Báo cáo khoa học: A steady-state modeling approach to validate an in vivo mechanism of the GAL regulatory network in Saccharomyces cerevisiae ppt

Eur. J. Biochem. 271, 4064–4074 (2004) Ó FEBS 2004

doi:10.1111/j.1432-1033.2004.04344.x

A steady-state modeling approach to validate an in vivo mechanism
of the GAL regulatory network in Saccharomyces cerevisiae
Malkhey Verma1, Paike J. Bhat2, Sharad Bhartiya1 and K. V. Venkatesh1,2
1

Department of Chemical Engineering and 2School 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, autoregulation, and compartmentalization and shuttling of regulatory proteins. Experiments in molecular biology have
identified these mechanisms recruited by a regulatory network. Mathematical models may be used to complement the
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 mechanism. The equilibrium dissociation constants
for the various interactions and the total component con-

centration constitute constraints on the candidate models. In
this work, we identify the most plausible in vivo network by
comparing the output response to the experimental data. We
demonstrate the methodology using the GAL system of
Saccharomyces cerevisiae for which the steady-state analysis
reveals that Gal3p neither dimerizes nor shuttles between the
cytoplasm and the nucleus.

Intracellular regulatory networks are complex systems
whose operation represents a highly coordinated orchestration connecting metabolic pathways, signal transduction

and gene expression in a hierarchical control structure. The
scope of experimental methods in molecular biology for
identifying the role of individual mechanisms in the overall
hierarchy is limited to a subset of the total in vivo
interactions. Quantitative analyses have been used to
integrate the metabolic pathways for signal transduction
and gene expression [1–3]. A large number of regulatory
networks have been described in literature for gene expression of various organisms. However, only a few of these
regulatory networks have been quantified with mathematical models to obtain meaningful insights. Examples of such
regulatory networks with detailed mechanisms include the
tryptophan and arabinose systems of Escherichia coli and
the phage lambda switch in bacteriophage.
The GAL regulatory network in Saccharomyces cerevisiae is a prototypical eukaryotic switch that is well
characterized at the biochemical and genetic level. The
switch constitutes elements for sensing of galactose and
transduction of the measurement of galactose to the
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
protein to interact with DNA may depend on its activity,
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 multiple copies 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 is termed autoregulation [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 to accomplish its regulatory goals. The complexity of the regulatory network arises
due to the interplay between these numerous coupled
elementary mechanisms.
Experimental methods in molecular biology have been
gainfully used to elicit parts of the overall mechanism.
However, evaluation of the exact mechanism of a regulatory
network requires extensive experimentation. Therefore,
mechanisms of only a few networks have been completely
elaborated, such as, phage lambda [4] and trp regulation in
E. coli [17,18]. Further, experimental methods establish and
quantify in vitro interactions, thus raising questions regarding prevalent in vivo mechanisms. Performance of the

Correspondence to K. V. Venkatesh, Department of Chemical
Engineering, Indian Institute of Technology, Bombay, Powai, Mumbai-400076, India. Fax: +91 22 25726895, Tel.: +91 22 25767233.
E-mail:
Abbreviations (used only in equations): Gal, galactose; G4, Gal4p;
G80, Gal80p; G3, Gal3p; G3*, activated Gal3p; D1, one binding site
for dimer Gal4p on GAL genes; D2, two binding sites for dimer Gal4p

on GAL genes.
(Received 24 July 2004, revised 13 August 2004,
accepted 23 August 2004)

Keywords: Gal4p binding sites; gene expression; nucleocytoplasmic shuttling; regulatory networks; Saccharomyces
cerevisiae.


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Mechanism of galactose signal transduction (Eur. J. Biochem. 271) 4065

regulatory network depends on the prevalent individual
elementary mechanisms and the sequence in which they are
connected. A mathematical representation of these elementary mechanisms, identified through experiments, will allow
postulation of candidate models for the network operation.
These candidate models may now be evaluated using
experimental data to converge on the realistic in vivo
mechanism. The in vivo model is selected from the candidate
models that best describe the input–output experimental
data. The individual components of the selected model
provide insights into the importance of their roles in the
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 analysis has been used in the past to quantify genetic regulatory
switches [2–4,12,17,19]. The 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 comparing the response of the
model with experimental steady-state expression of GAL
genes in response to galactose.
The GAL genetic switch
The GAL regulatory network is composed of three
regulatory proteins: a transcriptional activator Gal4p, a
negative regulator Gal80p and a signal transducer Gal3p
[6,7,20–23]. Gal4p binds exclusively as dimer [24] to 17 bp of
specific upstream activation sequences of the GAL genes
through its N-terminal DNA binding site. Gal80p inhibits
the transcriptional activity of Gal4p by binding to its 28
amino acid region at the carboxyl terminal [25–27]. In vitro
studies have demonstrated that dimerization of Gal80p
stabilizes the Gal4p–Gal80p and the DNA–Gal4p–Gal80p
complexes [7]. The GAL genes are expressed in presence
of galactose through Gal3p, which relieves the inhibitory
effect of Gal80p [20,22,24,28–30].
Previous in vitro studies indicate that Gal3p interacts
directly with Gal80p in the presence of galactose in an ATP
dependent manner. Platt & Reece [22] have demonstrated
the in vitro existence of the complex DNA–Gal4p–Gal80p–
Gal3p, which is thought to relieve the inhibition by Gal80p.
Based on this observation, the authors postulated that
Gal3p enters the nucleus and interacts with the DNA–
Gal4p–Gal80p complex to initiate transcription. However,

Peng & Hopper have recently demonstrated under in vivo
conditions that Gal3p is a cytoplasmic protein, whereas,
Gal80p is present both in the nucleus and in the cytoplasm
[11,23]. The above two studies indicate the existence of
following two contrasting in vivo mechanisms for GAL
protein expression: (a) regulatory protein Gal3p translocates into the nucleus to bind to the DNA complex to relieve
repression; (b) Gal3p sequesters Gal80p from the nucleus
into the cytoplasm to relieve repression. There is further
ambiguity regarding dimerization of Gal3p.

A fundamental question arises with regards to the
mechanism for transmission of the galactose signal from
the cytoplasm to the DNA–Gal4p–Gal80p complex present
in the nucleus to activate transcription. In particular, does
Gal3p enter the nucleus as suggested by Platt & Reece [22]
or does Gal80p shuttle between the nucleus and cytoplasm
as reported by Peng & Hopper [11], or are both of these
mechanisms prevalent in vivo. Questions of such nature
may be addressed by the modeling approach discussed
above. We postulate four different mechanistic models for
the interaction between Gal80p and Gal3p based on
translocation and dimerization possibilities of Gal3p. The
steady-state response analysis rules out dimerization or
translocation of Gal3p. Further, the analysis clearly demonstrates that the shuttling of Gal80p 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 the mechanism of induction of GAL
genes by galactose. In each of the models, cytoplasmic

Gal3p is activated by galactose. Further, Gal4p dimerizes
and interacts with 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 four candidate 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 this model, the Gal3p–
Gal80p interaction takes place exclusively in the nucleus.
Model II
Activated Gal3p enters the nucleus and interacts with free
Gal80p monomer alone to form Gal3p–Gal80p complex in
the nucleus. Thus, formation of the DNA–Gal4p–Gal80p–
Gal3p complex and interactions between Gal3p and
other complexes of Gal80p have not been considered here
(Fig. 2).
Model III
Activated Gal3p dimerizes and subsequently interacts with
dimer Gal80p in the cytoplasm alone without translocating
to the nucleus. The consequent nucleocytoplasmic shuttling
of the Gal80p monomer from the nucleus to the cytoplasm
relieves repression (Fig. 2).
Model IV

As in Model III, Gal80p shuttles between the nucleus and
the cytoplasm to regulate transcription. However, in this


4066 M. Verma et al. (Eur. J. Biochem. 271)

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Fig. 1. Schematic representation of candidate model, Model I, for 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
G3* represent regulatory proteins Gal4p, Gal80p, Gal3p and activated
Gal3p, respectively. Model I includes sequential binding of activated
Gal3p to DNA-Gal4p–Gal80p. Parameter m represents cooperativity
during binding of Gal4p to the second binding site. All other Ki valuess
(where i ¼ 1–5) represent dissociation constants for various interactions. Kd represents binding of Gal4p dimer with DNA. Parameter
values are provided in the Appendix.

case, Gal80p binds as a monomer to activated Gal3p in the
cytoplasm to relieve repression by Gal80p in the nucleus
(Fig. 3).
All of the above four models consider the activation of
Gal3p (G3 to G3*) at a given galactose (Gal) concentration
to follow a Michelis–Menten saturation relationship:


Gal
ẵG3 t ẳ ẵG3t
KS ỵ Gal
where, KS is the half saturation constant for activation of

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
( f1) or two ( f2) binding sites is given as follows:
f1 ẳ

ẵD1G42 ỵ ẵD1G42 G802 G32
ẵD1t

Fig. 2. Schematic representation of candidate models, Model II and
Model III, for the GAL genetic switch in the presence of galactose.
Model II assumes that activated Gal3p enters the nucleus and binds to
the Gal80p monomer to switch on the GAL genes. On the other hand,
Model III considers activated Gal3p as an exclusively cytoplasmic
protein that interacts with Gal80p as a dimer. K represents the
nucleocytoplasmic distribution coefficient of Gal80p. See Fig. 1, for
interpretation of other symbols.


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Mechanism of galactose signal transduction (Eur. J. Biochem. 271) 4067

modeled by an equilibrium distribution coefficient (K) as
follows:
K¼

Fig. 3. Schematic representation of candidate model, Model IV, for the
GAL genetic switch in the presence of galactose. Like in Model III,
Model IV also considers Gal3p to be an exclusively cytoplasmic protein. However, Gal3p can exist only as a monomer. See Fig. 1, for
interpretation of symbols.

f2 ẳ

ẵG80c
ẵG80n

where, [G80]n and [G80]c represent Gal80p concentrations
in the nucleus and cytoplasm, respectively. In order to relate
protein expression to galactose concentrations, component
molar balances along with equilibrium relationships (for all
interactions present in a model) are formulated and solved
(Appendix). The total concentrations of DNA, Gal4p,
Gal3p and Gal80p, along with the various binding
constants for the interactions were taken from literature
and are also listed in the Appendix. It is noted that all
component concentrations including [G80]n and [G80]c are
based on total cell volume. In summary, Model I and II
manifest the mechanism reported by Platt & Reece [22],
while Model III and IV are based on the mechanism
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 protein expression) steady-state responses for the candidate
models with experimental data reported and described in
Verma et al. [12], whose data for fractional protein expression 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]

ẵD2G42 ỵ ẵD2G42 G42 þ ½D2G42 G802 G32 Š þ ½D2G42 G802 G32 G42 G802 G32 Š
½D2Št

Note that the complex DNA-Gal4p–Gal80p–Gal3p will not
be present in Model II, Model III, or Model IV. The
fractional protein expression can be related to fractional
transcriptional expression through a co-response coefficient
[32], which is defined as the ratio of the log fold change in
protein expression to log fold change in mRNA expression
[33]. Thus, the following power law expression was used for
transforming fractional transcription ( fi) to fractional
translation ( fip) at steady state:
fip ¼ fin
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 concentrations are dependent
on the status of the switch. Thus, to account for autoregulation of Gal80p and Gal3p, the total concentrations of
these were related to the translation status of genes with one
binding site (f1p) [12] as shown below:
ẵG80t ẳ f1p ẵG80max
ẵG3t ẳ f1p ẵG3max
Models III and IV require shuttling of Gal80p across the
nucleocytoplasmic membrane. This mechanism has been

report distinct fractional protein expression for different
galactose concentrations (Fig. 4). Although the protein

expression of genes with one ( f1p) and two ( f2p) binding
sites, occurs at 0.5 mM galactose concentration, the expression levels at higher concentrations are observed as 64% and
82%, respectively, of the maximum feasible protein expression. The maximum feasible protein concentration is
obtained when all the Gal4p binding sites express themselves.
Furthermore, the enhanced expression level of GAL genes
with two binding sites relative to one binding site is
accompanied by saturation at lower galactose concentration,
implying a more sensitive response. Verma et al. [12] use the
Hill equation to describe the sensitivity of protein expression
to galactose and additionally report Hill coefficients of 1.2
and 2 for one and two binding sites, respectively. The
equations representing the four candidate models described
in the Appendix were simulated to yield f1p and f2p at various
galactose concentrations. Figure 4 shows comparisons of f1p
and f2p between the model simulation results for candidate
Model I and experimental data. The formation of the
DNA–Gal4p–Gal80p–Gal3p complex yields a very sensitive
response wherein the switch turns on at a very low galactose
concentration (about 10)4 mM). The Hill coefficients for
expression from genes with one and two binding sites for
Model 1 are 3.2 and 5, respectively, indicating an extremely


4068 M. Verma et al. (Eur. J. Biochem. 271)

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Fig. 4. Comparison of Model I simulation results with experimental data
for fractional protein expression of wild-type for genes with one binding
site (A) and genes with two binding sites (B). Solid circles and solid

triangles denote experimental data for a-galactosidase expression level
for genes with one binding site and for b-galactosidase expression level
for genes with two binding sites, respectively. Error bars show experimental deviation in fractional expression based on three independent
experiments. The solid line refers to simulation results for Model I.

Fig. 5. Comparison of Model II simulation results with experimental data
for fractional protein expression of wild-type for genes with one binding
site (A) and genes with two binding sites (B). Solid circles and solid
triangles denote experimental data for a-galactosidase expression level
for genes with one binding site and for b-galactosidase expression level
for genes with two binding sites, respectively. Error bars show experimental deviation in fractional expression based on three independent
experiments. The solid line refers to simulation results for Model II.

ultrasensitive response. Because only small concentrations of
DNA-Gal4p–Gal80p complex exist, the presence of a small
amount of activated Gal3p in the nucleus is sufficient to
switch on the GAL genes at very low galactose concentrations. This fact in conjunction with the autoregulation of
Gal3p ensures the steep response in Fig. 4 with maximum
feasible protein expression. The large mismatch between the
experiment and the response curve of Model I implies that
Model I may not be operable in vivo.
Comparison of experimental data with simulation of
Model II, where activated Gal3p monomer binds to Gal80p
monomer in the nucleus, is shown in Fig. 5. The regulatory
network represented by Model II responds at about 0.5 mM
galactose level, which matches with experimental data. The
Hill coefficients are noted as 2 and 3 for f1p and f2p,
respectively, with maximum feasible protein expression for
genes with two binding sites. Absence of direct binding of
Gal3p to the DNA implies that larger quantities of Gal3p

are necessary, relative to Model I, to switch on the GAL

genes. However, the protein expressions are steeper than
those observed experimentally and are caused by autoregulation and nonexistence of shuttling of Gal80p.
In Model III, the model predictions indicate that the
protein expressions are subsensitive and do not attain the
wild-type expression levels (Fig. 6, curve i). Model III
expression levels are observed as 48% and 40% of the
maximum feasible expression for f1p and f2p, respectively. As
the total available Gal3p concentration in vivo is 5 lM
(Appendix), the dimerization of Gal3p reduces the effective
amount of available Gal3p in the cytoplasm for 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 demonstrated by Verma et al. [12]. The experimentally observed
expression levels of 64% and 82% for f1p and f2p [12,34,35],
respectively, are a result of incomplete sequestration of


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Mechanism of galactose signal transduction (Eur. J. Biochem. 271) 4069

Fig. 6. Comparison of Model III (curve i) and Model IV (curve ii)
simulation results with experimental data for fractional protein expression of wild-type for genes with one binding site (A) and genes with two
binding sites (B). Solid circles and solid triangles denote experimental
data for a-galactosidase expression level for genes with one binding site
and for b-galactosidase expression level for genes with two binding

sites, respectively. Error bars show experimental deviation in fractional
expression based on three independent experiments.

Gal80p by Gal3p. The above values of percentage protein
expression levels have also been observed independently
[34,35]. The response of Model IV matches the experimental
observation given the constraints of total component
concentrations and binding constants.

Discussion
Studies in molecular biology have enumerated various
interactions resulting in a complex regulatory network.
Most of such studies demonstrate the in vitro interaction
between the various components. However, these in vitro
experiments may not yield the in vivo mechanism of the
regulatory system. An experimental determination of the
in vivo mechanism in a genetic regulatory network would
require generation of specific mutants, which is tedious.
Many factors contribute to the response of a regulatory
network for a given input. For example, the operation of the
switch is constrained by the number of binding sites and the

amounts of regulatory proteins. Further, numerous elements such as stoichiometry (dimerization), number of
binding sites, autoregulation and cooperativity are also
known to constrain the operation of the network. However,
the response for a specific system is constrained by the
connection between these elements. The response is also
influenced by the relative dominance of these individual
elements, which are captured by parameters such 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 accomplished via shuttling or modification, which 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 vivo
mechanisms reflected by the sequence of interactions;
(c) parameters quantifying strength of interactions; and
(d) spatial localization of protein 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 observations.
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 in the reported parameter value does not
significantly affect the model response. This indicates that
the network 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]max is five-fold of
[Gal80p]max and this constraint should not be violated while
exploring parametric sensitivity. Another issue that needs to
be considered is the experimental error in protein measurement, which may be large enough to fit more than one of the
candidate model responses. However, specific to the measurements reported in the current work, error bars indicate

that Model IV fits uniquely the experimental data. This
issue must be carefully considered when applying a similar
methodology to other systems for identification of the
possible in vivo mechanisms.
It is pertinent to pursue identification of the elements of
the mechanism through mathematical models. Development of a steady-state model requires the binding constants
between the various components and the total component
concentrations as model parameters, which can be obtained
through simpler experiments. Thus, steady-state analysis
can be used as a tool to establish the actual mechanism
prevalent inside the cell by eliminating infeasible mechanisms. The response curve can be quantified by a Hill
equation and is characterized by two parameters, namely,
the Hill coefficient and the half saturation constant. The Hill
coefficient is a measure of the steepness of the response,
while the half saturation constant measures the threshold
activator (inducer or repressor) concentration required for
the response (switching on or off). Thus, the steadystate input–output response analysis will yield these two


4070 M. Verma et al. (Eur. J. Biochem. 271)

parameters, which can then be compared with the experimentally obtained values to validate the model.
In this work, we demonstrate the above methodology to
identify the in vivo mechanism for the GAL system. Platt &
Reece [22] have demonstrated formation of 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 DNA–Gal4p–Gal80p complex (as
represented in Model I). However, Peng & Hopper [11] have
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 shows
that dimerization of Gal3p will violate the total concentration of Gal3p in the wild-type thus reducing the protein
expression as in Model III. This confirms the evidence
obtained through gel filtering and cross-linking that Gal3p is
monomeric in solution even at high concentrations.
Peng & Hopper [11] have experimentally verified that
Gal3p concentration is five times that of Gal80p in wild-type.
This constraint on the inventory of the two regulatory
proteins critically affects the protein expressions. For
example, the analysis using Model IV demonstrates that if
this constraint were to be violated by having a large excess of
Gal3p in the cytoplasm, the slightest amount of galactose
would sequester Gal80p in the cytoplasm (results not
shown). Here the protein expression would be similar to
that of a mutant strain lacking Gal80p. Also, the higher
sensitivity of the protein expression for genes with two
binding sites is a result of dimerization of Gal4p and
cooperativity [19]. The key mechanism that controls the
protein expression in the wild-type is the shuttling of Gal80p.
Increasing the amount of Gal80p in the cytoplasm by
increasing the distribution coefficient (K) causes the switch to
turn on at very low galactose concentrations. On the other
hand, decreasing the distribution coefficient would make the
response less sensitive to galactose. Thus, the performance of
the switch is critically dependent upon the parameter, K,

which determines the steady-state concentration of Gal80p
in the cytoplasm and the nucleus.
The above steady-state response methodology to predict
in vivo mechanisms prevalent in a regulatory network may
be extended to other systems. The ingredients necessary for
performing such an analysis include the experimental input–
output response curves (either transcription response or
protein expression) and in vitro binding coefficients. Further
results from studies in molecular biology and bioinformatics
can limit the number of candidate models. Finally, the
relevance of the different mechanisms at the system level can
be obtained by such a steady-state response methodology in
conjunction with the information and constraints established by molecular biology.

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Appendix
Nomenclature
Complexes formed between any two or more of the components below are represented by an en-rule (–) between the names of
the two components. Thus, X–Y represents the complex formed between components X and Y. However, this has been

removed when the components are referred to by their abbreviations within equations. A component or complex 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
G80
G80n
G80c
G3
G3*
D1
D2

Gal4p
Gal80p
Gal80p in nucleus
Gal80p in cytoplasm
Gal3p
Activated Gal3p
Operator of genes with one binding site for Gal4p
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 interactions specic to the
model:
Model I
ẵD1t ẳ ẵD1 ỵ ẵD1G42 ỵ ẵD1G42 G802 ỵ ẵD1G42 G802 G3* ỵ ẵD1G42 G802 G3*G3
ẵD2t ẳ ẵD2 ỵ ẵD2G42 ỵ ẵD2G42 G802 þ ½D2G42 G42 Š þ ½D2G42 G802 G42 Š þ ẵD2G42 G802 G42 G802
ỵ ẵD2G42 G802 G3* ỵ ẵD2G42 G802 G3*G3* ỵ ẵD2G42 G802 G3*G42 ỵ ẵD2G42 G802 G3*G3*G42
ỵ ẵD2G42 G802 G3*G42 G802 ỵ ẵD2G42 G802 G3*G3*G802 G802 ỵ ẵD2G42 G802 G3*G3*G42 G802 G3*

ỵ ẵD2G42 G802 G3*G3*G42 G802 G3*G3*Š


4072 M. Verma et al. (Eur. J. Biochem. 271)

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ẵG4t ẳ ẵG4 ỵ 2 ẵG42 ỵ 2 ẵG42 G802 ỵ 2 ẵD1G42 ỵ 2 ẵD1G42 G802
ỵ 2 ẵD1G42 G802 G3* þ 2  ½D1G42 G802 G3*G3*Š þ 2  ½D2G42
ỵ 2 ẵD2G42 G802 ỵ 4 ẵD2G42 G42 ỵ 4 ẵD2G42 G802 G42
ỵ 4 ẵD2G42 G802 G3*G42 ỵ 4 ẵD2G42 G802 G3*G3*G42
ỵ 4 ẵD2G42 G802 G42 G802 ỵ 2 ẵD2G42 G802 G3* ỵ 2 ẵD2G42 G802 G3*G3*
ỵ 4 ẵD2G42 G802 G3*G42 ỵ 4 ẵD2G42 G802 G3*G3*G42 G802
ỵ 4 ẵD2G42 G802 G3*G3*G42 G802 G3* ỵ 4 ẵD2G42 G802 G3*G3*G42 G802 G3*G3*
ẵG80t ẳ ẵG80 ỵ 2 ẵG802 ỵ 2 ẵG42 G802 ỵ 2 ẵD1G42 G802 ỵ 2 ẵD1G42 G802 G3*
ỵ 2 ẵD1G42 G802 G3*G3* þ 2  ½D2G42 G802 Š þ 2  ½D2G42 G802 G42
ỵ 4 ẵD2G42 G802 G42 G802 þ 2  ½D2G42 G802 G3*Š þ 2  ½D2G42 G802 G3*G3*
ỵ 2 ẵD2G42 G802 G3*G42 ỵ 2 ẵD2G42 G802 G3*G3*G42
ỵ 4 ẵD2G42 G802 G3*G42 G802 ỵ 4 ẵD2G42 G802 G3*G3*G42 G802
ỵ 4 ẵD2G42 G802 G3*G3*G42 G802 G3* ỵ 4 ẵD2G42 G802 G3*G3*G42 G802 G3*G3*
ỵ ẵG80G3*
ẵG3*t ẳ ẵG3* ỵ ẵD1G42 G802 G3* ỵ 2 ẵD1G42 G802 G3*G3*
ỵ ẵD2G42 G802 G3* ỵ 2 ẵD2G42 G802 G3*G3* ỵ ẵD2G42 G802 G3*G42
ỵ 2 ẵD2G42 G802 G3*G3*G42 ỵ ẵD2G42 G802 G3*G42 G802
ỵ 2 ẵD2G42 G802 G3*G3*G42 G802 ỵ 3 ẵD2G42 G802 G3*G3*G42 G802 G3*
ỵ 4 ẵD2G42 G802 G3*G3*G42 G802 G3*G3* ỵ ẵG80G3*
Model II
ẵD1t ẳ ẵD1 ỵ ẵD1G42 ỵ ẵD1G42 G802
ẵD2t ẳ ẵD2 þ ½D2G42 Š þ ½D2G42 G802 Š þ ½D2G42 G42 ỵ ẵD2G42 G802 G42 ỵ ẵD2G42 G802 G42 G802
ẵG4t ẳ ẵG4 ỵ 2 ẵG42 ỵ 2 ẵG42 G802 ỵ 2 ẵD1G42 þ 2  ½D1G42 G802 Š þ 2  ½D2G42

ỵ 2 ẵD2G42 G802 ỵ 4 ẵD2G42 G42 ỵ 4 ẵD2G42 G802 G42 ỵ 4 ẵD2G42 G802 G42 G802
ẵG80t ẳ ẵG80 ỵ 2 ẵG802 ỵ 2 ẵG42 G802 þ 2  ½D1G42 G802 Š þ 2  ½D2G42 G802
ỵ 2 ẵD2G42 G802 G42 ỵ 4 ẵD2G42 G802 G42 G802 ỵ ẵG80G3*
ẵG3*t ẳ ẵG3* ỵ ẵG80G3*
Model III
ẵD1t ẳ ẵD1 ỵ ẵD1G42 ỵ ẵD1G42 G80n2
ẵD2t ẳ ẵD2 ỵ ẵD2G42 ỵ ẵD2G42 G80n2 ỵ ẵD2G42 G42 ỵẵD2G42 G80n2 G42
ỵ ẵD2G42 G80n2 G42 G80n2
ẵG4t ẳ ẵG4 ỵ 2 ẵG42 þ 2  ½G42 G80n2 Š þ 2  ½D1G42 ỵ 2 ẵD1G42 G80n2 ỵ 2 ẵD2G42
ỵ 2 ẵD2G42 G80n2 ỵ 4 ẵD2G42 G42 ỵ 4 ẵD2G42 G80n2 G42 þ 4  ½D2G42 G80n2 G42 G80n2 Š


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Mechanism of galactose signal transduction (Eur. J. Biochem. 271) 4073

ẵG80t ẳ ẵG80n ỵ ẵG80c ỵ 2 ẵG80n2 ỵ 2 ẵG80c2 ỵ 2 ẵG42 G80n2 ỵ 2 ẵD1G42 G80n2
ỵ 2 ẵD2G42 G80n2 ỵ 2 ẵD2G42 G80n2 G42 þ 4  ½D2G42 G80n2 G42 G80n2 Š þ 2 ẵG80c2 G3*2
ẵG3*t ẳ ẵG3* ỵ 2 ẵG3*2 ỵ 2 ẵG80c2 G3*2
Model IV
ẵD1t ẳ ẵD1 ỵ ẵD1G42 ỵ ẵD1G42 G80n2
ẵD2t ẳ ẵD2 ỵ ẵD2G42 ỵ ẵD2G42 G80n2 ỵ ẵD2G42 G42 þ ½D2G42 G80n2 G42 Š þ ½D2G42 G80n2 G42 G80n2
ẵG4t ẳ ẵG4 ỵ 2 ẵG42 ỵ 2 ẵG42 G80n2 ỵ 2 ẵD1G42 ỵ 2 ẵD1G42 G80n2
ỵ 2 ẵD2G42 ỵ2 ẵD2G42 G80n2 ỵ 4 ẵD2G42 G42 ỵ 4 ẵD2G42 G80n2 G42
ỵ 4 ẵD2G42 G80n2 G42 G80n2
ẵG80t ẳ ẵG80n ỵ ẵG80c ỵ 2 ẵG80n2 ỵ 2 ẵG80c2 ỵ 2 ẵG42 G80n2 ỵ 2 ẵD1G42 G80n2
ỵ 2 ẵD2G42 G80n2 ỵ2 ẵD2G42 G80n2 G42 ỵ 4 ẵD2G42 G80n2 G42 G80n2
ỵ ẵG80cG3*
ẵG3*t ẳ ẵG3* þ ½G80cG3*Š
Equilibrium dissociation relationships

Concentrations of all complexes arising from various interactions in the GAL switch are obtained using equilibrium
dissociation relationships. The value of the dissociation constant enables expression of any complex in terms of the free
component concentration. For example, the concentration of the complex D1G42 resulting from the interaction between D1
and G42 can be expressed as,
ẵD1G42 ẳ

ẵD1 ẵG42
Kd K1

where K1 and Kd represent the respective equilibrium dissociation constants for the following reactions, respectively,
G4 ỵ G4 é G42
D1 ỵ G42 Ð D1G42
In order to identify an equilibrium dissociation constant with a specific interaction, the following terminology has been
adopted:
K1 Dissociation constant for dimerization of Gal4p
K2 Dissociation constant for dimerization of Gal80p
K3 Dissociation constant for interaction between Gal4p and its complex with Gal80p or its dimer
K4 Dissociation constant for interaction between Gal80p and its complex with Gal3p* or its dimer
K5 Dissociation constant for dimerization of Gal3p*
Kd 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 lm3 [36]. Binding constants and estimated
parameters used in the model are obtained from Verma et al. [9]. The set of equations were solved using the fsolve


4074 M. Verma et al. (Eur. J. Biochem. 271)

Ó FEBS 2004

function in MATLAB12 (The Math Works, Inc., Natick, MA, USA). Parameter values used in the steady-state model [9] are
shown.
Parameter

Value

Kd
K
Ks
K1
K2
K3
K4
K5
m
n
[D1]t
[D2]t
[Gal4p]t
[Gal80p]max
[Gal3p]max

2.0 · 10)10 M
0.4
1.0
1.0 · 10)7 M
1.0 · 10)10 M
5.0 · 10)11 M
6.3 · 10)11 M

1.0 · 10)10 M
30
0.5
3 · 2.372 · 10)11
7 · 2.372 · 10)11
5.47 · 10)9 M
1.0 · 10)6 M
5.0 · 10)6 M

M
M