A rationally engineered decoder of transient
Claude Lormeau 1,2, Fabian Rudolf1& Jörg Stelling 1✉
Cells can encode information about their environment by modulating signaling dynamics and
responding accordingly. Yet, the mechanisms cells use to decode these dynamics remain
unknown when cells respond exclusively to transient signals. Here, we approach design
principles underlying such decoding by rationally engineering a synthetic short-pulse decoder
in budding yeast. A computational method for rapid prototyping, TopoDesign, allowed us to
explore 4122 possible circuit architectures, design targeted experiments, and then rationally
select a single circuit for implementation. This circuit demonstrates short-pulse decoding
through incoherent feedforward and positive feedback. We predict incoherent feedforward to
be essential for decoding transient signals, thereby complementing proposed design princi-
ples of temporal ﬁltering, the ability to respond to sustained signals, but not to transient
signals. More generally, we anticipate TopoDesign to help designing other synthetic circuits
with non-intuitive dynamics, simply by assembling available biological components.
1Department of Biosystems Science and Engineering and SIB Swiss Institute of Bioinformatics, ETH Zurich, Mattenstrasse 26, CH 4058 Basel, Switzerland.
2Life Science Zurich Graduate School, Interdisciplinary PhD Program Systems Biology, Zurich, Switzerland. ✉email: email@example.com
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Cells can shape the dynamic responses of signaling path-
ways to encode information about their environment,
which then requires an interpretation of the resulting
dynamics (decoding) to elicit appropriate responses, for example,
in terms of gene expression programs1. The mammalian MAPK
pathway is a prominent example for such dynamic encoding and
decoding in cellular signaling. It responds to NGF with a sus-
tained Erk output to induce differentiation, but to EGF with a
transient output to induce proliferation2. A coherent feedforward
(CFF) on c-Fos, a network motif in which a signal activates the
target both directly and via an intermediary component3, decodes
the sustained output of MAPK signaling4,5. This architecture is
consistent with proposed design principles of temporal ﬁltering,
which is the ability to respond to sustained signals, but not to
However, it is unknown how cells decode the transient output
of MAPK signaling7. Corresponding mechanisms are unlikely to
reside only in the dynamics of a single promoter8; they are rather
established by interaction networks that are not yet identiﬁed.
More generally, beyond suggested signal processing with coop-
erative assemblies9, decoding mechanisms to generate a speciﬁc
response to a transient signal, while ignoring more sustained
signals and not responding without input, are currently unknown.
In addition to analyzing the natural system, the design of
simple synthetic circuits with the same phenotype can help
decipher complex phenotypes and extract the underlying prin-
ciples from which they emerge10. A comparatively simple sig-
naling pathway to investigate decoding principles by synthetic
circuit design is the mating pathway in the budding yeast Sac-
charomyces cerevisiae. It is well-characterized, accepts a sustained
stimulation with the α-factor pheromone as input11, and was
previously used, for example, to rationally tune G-protein coupled
receptor signaling in this model eukaryote12.
In this work, we elucidate decoding mechanisms by rationally
designing a synthetic short pulse decoder for the budding yeast
mating pathway (Fig. 1a). Speciﬁcally, we engineer a circuit that
responds to a 30 min pulse of α-factor, but not to no pulse or a 3 h
pulse, which is orthogonal to the natural mating response. Because
decoder network architectures are not known, we develop a
computational method for rapid prototyping of synthetic circuits
with complex target dynamics, TopoDesign. We show that the
method can explore thousands of possible circuit architectures,
design targeted experiments, and then rationally select a single
circuit for implementation. Our implemented circuit demonstrates
short pulse decoding through incoherent feedforward (IFF) and
positive feedback (PF), and we predict nested IFF loops to be
essential for decoding transient signals more generally.
Topological design framework. Because we did not know which
network structures (topologies) could generate a short pulse
decoder behavior, we deﬁned a master network (Fig. 1b) that
encompasses well-known motifs in signal processing: negative
and positive feedback (NF and PF)13,14 as well as IFF3,15 motifs.
We included IFFs in particular because they can retain memories
of pulses16, and thereby discriminate between transient and
sustained inputs17. Note, however, that we require a decoder
behavior that is different from the known behaviors of IFFs: it
should not respond to a long pulse at any point in time, not only
after an adaptation period.
Fig. 1 Initial decoder design. a Design objective for a short pulse (≤30 min duration) decoder of signals transmitted by the yeast mating pathway.
bStarting topology with α-factor and chemical (Ch
) input, citrine ﬂuorescence output, transcription factors (TF1,2), combinatorial promoters (trapezoids),
and activating (colored arrows) or inhibiting (bars) interactions; see also Supplementary Methods. cFirst step of TopoDesign, requiring a design objective
(a) and a starting topology (b) for topological ﬁltering25 to obtain functional topologies T
by deleting interactions from the starting topology; they achieve
the design objective for at least one parameter set θ(individual parameters: θ
). Viable regions V
in parameter space (boundaries Θ) allow to compute
robustness and feasibility metrics inspired by23, where pi
idealðθÞis an ideal parameter distribution. dRanking of the 109 topologies that can meet the design
objectives, comprising incoherent feedforward (IFF), negative feedback (NF), and positive feedback (PF) motifs. eTopologies highlighted in dand their
predicted behaviors (random viable parameter sets).
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In biological terms, the master network (Fig. 1b) involves an
activating transcription factor (TF1), a repressor (TF2) that
responds to a tuning chemical, six potential AND gate inducible
promoters (activated only if TF1 is present and TF2 is absent), and
two post-translational interactions inspired by ref. 18. At this stage,
the biological parts are hypothetical—they exist in principle, but
we do not know if speciﬁc instances with suitable quantitative
characteristics, such as repressor strength are available or will need
to be established by molecular engineering.
Enumeration of the master network’s sub-topologies yields a set
of 4122 possible decoder topologies. Experimentally testing that
many alternatives is impossible, although efﬁcient methods for
circuit construction exist6,9,13,14,19,20. Also, existing computational
design methods either help designing dynamic circuits for few
topologies that can be enumerated and analyzed individually21,or
focus on logical circuits using well-characterized components20,22.
Because neither condition applied here, we extended our Bayesian
circuit design method23 to a rapid prototyping method, TopoDe-
sign. Without requiring a catalog of speciﬁc biological parts, it
explores possible combinations of hypothetical parts. TopoDesign
accounts for uncertain knowledge about the parts and their
biological variability, which allows capitalizing on existing
biological parts that may be ill-characterized.
We deﬁne a design objective and a dynamic mathematical
model for the set of possible topologies (Fig. 1c, Supplementary
Fig. 1; Supplementary Methods). For the model, we used
commonly applied speciﬁcations of processes and interactions,
such as Hill functions for gene expression control; note that all
model inferences and predictions are contingent on this formula-
tion. Topological ﬁltering24,25 explores simultaneously model
topologies and parameters to ﬁnd functional topologies T
, at least one parameter set is viable: it achieves the design
objective. By efﬁcient sampling26, we also obtain the corresponding
viable space V
, that is, the parameter space for correct circuit
behavior. This allows us to deﬁne two metrics for topology
robustness and feasibility (Fig. 1c). Our robustness metric is a
quantitative version of the “Q-value”or “robustness score”4,27.It
measures globally how much of the parameter space is viable,
giving the theoretical probability of a circuit to achieve the design
objective, without prior knowledge on parameters. However, with
correlated parameters, a topology may not tolerate variation in
individual parameters. To account for such dependencies between
parts in practice, we therefore measure feasibility: the proportion of
a parameter distribution that ﬁts into the viable space (Fig. 1c). The
deﬁnition of the metric is distinct from23 and critical: it enables a
systematic integration of experimental data, and thereby all
iterations of computation and experiments. Without further
information, we compute ideal feasibility by assuming optimal
parameters with small variance (Fig. 1c; Supplementary Methods).
Functional topologies for a short pulse decoder. The search for
functional topologies is unbiased by experimental data, assuming
only broad, plausible ranges of parameters (Supplementary
Methods). It yields both a set of functional topologies that one
can analyze to reveal principles of decoder function and (via the
viable spaces) constraints on the characteristics of parts to be used
for circuit implementations. Speciﬁcally, TopoDesign found 109
topologies able to behave as short pulse decoders (Fig. 1d, Sup-
plementary Figs. 2 and 3). Robustness and ideal feasibility cor-
relate only moderately (Kendall’sτ=0.40, p<10
the need for two metrics to capture fully the size and shape of the
viable spaces. All circuits include at least one IFF motif. Some
have an additional NF, PF, or both. Apart from the omnipresent
IFF, the diversity of motifs in robust and feasible topologies does
not orient us towards one particular circuit architecture. For
are indistinguishable in our metrics
(Fig. 1d), but rely on very different topologies to generate similar
predicted decoder behaviors (Fig. 1e).
To understand how functional circuits decode the input
dynamics, we simulated the internal dynamics of four simple
circuits with a random viable parameter sample each (Fig. 2). At
the core of each circuit are interlocked incoherent (comprising
αfactor, TF1, and TF2) and coherent (TF2, TF1, and citrine)
feedforwards (for a more detailed analysis of the relations
between network motifs and decoder function, see also
Supplementary Fig. 3 and Supplementary Methods). In T
the minimal example, the IFF on the activator TF1 generates an
adaptive pulse of TF1 activity that has approximately the duration
of the input pulse we want to decode, independent of the input
duration. This adaptive TF1 response is crucial since all 109
circuits except one (with very low robustness) include an IFF on
TF1. Because the negative regulator TF2 always follows the input
with a pulse that has approximately the same duration as the
input, citrine appears only if TF2 disappears before the TF1 signal
disappears, hence only in response to short inputs. Circuits with
additional interactions employ the same principle (Fig. 2), with
additional increases of TF1 activity, for example, due to PF in T
that stabilizes the output in a high steady state.
Speciﬁcation of biological parts and rapid prototyping.To
specify biological parts, in principle, one can select parts from
established catalogs that are expanding in scope also for
S. cerevisiae22,28. The bottleneck is that quantitative parts char-
acterizations that allow checking if parts fulﬁll the requirements
on parameters for circuit function (via the viable spaces) remain
sparse. TopoDesign, however, can also consider less well-
characterized components by explicitly accounting for para-
meter uncertainties. We decided to use our available biological
components; we matched them to model predictions by identi-
fying recurrent constraints on parameters in circuits with ideal
feasibility >0.9 (Fig. 1d, Supplementary Fig. 4). They required TFs
with relatively high fold change and cooperativity (n> 2). We
selected a corresponding activating TF1 (Fig. 1b): LexA-ER-B112
acting on a target promoter with four lexA boxes29. Similarly, we
speciﬁed TF2 by a TetR-MBP fusion protein repressing a Tdh3
promoter ﬂanked by tetO sites30, tunable by anhydrotetracycline
(aTc), and we used the native, α-factor-inducible Fus1 promoter.
Inducible promoters could be hybrid: repressed by TetR-MBP
and activated by α-factor (P
) or LexA-ER-B112 (P
establish α-factor-responsive protein degradation, we tagged TF1
with a phospho-regulon18 (few functional topologies included
controlled TF2 degradation).
Different conﬁgurations of these few parts could yield 69
functional topologies. To select among them rapidly to reduce
experimental effort, we used prototyping, namely construction of
small informative synthetic networks. We built seven such
networks and measured their dynamics and dose-responses to
aTc and α-factor (Fig. 3a–c, Supplementary Fig. 5). With 984 data
points from ﬂow cytometry in total and a uniform prior
(Supplementary Table 7), we used approximate Bayesian
computation31 (ABC) to estimate the posterior probability
distribution of the 20 parameters for all parts, and thereby to
make the parts’characteristics usable for the evaluation of the 69
candidate topologies (Fig. 3d; Supplementary Methods). Narrow
distributions (Fig. 3e, Supplementary Fig. 6) indicate that the data
sufﬁce to obtain high-quality information on all parameters.
We used the ABC posterior to update the feasibility of all
circuits (Fig. 4a; Supplementary Fig. 2). Because the nonzero
regions of the posteriors did not overlap with the topologies’
viable spaces, all circuits had zero updated feasibility. To increase
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Fig. 3 Rapid prototyping. a Example module for characterization (strain yCL109; β-est: β-estradiol; aTc: anhydrotetracyclin). b,cCharacterization
experiments, citrine ﬂuorescence measured by ﬂow cytometry. All ﬂow cytometry measurements include at least 4000 cells after gating. Symbols show
experimental means, ±standard deviation, and lines simulations of the maximum likelihood parameter set estimated with all seven modules. 5 μM
β-estradiol were added at time 0, together with varying concentrations of α-factor (dose response at 18 h (b), dynamics after αaddition (c)), or varying
concentrations of aTc with 0 or 1 μMα(aTc dose response at 6 h (b)). For α-factor release (c), we removed αfrom the medium 18 h after induction.
dIllustration of the second step of TopoDesign to infer the posterior distribution pðθjDÞof the 20 parameters θ
for parts in Fig. 1b by approximate Bayesian
computation (ABC) using the likelihood pðDjθÞfor data D.eProjection of the joint posterior parameter distribution on two pairs of parameters; bright
contour lines indicate high probability density.
Fig. 2 Decoder design principles. Detailed (colors; see Fig. 1) and abstracted (black) topologies of four simple functional circuits (top; numbers indicate
topology variants). Internal dynamics of TF1 and TF2 were simulated for a random viable parameter sample for each circuit, with different input (α-factor)
durations (indicated by colors; bottom).
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feasibility, we allowed for the tuning of selected parameters.
Tunability is an intrinsic property of a parameter, reﬂecting the
experimental effort for modifying a parameter’s value in given
ranges. We devised discrete categories of tunability that account
for this effort and have different roles in TopoDesign (Supple-
mentary Methods). As simple tuning possibilities to increase
feasibility, we considered varying aTc concentrations and
promoter copy numbers (assuming those affect maximum
production rates proportionally).
After optimizing the location of the parameter posterior in the
tuning directions, feasibility clearly discriminated between the 69
topologies (Fig. 4b). Two circuits, T
, stood out by having
close to 50% feasibility. T
(Fig. 4c) was more robust and had
fewer interactions than T
(Supplementary Fig. 2). Importantly,
the additional induced degradation of LexA in T
is likely to
increase the circuit’s burden on the cell and thereby to make it
evolutionarily less stable32. Finally, tuning without molecular
engineering to modify parameters, such as the cooperativity of
LexA should make T
a functional decoder (Fig. 4d, Supplemen-
tary Figs. 6 and 7). We therefore selected T
Circuit implementation and validation. To decide how to
(Fig. 5a), we explored the parameter subspace for
copy number variations of the individual parts and aTc con-
centration; they are experimentally simple to control and there-
fore suitable for rapid prototyping. The sampling results
(Supplementary Fig. 8) indicated that the two P
required single copies; we integrated single copies using shuttle
vectors from ref. 33 to obtain strain yCL114 (Supplementary
Table 2). The model also predicted a need for high copy numbers
of the two α-factor-inducible constructs, and enough aTc to
substantially reduce TetR binding for a working decoder. For
those constructs, we implemented variants of T
copy numbers, determined a posteriori. Speciﬁcally, we cloned
each part in a multi-integration vector deﬁcient in auxotrophic
marker production and transformed a mixture of the two
resulting constructs in strain yCL114 (see “Methods”section).
Next, we used our α-factor-pulse ﬂow cytometry assay at
100 nM aTc (see “Methods”section) to screen for cells that did
not respond without α-factor or to a long pulse, but responded to
a short pulse. This yielded four strains with circuit variants T
(see Fig. 5b for T
) that could behave as short pulse decoders.
Indeed, in independent experiments in which we systematically
varied the pulse duration, T
’s responses increased and then
decreased again with pulse duration (Fig. 5c). In contrast, circuit
variants with only a PF and no IFF, which we constructed as
negative controls (C
, Fig. 5a), were non-functional (Fig. 5c), as
expected from their lack of IFFs.
To characterize circuit behaviors with respect to the aTc
concentration as tuning parameter, we varied aTc concentrations
and compared the responses of all strains to 30 min and 3 h pulses
Fig. 4 Bayesian updating. a The inferred parameter posterior p(θ|D)is
compared to the viable regions V
of all topologies to calculate each
topology’s feasibility; we shift p(θ|D) in tunable parameter directions to
tunedðθjDÞto maximize feasibility. bUpdated ranking of topologies for the
short pulse decoder, highlighting promising topologies. cCircuit diagram of
the best candidate, T
.dProjection of the viable space of T
, and of the
parameter posterior distribution before and after tuning, on two
parameters. Copy number N
enables tuning of promoter strength,
leading to a predicted feasibility of 48% (b).
Fig. 5 Implementation of the predicted decoder. a Variants of T
differ in the copy number Nof α-factor inducible TetR and LexA constructs. Control
circuit variants (C
) lack α-factor inducible TetR. bDistributions of single-cell responses of T
to 1 μMα-factor pulses (durations indicated by colors) at
100 nM aTc as determined experimentally by ﬂow cytometry. All ﬂow cytometry measurements include at least 4000 cells after gating. Fluorescence is
normalized to the FSC-A signal, see “Methods”section. cResponses of the indicated T
variants and control circuits at 6 h to different 1 μMα-factor pulse
durations at 100 nM aTc in percentages of cells above a ﬂuorescence threshold (unimodal response of C
to a 3 h pulse is 95%), to accommodate for
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of α-factor. This experiment conﬁrmed that T
as short pulse decoders, whereas C
could not (Fig. 6a for T
Supplementary Fig. 9a for all variants). It also identiﬁed variant-
speciﬁc optimal aTc concentrations (see Fig. 6a, aTcopt: highest
30/180 min response ratio, at least 50% of cells responding).
To compare model predictions and experimental data for the
circuit design, we then used the sampling results (Supple-
mentary Fig. 8) to deﬁne a region of high feasibility (>90% of
’s maximal feasibility) in the space of tunable parameters
(Fig. 6b). T
differ in copy numbers, which we determined by
qPCR. The combined data suggest that T
form a region with
the same shape as the predicted feasibility region, although it is
shifted (Fig. 6b). This is supported by aTcopt of T
with the number of TetR constructs (Pearson’sr=0.92, p<10
Supplementary Fig. 9b) as expected. To test the hypothesis of a
functional region, we selected three additional strains (T
with high copy numbers according to qPCR results, but located
outside the region of T
(Fig. 6b). We predicted T
non-functional, which experiments with varying aTc concentra-
tion conﬁrmed (Supplementary Fig. 9a).
Finally, we evaluated if the experimental decoder performance
is consistent with model predictions. For T
at their speciﬁc
aTcopt, we measured a fold change of response for discriminating
between 30 min and 3 h pulses between twofold and ﬁvefold
(Fig. 6c). To estimate the predicted behavior in a cell population,
we performed simulations of T
sim) with copy numbers and
aTc concentration optimized for feasibility (Fig. 6b), and each
simulated cell otherwise parametrized with samples from the ABC
posterior distribution (see Supplementary Methods for details).
Given the deﬁnition of feasibility, half of these simulated cells
achieve the design objective individually. In this best-case scenario,
sim showed a similar qualitative behavior as the experimental
data (Fig. 6a) and the predicted fold change was 31 (Fig. 6c). This
higher value compared to the experimental data resulted primarily
from fewer cells responding to the 3 h pulse. A comparison of ﬂow
cytometry data and simulation results (Fig. 6d) pointed to an
explanation: measured and simulated distributions for T
similar shapes, but a different prominence of the two modes for
the 3 h pulse. We speculate that a combination of gene expression
noise (not represented in our models) and PF stabilizing the high
output state (indicated by the control circuit’s unimodal
distribution) causes this difference. Overall, hence, predicted
functional circuits not only achieved the non-intuitive qualitative
behavior but also met the quantitative design objectives within a
meaningful margin of the best-case scenario.
Our decoder demonstrates that a purely transcriptional circuit
with four nodes combining an IFF with a nested CFF and a PF
can respond exclusively to short inputs. This is an example for
how nature could discriminate between input durations, but not
the only solution (Supplementary Fig. 3): our topology explora-
tion predicted many other possibilities. Intriguingly, they all
featured an IFF, pointing to a common design principle. Speci-
ﬁcally, we expect corresponding circuits to have nested IFFs at
their core because an adaptive response is required to dis-
criminate between short pulses on the one hand, and no or long
pulses on the other hand. Either an IFF itself, or a time-delayed
NF embedded in an IFF can generate the critical adaptive
response (Supplementary Fig. 3 and Supplementary Methods);
NFs and IFFs are the two known network motifs that can achieve
adaptation27. However, we cannot exclude that more complex
decoder architectures exist.
We argue that a perspective in terms of network motifs can
help identify and explain naturally occurring decoders of short
inputs. For example, interlocked feedforwards occur frequently in
gene regulatory networks involved in the development of multi-
cellular eukaryotes, such as Drosophila34. Intriguingly, short and
long pulses of Erk activity lead to the speciﬁcation of distinct cell
types during ﬂy development35, but the mechanisms for the
short pulse response are unclear. Similarly, many feedforwards
are known in mammalian Erk signaling36 and downstream gene
regulation can decode Erk dynamics37. Candidates for short
pulse decoding are the c-Fos transcription factor and the
mRNA-destabilizing protein ZFP36 involved in an IFF38, or Erk
and dual-speciﬁcity phosphatases involved in time-delayed NF as
well as IFF36, provided that these regulators act antagonistically
on common targets.
More generally, TopoDesign combines Bayesian accounting for
uncertainty in design21 with scalability in terms of the number of
possible topologies, relevant metrics for selecting topologies, and
rapid prototyping to reduce experimental effort. Scalability with
respect to circuit complexity (dimensions of parameter spaces),
however, is an open issue for future investigations. In addition,
one could develop model-based experimental design approaches
to identify small informative networks during rapid prototyping,
and expand the framework to account for cell-to-cell variability
explicitly. While being general, TopoDesign is customizable: the
Fig. 6 Decoder validation and performance. a Responses at 6 h to 0, 30,
or 180 min pulses (colors) of 1 μMα-factor for T
at varying aTc
concentrations as determined experimentally by ﬂow cytometry (see
Supplementary Fig. 9a for all circuits). All ﬂow cytometry measurements
include at least 4000 cells after gating. Experimental data (solid lines) are
complemented by model predictions (dashed lines) for an optimal T
sim, see Supplementary Methods). bExperimentally
determined copy numbers for seven implemented variants of T
s.d., n=3 technical replicates) and optimal aTc concentrations (aTcopt;
estimated for T
(red open symbols) and extrapolated for T
open symbols; see also Supplementary Fig. 9b)). Red contour line:
predicted region of high feasibility. Filled red symbol: copy numbers and aTc
concentration for T
sim.cResponses at 6 h for T
and for the optimal
simulated circuit at aTcopt. Numbers above bars: fold-changes in responses
to 30 min pulses relative to 180 min pulses. dDistributions of single-cell
responses of T
(pdf: probability density function) to input pulses at
aTcopt, determined experimentally as in Fig. 5b (left) and predicted
computationally (right; equivalent normalization).
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user deﬁnes available components and tunable parameters.
Similar to our study, we envisage that TopoDesign will accelerate
the engineering of synthetic circuits with complex dynamic
behavior, without detailed molecular engineering.
Plasmid construction. Plasmids (Supplementary Table 1) were constructed by
isothermal assembly using the pRG shuttle vector series33 as backbones, and inserts
were obtained by PCR. Primers used for plasmid assembly are listed in Supple-
mentary Table 4. All constructs were checked with Sanger sequencing (Microsynth).
The sequences of the three hybrid promoters cloned for this work are listed in
Supplementary Table 3. The fus1tet and lexAtet promoters were obtained by fusing
the core promoter sequence of P2tet from Azizoglu et al.30 to the upstream activating
sequence of either the Fus1 promoter or the 4 lexA boxes promoter from Ottoz
et al.29. Instead of using directly the Fus1 promoter when no repression by TetR was
needed, a non-repressible version of the Fus1tet fusion promoter (called Pfus1mut)
was used to keep exactly the same properties as Pfus1tet. The fus1mut promoter is
almost the same as the fus1tet promoter except that the sequences of the tetO sites
were shufﬂed to prevent binding of TetR. The LexA-ER-B112-phosphodegron was
obtained by inserting the phosphodegron sequence from Grodley et al.18 between the
end of the LexA-ER-B112 sequence from Ottoz et al.29 and the stop codon.
Yeast strain construction.S. cerevisiae strains are listed in Supplementary
Table 2. They were constructed for this work except for FRY6933, from which
yCL102 was derived with the modiﬁcations bar1::Nat and far1::KanMX. All other
strains were then derived from yCL102. Integration of single-copy constructs was
always done with one of the pRG20x vectors33, and checked for single-copy
integration at the correct site by multiplex colony PCR (protocol by Gnügge
et al.33). Integration of multiple copy constructs was done with the pRG235 vector,
with a co-transformation if different constructs had to be integrated in multiple
copies. The number of integrated copies for each construct was then checked by
quantitative real-time PCR (qRT-PCR).
Media and chemicals. All experiments were performed at 30° in YPD medium
containing 1% yeast extract (Thermoﬁsher, 212720), 2% bacto-peptone (Ther-
moﬁsher, 211820) and 2% glucose (Sigma, G8270).
α-factor mating pheromone (Zymo Research, Y1001) was directly used as
10 mM stock. aTc (Cayman Chemicals, 10009542) was prepared as a 10 mM stock
in ethanol. β-estradiol (Sigma-Aldrich, 107K1322) was prepared as a 100 mM stock
in ethanol. Pronase (protease from Streptomyces griseus, Sigma-Aldrich, P8811)
was prepared as a 40 mg/ml stock solution in sterile distilled water.
Flow cytometry. For all experiments we ﬁrst cultured cells to early exponential
phase (about 5e6 cells/mL), then we added β-estradiol to reach a concentration of
5μM. For aTc dose-response experiments, α-factor (ﬁnal concentration 1 μM) and
aTc (various concentrations) were added together with β-estradiol. For α-factor
dose-response experiments, only α-factor (various concentrations) was added
together with β-estradiol. For α-factor release experiments, cells were diluted when
adding β-estradiol and α-factor to make sure they are in exponential phase 18 h
later. 18 h after adding β-estradiol and α-factor, cells were taken to a Corning
FiltrEx 96-well white ﬁlter plate with 0.2 μm hydrophilic PVDF membrane to be
centrifuged for 3 min at 3000 g. They were then resuspended in new medium with
50 μg/mL pronase (to remove the remaining α-factor) and 5 μMβ-estradiol (no α).
For α-factor pulse experiments, α-factor was removed from an aliquot of the main
culture by centrifugation as for α-factor release experiments after each pulse
duration, and aTc was added to each aliquot after α-factor removal in the indicated
concentration together with pronase and β-estradiol.
For all experiments, at every time point indicated, cells were diluted in PBS and
measured using a BD LSR Fortessa cell analyzer equipped with a high-throughput
sampler. PMT voltages used for the different channels were always 480 mV for
forward scattering, 275 mV for side scattering, and 630 mV for the 488 nm excitation
laser. A 530/30 ﬁlter was used to measure Citrine ﬂuorescence. We gated broadly for
budding cells in the FSC-W-SSC-W plane29 as shown in Supplementary Fig. 10. Our
cells do not stop growing in the presence of α-factor due to far1 deletion, but they
tend to aggregate instead, leading to a higher ﬂuorescence signal in the presence of α
even for a constitutive promoter. In order to correct for the size of ﬂow cytometry
events, we normalize the ﬂuorescence of every event by its FSC-A signal. The
normalization corrects for the α-factor effect on cell size. However, we still observe a
small shift induced by α-factor for the act1 strain (yCL106). We included this
unexplained effect in our model of the act1 promoter (see methods about computing
the parameter posterior in Supplementary Information).
Quantitative real-time PCR. qRT-PCR was used to assess the number of copies
of lexA-ER-B112,tetR-nls-malE and citrine constructs in the genome for the strains
yCL110, yCL130-133, and yCL141-143. We extracted genomic DNA of dense
cultures with a YeaStar Genomic DNA Kit with Zymo-Spin III columns
(Zymo Research). We performed qRT-PCR on a LightCycler 480 Instrument using
the PowerUp SYBR Green Master Mix (ThermoFisher) with primers listed in
Supplementary Table 5. We ﬁtted all ﬂuorescence curves with the ﬁve-parameter
logistic curve from39 and used the analytical solution of the second derivative
maximum to determine the Ct values. For copy number quantiﬁcation, we used
citrine (always present as one copy) as an internal reference and we used the strain
yCL110 (containing one copy of each target) as a reference strain. Primer efﬁ-
, and E
were estimated with calibration curves, and copy
numbers were estimated as in Pfaff et al.40.
Software for data collection and analysis. BD FACSDiva 8.1 software was used to
collect the ﬂow cytometry data. Roche LightCycler®96 SW 1.1 software was used to
collect the RT-qPCR data. Matlab R2019a (Mathworks, Natick, MA) was used to
analyze the data, and to develop the TopoDesign method described in detail in Sup-
plementary Methods. To analyze FACS data, we used the toolbox MatlabCytofUtilities
available from https://github.com/nolanlab/MatlabCytofUtilities. The TopoDesign
method depends on the Matlab toolboxes Hyperspace (https://gitlab.com/csb.ethz/
HYPERSPACE, commit of 09/17/2018), TopoFilter v0.3.6 (https://git.bsse.ethz.ch/csb/
TopoFilter), IQM Tools v188.8.131.52 (https://iqmtools.intiquan.com/)andthe2014
MEIGO-M package (available from http://gingproc.iim.csic.es/meigom.html).
Statistics and reproducibility. Each experiment was repeated independently at
least three times with similar results, with the exception of the dynamic response of
small informative networks (columns 3 and 4 in Supplementary Fig. 5) which was
carried out once, and quantitative PCR measurements repeated twice. Models are
speciﬁed in Supplementary Methods and all data and code required to reproduce
the analysis are available open-source (see “Data availability”section).
Reporting summary. Further information on research design is available in the Nature
Research Reporting Summary linked to this article.
All code is available as a static snapshot at the ETH Research Collection with identiﬁer
[https://doi.org/10.3929/ethz-b-000471160]41 and in version-controlled form at https://
All computational and experimental data that support the ﬁndings of this study are
available at the ETH Research Collection with the identiﬁer [https://doi.org/10.3929/
ethz-b-000471160]41. Strains and plasmids used in this study are available from Addgene
(https://www.addgene.org/browse/article/28211930/). Any other relevant data are
available from the authors upon reasonable request.
Received: 6 August 2020; Accepted: 5 March 2021;
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We thank A. Azizoglu for experimental support, L. Widmer and H.-M. Kaltenbach for
discussions. This work was supported by the Swiss National Science Foundation via the
NCCR Molecular Systems Engineering (grant 182895).
C.L., F.R., and J.S. conceived the study. C.L. and J.S. conceived TopoDesign. C.L. and F.R.
designed experiments. C.L. performed modeling, experiments, and data analysis. C.L. and
J.S. wrote the manuscript.
The authors declare no competing interests.
Supplementary information The online version contains supplementary material
available at https://doi.org/10.1038/s41467-021-22190-4.
Correspondence and requests for materials should be addressed to J.S.
Peer review information Nature Communications thanks Diogo Camacho and the other,
anonymous, reviewer(s) for their contribution to the peer review of this work. Peer
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