2a and 3), iii) causes growth arrest in acetate, iv) causes growth arrest in galactose. These
functions of the C-terminal domain of Hsf1 were not previously described 60], 76].

Fig. 3. Increase of HSE-dependent gene expression, during the post-diauxic phase of liquid
cultures at 25 °C, requires Hsf1 activity. Strains containing plasmid pRY016 were
grown in SD medium at 25 °C and aliquots were taken at the indicated culture densities
(OD
₆₀₀
). Data shown represent the average and standard deviation of at least three independent
experiments. ?-galactosidase specific activities are reported as in Fig. 2. Bars that do not share at least a common letter differ significantly (P??0.05). Strains assayed were: WT (W303-6B), hsf1-?CTA (LM020), hsf1-?CTA cdc25? (SL6001), and cdc25? (SL5001)

To analyze the contribution of Skn7, the double mutant skn7? cdc25? was also transformed with reporter plasmid pRY016. The ?-galactosidase activity in
skn7? cdc25? cells at 25 °C or after heat shock was lower than that of cdc25? cells (Fig. 2b). In contrast to cdc25? hsf1-?CTA cells, ?-galactosidase activity increased upon heat shock at 39 °C. However, this
increase was not statistically significant (Fig. 2b). This indicates that, in the cdc25? strain, HSE-dependent expression is reliant on Skn7 for optimal temperature growth
to a greater extent than after a heat shock. Furthermore, the basal thermotolerance
and the duplication time of cdc25? skn7? cells decreased relative to cdc25? cells (Additional file 1: Table S2), while the inhibition of growth at 36 °C and in acetate or galactose as
sole carbon sources at 25 °C were suppressed by SKN7 deletion. In agreement with the involvement of Skn7 in the oxidative stress response
49], we observed that resistance of cdc25? cells to H
₂
O
₂
decreased by deletion of SKN7 (data not shown). The activity of the reporter gene in the single skn7? mutant was similar to the WT at 25 °C and after a heat shock at 39 °C (Fig. 2b). Together, these results indicate that, in cells growing at optimal temperature
or when their PKA activity is low, Skn7 is required to achieve maximal basal thermotolerance
and HSE-dependent gene expression. The contribution of Skn7 to the elevated HSE-dependent
gene expression in response to heat shock was only marginal (Fig. 2b). Thus, heat induction of HSE-dependent gene expression in cells with low or high
PKA activity depends mostly on Hsf1. However, we found that Skn7 plays new roles in
other cellular processes at low PKA activity: i) inhibits growth at 25 °C, ii) It
is required for H
₂
O
₂
resistance, iii) causes growth arrest in glucose at 36 °C, iv) causes growth arrest
in acetate at 25 °C, v) causes growth arrest in galactose at 25 °C.

Ras2 also regulates HSE-dependent gene expression

Ras2 is a positive regulator of the PKA-RN acting downstream of Cdc25. In a RAS2 deletion mutant, basal thermotolerance was 120-fold higher than in the WT strain
[P?=?0.002] (Additional file 1: Table S1). This difference was consistent with a constitutively elevated HSE-dependent
gene expression at 25 °C (Fig. 4). Growth rate of the RAS2 mutant was similar to the WT strain (Additional file 1: Table S1). The increased thermotolerance of CDC25 and RAS2 single mutants (Additional file 1: Table S1) confirmed that their PKA activity decreased. However, the growth rate
diminished only in the CDC25, but not in the RAS2 mutant. This finding indicates that the control of basal thermotolerance is more
sensitive to a low PKA cellular activity than duplication time is.

Fig. 4. Effect of RAS2, and BCY1 deletions on HSE-dependent gene expression. Strains were transformed with plasmid
pRY016 (2 ?) containing an HSE-CYC1-lacZ reporter gene. Growth and temperature treatments were performed as described in Methods
section. Data shown represent the average and standard deviation of at least three
independent experiments. ?-galactosidase specific activities are reported as in Fig. 2. Bars that do not share at least a common letter differ significantly (P??0.05). Strains assayed were: WT (W303-1a), ras2? (Wras2?) and bcy1? (CM0095)

Deletion of BCY1 represses the HSE-dependent gene expression

To evaluate whether cells with high PKA activity altered HSE-dependent gene expression
in the opposite way to mutants with low PKA activity, such as cdc25? and ras2?, a deletion mutant of BCY1 was studied. Indeed, HSE-dependent expression was repressed in bcy1? cells relative to the WT strain at 25 °C and after heat shock at 39 °C (Fig. 4). Consistent with these results, duplication time decreased in the bcy1? mutant, while basal thermotolerance remained the same as in the WT strain (Additional
file 1: Table S1). Induced thermotolerance decreased dramatically in bcy1? cells (0.22?±?0.4 % in the mutant vs. 72?±?12 % in the WT with a P?=? 0.001). Moreover,
cell viability in bcy1? cells was very poor, in agreement with previous results 85].

Tpk1 and Tpk3 inhibit HSE-dependent gene expression in the absence of Tpk2

To explore the possible differences between the CS of PKA, we first analyzed HSE-dependent
expression in single TPK gene deletion mutants. In tpk1? cells HSE-dependent expression was slightly reduced at 39 °C but not at 25 °C when
compared to the WT (Fig. 5). In tpk3? cells HSE-dependent expression was not affected. Interestingly, HSE-dependent expression
in the tpk2? mutant was highly repressed both at 25 °C and 39 °C. The basal thermotolerance of
the three single mutants was similar to the WT strain (Additional file 1: Table S3). Duplication times of tpk2? or tpk3? mutants were similar to the WT strain. However, the tpk1? mutant showed a slower growth rate (Additional file 1: Table S3). Induced thermotolerance was reduced relative to WT in tpk1? and tpk2? mutants, but not in tpk3?. These results suggested that each CS plays a different role in the control of HSE-dependent
gene expression, growth, and in basal- and induced-thermotolerance. In order to analyze
the role of individual Tpk’s, double TPK deletion mutants were studied. The ?-galactosidase activities of tpk1? tpk3? cells growing at 25 °C or after heat shock at 39 °C were similar to their isogenic
WT strain (Fig. 5). However, its basal thermotolerance and duplication time increased relative to the
WT strain (Additional file 1: Table S3). In contrast, the ?-galactosidase activities at 25 and 39 °C in cells
containing only Tpk1 (tpk2? tpk3?) or Tpk3 (tpk1? tpk2?) were very low (Fig. 5), whereas their basal thermotolerance and duplication time were similar to the WT.
However, the level of induced thermotolerance of tpk1? tpk2? was lower [P?=?0.05] than in WT cells (Additional file 1: Table S3). In tpk2? tpk3? and tpk1? tpk3? cells, the induced thermotolerance levels were similar to the WT cells, supporting
the idea that Tpk3 and Tpk1 hyper-repress the HSE-dependent gene expression when acting
as the sole PKA CS, and that Tpk3 represses the induced thermotolerance if acting
as sole PKA CS. These results confirm the hypothesis that the activities of the CS
are not redundant for the control of HSE-dependent gene expression, growth, basal
or induced thermotolerance. Also, these findings imply that Tpk2 activity antagonizes
Tpk1 and Tpk3 action, as has been suggested by other studies on the control of iron
uptake and pseudohyphal growth 61], 68], 69].

Fig. 5. Effect of TPK gene deletions on HSE-dependent gene expression. Strains were transformed with plasmid
pRY016 (2 ?) containing an HSE-CYC1-lacZ reporter gene. Growth and temperature treatments were performed as described in Methods
section. Values are reported as ?-galactosidase specific activity (nmol of hydrolyzed
ONPG min
^?1
 mg
^?1
protein) and are the average and standard deviation of at least three independent
experiments. Bars that do not share at least a common letter differ significantly
(P??0.05). Strains assayed were: WT (W303-1a), tpk1? (KG712), tpk2? (KG604), tpk3? (KS580), tpk2? tpk3? (KS590), tpk1? tpk3? (KS700), tpk1? tpk2? (KS710), tpk2?:: TPK2 tpk3? (KS590-URA3-TPK2)

Heat shock gene transcript levels are reduced when Tpk3 is the only CS

To learn more about the strong repressing activity of Tpk3 upon Hsf1, when Tpk1 and
Tpk2 are absent, we studied the levels of several stress genes within the context
of their natural promoters. As shown in Additional file 2: Figure S1, expression of the heat shock genes HSP104, HSP82, SSA3, HSP26, and HSP12 at 25 °C was reduced in the tpk1? tpk2? mutant relative to the WT strain. This result is consistent with the low level of
induced thermotolerance displayed by the tpk1? tpk2? mutant (Additional file 1: Table S3). Transformation of tpk1? tpk2? cells with TPK2 in a CEN plasmid did not complement fully the HSE-dependent gene expression at WT
levels (data not shown), most likely because TPK2 gene copy number per cell was not 1, but 2.8 copies/cell. Transformation of the tpk1? tpk2? cells with TPK2 in a 2 ? plasmid was toxic to the cell, explaining the surprisingly low copy number
in the surviving cells (1.7 copies/cell).

Tpk2 antagonizes the activity of Tpk1

To further test the hypothesis that the loss of TPK2 in the tpk2? tpk3? double mutant causes repression of HSE-dependent gene expression, the TPK2 gene was returned to the tpk2? tpk3? double mutant using the delitto perfetto technique (see Methods) 30], 79], restoring the native copy number of the gene. This modification (tpk2?::TPK2 tpk3?) returned HSE-dependent expression to WT levels (Fig. 5), supporting the idea that Tpk2 antagonizes the activity of Tpk1 on HSE-dependent
expression.

Catalytic activity of PKA in extracts from TPK mutants

We hypothesized that antagonism between Tpk2 and the other CS (Tpk1 and Tpk3) was
due to drastic changes in the total PKA activity of the cell. Accordingly, we could
expect that the total PKA activity in TPK2 mutants (tpk2?, tpk1? tpk2?, and tpk2? tpk3?) would be high, whereas in the WT, tpk1?, tpk3?, and tpk1? tpk3? mutants the PKA activity would be low. After addition of cAMP, PKA activity in extracts
from mutants tpk1?, tpk3?, and tpk1? tpk3? was similar to the WT (Additional file 2: Figure S2). On the contrary, cAMP-dependent PKA activity decreased in tpk2?, tpk1? tpk2?, and tpk3? mutants. These results indicate that HSE-dependent expression is not a simple reflection
of the overall PKA activity within the cell. Alternatively, one could also propose
that deletion of a given TPK gene reduced the PKA activity in the cell in a proportional manner to its abundance
in the WT. It is established that during exponential growth in liquid cultures yeasts
contain a large proportion of Tpk1, followed by Tpk2, and Tpk3 being the one with
the lowest abundance 88]. Thus, elimination of TPK1 and/or TPK2 should diminish dramatically the PKA activity in the cell. This was the case for
TPK2 deletions but not for TPK1 deletions (Additional file 2: Figure S2), indicating again that deletion of a given TPK gene does not influence arithmetically the overall PKA activity in the cell. Therefore,
dynamic mechanisms seem to define the final PKA activity in the WT and in a given
TPK mutant (interactions between CS, compartmentalization, stability, etc.).

Ssa1 and Ssa2 mediate the inhibition of HSE-dependent gene expression

Our initial computational model assumed that the regulation of Hsf1/Skn7 by the CS
was direct. However, under this design, predicted and experimental HSE-activities
for several PKA-RN mutants gave contrasting results. Complete agreement between experimental
and computational data was not achieved until a negative regulator was placed as an
intermediary between the CS and Hsf1/Skn7 (see Fig. 1 and the following subsection). This idea was in accordance with previous findings
demonstrating that the CS’s do not interact directly with Hsf1 20]. Therefore, we considered Hsp70 chaperones as putative intermediate inhibitors, because
they are well-known negative regulators of Hsf1. Yeast mutants with decreased Hsp70
levels increase the expression of Hsps, enhance thermotolerance, and grow slowly.
Additionally, these phenotypes are suppressed by a mutation in HSF1 that decreases its DNA binding affinity 13], 34], 92]. These observations and others from both mammals and yeast reinforce a model that
includes an auto-regulatory loop in which Hsp70 represses Hsf1 activity 4], 12], 94]. Moreover, Ssa1 positively controls the PKA-RN by stabilizing Cdc25 at optimal temperatures
26] and, under stress, the Cdc25-Hsp70 complex dissociates leading to a loss of Cdc25
levels and a decrease in the activity of the PKA pathway 26]. Our experiments revealed that deletion of SSA2 increased HSE-dependent gene expression (Fig. 6). Deletion of SSA1 did not affect HSE-dependent gene expression significantly, indicating that SSA2 suffices for maintaining WT activity. Deletion of both SSA1 and SSA2 largely increased the reporter activity, uncovering the contribution of both Hsp70
genes as repressors of HSE-dependent gene expression in WT cells. Interestingly, deletion
of SSA1 or SSA2 in a tpk2? background did not suppress the strong repression of HSE-dependent gene expression
characteristic of the tpk2? single mutant (Fig. 6). However, the phenotype of the tpk2? mutant was suppressed in the triple mutant ssa1? ssa2? tpk2?, as its HSE-dependent expression was higher than in tpk2? cells (at 25 °C and 39 °C), similar to that of the ssa1? and the WT at 25 °C, and lower compared to ssa1? and the WT at 39 °C. These results implicated Ssa1 and Ssa2 not only as mediators
of the strong repression of HSE-dependent gene expression, but also suggest the existence
of an additional repressor of Hsf1/Skn7, active in the absence of Tpk2.

Fig. 6. A role for SSA1 and SSA2 in the repression of HSE-dependent gene expression. Strains transformed with reporter
plasmid pRY016 were grown in SD medium at 25 °C until mid-exponential phase and treated
at different temperatures as described in Methods section. Data shown represent the
average and standard deviation of at least three independent experiments. ?-galactosidase
specific activities are reported as in Fig. 2. Bars that do not share at least a common letter differ significantly (P??0.05). Strains assayed were: WT (W303-1a), tpk2? (KG604), ssa1? (S001), ssa1? tpk2? (S002), ssa2? (SL622), ssa2? tpk2? (SL623), ssa1? ssa2? (SL625), ssa1? ssa2? tpk2? (SL708)

The dynamical model of the PKA-RN revealed an additional negative regulator of Hsf1

To thoroughly understand the implications of our observations we constructed a discrete
dynamical model of the PKA-RN based both on our results and in the literature 4], 10], 19], 20], 23], 26], 60], 61], 66], 68], 69], 76], 78], 84], 89], 94]. As described in the Methods section, we have used an extension of a synchronous
discrete modeling framework, as this type of modeling is known to accurately predict
the behavior of several biological networks. One of the advantages of the discrete
framework is that it only requires knowledge about the regulatory nature of the interactions
involved, contrary to reaction-kinetic differential equations that require the precise
values for all the kinetic parameters and cooperativity exponents of the network elements.
For a detailed review of the advantages and disadvantages of discrete and Boolean
models compared to other frameworks consult 1], 38], 71], 90].

Briefly, our model consists on N elements {? ₁ , ? ₂ ,…, ? _N
} whose dynamical states take integer values ranging from 0 to m _i
, where m _i
is the maximum level of activity (or level of expression) for element ? _i
. Usually only two levels of activity are implemented: either the node is active (? _i
?=?1) or it is inactive (? _i
?=?0). However, often the functionality of a given node depends on whether it has
a low, mild or high level of activity 9] and the binary description is not enough. This is the case here, as our experiments
indicate that some nodes of the TPK-RN require distinction of up to six levels of
activity (see Additional file 3: Sections 3 and 4 in the Supplementary Information). Additionally, as currently there
is no information about the time scales implicated in the dynamics of the PKA-RN elements,
for graphing we used a synchronous updating scheme (see Methods).

For each network (we will consider WT, tpk1?, etc., as different networks) we sampled about 10 % of the complete set of initial
conditions (which consists of more than 4 billion points) looking for steady states
of expression (attractors) (see Additional file 4: Text S1). As several initial conditions may fall into the same attractor, we define
the size of the basin of attraction B _k
as the number of initial conditions that fall into attractor K. Our extension of this traditional modeling framework consists in two simple modifications.
First we averaged the level of expression for each element over a time window whose
length equaled the attractor period. This gave us a single continuous value A _ik
for each element ? _i
in the k ^th
attractor. Then, to better represent the experimental measurements from liquid batch
cultures where a single average expression level is obtained, we averaged the quantities
A _ik
over all the attractors of the network, weighted by the size of the corresponding
basin of attraction (see Methods). Thus, contrary to other studies 9], 46], 52], we avoided discarding any attractor reached by the network deeming it as “non-biologically
relevant”.

From now on, we will refer to this extension as the Windowed Discrete Model (WDM).
This statistical treatment of data is supported by experimental studies showing that
individual yeast cells in batch cultures exhibit different cell cycle phases, physiological
states, and gene expression patterns that result in a heterogeneous population 23], 40], 53]. With this procedure, we were able to make a direct and semi-quantitative comparison
between the model predictions and the experimental measurements. The WT interaction
network considered is shown in Fig. 1 and the logic rules governing the dynamics of the system are presented on the Supplementary
Information (see Additional file 3: Section 3).

The modeled PKA-RN starts with the Cdc25-Ras branch. Cdc25 abundance and function
are dependant on the activity of the Hsp70 chaperones (Ssa1 and Ssa2) 26]. Under optimal temperature and nutrients conditions, Cdc25 acts as the positive regulator
of Ras2 activity 6], 22], which in turn activates Cyr1 (adenylate cyclase) 43]. The product of Cyr1, cAMP, negatively regulates the inhibition imposed by Bcy1 upon
the CS Tpk1, Tpk2, and Tpk3 84]. The CS were modeled as a module showing antagonism, as our results (Figs. 1 and 5) and those from others have suggested 61], 68], 69]. We propose that Tpk2 activity inhibits the activation of Ssa1 and Ssa2 by the Tpk1
and Tpk3 subunits. The implication for this interaction is that, in a WT background
where the three CS are active, only the activity of Tpk2 is effective in activating
Ssa1 and Ssa2 chaperones. The mechanistic basis for this antagonism remains to be
studied. A systematic study of yeast kinases, made in vitro, showed that some CS have as substrates other CS. In particular, Tpk1 phosphorylates
Tpk2 and Tpk3; Tpk3 phosphorylates Tpk2; and Tpk2 phosphorylates Tpk3 65]. It remains to be seen whether the antagonism between the CS is caused by their mutual
phosphorylation or whether it occurs via other indirect mechanisms.

As mentioned above (Fig. 6), the inhibition of the HSE-dependent expression by the PKA-RN requires the activation,
by the TPKs, of an inhibitor of Hsf1 and Skn7. Ssa1 and Ssa2 (Hsp70 proteins) were
introduced into the model as repressors of the HSE-dependent expression 4], 78] (Fig. 6). Moreover, based on the expression levels of the triple mutant ssa1? ssa2? tpk2? (Fig. 6), we included a third repressor of Hsf1/Skn7 that gets activated exclusively when
Tpk1 and Tpk3 become the only CS (i.e., when Tpk2 is absent or at minimum levels).
We believe that a very plausible candidate for such a repressor could be Hsp90, given
that Hsp90 binds to Hsf1 59], 96] and its deletion increases HSE-dependent expression 16]. Moreover, Tpk1 and Tpk3 phosphorylate Hsp82 (Hsp90) in vitro65]; although the functional significance of this phosphorylation is unknown. It is plausible
that the binding of Hsp90 to Hsf1 could be enhanced upon phosphorylation by Tpk1 or
Tpk3, but this needs to be addressed experimentally. Similarly, Tpk1 and Tpk3 could
enhance the repression of Hsf1 by other members of the Hsp70 family, such as Ssb1
or Ssb2, as it is known that Ssb1 and Ssb2 form complexes with Hsf1 and deletion of
their genes also increases HSE-dependent expression 4]. However, more work is needed to identify the third repressor that is unleashed in
the absence of Tpk2. In any case, it is important to stress that only by including
the three repressors (Ssa1, Ssa2, and the putative third repressor), the experimental
measurements could be reproduced by the model.

Quantitative comparison between theoretical and experimental results corroborates
the proposed regulatory interactions

To validate the simulations of our model, we compared the HSE-dependent expression
results obtained computationally and those obtained experimentally in a number of
mutant strains. Population measurements were reported as the ratio (strain expression
level)/(WT expression level) and are presented in Additional file 1: Table S4. Figure 7 shows that the results obtained with the WDM closely resembled the experimental results
obtained for all strains. The great concordance between theory and experiment suggests
that the novel interactions proposed here for the PKA-RN are very likely true. Additionally,
we also implemented several asynchronous updating schemes and the results that we
obtained for the population expression level were almost identical regardless of the
synchronicity or asynchronicity of the updating scheme (Additional file 2: Figure S3). This feature is quite relevant because, for a particular network (single-cell
level) the use of asynchronous updating can significantly change the dynamical attractors
of the network 15], 36] to the point that random asynchronous updating has been called inadequate in some
scenarios 15]. We present the structure of the attractor landscape for the 25 °C WT network using
synchronous updating (Additional file 2: Figures S5 and S6). As this example shows, different basins of attraction varying
in size can be visualized. The WDM takes this fact into account to simulate subgroups
of cells that might correspond to the different basins of attraction.

Fig. 7. Comparison between experimental data and predictions by the WDM. Comparison between
experimental and theoretical measurements for HSE-lacZ activity. Values are given as average ratios between strain expression and WT expression
at 25 °C, making the average expression ratio of the WT strain at 25 °C equal to one.
Theoretical and experimental values show similar quantitative behavior across strains.
Moreover, since the theoretical values are no longer discrete, subtle differences
occurring experimentally are reproduced also by the model. a Ratios at 25 °C, b ratios after a heat shock at 39 °C

In addition to the population measurements, we present simulations for the temporal
dynamics of Bcy1, cAMP, HSE-lacZ, and Tpk3 that, presumably, could be valid for single-cell measurements (Fig. 8). Each curve represents a simulation corresponding to a different strain (WT, ssa1? ssa2?, tpk2?, and tpk1? tpk3?) starting from a random initial condition. At time t_0,
an increase in the temperature was simulated by turning on the heat shock node. In
the absence of Ssa1 and Ssa2 (Fig. 8, red lines), the levels of HSE-lacZ activity and Bcy1 increased dramatically, while the levels of cAMP and Tpk3 were
very low. In the absence of Ssa1 and Ssa2, the dynamics of Tpk1 and Tpk2 were identical
to Tpk3 (data not shown). The particular temporal dynamics observed in these simulations
(oscillatory behavior, spikes, etc.) remain to be experimentally confirmed through
the use of single-cell measurements. Nonetheless the predictions reported in Fig. 8 fit well the experimental data showing that ssa1? ssa2? mutants are constitutively resistant to high temperature and display elevated production
of Hsp’s and slow growth rates 34]. Deletion of TPK2 also decreased the expression of HSE-lacZ with respect to the WT, but more conspicuously at 39 °C than at 25 °C, consistent
with the lower induced thermotolerance level in this mutant (Additional file 1: Table S3).

Fig. 8. Single-cell predictions of the temporal dynamics for Bcy1, cAMP, HSE-lacZ, and Tpk3 in WT and three mutants. Temporal dynamics for four selected nodes: Bcy1
(a), cAMP (b), HSE-lacZ (c), and Tpk3 (d). Line colors correspond to different strains. Simulations were made starting from
a random initial condition for each strain. Expression and time are given in arbitrary
units. Background color represents the temperature of the culture: 25 °C (blue) and
39 °C (pink)