Design of a MAPK signalling cascade balances energetic cost versus accuracy of information transmission

Abstract

Cellular processes are inherently noisy, and the selection for accurate responses in presence of noise has likely shaped signalling networks. Here, we investigate the trade-off between accuracy of information transmission and its energetic cost for a mitogen-activated protein kinase (MAPK) signalling cascade. Our analysis of the pheromone response pathway of budding yeast suggests that dose-dependent induction of the negative transcriptional feedbacks in this network maximizes the information per unit energetic cost, rather than the information transmission capacity itself. We further demonstrate that futile cycling of MAPK phosphorylation and dephosphorylation has a measurable effect on growth fitness, with energy dissipation within the signalling cascade thus likely being subject to evolutionary selection. Considering optimization of accuracy versus the energetic cost of information processing, a concept well established in physics and engineering, may thus offer a general framework to understand the regulatory design of cellular signalling systems.

Full text

ARTICLE
Design of a MAPK signalling cascade balances
energetic cost versus accuracy of information
transmission
Alexander Anders1,2,4, Bhaswar Ghosh1,2,3,4 ✉, Timo Glatter1& Victor Sourjik 1,2✉
Cellular processes are inherently noisy, and the selection for accurate responses in presence
of noise has likely shaped signalling networks. Here, we investigate the trade-off between
accuracy of information transmission and its energetic cost for a mitogen-activated protein
kinase (MAPK) signalling cascade. Our analysis of the pheromone response pathway of
budding yeast suggests that dose-dependent induction of the negative transcriptional feed-
backs in this network maximizes the information per unit energetic cost, rather than the
information transmission capacity itself. We further demonstrate that futile cycling of MAPK
phosphorylation and dephosphorylation has a measurable effect on growth fitness, with
energy dissipation within the signalling cascade thus likely being subject to evolutionary
selection. Considering optimization of accuracy versus the energetic cost of information
processing, a concept well established in physics and engineering, may thus offer a general
framework to understand the regulatory design of cellular signalling systems.
https://doi.org/10.1038/s41467-020-17276-4 OPEN
1Max Planck Institute for Terrestrial Microbiology, 35043 Marburg, Germany. 2LOEWE Center for Synthetic Microbiology (SYNMIKRO), 35043
Marburg, Germany.
3
Present address: International Institute of Information Technology, Gachibowli, Hyderabad, India.
4
These authors contributed equally:
Alexander Anders, Bhaswar Ghosh. ✉email: bhaswar.ghosh@iiit.ac.in;victor.sourjik@synmikro.mpi-marburg.mpg.de
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Living organisms have the ability to sense cues in the external
and internal environment in order to initiate appropriate
cellular responses. Inherent stochasticity of events involved
in sensing and downstream transmission of signals may lead to
noise, which is manifested as the variability in signalling outputs,
e.g. morphological changes or reporter gene expression, across a
population of clonal cells, leading to loss of information about
the strength of the input1–4. While heterogeneity within a cell
population can be beneficial in some cases5, typical signalling
pathways rather evolved to transmit information precisely in
order to enable reliable input-dependent cellular responses.
The precision of signal decoding by cellular networks can be
estimated using information theoretic approaches6–11. As the
input (e.g. concentration of a chemical stimulant) varies and this
change is transmitted via a signalling pathway, the change in the
output (e.g. stimulated expression of a gene) carries information
about the input variable. In general, the precision with which the
input value can be estimated from measuring the output
improves with larger changes (i.e. dynamic range) of the output
and with lower output noise. According to Cramėr–Rao
inequality, the error in estimating the input from the output is
bounded by the Fisher information12,defined as the relative
entropy change of the output distribution for an infinitesimal
change in the input around a given input value.
Furthermore, information transmission capacity of signalling
systems can also be estimated by calculating the mutual infor-
mation2,13, which is increasingly being used to characterize bio-
chemical signalling networks1,6,8–11,14. The mutual information
measures the mutual interdependence between the input and the
output distributions by calculating the relative entropy of the
output distributions conditioned on the input with respect to the
unconditioned output distributions. In both cases, more infor-
mation can be extracted about the input from the output dis-
tribution if the relative entropy change is large.
Cells apparently evolved several strategies to improve infor-
mation transmission in the presence of the stochastic noise, using
multiple genes2or multiple time points (i.e. time-averaging)15 for
readout or by actively suppressing noise16,17. The latter includes
utilization of negative feedbacks, which have been shown both
theoretically and experimentally to reduce signalling noise and
therefore to enhance the information transfer16–18. Furthermore,
negative feedbacks can reduce basal activity (i.e. activity in
the absence of signal) and/or the activity of fully stimulated
network—which can, dependent on the system, either increase or
decrease the output range and thus information transfer2,13.
Although increasing the accuracy of signalling typically imposes
additional energetic cost19–21, to which extent this fundamental
trade-off between information and energy is reflected in the
properties of cell signalling networks remains largely unclear.
We address this question by focusing on the negative feedback
regulation within the pheromone response (or mating) pathway in
Saccharomyces cerevisiae, one of the most studied examples of
eukaryotic signalling. This pathway mediates communication and
ultimately mating between two haploid mating types of S. cere-
visiae,MATaand MATα, which secrete a- and α-pheromones,
respectively. Each pheromone is sensed by the opposite mating
type, whereby perception of pheromone by a G protein-coupled
receptor (Ste2 in MATa) stimulates the canonical mitogen-
activated protein kinase (MAPK) cascade, leading to activation
of the MAPKs Fus3 and Kss122–24. Fus3, the major MAPK of the
mating pathway, induces cell-cycle arrest, mating-specific changes
in cell morphology and, via activation of the transcriptional acti-
vator Ste12, expression of mating genes including genes that
encode components or regulators of the MAPK cascade25–29.
Previous studies demonstrated that the pheromone pathway
transmits information with high precision, as exemplified by a
linear relationship between receptor occupancy and downstream
responses (“dose–response alignment”)30 and by a uniform mor-
phological transition of cell population into a mating-competent
state (“shmooing”) at a critical pheromone concentration27,31.
Such uniformity in the output implies existence of, likely multiple,
mechanisms to improve precision of information transmission
within the pathway. Indeed, the negative feedback within the
pheromone pathway provided by Sst2, a GTPase-activating pro-
tein (GAP) for the receptor-coupled G protein α-subunit, appears
to fulfil such function30,32.
Here, we primarily investigate the feedback regulation by
Msg5, a dual-specific phosphatase for Fus3. Our experimental
and computational analyses show that the pheromone-dependent
transcriptional induction of Msg5 reduces variability and
increases the dynamic range of the pathway output, hence
increasing information transmission. Selection for increased
accuracy could thus explain the presence of negative feedback
regulation mediated by phosphatases as a common feature of the
MAPK pathway topology. We further investigate the sensitivity
of induction of the negative feedback provided by Msg5, which is
activated at much higher pheromone dose than the upstream-
acting negative feedback provided by Sst228,29. We demonstrate
that, while the precision of input estimation could be significantly
enhanced by artificially increasing the sensitivity of MSG5 gene
induction, the naturally observed regulation appears optimal
when considering energy investment into operation of the sig-
nalling pathway. We argue that such regulatory design, with
lower induction sensitivity of the downstream feedback, might
in general (optimally) balance accuracy of signalling against
the energetic cost of pathway operation. Finally, we confirm
experimentally that the phosphorylation/dephosphorylation
cycle at the core of the MAPK signalling pathway has measurable
fitness cost, thus likely placing it under evolutionary selection
pressure.
Results
MSG5 and SST2 are induced at different pheromone doses.
Since we were interested in feedback regulation within the
S. cerevisiae pheromone pathway that could be provided by
transcriptional induction (i.e. transcriptional feedback regula-
tion), we first determined which pathway-associated genes, and at
what dose, are activated by the pheromone stimulation using
transcriptomics (see “Methods”). Here, we exclusively focused on
the branch of pheromone signalling mediated by MAPK Fus3, by
utilizing strains devoid of the functional Kss1. Furthermore, all
strains used for quantitative measurements of the α-pheromone
responses were deleted for the α-pheromone-protease gene BAR1
and for α-pheromone genes MFα1and MFα2to respectively
avoid pheromone degradation or possible self-stimulation due to
background expression of α-pheromone by MATacells.
We find that, of the core pathway and regulatory components,
expression of genes encoding the receptor Ste2, the GAP of
the receptor-coupled Gαprotein (Sst2), the kinase Fus3, its
phosphatase Msg5 and the inhibitor of transcriptional activator
Ste12 (Dig2) were upregulated (Supplementary Fig. 1), in a
general agreement with the previous reports28,29,33. This suggests
that the pheromone pathway is regulated by at least two pairs of
positive/negative feedback loops, respectively, at the upper and
lower levels of the cascade (Fig. 1a). We quantified induction
sensitivities to pheromone of feedback regulators by determining
EC
50
values, i.e. pheromone concentrations for achieving half-
maximal induction (Fig. 1b). Notably, while both positive
feedbacks (Ste2 and Fus3) and the upstream-acting negative
feedback mediated by Sst2 become induced already at the low
pheromone dose, the downstream-acting Msg5 negative feedback
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was upregulated only at much higher pheromone levels (Fig. 1b
and protein colouring in Fig. 1a).
Negative feedbacks improve information transmission.We
subsequently investigated the role of the negative feedbacks and
their different induction sensitivities in the regulation of the
pathway output. Since negative regulation by Sst2 has been
already shown to suppress noise in the pheromone pathway32,we
focused on the negative feedback regulation by Msg5. To examine
the noise-suppressing capability of Msg5, we measured the output
fluorescence of the pheromone-responsive P
FUS1
-GFP reporter in
individual cells by fluorescence microscopy (see “Methods”).
Indeed, we found that in the absence of either Sst2 or Msg5 the
reporter output became more sensitive to low doses of pher-
omone (Fig. 2a). Moreover, the intercellular variability of the
output in the population—total noise (η
tot
), determined as the
coefficient of variation (CV) of reporter activity—significantly
increased (Fig. 2b). While the effect of MSG5 deletion (msg5Δ)
was mild compared to sst2Δ, it was further unmasked by deletion
of phosphatase Ptp3. Ptp3 thus seems to partly compensate the
loss of Msg5, although it is not transcriptionally induced by
pheromone (Supplementary Fig. 1A) and in itself had nearly no
impact on pathway response and noise (Fig. 2a). Another phos-
phatase, Ptp2, that was induced by the pheromone (Supplemen-
tary Fig. 1B) had virtually no effect on pheromone signalling
(Supplementary Fig. 2). Besides increasing output noise, absence
of either Msg5 or Sst2 lowered the threshold of pheromone
stimulation and also elevated the basal pathway activity. Since
the maximal output responses remained nearly unaffected, these
deletions thus effectively reduced the output range.
In order to quantify signalling accuracy in wild type and
mutant strains, we invoked an information theory approach. As
mentioned above (see “Introduction”), both output range and
pathway noise impact the signalling precision and amount of
information that can be transmitted through a signalling
pathway2,13,16,30. Precision in the input estimation can be
characterized locally (i.e. at different pathway outputs) by the
Msg5 Fus3
Ste12
Sst2 Gpa1
Ste2
ab
1 10 100
[-pheromone] (nM)
0.2
0.4
0.6
0.8
1.0
0
Normalized RPKM
0.1
STE2
SST2
FUS3
MSG5
Relative EC50
5
4
3
2
1
Fig. 1 Activation of the pheromone response pathway induces multiple
feedback loops. a Simplified depiction of the pathway and its feedback
regulators. Activation of the pheromone receptor Ste2 leads, through a
signalling cascade, to activation of MAP kinase Fus3. Fus3-dependent
phosphorylation of transcriptional activator Ste12 stimulates the expression
of Ste2 and Fus3 as well as of two negative pathway regulators: Sst2, a
GTPase activating protein (GAP) for Gαprotein Gpa1; and Msg5, a
phosphatase for Fus3. These upregulated components are coloured
according to relative EC
50
values (normalized to the lowest value,
approximately 4 nM for STE2) of their mRNA dose responses; mRNA levels
of pathway components in white boxes were not upregulated. Black arrows
denote transcriptional feedback regulation, green (dashed) arrows denote
(indirect) activation and red blunt-end arrows indicate inhibiting activity.
bDose dependence of pheromone activation for the indicated genes
encoding pathway components. Shown are normalized RNA levels as
measured in two independent RNA sequencing experiments (symbols with
and without frames, respectively) at 60 min after addition of respective
dose of pheromone in a strain deleted for α-pheromone protease gene BAR1
(Supplementary Table 1). Lines are fits with a sigmoidal function used to
infer EC
50
values, used for the colour scale in a,b.
0.02 0.06 0.10
0.0
0.3
0.6
0.9
Mutual information
FUS1 promoter output (A.U.)
d
0.02 0.06 0.10
0
1
2
3
Fisher information
FUS1 promoter output (A.U.)
c
e
0.02 0.06 0.10
0.0
0.2
0.4
0.6
FUS1 promoter output (A.U.)
tot
2
b
FUS1 promoter output (A.U.)
[α-pheromone] (nM)
0 0.01 0.1 1 10
0.05
0.00
0.10
0.15
a
Wild type
msg5
ptp3
msg5 ptp3
sst2
0.01 0.1 1 10
0.2
0.4
0.6
0.8
1.0
0.60.4 0.8 1.0
0.1
0.2
0.3
0.4
0246
Fisher information Mutual information
0.05
0.025
0.125
0.075
0.10
Output
00.51 21.5
0.2 0.4 0.6 0.8 1.0
0.0
0.2
0.4
0.6
0.8
0.2 0.4 0.6 0.8 1.0
0.0
0.1
0.2
0.3
0.4
0.5
Fig. 2 Negative feedback regulators improve accuracy of input estimation
and information transmission. a Dose dependence of pathway activation,
measured using activity of a P
FUS1
-GFP pathway reporter, for wild type
(black) and strains deleted for negative regulators (colours as indicated).
Data were collected between 140 and 210 min after pheromone addition,
using time-lapse microscopy (see “Methods”), in two independent
experiments (shown with different symbols). Dashed lines connect means
for both experiments and serve as a guide to the eye; shaded areas centred
on those lines show cell-to-cell variabilities (s.d.) across the cell
populations, again averaged over both experiments with at least 300 cells
per point and experiment. bPathway noise, calculated as the coefficient of
variation of P
FUS1
-GFP levels across the population, in the individual
experiments (symbols as in a), plotted against the P
FUS1
-GFP output.
Dashed lines connect the means of noise and P
FUS1
-GFP output for both
independent experiments. c,dFisher (c) and mutual (d) information,
calculated as described in “Methods”independently for both experiments
(symbols are as in a). Notably, although mutual information was calculated
between the pheromone input and the pathway output, it was plotted
against the pathway output at a particular pheromone input for better
comparison between strains that have different sensitivities to pheromone.
Dashed lines connect means for both independent experiments. Fisher and
mutual information are not shown for sst2Δstrain. Insets in a–dshow
results of stochastic simulations using a simplified mathematical model of
the pheromone pathway (see main text). eAggregated, i.e. summed up
over the whole output range, Fisher (left) and mutual (right) information,
with individual contributions at different output levels shown in different
shades of grey. Aggregated information was calculated from means for
both independent experiments. Edges of bars are coloured according to the
strains as indicated in a.
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Fisher information12,34 (see Supplementary Note 1 for more
details). Fisher information was indeed significantly higher,
virtually over the whole range of pathway outputs, for the wild
type as compared to msg5Δor msg5Δptp3Δstrains (Fig. 2c).
Consequently, aggregated Fisher information was highest for the
wild type, too (Fig. 2e, left). In order to distinguish respective
contributions of increased output range and decreased noise to the
Msg5-mediated improvement of information transmission, Fisher
information was also calculated when projecting noise levels of the
wild type onto msg5Δdose responses and vice versa. We found that
individual contributions of the output range expansion and noise
suppression by Msg5 to the improved information transmission
were roughly equal and synergistic (Supplementary Fig. 3).
Thus negative feedbacks improve accuracy of input estimation by
both expanding the dynamic range of the output and lowering the
output noise.
To confirm these results obtained using Fisher information, we
also calculated mutual information, another frequently used
measure of information transmission35. To directly compare these
two measures of information transmission, mutual information was
calculated locally at a particular level of pathway stimulation, as
done previously14 (Supplementary Note 1). Relative differences in
transmitted mutual information between strains were comparable
to those observed for Fisher information (Fig. 2d, e, right panel).
Notably, similar differences between strains were observed at other
time points of stimulation for both Fisher and mutual information
(Supplementary Fig. 4).
Finally, we tested whether it is the negative transcriptional
feedback or simply the negative regulation of the pathway that are
important for enhanced precision, by constitutively expressing
MSG5 under control of a doxycycline-inducible promoter. Such
constitutive Msg5 production could only partially rescue the
output range, noise suppression and precision (Supplementary
Fig. 5), implying that pathway-dependent induction of the
transcriptional feedback is indeed crucial.
Sensitized MSG5 induction improves information transmis-
sion. Although both Sst2 and Msg5 negative feedback regulators
improve information transmission, they display different induc-
tion sensitivities, with Sst2 that acts upstream in the pathway
being induced at lower dose than the downstream-acting Msg5.
In order to study the impact of the dose dependence of feedback
induction in silico, we constructed a simplified mathematical
model of pheromone signalling that consists of a two-step
phosphorylation cascade activated by pheromone at the upper
level and incorporates two negative (Sst2 and Msg5) as well
as two positive (Fus3 and Ste2) feedbacks (Supplementary
Fig. 6A, see “Methods”and Supplementary Note 2 for details).
Simulations of this model qualitatively confirmed that negative
feedbacks reduce basal activity and noise of the pathway output,
therefore enhancing Fisher and mutual information (Fig. 2a–d
insets).
We then used this model to investigate the dependence of the
signalling accuracy on induction sensitivity of the Msg5 feedback
by systematically varying K
D
value that quantifies binding
strength of active Ste12 (i.e. phosphorylated Ste12-P) to MSG5
promoter and calculating resulting dose responses to pheromone,
output noise and Fisher information (Fig. 3a, Supplementary
Fig. 6B, C). Interestingly, simulations predicted that maximum
information would be transmitted by the pathway at the highest
sensitivity of MSG5 induction (Fig. 3a), in contrast to the
experimentally observed low induction sensitivity.
To test this model prediction experimentally, we replaced the
native promoter of MSG5 with P
FUS1
promoter that is induced
by lower levels of pheromone (Supplementary Fig. 1). The
modified induction of MSG5 both decreased basal pathway
activity and improved suppression of noise, particularly in the
lower range of activity (Fig. 3b, c), similar to the results of
model simulations (Supplementary Fig. 6B). Consequently, the
overall information transmission increased, while its range
slightly shifted to lower activity as compared to the wild type
(Fig. 3d), again confirming model predictions. We obtained
similar results for high-sensitivity induction of MSG5 by other
pathway-dependent promoters, in these cases measured using
flow cytometry (Supplementary Fig. 7). Notably, our analysis
showed that both lowered basal pathway activity and reduced
noise at low pathway activity contributed to the observed
increase in Fisher information (Supplementary Fig. 8).
Sensitive feedback induction maximizes information. We next
systematically investigated the dependence of information trans-
mission through the pathway on the induction sensitivities of
both negative feedbacks, Sst2 and Msg5. Since in our simulations
information transmission to the downstream transcriptional
0 0.1 101
0.05
0.10
0.15
ab c d
0.0 0.2 0.4 0.6 0.8 1.0
1.5
2.0
FUS1 promoter output
16
64
256
1024
4096
K
D
P
MSG5
(nM)
Simulated information
Fisher information
[-pheromone] (nM)
FUS1 promoter output (A.U.)
0.05 0.10 0.15
0.4
FUS1 promoter output (A.U.)
0
1
2
3
4
Fisher information
FUS1 promoter output (A.U.)
0.05 0.10 0.15
0.2
0.6
0.5
1.0
0.0
Output
0.05
0.10
Fisher information
5
10
Wild type
P
FUS1
-MSG5
tot
2
Fig. 3 Sensitized MSG5 induction leads to improved input estimation. a Dependence of simulated Fisher information on sensitivity of MSG5 feedback
induction, altered by adjusting the parameter defining binding affinity of active Ste12-P to the MSG5 promoter (K
D
P
MSG5
). For simulation of the wild type in
Fig. 2,K
D
was 700 nM. b–dEffect of sensitized MSG5 feedback induction on dose dependence of the pathway response (b), noise (c) and Fisher
information (d). MSG5 induction was sensitized by replacing its native promoter with P
FUS1
promoter that responds with higher sensitivity to pheromone.
Data were acquired between 110 and 170 min after pheromone addition in two independent experiments (shown with different symbols in b–d). Dashed
lines serve as guides to the eye and connect means for both experiments; shaded areas in bcentred on those lines show cell-to-cell variabilities (s.d.)
across the cell populations, again averaged over both experiments. Similar results were observed when MSG5 induction was sensitized using other
promoters (Supplementary Fig. 6). Inset in dshows aggregated Fisher information calculated with means for both experiments.
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reporter is reduced by saturation of the phosphorylation and
DNA-binding functions of Ste12 (Supplementary Fig. 9A),
we calculated total information (i.e. information averaged over
all simulated inputs) based on active Fus3 (i.e. double-
phosphorylated Fus3-PP) as the output. Also at this level, the
information transmission was reduced in the absence of negative
feedback regulators Sst2 and Msg5 (Supplementary Fig. 9B).
Consistent with simulation of the transcriptional output (Fig. 3a),
maximal aggregated (total) transmission information contained
in Fus3-PP was observed at similarly high induction sensitivities
(i.e. low K
D
values) for Msg5 and Sst2 (Fig. 4a, Supplementary
Fig. 10). Notably, similar to our experiments, varying K
D
values
in the simulations not only changed the sensitivity of induction
(i.e. EC
50
value) but, at the same time, also altered dynamic
ranges of the analysed output.
Information transmission is balanced by energy consumption.
Since both experiments and modelling suggest that induction
sensitivity of the Msg5-mediated negative feedback in the
pheromone signalling pathway may not to be optimized for
maximizing information transmission, we asked in which respect
the naturally observed design might be superior to a potential
information-maximizing design. While having the capacity to
reduce noise and/or increase the output range, negative (feed-
back) regulation requires energy. In the cases of Msg5 and Sst2
feedbacks, this means consumption of adenosine triphosphate
(ATP) in cycles of phosphorylation and dephosphorylation
(subsequently simply referred to as phosphorylation cycles) and
increased consumption of guanosine triphosphate (GTP) for
activation and de-activation cycles of receptor-coupled G protein,
respectively. Generally, maintaining a given pathway output in
the presence of negative (feedback) regulation entails higher
energy consumption than its absence, which might constrain
optimization of negative feedback regulation. We estimated that
the rate of ATP consumption that is required to maintain half of
total Fus3 molecules phosphorylated36, ~104molecules/cell at full
pathway induction, amounts to 0.2% of total cellular energy use
in rich medium (Supplementary Note 5). Thus the cost of energy
investment in operating the MAPK signalling pathway might be
ac
Information
bd
Relative active Fus3 (–)
0.01 0.05 0.20.02 1.00.1 0.5
Relative active Fus3 (–)
0.01 0.05 0.20.02 1.00.1 0.5
101
100
102
ATP+GTP cons. rate (nM/s)
16
64
256
1024
4096
KDPSST2 (nM)
16
64
256
1024
4096
KDPMSG5 (nM)
0
0.2
0.4
0.6
8
16
32
64
128
256
512
1024
2048
4096
4096
2048
1024
512
256
128
64
32
16
8
Information/energy (nM/s)
–1
Information per energy
Energy consumption (KD PSST2)
K
D
P
SST2
(nM)
KD PMSG5 (nM)
KD PMSG5 (nM)
8
16
32
64
128
256
512
1024
2048
4096
4096
2048
1024
512
256
128
64
32
16
8
Total Fisher information
0.6
1.0
1.4
Quantity compared to initial situtation
Unchanged Higher
Increase of rX
Xactive •
Increase of rY
Yactive •
Energy consumption (KD PMSG5)e
active
active
X
Y
Xactive •rX
Yactive •rY
Initial situation
0.2
K
D
P
SST2
(nM)
101
100
102
ATP+GTP cons. rate (nM/s)
rX
rY
Fig. 4 Induction of negative feedback regulators may balance accuracy versus energy investment. a Simulated dependence of pathway accuracy
(information) on sensitivities of SST2 and MSG5 induction. The heat map shows total Fisher information of active Fus3 (Fus3-PP) over the same 5 × 106
range of stimulus strength (see main text and Supplementary Fig. 8 for details) for varying binding affinities (K
D
) of Ste12-P to SST2 and MSG5 promoters.
b,cSimulated energy (ATP+GTP) consumption rates as a function of relative active Fus3 (Fus3-PP normalized to maximum per plot) for different
induction sensitivities of SST2 (b) and MSG5 (c). Binding affinities of Ste12-P to SST2 and MSG5 promoters were changed individually while keeping affinity
to the respective other promoter fixed at 8 nM. dSimulated dependence of information per energy on sensitivities of feedback induction. The heat map
shows total Fisher information per energy (see text for details) simulated as in a.eCartoon illustrating difference between energetic costs of negative
feedback regulation at two stages of a simulated signalling cascade. Here, activities of two consecutive positive regulators (Xand Y), indicated by filling
heights of the respective circles, are determined by the influx (e.g. phosphorylation) and outflux (e.g. dephosphorylation) rates of energy. Influx rates at the
upper (lower) level depend on the signal strength (e.g. pheromone stimulation) and activity of the upstream regulator, respectively. Outflux rate constants
(r
X
,r
Y
) correlate with the activities of negative regulators (e.g. phosphatases). Red colour indicates increase in quantities compared to the initial situation
(upper panel). In order to sustain constant cascade output Y
active
while increasing r
x
(middle panel), the increased outflux requires compensation by higher
influx into X(i.e. stronger stimulation is required to achieve the same output). In this case, increased flux of energy solely at the affected level is sufficient
for compensation. However, when increasing r
Y
(lower panel), the compensatory higher influx into Yadditionally requires an increase in X
active
, which in
turn requires higher influx into X. Thus compensation of increased r
Y
entails increased energy fluxes on both cascade levels.
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sufficiently high to affect cellular fitness. This estimated cost of
continuous phosphorylation cycle of Fus3 is comparable to the
cost of cellular investment into the biosynthesis of signalling
proteins (Supplementary Note 5), reminiscent of signalling in
bacterial chemotaxis19, and thus, indeed, might be subject to
evolutionary optimization.
Consequently, in our model simulations, we took into
consideration the energy consumed during the signalling process,
GTP at the upper level and ATP at the lower level. Intuitively, in
order to maintain a given pathway output, higher activity of a
negative regulator requires stronger pathway activation by the
pheromone, which increases turnover of GTP and/or ATP.
Induction of a negative feedback regulator already at low levels of
pathway stimulation should result in increased energy consump-
tion over a wide range of pathway activities. This effect is indeed
apparent when varying induction sensitivities of both SST2
(Fig. 4b) and MSG5 (Fig. 4c). However, while the increase in
energy consumption with increased sensitivity is relatively
modest for SST2, it is much more pronounced for MSG5.
To take into account both information transmission and energy
consumption in our simulations, we calculated integrated
information per energy37, or energy efficiency, for different
sensitivities of feedback induction:
Efficiency ¼Zθ2
θ1
FθðÞ
EθðÞ
PθðÞdθ:ð1Þ
Here, F(θ)is the Fisher information, E(θ)is the energy expenditure
and P(θ)is the probability of the input (Supplementary Notes 1
and 4). This definition is convenient in restricting our energy
calculation to the range of pathway stimulation that contains
information. In contrast to the maximal information transmission
(Fig. 4a), maximal information per energy was obtained at high-
sensitivity SST2 and low-sensitivity MSG5 induction (Fig. 4d and
Supplementary Note 4), which is consistent with our experimental
observations. This finding indicates that the natural design of the
MAPK pathway might be tuned to balance the precision of
information transmission with energy investment needed to
enable high precision. More generally, our analysis suggests that
for signalling cascades that include negative feedbacks acting at
different levels of the cascade—a common feature of eukaryotic
signalling38,39—induction of downstream-acting regulators
with lower sensitivity than those acting upstream might be
fundamentally beneficial from an energetic perspective (Fig. 4e,
see “Discussion”).
Cycling of MAPK phosphorylation reduces growth fitness.
While theoretically deducible, the effect of energy consumption
within the signalling cascade on cellular fitness has not been
shown experimentally. Given its small cost in comparison to total
cellular energy consumption, direct measurement of the
phosphorylation-cycle effect on cellular energy turnover would
not be feasible. However, the effect could become measurable
as growth disadvantage under long-term competition with
continuous activity of the phosphorylation cycle. We hence per-
formed such experiment by using two different enzymatically
inactive Fus3 variants, one of which could, however, still be
phosphorylated (Fus3-K42R) while the other could not (Fus3-
KTY) (Fig. 5a and Supplementary Fig. 11A)40. Since the back-
ground strain used for our experiments lacks functional Kss1 (see
above), replacement of wild-type Fus3 with these inactive variants
completely abolished transmission of the pheromone signal fur-
ther downstream (Supplementary Fig. 11B, C). Thus comparing
growth of strains expressing either of the two Fus3 variants along
with mNeongreen or mTurquoise to allow their discrimination
enabled us to selectively assess the effect of pheromone-
dependent Fus3 phosphorylation cycle.
To confirm that Fus3-K42R becomes phosphorylated in a
pheromone-dependent manner in vivo40, we identified the
corresponding phosphorylated peptide using mass spectrometry
(Supplementary Fig. 12). Indeed, the degree of phosphorylation
of this peptide was higher in the presence of pheromone
(Supplementary Fig. 12). Moreover, the phosphorylation was
also elevated in the absence of Msg5, suggesting that K42R is
dephosphorylated by Msg5.
When the MAPK pathway activity was stimulated by
pheromone, the relative abundance of strains carrying Fus3-
K42R steadily decreased in the co-culture with Fus3-KTY-
expressing cells (Fig. 5b, see Supplementary Fig. 13 for individual
experiments). The rates of growth divergence were, depending on
growth conditions, between about 0.02 and 0.07 per day (insets in
Fig. 5b–d). Assuming a constant doubling time of 100 min, and
thus a growth rate of approximately 10 day−1, this translates into
about 0.2–0.7% growth fitness defect of Fus3-K42R- compared to
-KTY-expressing cells in the presence of pheromone. This
decrease did not depend on which of the strains was labelled
with mNeongreen or mTurquoise, confirming that labelling itself
introduced no bias in growth (also apparent in the co-culture of
two differently labelled fus3Δstrains, Fig. 5a). Furthermore, we
performed control experiments to assess whether experimental
results were in line with our interpretation that indeed
phosphorylation cycle of Fus3-K42R was causing the observed
pheromone-dependent growth deficit. Under this assumption, we
expected (i) absence of phosphorylation cycle with deletion
of Fus3-phosphorylating kinase Ste7 and thus equal growth of
strains expressing Fus3-K42R and -KTY in the presence of
pheromone and (ii) slow-down of phosphorylation cycle in the
absence of phosphatase Msg5 due to decreased dephosphoryla-
tion rates and thus reduction of growth difference between
Fus3-K42R and -KTY cells compared to competition between
Msg5-expressing cells. We tested both predictions and indeed
could confirm them experimentally (Fig. 5c, d). Taken together,
we hypothesize that pheromone-dependent growth deficiency of
cells expressing Fus3-K42R is caused by the energetic burden
of its phosphorylation cycle and, consequently, that energetic cost
of enhanced information transmission was subject to evolu-
tionary selection, shaping the negative feedback design of the
yeast MAPK pathway.
Discussion
Cells need to reliably respond to the external cues in spite of the
inherent stochasticity of the events involved in sensing and
downstream signalling. This stochastic noise may lead to the
intercellular variability of responses, and single-cell measure-
ments indeed revealed that expression of the same gene can be
highly variable across apparently homogeneous cell popula-
tions3,4. Besides intrinsic stochasticity of individual processes, the
observed variability in gene expression might also have extrinsic
sources, e.g. variable levels of global transcription and translation
factors41.
Negative feedbacks have been shown to reduce cellular noise
and thus enhance information transmission capacity of sig-
nalling pathways16–18. This includes noise suppression through
negative feedback regulation provided by Sst2 within the yeast
pheromone signalling cascade30,32. Furthermore, negative
feedbacks can suppress pathway activity both in the absence
and/or presence of stimulation2. Dependent on the specific
parameters of a signalling pathway, suppression of the basal
activity can lead to enhanced response output range and thus
information transmission2,13.
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In general, negative feedback regulation entails dissipation of
energy and energy requirements for accurate information trans-
mission in signalling cascades have been emphasized in several
studies19–21,42–44. Nevertheless, the trade-off between potentially
conflicting optimization of negative feedbacks for energy dis-
sipation and for information transmission remained unexplored.
In this study, we demonstrate that negative feedback mediated by
the phosphatase Msg5 reduces the pathway noise and amplifies
the response output range, thus improving the precision of input
estimation and the information transmission capacity of the
signalling cascade, as measured by Fisher and mutual informa-
tion, respectively.
We observed that, whereas Msg5 at a lower level of the cascade
complements the Sst2 negative feedback at the upper level, MSG5
transcription is induced at much higher dose of the input signal
than that of SST2. This seeming correlation between the order of
negative feedback induction and the cascade stage could not be
simply rationalized in the context of information transmission,
since both our simulations and experiments showed that similar
and sensitive induction of both SST2 and MSG5 improves the
information capacity of the cascade. Furthermore, according to
our simulations, information was largely symmetric regarding the
induction order of both feedback regulators, meaning that the
precision of input estimation was virtually the same regardless of
SST2 being induced with higher sensitivity than MSG5 or vice
versa. However, a striking difference between high- and low-
sensitivity induction of MSG5 was observed when energy con-
sumption during signalling was additionally considered in our
mathematical model, with the latter configuration consuming less
energy for achieving the same output. Thus both high-sensitivity
induction of both negative feedbacks as well as a reversed order of
induction are energetically inferior to the observed induction
order. More generally, our analysis indicates that, for signalling
cascades that include negative feedbacks acting at different levels
of the cascade, induction of downstream regulators might be
generally energetically more expensive than those acting more
upstream (Fig. 4e). Notably, we further demonstrate experimen-
tally that futile cycling of Fus3 phosphorylation and depho-
sphorylation indeed can bear measurable fitness cost. Thus
dissipation of energy at this step likely resulted in evolutionary
selection for trade-off optimization between information and
energy consumption.
Notably, instead of using the more conventional method of
calculating channel capacity over all possible inputs2, here we
used metrics that enabled us to quantify information at every
input, which was necessary for defining the cost of energy con-
sumption for information transmission at a particular input. We
hence primarily used Fisher information, since it is naturally
Fus3
PP
K42R
PP
KTY
ab
–0.3
0.0
0.3
258
Time after mixing (days) Time after mixing (days) Time after mixing (days)
Log (growth divergence
+/– pheromone)
fus3/fus3
K42R/KTY
KTY/K42R
–0.04
0.00
0.04
Divergence
rate (day–1)
0
–0.6
–0.3
0.3
258
–0.2
–0.4
0
0.2
0.4
0.04
0.08
0
msg5
wt ste7wt
Divergence rate
KTY vs. K42R (day–1)
msg5
wt
ste7
wt
258
0
0.04
c
Log (growth divergence
+/– pheromone)
Fig. 5 Continuous dephosphorylation/phosphorylation of enzymatically inactive Fus3 lowers competitive growth fitness. a Schematic depiction of
employed Fus3 variants. A single amino acid replacement renders Fus3-K42R and -KTY enzymatically inactive and thus incapable of transmitting the
signal. Fus3-KTY additionally carries amino acid replacements at both phosphorylation sites. bFitness cost of phosphorylation cycle, monitored over time
as the ratio between mNeongreen (Ng)- and mTurquoise (Tq)-expressing cells grown in a co-culture in the presence of pheromone (20 nM), normalized
to the corresponding ratio in absence of pheromone. Different colours depict co-cultures of competing strains that carry different fus3 alleles and
fluorescent markers: fus3Δ+Ng vs. fus3Δ+Tq (black), fus3-K42R+Ng vs. fus3-KTY+Tq (green) and fus3-KTY+Ng vs. fus3-K42R+Tq (blue). For each pair,
four co-cultures per genotype with independent transformants were tested. Co-cultures were grown for several days with re-inoculation twice a day and
flow cytometric measurements once a day to determine ratios of Ng- to Tq-expressing cells. Combinations of fus3-K42R- and -KTY-expressing cells were
analysed in two independent experiments (depicted by different symbols), while control of fus3Δvs. fus3Δwas analysed in one experiment. Lines are linear
fits for individual co-cultures. Slopes derived from these fits quantify the rate of divergence of Ng/Tq ratios between co-cultures grown in the presence and
absence of pheromone (Inset). Centres and boundaries of boxes in the Inset depict means +/−s.d.; colouring for different co-cultures is according to the
main plot. In pairwise comparisons using two-sided ttest, pvalue was 7.08e−5 with 95% confidence interval (CI) ranging from 0.0169 to 0.0338 for
fus3Δ-fus3Δ(black, n=4 biologically independent samples) against K42R-KTY co-cultures (green, n=4 biologically independent samples examined over 2
independent experiments) and pvalue was 9.0e−4 with CI from −0.0287 to −0.0105 for fus3Δ-fus3Δ(black) against KTY-K42R co-cultures (blue, n=4
biologically independent samples examined over 2 independent experiments). cFitness of mutants with reduced dephosphorylation rate (msg5Δ, left) or
abolished phosphorylation (ste7Δ, right) compared to wild type. Wild-type pairs (wt, symbols and colours as in b, dashed lines for linear fits) in co-cultures
were same as in b. Each of those strains was subjected to gene deletion and the resulting deletion strains (one and two clones per parental strain for msg5Δ
and ste7Δ, respectively) were grown in co-cultures (diamond symbols, solid lines for linear fits) in a competition experiment alongside parental/wild-type
co-cultures. Insets show divergences of ratios between fus3-KTY- and -K42R-expressing cells between co-cultures grown in the presence or absence of
pheromone, as derived from the slopes of linear fits shown in the main figures. Centres and boundaries of boxes in the inset depict means +/−s.d. In
pairwise comparisons with two-sided ttest, pvalue was 4.62e−5 with CI from 0.0198 to 0.0429 for wild type (n=8 biologically independent samples)
against msg5Δ(n=8 biologically independent samples) co-cultures and pvalue was 4.32e−12 with CI from 0.0445 to 0.0577 for wild type against ste7Δ
(n=16 biologically independent samples) co-cultures. To increase throughput, co-cultures were grown here in 96-well plates without shaking, which might
explain slightly higher absolute divergence rates in these experiments compared to bwhere co-cultures were grown in 24-well plates with shaking.
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defined for a particular input. Nevertheless, we also calculated
local mutual information as done previously14, thus allowing us
to confirm that both information metrics give qualitatively similar
results.
Here, our analyses focused on Msg5 and, to a lesser extent, on
Sst2, the two major negative transcriptional feedback regulators in
the pheromone signalling pathway. Although Dig1, an inhibitor
of Ste12, has been previously reported to suppress noise in basal
pathway activity45, we observed no pheromone-dependent tran-
scriptional induction of DIG1 and thus did not consider it as a
bona fide negative transcriptional feedback. And, while closely
related regulator Dig2 was indeed transcriptionally induced at
high levels of pheromone stimulation, its exact role in the path-
way regulation remains unclear.
Taken together, our analysis provides evidence that evolu-
tionary selection on signalling networks not only maximizes
precision of information transmission but also minimizes the
corresponding energy investment. Such trade-offs between mul-
tiple (conflicting) objectives may be the fundamental principle in
many biological system designs46. Although individual details of
the cost-accuracy trade-off will likely depend on the importance
of signalling accuracy for fitness in a specific system, this trade-off
is likely to play a major role in the evolution of signalling and thus
to shape the architecture of cellular signalling networks.
Methods
Strains and growth conditions.S. cerevisiae strains used in this study are of
mating type MATaand derivatives of SEY6210a (MATaleu2-3,112 ura3-52
his3Δ200 trp1Δ901 lys2-801 suc2Δ9). Notably, this strain caries loss-of-function
mutations in the kss1 gene (our unpublished data), allowing us to exclusively
analyse the major, Fus3-mediated signalling branch of the pheromone pathway.
Generally, strains used for quantitatively measuring responses to α-pheromone
were deleted for α-pheromone-protease gene BAR1 and α-pheromone genes MFα1
and MFα2. All strains are listed in Supplementary Table 1.
Generally, the synthetic defined media (SD or LoFlo-SD) for growing yeast in
liquid were composed of yeast nitrogen base (YNB, Formedium) or low-
fluorescence YNB (LoFlo-YNB, Formedium) with complete supplement mix
(Formedium) and 2% glucose. Routinely, cells in liquid media were incubated
overnight in an orbital shaker at 200 rpm, diluted 1:50 to 1:100 into fresh media the
following morning and grown to mid-exponential phase prior to starting the
experiment.
For RNA sequencing experiments, strain yAA95 was grown in 500 ml SD at
30 °C. At mid-exponential phase (OD
600
approximately 0.5), pheromone
stimulation was initiated by transferring aliquots of the suspension into separate
flasks with prepared stock solutions of synthetic α-pheromone (Sigma). After
incubation for 60 min, cells were harvested by transferring 5 ml of suspension into
15-ml tubes containing 5 ml ice and mixed to immediately cool down the
suspension. Further steps were carried out on ice or at 4 °C. After centrifugation
and removal of supernatant, cell pellets were re-suspended in ice-cold water and
transferred to 2-ml Eppendorf tubes. After another centrifugation step, the
supernatant was carefully removed, and the cell pellets were stored at −20 °C until
further processing. For the time-course experiments, the harvesting procedure was
repeated at different time points.
For microscopic experiments, cells were grown in LoFlo-SD with 2 µM casein at
25 °C. Where applied, doxycycline was already present during overnight growth
and was kept at the same concentrations for day cultures and during microscopy.
Note that addition of casein results in higher apparent sensitivities of cell responses
to pheromone likely due to prevention of pheromone adsorption to surfaces47.
Thus absolute sensitivities reported here are higher for microscopy compared to
RNA sequencing experiments.
For growth-competition experiments, growth media were composed of LoFlo-
SD (experiment 2 in Supplementary Fig. 13) or SD (all other experiments) with
2 µM casein and supplemented with 20 µg/ml doxycycline and/or 20 nM α-
pheromone where applicable. Cells were grown in 24-well plates (Greiner Bio-One)
in 1 ml medium at 30 °C with shaking at 200rpm and diluted twice a day (in the
morning and evening) 1:50 into fresh medium of the same composition. For
higher-throughput experiments with wild type and deletion strains (Fig. 5c), cells
were grown in 96-well plates (Greiner Bio-One) in 250 µl medium at 30 °C without
shaking. Again, cells were diluted twice a day 1:50 into fresh medium.
Fluorescence time-lapse microscopy and analysis. The microscopic assay48 is
illustrated in Supplementary Fig. 14. Briefly, images were acquired on a wide-field
fluorescence microscope (Nikon Ti-E) equipped with a solid-state white-light light-
emitting diode source (Sola SE-II), a motorized stage, a ×40 dry objective (Nikon
Plan Apo ×40 Lambda, 0.95 N/A), a sCMOS camera (Andor Zyla) and an incu-
bator with heater controller (Digital Pixel). The green fluorescent protein (GFP)
signal was acquired using a 470/40 nm excitation filter and a 525/50 nm emission
filter, and the mCherry signal was acquired with 575/25 nm and 647/57 nm,
respectively. Cell suspensions were transferred to a 96-well glass-bottom plate
(Greiner Bio-One) coated with type-IV Concanavalin A (Sigma-Aldrich), and
addition of α-pheromone stock solutions was performed after allowing cells to
settle down for approximately 30 min. Image acquisition was started immediately
after addition of pheromone and repeated periodically at defined time intervals
over the course of several hours at 25 °C.
Single-cell median values of fluorescence intensities were extracted from the
images with the freely available software CellProfiler version 249 by performing cell
segmentation on the bright-field images and using the defined masks for measuring
intensities in the corresponding fluorescence images. Raw data extracted by
CellProfiler were further processed using the statistical software R version 350.
Upper and lower three percentiles per field of view and time point in either
fluorescence channel were routinely removed from further analysis. Fluorescence
intensities of GFP-only and mCherry-only expressing strains were used to correct
fluorescence intensities of single cells for autofluorescence and bleed-through
between the fluorescence channels. The corrected values were used for further
analysis. The final number of analysed cells per well and time point was between
300 and 4000. Original images and tables containing single cell data are available
on request.
Flow cytometric measurements. Cell suspensions were injected from a 96-well
plate (Greiner Bio-One) with a high-throughput sampler into an LSR Fortessa
Special Order flow cytometer (BD Biosciences). Fluorescence was measured with
lasers of different wavelengths: 488 nm for GFP, 447 nm for mTurquoise (Tq),
561 nm for mCherry, and 514 nm for mNeongreen (Ng). Using the BD FACS
DIVA software (BD Biosciences), cells were gated in a FSC-A/SSC-A plot to
exclude debris. Ten thousand cells from within the gate were acquired per sample.
For growth-competition experiments, cells were gated in a Ng/Tq plot to determine
the relative amounts of Ng- and Tq-expressing cells in the co-culture.
RNA preparation and sequencing. Frozen cell pellets were re-suspended in 500 µl
ProtK buffer (100 mM Tris/Cl pH 7.9, 150 mM NaCl, 25 mM EDTA, 1% sodium
dodecyl sulfate) with freshly added 100 µg/ml Proteinase K (ThermoFisher). Five
hundred microlitres of glass beads were added, and cells were disrupted by strong
vortexing for 5 min. The resulting lysate–glass bead mixture was incubated for
60 min at 37 °C. The RNA was isolated by 25:24:1 aqua-phenol:chloroform:isoamyl
alcohol (Carl Roth) extraction followed by a chloroform extraction and precipitated
with ethanol. The RNA pellet was washed once with 75% ethanol, re-suspended in
water and treated with RNase-free DNaseI (Roche Life Science) according to the
manufacturer’s protocol. After another precipitation/wash step, the RNA was
dissolved in nuclease-free water and analysed for integrity on a formaldehyde/
agarose gel. The RNA was depleted of ribosomal RNAs with the Ribo-Zero Gold
rRNA Removal Kit (Illumina) and reverse-transcribed with random hexamers at
the deep-sequencing facility at BioQuant, Heidelberg. Sequencing was performed at
the GeneCore facility at EMBL Heidelberg, with 50 bp read length, single-end re ads
and 9 samples per lane, by Illumina (Solexa) sequencing.
Analysis of RNA sequencing data. Sequence reads were mapped onto the yeast
genome (ensemble S. cerevisiae genome) with Bowtie 251. The resulting strand-
specific read densities were used to calculate the RPKM (reads per kilobase of
transcript, per million mapped reads) values for all annotated genes (ensemble S.
cerevisiae genome). A threshold of twofold higher (lower) expression than in the
non-pheromone-treated sample was used for designating genes as being induced
(repressed) genes. The dose–response curves were generated from the RPKM
values at different pheromone concentrations, and EC
50
values were determined by
fitting the dose–response curves using a sigmoidal function.
Calculation of noise and information. Time-lapse single-cell measurements of the
P
FUS1
-GFP reporter were used to calculate the CV, used as a measure of the total
noise of gene expression. The accuracy of signal transduction was determined using
Fisher information, which was calculated by smoothing the dose dependence of the
response and of standard deviation with a spline interpolation in order to obtain
the derivatives of the log-likelihood function at different inputs. The distribution of
the outputs at each input was assumed to be normal to numerically calculate the
integral for taking average of the derivatives over the distribution function (Sup-
plementary Note 1). Information transmission was further quantified by calcu-
lating mutual information at every input by taking a sliding window of three
inputs. Mutual information within this window was estimated by binning the
distribution of the output values in 20 bins to calculate the conditional and
unconditional entropy (Supplementary Note 1). Numerical integration for the
Fisher information and the entropy calculation for the mutual information were
carried out using the Package entropy and the spline function in R software.
Mathematical model of the pheromone response pathway. We considered a
two-step phosphorylation cascade model of the pathway (Supplementary Fig. 6A),
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where the receptor Ste2 activates kinase Fus3 and the activated Fus3 further
induces the activity of the transcription factor Ste12, which in turn stimulates the
transcription of the FUS1 gene. The system is modelled as a set of ordinary dif-
ferential equations (ODEs; Supplementary Note 2)32,39,52,53, and noise is intro-
duced by randomly selecting production rates as well as initial concentrations of
the pathway components from a log-normal distribution of values. The simulations
were performed by solving the ODEs using CVode54 interfaced with MATLAB in a
population of 500 cells for 1000 s. By default, simulations covered a pheromone-
concentration range of 314-fold with serial 3-fold increases, usually starting with
10−4nM and leading up to approximately 480 nM. Noise, Fisher information and
mutual information were calculated from the simulated data following the same
methods as in the case of the experimental data (see above). We considered that
energy is consumed in signal transduction at two levels: at the receptor level in the
process of GTP hydrolysis during inactivation of the receptor by Sst2 as well as in
the two-stage phosphorylation reactions (Supplementary Note 2). Simulations with
different feedback strengths were carried out by varying the parameters quantifying
binding strengths of active activator Ste12 (Ste12-P) to the respective promoters.
Reporting summary. Further information on research design is available in
the Nature Research Reporting Summary linked to this article.
Data availability
RNA sequencing data have been deposited in the Gene Expression Omnibus (GEO)
database under accession code GSE151729. Further data supporting the findings of this
study, including raw images, tables with single-cell data and flow cytometric data, are
available upon request from the corresponding authors.
Code availability
The code for simulations is available on request from the corresponding authors. Custom
scripts for CellProfiler, MATLAB and R used for the analysis of data are likewise
available upon request.
Received: 20 March 2019; Accepted: 22 June 2020;
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Acknowledgements
We thank Pieter Rein ten Wolde, Giulia Malaguti and Sean Murray for insightful
comments on the manuscript. This work was supported by grant 294761-MicRobE from
the European Research Council.
Author contributions
A.A., B.G. and V.S. conceived experiments; A.A. performed experiments; B.G. and A.A.
analysed the data; B.G. performed computational modelling; T.G. performed mass
spectrometric experiments; B.G., A.A. and V.S. wrote the paper.
Competing interests
The authors declare no competing interests.
Additional information
Supplementary information is available for this paper at https://doi.org/10.1038/s41467-
020-17276-4.
Correspondence and requests for materials should be addressed to B.G. or V.S.
Peer review information Nature Communications thanks the anonymous reviewer(s) for
their contribution to the peer review of this work. Peer reviewer reports are available.
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ARTICLE NATURE COMMUNICATIONS | https://doi.org/10.1038/s41467-020-17276-4
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