A steady-state modeling approach to validate an
in vivo
mechanism
of the GAL regulatory network in
Saccharomyces cerevisiae
Malkhey Verma
1
, Paike J. Bhat
2
, Sharad Bhartiya
1
and K. V. Venkatesh
1,2
1
Department of Chemical Engineering and
2
School of Biosciences and Bioengineering, Indian Institute of Technology Bombay,
Powai, Mumbai, India
Cellular regulation is a result of complex interactions arising
from DNA–protein and protein–protein binding, autoreg-
ulation, and c ompartmentalization and shuttling o f regula-
tory proteins. Experiments in molecular biology have
identified these mechanisms recruited by a regulatory net-
work. M athematical m odels may be u sed t o c omplement t he
knowledge-base provided by in vitro experimental methods.
Interactions identified by in vitro experiments can lead to the
hypothesis of multiple candidate models explaining the
in vivo mechan ism. The e quilibrium disso ciation constants
for the various interactions and t he total component con-
centration c onstitute constraints o n t he candidate models. I n
this work, we identify t he most plausible in v ivo network by

nucleus through protein–protein interaction leading to
gene expression. The status of the switch is determined by
the state of the upstream regulatory element of the GAL
genes in the nucleus. The regulatory protein may bind to
the upstream regulatory element constituting a protein–
DNA interaction [4–6]. The availability of the regulatory
proteintointeractwithDNAmaydependonitsactivity,
which is generally established through a protein–protein
interaction [6,7]. It should be noted that the two interacting
molecules might represent the same protein, implying
dimerization. The upstream regulatory element itself may
be present in m ultiple c opies representing variable binding
sites. Furthermore, the status of one binding site could
influence the binding of the regulatory protein to the other,
representing cooperativity [5,6]. A regulatory protein may
be the product of the same genetic switch that it regulates
and i s termed a utoregulation [8,9]. Another mechanism
that plays an important role in deciding the status of the
switch is the distribution of the protein between the
nucleus and cytoplasm. This is accomplished either by
nucleocytoplasmic shuttling [10–12] of the protein or by
covalent modification [12–16]. The regulatory switch
recruits various elementary mechanisms, such as protein–
DNA and protein–protein interactions, stoichiometry
(number of binding sites and dimerization), shuttling,
cooperativity and autoregulation t o accomplish its regula-
tory goals. The complexity of the regulatory network arises
due to the i nterplay between these numerous coupled
elementary mechanisms.
Experimental methods in molecular biology have been

overall performance of the network. A similar experimental
evaluation of the roles of individual elementary mechanisms
in vivo is very difficult and tedious to obtain.
Among modeling strategies, steady-state response analy-
sis has been used in the past t o quantify genetic regulatory
switches [2–4,12,17,19]. T he input–output relationships were
mainly quantified by assuming interactions at equilibrium
and applying molar balances for the different components.
Thermodynamic parameters and total concentrations for
the various components are obtained by in vitro studies and
represent constraints on the candidate models. In this work,
we analyze the GAL genetic switch in S. cerevisiae to
demonstrate such an approach towards identifying the
in vivo mechanism from a pool of candidate models. We
validate the mechanism by c omparing the response of the
model with experimental steady-state expression of GAL
genes in response to galactose.
The GAL genetic switch
The G AL regulatory network is c omposed of three
regulatory proteins: a transcriptional a ctivator Gal4p, a
negative regulator Gal80p and a signal transducer Gal3p
[6,7,20–23]. Gal4p binds exclusiv ely a s d imer [24] to 17 bp of
specific upstream activation sequences of the GAL genes
through i ts N -terminal DNA binding site. Gal80p inhibits
the transcriptional activity of Gal4p b y binding to its 2 8
amino acid region at the carboxyl terminal [25–27]. In vitro
studies have demonstrated that dimerization of Gal80p
stabilizes the G al4p–Gal80p and the DNA–Gal4p–Gal80p
complexes [ 7]. The GAL genes are expressed in presence
of galactose through Gal3p, which relieves the inhibitory

translocation and dimerization possibilities of Gal3p. The
steady-state response analysis rules out dimerization or
translocation of Gal3p. Further, the analysis clearly dem-
onstrates that the shuttling of G al80p and monomer
binding of Gal80p with Gal3p are prevalent in vivo.
Experimental procedures
We consider four candidate models, Models I–IV, shown in
Figs 1–3, to validate t he mechanism of induction of GAL
genes by galactose. In each o f the models, cytoplasmic
Gal3p is activated by galactose. Further, Gal4p dimerizes
and i nteracts wit h the DNA to form the DNA–Gal4p
complex in the nucleus. The GAL genes can have either one
(D1) or two ( D2) binding sites for dimer Gal4p. Also,
Gal80p dimerizes and subsequently interacts with the
DNA–Gal4p complex. The above mechanisms have been
elucidated by experiments [18]. The issues that differentiate
the f our cand idate models, described below, relate to
interactions between Gal3p and Gal80p.
Model I
As depicted in Fig. 1, activated Gal3p enters the nucleus
and binds to free as well as bound Gal80p to form Gal80p–
Gal3p and DNA–Gal4p–Gal80p–Gal3p complexes,
respectively. This relieves repression from Gal80p, leading
to expression of the GAL genes. In t his model, the Gal3p–
Gal80p interaction takes place exclusively in the nucleus.
Model II
Activated Gal3p enters the nucleus and i nteracts with free
Gal80p monomer alone to form Gal3p–Gal80p complex in
the nucleus. Thus, formation of the DNA–Gal4p–Gal80p–
Gal3p c omplex an d interactions between Gal3p and

S
is the half saturation constant for activation o f
Gal3p by galactose and t refers to the total component
concentration. The expression of GAL genes is determined
by the binding of the operator to either the dimer Gal4p
(G4) alone, that is DNA-Gal4p, or the complex Gal4p–
Gal80p–Gal3p, that is, DNA-Gal4p–Gal80p–Gal3p.
Therefore, the probability of expression of genes with one
( f
1
)ortwo(f
2
) binding sites is given as follows:
f
1
¼
½D1G4
2
þ½D1G4
2
G80
2
G3
2

½D1
t
Fig. 1. Sc hem atic represe ntatio n of cand idate m odel, M odel I, fo r the
GAL genetic switch in the presence of galactose. D1 and D2 represent
genes with one and two binding sites, respectively. G4, G80, G3 and

translation ( f
ip
) at steady state:
f
ip
¼ f
n
i
where, n is the co-response coefficient for translation [12],
i indicates the number of binding sites and p refers to the
protein. Because Gal80p and Gal3p are also regulated by
the GAL system, their total c oncentrations are dependent
on the status o f the switch. T hus, to a ccount for autoreg-
ulation of Gal80p and Gal3p, the total concentrations of
these were related to the translation status of genes with one
binding site (f
1p
) [12] as shown below:
½G80
t
¼ f
1p
½G80
max
½G3
t
¼ f
1p
½G3
max

reported by Peng & Hopper [11]. In this work, the basis for
identifying the in vivo mechanism was based on comparing
the input (galactose concentration)–output (fractional pro-
tein expression) steady-state responses for the candidate
models with experimental data reported and described in
Verma et al . [12], whose data for fractional protein expres-
sion has a maximum error of 9%.
Results
Depending upon the number of binding sites available to
Gal4p, i.e. either one or two binding sites, Verma et al.[12]
report distinct fractional protein expression for different
galactose concentrations (Fig. 4). Although the protein
expression of genes with one ( f
1p
)andtwo(f
2p
) binding
sites, occurs at 0.5 m
M
galactose concentration, the expres-
sion levels at higher concentrations ar e observe d a s 64% and
82%, re spectively, of the maximum feasible protein expres-
sion. The m aximum feasible protein concentration is
obtained when a ll the Gal4p binding sites express themselves.
Furthermore, the enhanced expression level of GAL genes
with two binding sites r elative to one binding site is
accompanied by s aturation at lower galactose concentration,
implying a more sensitive response. Verma et al.[12]usethe
Hill equation to describe the sensitivity of protein expression
to galactose and additionally report Hill coefficients of 1.2

½D2G4
2
þ½D2G4
2
G4
2
þ½D2G4
2
G80
2
G3
2
þ½D2G4
2
G80
2
G3
2
G4
2
G80
2
G3
2

½D2
t
Ó FEBS 2004 Mechanism of galactose signal transduction (Eur. J. Biochem. 271) 4067
ultrasensitive response. Because only small concentrations of
DNA-Gal4p–Gal80p complex exist, the presence of a small

1p
and f
2p
, respectively. As
the t otal available Gal3p concentration in vivo is 5 l
M
(Appendix), the dimerization of Gal3p reduces the effective
amount of available Gal3p in the c ytoplasm f or sequestering
Gal80p from the nucleus, yielding a subsensitive response.
In Model IV, where activated Gal3p binds as a monomer
to Gal80p in the cytoplasm and Gal80p shuttles between
nucleus and the cytoplasm, the prediction matches the
experimental data (Fig. 6, curve ii), as previously demon-
strated by Verma et al . [12]. The experimentally observed
expression levels of 64% and 82% for f
1p
and f
2p
[12,34,35],
respectively, are a result of incomplete sequestration o f
Fig. 5. Comparison of Model II simulation r esu lts w it h experimental da ta
for fractional protein expression of wild-type for genes with one binding
site (A) and gen es w ith t wo binding site s ( B). Solid circles and solid
triangles denote experimental data for a-galactosidase expression level
for g enes with one binding site and for b-galactosidase expression level
for genes with two binding sites, respectively. Error bars show experi-
mental deviation in fractional expression based on three independent
experiments. The solid line refers to si mulation r esults for Model II.
Fig. 4. Comparison of Model I simulation results w ith experimental d ata
for fractional protein expression of wild-type for genes with one binding

influenced by the relative dominance of these individual
elements, which are captured by parameters s uch as the
binding constants and the extent of autoregulation. The
regulatory proteins may reside either in the nucleus or in
the cytoplasm or in both, thus controlling the network. The
existence of a protein in multiple compartments is accom-
plished via s huttling o r mod ification, wh ich act as additional
constraints on the response. In summary, the response of
regulatory system is uniquely determined by (a) resources
available in terms of total concentrations; (b) in v ivo
mechanisms reflected by the sequence of interactions;
(c) parameters quantifying strength of interactions; a nd
(d) spatial localization of p rotein in a compartment or
shuttling of proteins between compartments.
It is evident that a large number of parameters play a role
in the response of the GAL system. One may attempt to use
parameter-fitting procedures to alter the numerical values
for parameters in Models I–III such that the altered model
response is consistent with experimental ob servations.
However, the numerical values for the parameters (such as
the binding constants) reported in literature are obtained
experimentally and cannot assume arbitrary values. It is
noted that, with the exception of the shuttling constant, K,a
10-fold change i n the reported parameter value does not
significantly affect the model response. This indicates that
the n etwork response does not significantly depend on the
model parameters (except for K). Among the parameters
utilized in the four candidate models, those indicating total
component concentrations are well characterized. Thus, for
example, experiments indicate that [Gal3p]

Fig. 6. Co mpar ison of Model III (curve i) and Model IV (curve ii)
simulation results with experimental data for fractional protein expres-
sion of wild-type for genes with one binding site (A) and genes with two
binding sites (B). Solid circles and solid triangles denote e xperimenta l
data for a-galactosidase expression l evel for genes with o ne bi nding site
and f or b-galactosidase e xpression level for genes with t wo binding
sites, respectively. Error bars show experimen tal deviation in fractional
expression based on three independent experiments.
Ó FEBS 2004 Mechanism of galactose signal transduction (Eur. J. Biochem. 271) 4069
parameters, which can th en be compared with the e xperi-
mentally obtained values to validate the model.
In this work, we demonstrate the above methodology to
identify the in vivo mechanism for th e GAL system. Platt &
Reece [22] have demonstrated formation o f the DNA–
Gal4p–Gal80p–Gal3p complex in vitro. This prompts entry
of Gal3p into the nucleus to relieve repression caused by
Gal80p by binding to the D NA–Gal4p–Gal80p complex (as
represented in M odel I). However, Peng & Hopper [ 11] h ave
demonstrated that Gal3p is a cytoplasmic protein, thus
contradicting Model I . Simulations of Model I and Model II,
which postulated the shuttling of Gal3p, could not be
validated, thereby confirming the fact that Gal3p is a
cytoplasmic protein. Gal4p and Gal80p are shown to
dimerize in vitro [6,7]. However, dimerization of Gal3p
in vivo has not been reported in literature. Our analysis s hows
that dimerization of Gal3p will violate the total concentra-
tion of Gal3p in the wild-type thus reducing the protein
expression as in Model III. T his confirms the evidence
obtained t hrough g el filtering and c ross-linking that Gal3p is
monomeric in solution even at high concentrations.

relevance of t he different m echanisms at the s ystem le vel can
be obtained by such a steady-state response methodology in
conjunction with the information and constraints estab-
lished by molecular biology.
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Appendix
Nomenclature
Complexes formed b etween any t wo or more of the components b elow are r epresented by an en-rule (–) between t he names of
the two comp onents. Thus, X –Y represents the complex formed between c omponents X and Y. However, this h as been
removed when t he comp onents a re referred t o b y t heir abb reviations within equations. A component or co mplex X appearing
within square bracket, [X], refers to concentration of X. Subscript Ô2Õ indicates a dimer of a component, while a subscript ÔtÕ
refers to the total component concentration.
G4 Gal4p
G80 Gal80p
G80
n
Gal80p in nucleus
G80
c
Gal80p in cytoplasm
G3 Gal3p
G3* Activated Gal3p
D1 Operator of genes with one binding site for Gal4p
D2 Operator of genes with two binding site for Gal4p
Molar balance equations
The following are the molar balance equations for the four candidate models after considering interaction s specific to the
model:
Model I
½D1
t
¼½D1þ½D1G4

G4
2
þ½D2G4
2
G80
2
G4
2
G80
2

þ½D2G4
2
G80
2
G3*þ½D2G4
2
G80
2
G3*G3*þ½D2G4
2
G80
2
G3*G4
2
þ½D2G4
2
G80
2
G3*G3*G4

2
G3*G3*G4
2
G80
2
G3*G3*
Ó FEBS 2004 Mechanism of galactose signal transduction (Eur. J. Biochem. 271) 4071
½G4
t
¼½G4þ2 ½G4
2
þ2 ½G4
2
G80
2
þ2 ½D1G4
2
þ2 ½D1G4
2
G80
2

þ 2 ½D1G4
2
G80
2
G3*þ2 ½D1G4
2
G80
2


þ 4 ½D2G4
2
G80
2
G4
2
G80
2
þ2 ½D2G4
2
G80
2
G3*þ2 ½D2G4
2
G80
2
G3*G3*
þ 4 ½D2G4
2
G80
2
G3*G4
2
þ4 ½D2G4
2
G80
2
G3*G3*G4
2

G80
2
þ2 ½D1G4
2
G80
2
G3*
þ 2 ½D1G4
2
G80
2
G3*G3*þ2 ½D2G4
2
G80
2
þ2 ½D2G4
2
G80
2
G4
2

þ 4 ½D2G4
2
G80
2
G4
2
G80
2

þ4 ½D2G4
2
G80
2
G3*G3*G4
2
G80
2

þ 4 ½D2G4
2
G80
2
G3*G3*G4
2
G80
2
G3*þ4 ½D2G4
2
G80
2
G3*G3*G4
2
G80
2
G3*G3*
þ½G80G3*
½G3*
t
¼½G3*þ½D1G4

2
G80
2
G3*G4
2
G80
2

þ 2 ½D2G4
2
G80
2
G3*G3*G4
2
G80
2
þ3 ½D2G4
2
G80
2
G3*G3*G4
2
G80
2
G3*
þ 4 ½D2G4
2
G80
2
G3*G3*G4

G4
2
þ½D2G4
2
G80
2
G4
2
G80
2

½G4
t
¼½G4þ2 ½G4
2
þ2 ½G4
2
G80
2
þ2 ½D1G4
2
þ2 ½D1G4
2
G80
2
þ2 ½D2G4
2

þ 2 ½D2G4
2

2
G80
2
þ2 ½D2G4
2
G80
2

þ 2 ½D2G4
2
G80
2
G4
2
þ4 ½D2G4
2
G80
2
G4
2
G80
2
þ½G80G3*
½G3*
t
¼½G3*þ½G80G3*
Model III
½D1
t
¼½D1þ½D1G4

2
G80n
2

½G4
t
¼½G4þ2 ½G4
2
þ2 ½G4
2
G80n
2
þ2 ½D1G4
2
þ2 ½D1G4
2
G80n
2
þ2 ½D2G4
2

þ 2 ½D2G4
2
G80n
2
þ4 ½D2G4
2
G4
2
þ4 ½D2G4

þ 2 ½D2G4
2
G80n
2
þ2 ½D2G4
2
G80n
2
G4
2
þ4 ½D2G4
2
G80n
2
G4
2
G80n
2
þ2 ½G80c
2
G3*
2

½G3*
t
¼½G3*þ2 ½G3*
2
þ2 ½G80c
2
G3*

þ½D2G4
2
G80n
2
G4
2
G80n
2

½G4
t
¼½G4þ2 ½G4
2
þ2 ½G4
2
G80n
2
þ2 ½D1G4
2
þ2 ½D1G4
2
G80n
2

þ 2 ½D2G4
2
þ2 ½D2G4
2
G80n
2

þ2 ½D1G4
2
G80n
2

þ 2 ½D2G4
2
G80n
2
þ2 ½D2G4
2
G80n
2
G4
2
þ4 ½D2G4
2
G80n
2
G4
2
G80n
2

þ½G80cG3*
½G3*
t
¼½G3*þ½G80cG3*
Equilibrium dissociation relationships
Concentrations of all complexes arising from various i nteractions in the GAL switch are obtained using equilibriu m

1
Dissociation constant for dimerization of Gal4p
K
2
Dissociation constant for dimerization of Gal80p
K
3
Dissociation constant for interaction between Gal4p and i ts complex with Gal80p or its dimer
K
4
Dissociation constant for interaction between Gal80p and its complex with Gal3p* or its dimer
K
5
Dissociation constant for dimerization of Gal3p*
K
d
Dissociation constant for interaction between operator site (D1 or D2) and Gal4p dimer
K Nucleocytoplasmic distribution coefficient
Model parameters
The total regulatory proteins and DNA concentrations should be known to solve the model equilibrium relationship, for
this purpose we have considered a haploid yeast cell with total volume of 70 lm
3
[36]. B inding constants and estimated
parameters used in the m odel are obtained from Verma et al. [ 9]. The set of equations were solved using the fsolve
Ó FEBS 2004 Mechanism of galactose signal transduction (Eur. J. Biochem. 271) 4073
function in
MATLAB
12 (The Math Works, Inc., Natick, MA, USA). Parameter values used in the steady-state model [9] are
shown.
Parameter Value

5
1.0 · 10
)10
M
m 30
n 0.5
[D1]
t
3 · 2.372 · 10
)11
M
[D2]
t
7 · 2.372 · 10
)11
M
[Gal4p]
t
5.47 · 10
)9
M
[Gal80p]
max
1.0 · 10
)6
M
[Gal3p]
max
5.0 · 10
)6