Predicting Synthetic Gene Networks
Diego di Bernardo , Lucia Marucci , Filippo Menolascina ,
and Velia Siciliano
Synthetic biology aims at designing and building new biological functions in living organisms. The
complexity of cellular regulation (regulatory, metabolic, and signaling interactions, and their coordinated
action) can be tackled via the development of quantitative mathematical models. These models are useful
to test biological hypotheses and observations, and to predict the possible behaviors of a synthetic net-
work. Indeed, synthetic biology uses such models to design synthetic networks, prior to their construction
in the cell, to perform specifi c tasks, or to change a biological process in a desired way. The synthetic net-
work is built by assembling biological “parts” taken from different systems; therefore it is fundamental
to identify, isolate, and test regulatory motifs which occur frequently in biological pathways. In this
chapter, we describe how to model and predict the behavior of synthetic networks in two difference cases:
(1) a synthetic network composed of fi ve genes regulating each other through a variety of regulatory inter-
actions in the yeast Saccharomyces cerevisiae (2) a synthetic transcriptional positive feedback loop stably
integrated in Human Embryonic Kidney 293 cells (HEK293).
Key words: Synthetic biology , Mathematical modeling , Positive feedback loop , S. cerevisiae , HEK
293 , Microfl uidics
The synthetic network described herein has been built for
benchmarking modeling and reverse-engineering approaches
( 1, 3 ) . IRMA was designed to be isolated from the cellular envi-
ronment (Cuccato et al., Heredity 102:527–532, 2009), and to
respond to galactose or glucose, which respectively “switch” the
network on and off by triggering transcription of its genes. This
network (Fig. 1 ) is very articulated in its interconnections, which
include regulator chains, single input motifs, and multiple feedback
Network in Yeast
Wilfried Weber and Martin Fussenegger (eds.), Synthetic Gene Networks: Methods and Protocols,
Methods in Molecular Biology, vol. 813, DOI 10.1007/978-1-61779-412-4_4, © Springer Science+Business Media, LLC 2012
58 D. di Bernardo et al.
loops generated by the combination of transcriptional activa-
tors and repressors. We selected well-characterized promoter/
TF-encoding-genes pairs. We chose nonessential and nonredun-
dant TF-genes that can be knocked out without affecting yeast
viability. The following genes have been chosen for IRMA: as
activators and repressors encoding genes: SWI5, ASH1, CBF1,
GAL4 , and GAL80 ; as promoter genes: HO , ASH1 , MET16 ,
GAL10 (Fig. 1 ).
This synthetic network is shown in Fig. 2 . We took advantage of
the inducible Tet regulatory system: the expression of Tetracycline-
controlled transactivator tTA is self-controlled by a CMV-TET
promoter responsive to thetTA itself unless Tetracycline, or its
analogous Doxycycline, is added to the medium in which cells are
grown ( 4 ) . To follow the protein dynamics of the positive feedback
loop, a destabilized yellow variant of the enhanced green fl uores-
cent protein (d2EYFP) (Clontech), with a half-life of approxi-
mately 2 h, was expressed together with the tTA transactivator
from the same mRNA, via an Intra Ribosomal Entry Sequence
(IRES) in between of the transactivator tTA and the d2EYFP
(Fig. 2 ). In order to stably express in HEK293 cells the inducible
feedback loop and to better characterize its dynamics overtime, we
used a lentiviral vector ( 5, 6 ) , based on the multisite Gateway
technology provided by Invitrogen.
When deriving a model from experimental data, three major
approaches can be used: white-box, black-box, and gray-box. In
white-box modeling, the model and parameter values are entirely
derived from fi rst principles, while in black-box, the model is
completely derived from input–output data. The third alternative,
the so-called gray-box approach ( 7 ) , combines the two above
Loop in Mammalian
1.3. Derivation of
for Synthetic Network
Fig. 1. Diagram of the synthetic network in yeast. Solid lines model transcriptional interactions while dashed lines are
meant to represent protein-protein interactions.
594 Predicting Synthetic Gene Networks
approaches. Specifi cally, fi rst principles are used to partially derive
the model structure, while parameters in the model are estimated
from experimental data. The approach described in this chapter,
both for the yeast and the mammalian synthetic network, is a gray-
box one. In this case, modeling entails the following main steps to
be executed iteratively: (1) derivation of the model equations and
(2) estimation of the model parameters from experimental data
and/or literature. Step (1) requires introducing simplifying hypoth-
esis and choosing a proper formal framework. Among the different
mathematical formalisms, those based on differential equations are
commonly used to describe the average behavior of a population of
cells ( 8 ) . The Differential Equations modeling approach is based
on the following biological assumptions: the quantifi ed concentra-
tions are homogeneous in space and they are continuous quantities
in time. These assumptions hold true for processes evolving on
long time scales in which the number of molecules of the species in
the reaction volume is suffi ciently large. Step (2) is required to
estimate unknown model parameters from the available experimental
data. Experimental data are strongly affected by noise. Hence,
classical optimization methods, based on gradient descent from an
arbitrary initial guess of the parameters’ value, can be unfeasible.
The above considerations suggest looking at stochastic optimization
algorithms, such as Genetic Algorithms (GA) ( 9 ) , which provide a
fl exible approach to nonlinear optimization. Their application has
been proved to yield good results in the parametrization of syn-
thetic networks ( 10, 11 ) .
When the network is quite complex in terms of the number of
the unknown parameters, there is the need of going through itera-
tion between experiments and modeling, to gather more experi-
mental data if needed. We show an example of such iteration, in
the case of the yeast network.
Fig. 2. Design of the positive feedback loop in mammalian cells. The promoter CMV-TET
consist of seven direct repeats of a 42-bp sequence containing the tet operator sequences
( tetO ), located just upstream of the minimal CMV promoter (P min CMV ). The tetracycline-
controlled transactivator tTA derives from the addition of the VP16 activation domain to
the transcriptional repressor TetR. The d2EYFP is the destabilized yellow-green variant of
enhanced green fl uorescent protein with a half-life of approximately 2 h.
60 D. di Bernardo et al.
Once a model of a synthetic network has been derived, it is possible
to refi ne it by means of several alternative strategies. The primary
goal of model refi nement is the improvement of model predictions
as regards the network dynamics, i.e., how gene and protein expres-
sion change in time following a perturbation; in order to accomplish
this task, the experimenter may need to stimulate its synthetic net-
work with highly dynamical signals. This is usually done to elicit
nonlinear modes or other peculiar characteristics of the network
under development. Most of the synthetic networks documented so
far ( 12 ) use chemical compounds as inducers and thus the previous
requirement often translates in the need to quickly change the con-
centration of these compounds in the media where cells are grown.
On the contrary, effective strategies for data acquisition are needed
to measure changes in the concentration of the species of interest in
live cells. Here, we propose an integrated strategy intended to solve
both of these issues at once via “microfl uidics” devices and time-
lapse fl uorescence microscopy. Microfl uidics involves the manipula-
tion of very small fl uid volumes, enabling creation and control of
nanoliter-volume reactors, thus mimicking cellular microenviron-
ments. Microfl uidics devices can be conveniently used to fi nely con-
trol the concentration of compounds in the extracellular environment
during time lapse microscopy experiments. Data acquired from long
term stimulation of cells carrying fl uorescent tags and tracked by the
microscopy imaging can be conveniently used to improve the quality
of the mathematical model of the circuit of interest.
In the following sections, we illustrate how this platform can be
adapted in experimental contexts involving both simpler and higher
eukaryotic systems, namely mammalian cell lines and S. cerevisiae .
1. S. cerevisiae strains YM4271 background ( MATa ura3-52 his3-
D200 ade2-101 lys2-801 leu2-3 trp1-901 gal4-D542 gal80-D538
ade5::hisG ) ( 3 ) .
2. YEP medium: 10 g/L Bacto yeast extract, 20 g/L Bacto
3. YEPD medium: YEP containing 2% glucose.
4. YEPGR medium: YEP containing 2% galactose and 2% raffi nose.
5. SC medium: 6.7 g/L yeast nitrogen base without amino acids,
1.35 g/L amino acid powder mix.
6. 2 U/ul DNAse I (Roche).
7. Rneasy MiniElute Cleaneup Kit (Quiagen).
8. SuperScript III First-Strand Synthesis System (Invitrogen).
9. Platinum SYBR Green qPCR SuperMix-UDG with ROX
1.4. Refi ning
by Means Of
2.1. Yeast Culture,
614 Predicting Synthetic Gene Networks
10. 7000 ABI Real-Time PCR machine.
11. Applied Biosystems SDS software version 1.2.3 to perform
1. Cole-Parmer nano syringe pump (Cole-Parmer).
2. USB valve control system.
3. Pneumadyne 8-Valve Manifold.
4. Tygon Microbore Tubing I.D.: 0. 25” O.D.: 0.125” (Swagelok).
5. Tygon Microbore Tubing I.D.: 0.020” O.D.: 0.060” (VWR).
6. Double distilled H 2 O.
7. Sulforhodamine B (Sigma-Aldrich).
8. 60-mL syringe (BD).
9. 10-mL syringes (BD).
10. 22G sterile needles (BD).
11. 2 mL cryovials (BMA).
12. Microfl uidic device.
13. Inverted fl uorescence microscope with temperature and CO 2
conditioning and appropriate fl uorescence fi lters.
1. 293FT cells maintained at 37°C in a 5% CO 2 -humidifi ed
incubator, and cultured in Dulbecco’s Modifi ed Eagle’s
Medium DMEM (GIBCO BRL) supplemented with 10%
heat-inactivated fetal bovine serum (FBS) (Invitrogen), 1%
L -glutammine, 1% MEM Nonessential Amino Acids, 1% MEM
Sodium pyruvate, and 1% antibiotic/antimycotic solution
2. Hek 293 cells maintained at 37°C in a 5% CO 2 -humidifi ed
incubator, and cultured in Dulbecco’s Modifi ed Eagle’s
Medium DMEM (GIBCO BRL) supplemented with 10%
heat-inactivated fetal bovine serum (FBS) (Invitrogen), 1%
L -glutamine, and 1% antibiotic/antimycotic solution
3. Doxycicline (Clontech) dissolved in tissue-culture water to a
fi nal concentration of 10 m g/mL, stored in aliquots at −20°C,
and then added to tissue culture dishes as required.
4. Polybrene (Invitrogen) dissolved in tissue-culture water to a
fi nal concentration of 6 mg/mL, stored in aliquots at −20°C,
and then added to tissue culture dishes to a fi nal concentration
of 6 m g/mL.
5. Blasticidin (Sigma) dissolved in tissue-culture water to a fi nal
concentration of 100 mg/mL stored in aliquots at −20°C, and
then added to tissue culture dishes to a fi nal concentration
of 3 m g/mL.
2.2. Microfl uidics and
2.3. Mammalian Cells
Culture and Lentiviral
62 D. di Bernardo et al.
1. Taq Phusion (Fynnzymes) is used to a fi nal concentration of
0.02 U/ m L; the HF buffer is added to a fi nal concentration
of 1×, primers and dNTPs are supplied to a fi nal concentra-
tion of 0.5 m M each and 200 m M each, respectively.
2. Taq DNA polymerase (Invitrogen) is used to a fi nal concentra-
tion of 1 U/ m L; the PCR buffer is added to a fi nal concen-
tration of 1× MgCl 2 1.5 mM, primers, and dNTPs are supplied
to a fi nal concentration of 0.5 m M each and 200 m M each
3. 5 U/ m L of NheI and EcoRV restriction enzymes (Roche).
4. 2 U/ m L of T4 DNA Ligase, and T4 DNA Ligase buffer to a
fi nal concentration of 1×.
5. LR Clonase II plus enzyme mix (Invitrogen).
1. Personal computer equipped with MATLAB Simulink
2. Image processing algorithm implemented in the control
To construct the IRMA containing strain, sequential PCR-based
genomic integrations were made sequentially. All the integrations
were confi rmed by PCR.
1. The 2× HA-hphMX4 cassette was amplifi ed by PCR and
inserted in front of the stop codon of ASH1 gene in YM4271
strain resulting in P278 strain.
2. To generate P280 strain MET16 promoter was amplifi ed from
W303 and cloned in YIplac128 between Hind III and Sac I.
3. GAL4 ORF was cloned between Sac I and Nde I, thus resulting
in p MET16pGAL4 .
4. The MET16pGAL4-LEU2 cassette was integrated in SHE2
5. CBF1 ORF was amplifi ed from W303 and cloned among Bam
HI and Pac I of p FA6a-GFP (S65T)-kanMX6 .
6. The CBF1-GFP-kanMX6 cassette was integrated downstream
of the HO promoter of P280 strain, obtaining P324.
7. ASH1 promoter was cloned in Pst I and Bam HI of YIplac211,
and then GAL80-3xFLAG was inserted between Bam HI and
8. The ASH1pGAL80-3XFLAG-URA3 was integrated in SWI5
locus, thus yielding P326.
of Gene Circuit
3.1. Construction of
S. cerevisiae Strains
634 Predicting Synthetic Gene Networks
9. ACE2 gene was deleted in the strain P326 by integrating
natMX4cassette from pAG25.
10. GAL10pSWI5AAA-MYC9-KlTRP1 was integrated in CBF1
locus resulting in IRMA containing strain.
Further details can be found in ( 3 ) .
In order to analyze the dynamic behavior of the network, we analyzed
expression profi les of network genes by quantitative real-time
RT-PCR following two different perturbation experiments; in the
fi rst we shifted cells from glucose (YEPD medium) to galactose
(YEPGR medium) (“switch-on” experiments) and from galactose
to glucose (“switch-off” experiments). In the second, we overex-
pressed each of the fi ve network genes in cells that were grown
either in glucose or galactose ( 3 ) .
1. Prepare the total RNA.2. Treat 1 m g of RNA with 2.5 U of
2. Clean up with RNeasy MiniElute Cleaneup Kit (Quiagen).
3. Reverse-transcribe the RNA cleaned using SuperScript III
First-Strand Synthesis System.
4. Set up quantitative real-time PCR reactions in duplicates using
Platinum SYBR Green qPCR SuperMix-UDG with ROX.
5. Amplify the cDNA thus obtained using a 7000 ABI Real-Time
We constructed the synthetic positive feedback loop into a lentivi-
ral vector system to allow integration of the circuit in mammalian
cells. To this end, we used the ViraPower Promoterless Lentiviral
Gateway Expression System (Invitrogen), which takes advantage
of the site-specifi c recombination properties of bacteriophage
lambda, making the transfer of single DNA sequences faster than
the usual cloning strategies.
1. Cloning of a destabilized yellow-green variant of enhanced
green fl uorescent protein (d2EYFP) in the p MAtTA-IRES-
EGFP vector: the d2EYFP was amplifi ed from pd2EYFP-1
(Clontech) by PCR using the High-Fidelity DNA Polymerase
Taq Phusion, with a forward primer containing a NheI recognition
sequence and a reverse primer containing an EcoRV recogni-
tion sequence. The PCR product and p MAtTA-IRES-EGFP
were then digested with NheI-EcoRV restriction enzymes and
the d2EYFP ligated in place of EGFP (ratio ng of vector/ng of
d2EYFP = 1/3–1/5).
2. Generating the pENTR vectors: in order to produce a lentiviral
vector by using the gateway system we fi rst generated the pENTR
vectors containing the genes and the promoters of interest fl anked
by specifi c recombination sites. The p MAtTA-IRES-d2EYFP
and Testing of the
in Hek293 Cells
64D. di Bernardo et al.
was linearized with the AseI restriction enzyme and recombined
with the pDONR221 (invitrogen) following the manufacturer
instruction. In this way we generated p ENTRtTA-IRES-
d2EYFP vector with specifi c recombination sites. The CMV-
TET promoter was amplifi ed from pTRE2 (clontech) by PCR.
The PCR was performed with the Taq polymerase provided by
Invitrogen that adds a single deoxyadenosine (A) to the 3 ¢ ends
of PCR products. This allows PCR inserts to ligate effi ciently
with the pENTR5 ¢ -TOPO vector which is supplied linearized
with single 3 ¢ -deoxythymidine (T) overhangs, obtaining the
pENTR5 ¢ -TOPO- CMV-TET with specifi c recombination sites.
Finally, we performed a recombination reaction between the
pENTR tTA-IRES-d2EYFP ,
and the p Lenti/R4R2/V5-DEST using the LR clonase enzyme
according to manufacturer instructions. The lentivirus was
then produced in 293FTcells as described in the instructions
provided by Invitrogen.
3. Cell culture for lentiviral transduction: To transduce cells with
the virus produced, 500000 HEK293 cells were plated and
incubated overnight. The day of transduction the medium was
removed and 1 mL of the virus was added to the cells together
with polybrene to a fi nal concentration of 6 m g/mL. After an
overnight incubation the medium containing the virus was
removed and replaced with complete culture medium containing
the blasticidin to a fi nal concentration of 3 mg/mL to select
for stably transduced cells.
4. To test the dynamics of the autoregolatory loop, we performed
two sets of time-series experiments in which stably integrated
HEK293 cells were imaged using time-lapse microscopy and
fl uorescence of d2EYFP was quantifi ed. For both the experi-
mental designs in the fi rst time point, cells were treated with
Doxycycline to “switch off” the network, since Doxycycline
prevents the tTA transactivator to bind the CMV-TET respon-
sive promoter. In the fi rst set of experiments, the dynamics
were followed for 37 h at 37°C, while in the second set the
temperature was reduced to 32 °C to limit cell motility and
thus facilitate image analysis ( 13 ) .
pENTR5 ¢ -TOPO- CMV-TET ,
The network of interest it the one showed in Fig. 1 . Details about
the network construction are reported in Subheadings 2.1 and 3.1 .
For each species in the network, i.e., each mRNA (capital letters)
and correspondent protein concentration (small letters), we wrote
one equation, which expresses its change in time as the result of
production and degradation:
Modeling the Yeast
3.4.1. Step (i). Derivation
of the Model from First
65 4 Predicting Synthetic Gene Networks
([ 5],[ 1]; ,,,)[ 1],
[ 1][ 1],
(; ,)[ 4],
[ 4][ 4],
([4 ];,)[ 5],
v HSwiAshk k h h d CBF
CBF d Cbf
v H Cbf k hd GAL
v H Galk hd SWI
[ 5][ 5],
([ 5]; , )
([ 5];,)[ 1],
[ 1][ 1].
SWI d Swi
v HSwi d GAL
v HSwi k h d ASH
The fi rst two terms on the right-hand side of the mRNA equations
represent the production, where a are the basal transcription rates;
v are the maximal transcription rates modulated by the Hill
( ; , )
y k h
( ; , )
z k h
( , ; , , , )
y z k h k h
( ; , )
y k h H
( ; , ).
z k h
These are used to model transcriptional activation, or repression;
y and z represent transcription factor levels, h are the Hill coeffi -
cients (pure numbers that refer to the cooperativity of the activa-
tion binding reaction) and k are the Michaelis-Menten constants,
equal to the amount of transcription factor needed to reach half
maximal activation (or repression). For protein equations, the pro-
duction rates are b , i.e., the maximal translation rates. Degradations
of mRNAs and proteins are represented by d , i.e., the degradation
constants. The amount of free Gal4 depends on the interactions
of the galactose pathway with the network genes. For the units of
measurement, please refer to Table 1 . Summing up, when writing
the above model, we made the following assumptions: (A1) the
66D. di Bernardo et al.
transcriptional activity of each promoter is leaky ( a ); (A2)
the degradation kinetics of both mRNAs and proteins are
first-order; (A3) the protein production terms are proportional to
the corresponding mRNA concentrations; (A4) the transcriptional
activation–repression of each promoter by a transcription factor can
be modeled as a Hill function ( 2 ) .
Note that the concentration of Gal4free is the amount of Gal4
protein that is not involved in the formation of the protein-protein
complex with Gal80 and hence activates the GAL10 promoter
driving SWI5 expression.
Parameters of the mathematical model the yeast synthetic
model Refi ned model Exp. id.
k 1 (a.u.)
k 2 (a.u.)
k 3 (a.u.)
k 4 (a.u.)
1.884 1 1
30 0.035 0.035
0.229 0.037 0.037
0.216 0.09 Glu 0.09 Glu
0.01 Gal 0.01 Gal
k 5 (a.u.)
k 6 (a.u.)
a 1 (a.u. min. −1 )
a 2 (a.u. min. −1 )
a 3 (a.u. min. −1 )
a 4 (a.u. min. −1 )
a 5 (a.u. min. −1 )
v 1 (a.u. min. −1 )
v 2 (a.u. min. −1 )
v 3 (a.u. min. −1 )
0.16 1.884 1.884
0.160 1.884 1.884
0 0 –
1.10 × 10 −4 1.49 × 10 −4 –
3.2 × 10 −4 3 × 10 −3 –
0 7.4 × 10 −4 –
7.37 × 10 −5 6.1 × 10 −4 –
0.065 0.04 –
0.002 8.82 × 10 −4 –
0.025 0.002 Glu
v 3 Glu /v 3 Gal 9
v 4 (a.u. min. −1 )
v 5 (a.u. min. −1 )
d 1 (min −1 )
d 2 (min −1 )
d 3 (min −1 )
d 4 (min −1 )
0.007 0.014 –
0.002 0.018 –
0.033 0.022 –
0.042 0.047 –
0.047 0.421 –
0.141 0.098 –
674 Predicting Synthetic Gene Networks
In order to identify model’s parameters and validate the model, we
collected mRNAs expression levels during a time course experi-
ment, by shifting cells from glucose (YEPD medium) to galactose
(YEPGR medium) (“switch-on” experiment) as described in ( 3 )
and in Subheadings 2.1 and 3.2 . Data are shown in Fig. 3a .
We included as the fi rst point of the time-series the expression
level of the network genes after growing cells overnight in glucose,
just before shifting them from glucose to galactose ( 3 ) . The second
point, taken after 10 min, is measured just after the shift has
occurred. The averaged gene expression profi les (Fig. 3a ) show that
the standard washing steps, needed to shift cells from glucose
medium to the fresh new galactose-containing medium, induce a
transient increase in mRNA levels of GAL4 and GAL80 (Fig. 3a ,
gray bars). This effect is not dependent on galactose addition, but
uniquely on the washing steps ( 3 ) , and it is probably due to the
transient deprivation of carbon source during washing, which atten-
uates the degradation levels of GAL4 and GAL80 mRNAs ( 14 ) .
Moreover, the activation of CBF 1 appears to be delayed with
respect to the other Swi5 targets, respectively GAL80 and ASH1
(Fig. 3a ). Such delay is physically due to the sequential recruitment
of chromatin modifying complexes to the HO promoter, which
follows binding of Swi5 ( 15, 16 ) .
We then performed four additional experiments, shifting cells
from galactose to glucose, thus “switching off” gene expression in
the network, as described ( 3 ) and in Subheadings 2.1 and 3.2 .
model Refi ned model Exp. id.
d 5 (min −1 )
b 1 (min −1 )
b 2 (min −1 )
0.018 0.050 –
1 1 1
1 1 1
1 1 1
1 4 4
1 1 1
1 1 1
1 4 4
0.223 0.201 –
0.285 0.167 –
10 −4 Glu
t (min) 100 100 –
68D. di Bernardo et al.
The averaged time-series gene expression profi les (Fig. 3b ) were
used for validating model predictive performance. We refer to this
dataset as the “switch-off” dataset.
Finally, we collected another set of experiments to be used to fur-
ther validate the model’s predictive ability. We measured gene expres-
sion responses of the fi ve network genes following exogenous
overexpression of each of the fi ve genes under the control of a strong
constitutive promoter, as described in ( 3 ) and in Subheadings 2.1 and
3.2 . Such overexpression experiments were performed both in glucose
Fig. 3. Identifi cation and validation results of time-series, phenomenological model. Circles
represent average expression data for each of the IRMA genes at different time points.
Dashed lines represent standard errors. Solid lines represent in silico data. ( a ) Identifi cation
results of the phenomenological model on the average 5 h “switch-on” time-series. ( b )
Validation of the phenomenological model on the average 3 h “switch-off” dataset.
694 Predicting Synthetic Gene Networks
and in galactose. We refer to these two experimental datasets as the
“Galactose steady-state” and “Glucose steady-state” (Fig. 4a, c ).
At this stage, we had to properly refi ne the model both to be able
to capture the features highlighted by the gene expression profi les
and to reduce the number of parameters to be estimated. First of
all, we made the following extra modeling assumptions: (A5) a fi x
time delay, t , equal to 100 min, is added in the activation of the
HO promoter by Swi5; (A6) a transient decrease in the mRNA
degradation of GAL4 and GAL80 of value Db1 and Db2 is added for
an interval of 10 min to describe the effect of the washing steps.
Due to the lack of protein concentrations measurements, we
also assumed that the protein concentrations are monotonically
increasing functions of their corresponding mRNA concentrations
at any time (A7).
In order to defi ne the active amount of Gal4 (GAL4 free in the
above Equations), we needed to describe the effect of the galactose
pathway on the network dynamics. In the literature, very detailed
models of the galactose pathway have been presented ( 17 ) . Such
paradigms can be simplifi ed in a number of ways, but it often leads
to include in the model nonmeasurable complexes concentrations.
Thus, we decided to use a phenomenological approach, assuming
that (A8) the protein-protein interaction between Gal80 and Gal4
can be modeled as a direct inhibition of GAL80 on the promoter of
SWI5 , and that the strength of such inhibition depends on the
medium (strong inhibition in glucose, weak inhibition in galactose).
Actually we assumed that the GAL10 promoter is activated by
GAL4 and noncompetitively inhibited by GAL80. The resulting
phenomenological Delay Differential Equations (DDEs) model is:
SWI5(t - )
 ([ 4])
We use the symbol ^ to indicate medium-dependent quanti-
ties. Thus, we are assuming that the Michaelis-Menten coeffi cient
of the phenomenological description of the inhibition of GAL80 is
dependent on the medium.
3.5.1. Step (i). Derivation
of the Phenomenological
70D. di Bernardo et al.
Fig. 4. Experimental and simulated overexpression experiments ( a , c ). In vivo expression levels of IRMA genes after
overexpression of each gene (perturbed gene; indicated by the black dots on the bars) from the constitutive GPD promoter
( gray bars ) and after transformation of the empty vector ( white bars ). IRMA cells were transformed with each of the constructs
containing one of the fi ve genes or with the empty vector. At least, three difi erent colonies were grown in glucose ( b ) and
in galactose-rafi nose ( a ) up to the steady-state levels of gene expression. Quantitative PCR data are represented (average
data from different colonies) ( b , d ). In silico expressionlevels of IRMA genes obtained by simulating the overexpression of
each gene with the phenomenological model ( e , f ). In silico expression levels of IRMA genes obtained by simulating the
overexpression of each gene with the refi ned model.
714 Predicting Synthetic Gene Networks Download full-text
For the sake of simplicity, we set all of the Hill coeffi cients to 1. For
the identifi cation of the remaining parameters, we used the “switch-
on” dataset, using as initial values the simulated steady-state mRNA
levels in glucose. Parameters’ identifi cation results, obtained by
using the Genetic Algorithm and hand refi nement ( see Note 6 ) are
shown in Fig. 3 a and the inferred parameters in Table 1 . The model
captures the delay in CBF1 activation and the small variations of
GAL4 and GAL80 .
In order to validate the model predictive performance, we used
the “Glucose steady-state” and “Galactose steady-state” over-
expression experiments, and compared them with their in silico
counterparts by simulating the overexpression of each of the fi ve
genes (Fig. 4b ), (D)). We further validated the predictive perfor-
mance against the “switch-off” time-series by simulating in silico
the “switch-off” experiment (i.e., setting the medium-dependent
parameters to their values in glucose and starting the simulation
from the steady-state equilibrium in galactose) (Fig. 3b ). The phenom-
enological DDEs model has good descriptive and predictive
performance. However, the 24 identifi ed parameter values are
likely to be different from their physical values. For example, model
parameters (Table 1 ) indicate that the inhibition of Ash1 on CBF1
is so weak that can be neglected, even if in the literature it has been
reported otherwise ( 16 ) .
At this point, we needed to clarify the biological properties of the
HO promoter by taking direct measurements of the promoters’
parameters ( 3 ) . We thus measured the transcriptional response of
the promoters of GAL10 , MET16 , ASH1 , and HO; the latter when
regulated by both Swi5 and Ash1 ( see Note 7 ). For each promoter,
we fi tted to data the equation at steady state of the gene whose
expression the promoter drives. Of note, it became apparent from
the new experimental data and the fi tting results that galactose not
only weakens the inhibition of Gal80 on the GAL1 0 promoter
(assumption (A8)), but also allows a faster activation of the GAL10
promoter. Moreover, in galactose such activation is possible for
values of GAL4 lower than in glucose.
In order to capture the behavior observed from the new experiments,
we considered two additional parameters in the model to be explic-
itly dependent on the medium. Thus, we refi ned the previous
model by changing the equation of SWI5 , which became
d [ 15],
3.5.2. Step (II).
Identifi cation of Model’s
Parameters and Model
and Reidentifi cation
of the Correspondent
Parameters (Step (II))
3.5.4. Step (i).
Refi ned Model