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 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: venks@che.iitb.ac.in 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 Ó FEBS 2004 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) Ó FEBS 2004 Fig 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 ½G3à 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 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 Ó FEBS 2004 Mechanism of galactose signal transduction (Eur J Biochem 271) 4067 modeled by an equilibrium distribution coefficient (K) as follows: K¼ Fig 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 ỵ ẵD2G42 G802 G32 ỵ ẵD2G42 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 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 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 are 3.2 and 5, respectively, indicating an extremely 4068 M Verma et al (Eur J Biochem 271) Ó FEBS 2004 Fig 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 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 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 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 and 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 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 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 Ó FEBS 2004 Mechanism of galactose signal transduction (Eur J Biochem 271) 4069 Fig 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 References Zaslaver, A., Mayo, A.E., Rosenberg, R., Bashkin, P., Sberro, H., Tsalyuk, M., Surette, M.G & Alon, U (2004) Just-in-time transcription program in metabolic pathways Nat Genet 36, 486–491 Ó FEBS 2004 Fuente, A., Snoep, J.L., Westerhoff, H.V & Mendes, P (2002) Metabolic control in integrated biochemical systems Eur J Biochem 269, 4399–4408 Bruggeman, F.J., Westerhoff, H.V., Hoek, J.B & Kholodenko, B.N (2002) Modular Response Analysis of Cellular Regulatory Networks J Theor Biol 218, 507–520 Ackers, G.K., Johnson, A.D & Shea, M.A (1982) Quantitative model for gene regulation by k-phage repressor Proc Natl Acad Sci USA 79, 1129–1133 Ptashne, M.S (1986) Eukaryotic gene regulation: experiments and examples In A Genetic Switch: Phage Lambda and Higher Organisms 2nd edn pp 133–146 Cell Press and Blackwell Scientific, Cambridge, MA Lohr, D., Venkov, P & Zlatanova, J (1995) Transcriptional regulation in the yeast GAL gene family: a complex genetic network FASEB J 9, 777–786 Melcher, K & Xu, H.E (2001) Gal80–Gal80 interaction on adjacent Gal4p binding sites is required for complete GAL gene repression EMBO J 20, 841–851 Goldberger, R.F (1974) Autogenous regulation of gene expression: The mechanism by which protein directly controls expression of its own structural gene is described Science 183, 810–816 Savageau, M.A (1975) Significance of autogenously regulated and constitutive synthesis of regulatory proteins in repressible biosynthetic systems Nature 258, 208–214 10 Vencchi, M., Polo, S., Poupon, V., von de Loo, J.W., Benmerah, A & Di Fiore, P.P (2001) Nucleocytoplasmic shuttling of endocytic proteins J Biol Chem 153, 1511–1517 11 Peng, G & Hopper, J.E (2002) Gene activation by interaction of an inhibitor with a cytoplasmic signaling protein Proc Natl Acad Sci USA 99, 8548–8553 12 Verma, M., Bhat, P.J & Venkatesh, K.V (2003) Quantitative analysis of GAL genetic switch of Saccharomyces cerevisiae reveals that nucleocytoplasmic shuttling of Gal80p results in a highly sensitive response to galactose J Biol Chem 278, 48764– 48769 13 Kaffman, A., Herskowitz, I., Tijan, R & O’Shea, E.K (1994) Phosphorylation of the Transcription Factor PHO4 by a CyclinCDK Complex, PHO80-PHO85 Science 263, 1153–1156 14 O’Neill, E.M., Kaffman, A., Jolly, E.R & O’Shea, E.K (1996) Regulation of PHO4 nuclear localization by the PHO80-PHO85 cyclin-CDK complex Science 271, 209–212 15 Pemberton, L.F., Blobel, G & Rosenblum, J.S (1999) Nuclear import of the TATA-binding protein: Mediation by the karyopherin kap114p and a possible mechanism of intrecellular targeting J Cell Biol 145, 1407–1417 16 Komeili, A & O’Shea, E.K (2000) Nuclear transport and transcription Curr Opin Cell Biol 12, 355–360 17 Santillan, M & Mackey, M.C (2001) Dynamic regulation of the tryptophan operon: a modeling study and comparison with experimental data Proc Natl Acad Sci USA 98, 1364–1369 18 Bhartiya, S., Rawool, S & Venkatesh, K.V (2003) Dynamic model of Escherichia coli tryptophan operon shows an optimal structural design Eur J Biochem 270, 2644–2651 19 Verma, M., Bhat, P.J & Venkatesh, K.V (2004) Expression of GAL genes in a mutant strain of Saccharomyces cerevisae lacking GAL80: Quantitative Model and Experimental Verification Biotechnol Appl Biochem 39, 89–97 20 Broach, A.R (1979) Galactose regulation in Saccharomyces cerevisae The enzyme encoded by GAL7, 10, cluster are coordinately controlled and separately translated J Mol Biol 131, 41–53 21 Johnston, M & Carlson, M (1992) Regulation of carbon and phosphate utilization In The Molecular and Cellular Biology of the Yeast Saccharomyces (Johnes, E.W., Pringle, J.R & Broach, J.R., eds) Cold Spring Harbor Laboratory Press, Plainveiw, New York Ó FEBS 2004 Mechanism of galactose signal transduction (Eur J Biochem 271) 4071 22 Platt, A & Reece, R.J (1998) The yeast galactose genetic switch is mediated by the formation of a Gal4p-Gal80p-Gal3p complex EMBO J 17, 4086–4091 23 Bhat, P.J & Murthy, T.V.S (2001) Transcriptional control of the GAL/MEL regulon of yeast Saccharomyces cerevisae: mechanism of galactose mediated signal transduction Mol Microbiol 40, 1059–1066 24 Carey, M., Kakidani, H., Leatherwood, J., Mostashari, F & Ptashane, M (1989) An amino terminal fragment of Gal4p binds DNA as dimer J Mol Biol 209, 423–432 25 Nogi, Y & Fukasawa, T (1984) Nucleotide sequence of the yeast regulatory gene, Gal80 Nucleic Acids Res 12, 9287– 9298 26 Giniger, E., Varnum, S.M & Ptashne, M.S (1985) Specific DNA binding of GAL4, a positive regulatory protein of yeast Cell 40, 767–774 27 Koh, S.S., Ansari, A.Z., Ptashne, M.S & Young, R.A (1998) An activator target in the RNA polymerase II holoenzyme Mol Cell 1, 895–904 28 Kew, O.M & Douglas, H.C (1976) Genetic co-regulation of galactose and melibiose utilization in Saccharomyces cerevisae J Bacteriol 125, 33–41 29 Bhat, P.J., Oh, D & Hopper, J.E (1990) Analysis of the GAL3 signal transduction pathway activating GAL4 protein-dependent 30 31 32 33 34 35 36 transcription in Saccharomyces cerevisiae Genetics 125, 281– 291 Yano, K & Fukasawa, T (1997) Galactose dependent reversible interaction of Gal3p with Gal80p in the induction pathway of Gal4p activated genes of Saccharomyces cerevisiae Proc Natl Acad Sci USA 94, 1721–1726 Peng, G & Hopper, J.E (2000) Evidence for Gal3p’s cytosolic location and Gal80p’s dual cytosolic/nuclear location suggests new mechanisms for controlling Gal4p activity in Saccharomyces cerevisiae Mol Cell Biol 20, 5240–5148 Hofmeyr, J.-H.S., Cornish-Bowden, A & Rohwer, J.M (1993) Taking enzyme kinetics out of control; putting control into regulation Eur J Biochem 212, 833–837 Fell, D.A (2001) Beyond genomics Trends Genet 17, 680–682 Johnston, M., Flick, J.S & Pexton, T (1994) Multiple mechanisms provide rapid and stringent glucose repression of GAL gene expression in Saccharomyces cerevisiae Mol Cell Biol 14, 3834– 3841 Ostergaard, S., Olsson, L., Johnston, M & Nielsen, J (2000) Increasing galactose consumption by Saccharomyces cerevisiae through metabolic engineering of the GAL gene regulatory network Nat Biotechnol 18, 1283–1286 Shermann, F (1991) Methods in Enzymology (Abelson, J.N & Simon, M.I., eds), pp 3–21 Academic Press Inc., New York 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 specific to the model: Model I ẵD1t ẳ ẵD1 ỵ ẵD1G42 þ ½D1G42 G802 Š þ ½D1G42 G802 G3*Š þ ½D1G42 G802 G3*G3 ẵD2t ẳ ẵD2 ỵ ẵD2G42 ỵ ẵD2G42 G802 ỵ ẵD2G42 G42 ỵ ẵD2G42 G802 G42 ỵ ẵD2G42 G802 G42 G802 ỵ ẵD2G42 G802 G3* ỵ ẵD2G42 G802 G3*G3* ỵ ẵD2G42 G802 G3*G42 þ ½D2G42 G802 G3*G3*G42 Š þ ½D2G42 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* 4072 M Verma et al (Eur J Biochem 271) Ó FEBS 2004 ẵG4t ẳ ẵG4 ỵ ẵG42 ỵ ẵG42 G802 ỵ ẵD1G42 þ  ½D1G42 G802 Š þ  ½D1G42 G802 G3* ỵ ẵD1G42 G802 G3*G3* ỵ ẵD2G42 ỵ ẵD2G42 G802 ỵ ẵD2G42 G42 ỵ ẵD2G42 G802 G42 ỵ ẵD2G42 G802 G3*G42 ỵ ẵD2G42 G802 G3*G3*G42 ỵ ẵD2G42 G802 G42 G802 ỵ ẵD2G42 G802 G3* þ  ½D2G42 G802 G3*G3*Š þ  ½D2G42 G802 G3*G42 ỵ ẵD2G42 G802 G3*G3*G42 G802 ỵ ẵD2G42 G802 G3*G3*G42 G802 G3* ỵ ẵD2G42 G802 G3*G3*G42 G802 G3*G3* ẵG80t ẳ ẵG80 þ  ½G802 Š þ  ½G42 G802 ỵ ẵD1G42 G802 ỵ ẵD1G42 G802 G3* ỵ ẵD1G42 G802 G3*G3* ỵ ẵD2G42 G802 ỵ ẵD2G42 G802 G42 ỵ ẵD2G42 G802 G42 G802 þ  ½D2G42 G802 G3*Š þ  ½D2G42 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*G42 G802 ỵ ẵD2G42 G802 G3*G3*G42 G802 G3* þ  ½D2G42 G802 G3*G3*G42 G802 G3*G3*Š þ ½G80G3*Š ẵG3*t ẳ ẵG3* ỵ ẵD1G42 G802 G3* ỵ ẵD1G42 G802 G3*G3* 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*G42 G802 ỵ ẵD2G42 G802 G3*G3*G42 G802 G3* ỵ ẵD2G42 G802 G3*G3*G42 G802 G3*G3* ỵ ẵG80G3* Model II ẵD1t ẳ ẵD1 ỵ ẵD1G42 ỵ ẵD1G42 G802 ẵD2t ẳ ẵD2 ỵ ẵD2G42 ỵ ẵD2G42 G802 ỵ ẵD2G42 G42 ỵ ẵD2G42 G802 G42 ỵ ẵD2G42 G802 G42 G802 ẵG4t ẳ ẵG4 ỵ ẵG42 ỵ ẵG42 G802 ỵ ẵD1G42 ỵ ẵD1G42 G802 ỵ ẵD2G42 ỵ ẵD2G42 G802 þ  ½D2G42 G42 Š þ  ½D2G42 G802 G42 ỵ ẵD2G42 G802 G42 G802 ẵG80t ẳ ẵG80 ỵ ẵG802 ỵ ẵG42 G802 ỵ ẵD1G42 G802 ỵ ẵD2G42 G802 ỵ ẵD2G42 G802 G42 ỵ 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 ẵG42 ỵ ẵG42 G80n2 ỵ ẵD1G42 ỵ ẵD1G42 G80n2 ỵ ẵD2G42 ỵ ẵD2G42 G80n2 þ  ½D2G42 G42 Š þ  ½D2G42 G80n2 G42 ỵ ẵD2G42 G80n2 G42 G80n2 Š Ó FEBS 2004 Mechanism of galactose signal transduction (Eur J Biochem 271) 4073 ẵG80t ẳ ẵG80n ỵ ẵG80c ỵ ẵG80n2 ỵ ẵG80c2 ỵ ẵG42 G80n2 ỵ ẵD1G42 G80n2 ỵ ẵD2G42 G80n2 ỵ ẵD2G42 G80n2 G42 ỵ ẵD2G42 G80n2 G42 G80n2 ỵ ẵG80c2 G3*2 ẵG3*t ẳ ẵG3* ỵ ẵG3*2 ỵ ẵG80c2 G3*2 Model IV ẵD1t ẳ ẵD1 ỵ ẵD1G42 ỵ ẵD1G42 G80n2 ẵD2t ẳ ẵD2 ỵ ẵD2G42 þ ½D2G42 G80n2 Š þ ½D2G42 G42 Š þ ½D2G42 G80n2 G42 ỵ ẵD2G42 G80n2 G42 G80n2 ẵG4t ẳ ẵG4 ỵ ẵG42 ỵ ẵG42 G80n2 ỵ ẵD1G42 ỵ ẵD1G42 G80n2 ỵ ẵD2G42 ỵ2 ẵD2G42 G80n2 ỵ ẵD2G42 G42 ỵ ẵD2G42 G80n2 G42 ỵ ẵD2G42 G80n2 G42 G80n2 ẵG80t ẳ ẵG80n ỵ ẵG80c ỵ ẵG80n2 ỵ ẵG80c2 ỵ ẵG42 G80n2 ỵ ẵD1G42 G80n2 ỵ ẵD2G42 G80n2 ỵ2 ẵD2G42 G80n2 G42 ỵ ẵD2G42 G80n2 G42 G80n2 ỵ ẵG80cG3* ẵG3*t ẳ ẵG3* ỵ ẵG80cG3* 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  ½G4Š2 Kd K1 where K1 and Kd represent the respective equilibrium dissociation constants for the following reactions, respectively, G4 þ G4 Ð G42 D1 þ 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 · 2.372 · 10)11 · 2.372 · 10)11 5.47 · 10)9 M 1.0 · 10)6 M 5.0 · 10)6 M M M ... to validate the mechanism of induction of GAL genes by galactose In each of the models, cytoplasmic Gal3 p is activated by galactose Further, Gal4 p dimerizes and interacts with the DNA to form the. .. 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 Gal4 p, a negative regulator Gal8 0p... 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