Dynamic analysis of the KlGAL regulatory system in Kluyveromyces lactis: a comparative study with Saccharomyces cerevisiae

Abstract

The GAL regulatory system is highly conserved in yeast species of Saccharomyces cerevisiae and Kluyveromyces lactis. While the GAL system is a well studied system in S. cerevisiae, the dynamic behavior of the KlGAL system in K. lactis has not been characterized. Here, we have characterized the GAL system in yeast K. lactis by developing a dynamic model and comparing its performance to its not-so-distant cousin S. cerevisiae. The present analysis demonstrates the significance of the autoregulatory feedbacks due to KlGal4p, KlGal80p, KlGal1p and Lac12p on the dynamic performance of the KlGAL switch. The model predicts the experimentally observed absence of bistability in the wild type strain of K. lactis, unlike the short term memory of preculturing conditions observed in S. cerevisiae. The performance of the GAL switch is distinct for the two yeast species although they share similarities in the molecular components. The analysis suggests that the whole genome duplication of S. cerevisiae, which resulted in a dedicated inducer protein, Gal3p, may be responsible for the high sensitivity of the system to galactose concentrations. On the other hand, K. lactis uses a bifunctional protein as an inducer in addition to its galactokinase activity, which restricts its regulatory role and hence higher galactose levels in the medium are needed to trigger the GAL system.

Electronic supplementary material

The online version of this article (doi:10.1007/s11693-011-9082-7) contains supplementary material, which is available to authorized users.

Introduction

Organisms live under changing environmental conditions. The successful adaptation to these changes is determined by an appropriate response to external or internal perturbations through the simultaneous expression of a large set of genes. Transcriptional regulation serves as the mechanism to perform these tasks through interplay of various proteins. However, network regulation is hierarchal in nature with controls residing at metabolite, protein, mRNA, and DNA levels (Ruhela et al. 2004). These controls are achieved through complex interactions among the network components. Feedback is the common theme in all these control strategies with complex feedback motifs residing in signaling, metabolic and genetic regulatory networks. These nested feedback loops are key to a robust performance of the regulatory system (Venkatesh et al. 2004). However, other than these feedback loops, there exist other regulatory features such as compartmentalization and stoichiometry, which also play a crucial role in the overall performance of the regulatory system. For example, it has been shown that the nucleocytoplasmic shuttling of repressor protein Gal80p1 in GAL system of S. cerevisiae plays a crucial role in the performance of the switch (Verma et al. 2003).

Although S. cerevisiae and K. lactis have originated from a common ancestor, they have evolved differently in nature due to their respective environmental niche. The former has evolved in a melibiose environment while the latter in a lactose environment. While the GAL regulatory network in these organisms share similarities in the molecular components of the GAL system, their compartmentalization and stoichiometry are considerably different from each other (Rubio-Texeira 2005). For example, the repressor protein Gal80p is nucleocytoplasmic in S. cerevisiae, where as in K. lactis it is confined to the nucleus. Similarly, the opposite is observed in the case of inducer proteins, Gal3p and KlGal1p, where the former is cytoplasmic and the latter is nucleocytoplasmic protein. Although the regulatory proteins Gal80p and Gal3p/KlGal1p perform similar function in both species, the genes (GAL3/KlGAL1, GAL80) encoding them have varied binding sites for activator Gal4p in their promoter regions. The activator protein Gal4p is conserved in both species with the exception that its autoregulation (or self-regulation) is observed in the case of K. lactisKlGAL system, whereas in S. cerevisiae the activator is constitutively expressed. Furthermore, the mechanism for activation of inducer protein (Gal3p/KlGal1p) with galactose, and the interaction of inducer with the repressor protein Gal80p is not clearly understood.

In silico modeling studies have been successful in elucidating the network structure of various organisms (Ackers et al. 1982; Chung and Stephanopoulos 1996; Santillan and Mackey 2001). The GAL system in S. cerevisiae is a well studied regulatory network for which both steady-state and dynamic models have been developed to understand the regulatory structure (Ruhela et al. 2004; Verma et al. 2003). However, such an in-depth dynamic analysis of K. lactis has not been reported in literature. Therefore, a detailed dynamic model was developed for the KlGAL system of K. lactis and further validated using experimental data. The present study provides an opportunity to study the influence of the differences in the regulatory structure in the GAL system of S. cerevisiae and K. lactis on the dynamic performance of the system through a modeling approach. The developed model was used to compare the performance of the KlGAL system of K. lactis to that of S. cerevisiae GAL system for which a dynamic model reported in literature (Ruhela et al. 2004). We begin with the description of the key features of the KlGAL system in K. lactis and followed by its model development.

KlGAL system

The KlGAL system in K. lactis contains two regulatory genes (LAC9 or KlGAL4 and KlGAL80), a bifunctional regulatory gene KlGAL1 and four structural genes (LAC12, LAC4, KlGAL7 and KlGAL10). The KlGAL switch is found in three regulatory states in response to the availability of various carbon sources. In the presence of a non-inducing-non-repressing medium (NINR) such as glycerol or raffinose, the KlGAL switch is in an uninduced state. Under such a condition, the KlGal4p activity is inhibited by the binding of KlGal80p protein to the C-terminal activation domain of KlGal4p. In this state, the KlGAL genes are poised for induction as they are not subjected to carbon catabolite repression. In the presence of lactose/galactose medium, the KlGAL switch is in an induced state. The enzyme permease (Lac12p) transports lactose/galactose into the cytoplasm, which then in combination with ATP activates the protein KlGal1p. The protein KlGal1p, being bifunctional, has both inducer and galactokinase activity. The activated KlGal1p then shuttles into the nucleus and interacts with the repressor protein KlGal80p, thereby relieving the inhibition of KlGal80p on KlGal4p (Anders et al. 2006). In the presence of glucose, the KlGAL switch is in a repressed state. In S. cerevisiae, glucose represses the GAL genes by having a specific repressor protein Mig1p, which binds to the upstream repressor sequences (URS_G) present in the GAL genes (Nehlin et al. 1991). In case of K. lactis, the repression on KlGAL4 is Mig1p-independent, since KlGAL4 has no URS_G in its promoter for Mig1p but glucose indirectly represses the GAL system by a Mig1p binding site in KlGAL1 gene (Dong and Dickson 1997; Lamphier and Ptashne 1992). However, it has been experimentally shown that glucose affects the ability of KlGAL4 to activate transcription of KlGAL genes (Breunig 1989; Flick and Johnston 1990). Thus, while KlGal4p has no Mig1p binding site on its gene promoter, its activity is inhibited in the presence of glucose. The activator Gal4p in yeast contains at least three inhibitory domains in its central region and a glucose response domain between the activator domains, which become active in the presence of glucose, which, however are independent of repressor Mig1p (Stone and Sadowski 1993).

In all of the above three states, the concentration of activator KlGal4p plays a vital role in the induction mechanism of the KlGAL system. KlGAL4 gene contains a UAS_G in its own promoter for binding of KlGal4p resulting in an autoregulatory circuit which causes a two to fivefold increase in KlGal4p concentration in presence of lactose/galactose. This increase is essential for maximal growth rate on lactose and has probably evolved to give the organism a selective advantage in its natural habitat (Czyz et al. 1993). On the other hand, to maintain the repressed state of the KlGAL4-controlled genes in a glucose containing medium, the KlGal4p concentration has to be held below a certain threshold concentration (Zachariae et al. 1993). Quantification of the expression of GAL genes in K. lactis strain using equilibrium considerations for all the molecular interactions in the genetic network has been reported (Pannala et al. 2010). However, the model is not based on kinetic rate expressions for the various molecular mechanisms and does not include growth of cells and substrate consumption. Further, the glucose effect on the expression in a wild-type strain has not been characterized. It has been shown using the equilibrium modeling approach that the concentration and autoregulation of activator, KlGal4p plays a major role in giving a leaky expression of KlGAL genes in a K. lactis mutant strain lacking KlGAL80 even at high glucose concentrations (Pannala et al. 2010). Further, the model predicted that in a K. lactis wild-type strain the genes with two binding sites are expressed only 35% relative to its KlGAL80 mutant strain and the system demonstrated a leaky expression of about 2.5% at low galactose concentration. The study also demonstrated that the low expression levels were due to the limiting function of the bi-functional protein KlGal1p towards the induction process in order to cope with the need for the metabolism of lactose/galactose.

Although, the steady-state modeling analysis predicts the system behavior based on molecular mechanisms underlying the network, it fails to capture the temporal dominance of the individual mechanisms in the overall performance of the network. The model also captures cellular growth and the dynamics of substrate consumption. This motivates the development of a dynamic modeling approach. For example, a dynamic model developed for GAL system in S. cerevisiae illustrates that the autoregulation of regulatory proteins is the key for the dynamic operation of the GAL system (Ruhela et al. 2004). Here, the dynamic model was used to identify the relevance of autoregulation of regulatory proteins Gal3p and Gal80p as well as the importance of nucleocytoplasmic shuttling of Gal80p. Further, the dynamic model approach can be used to elucidate the systems-level properties of the network such as bi-stability, sensitive response and robustness. The following section describes the key features of the dynamic model of the KlGAL system in K. lactis.

Materials and methods

Model development

The dynamic model has been developed by assuming the interactions shown in Fig. 1. All genes with one binding site in the network are lumped as D1, while genes with two or more binding sites are clubbed as D2. The model accounts for the transcriptional interaction of activator KlGal4p with genes having one and two binding sites to produce the enzymes required for Leloir pathway and their regulatory proteins. The fractional transcriptional expressions are calculated as the fraction of the activator bound DNA [KlGal4p-DNA] to the total available DNA. The fractional transcriptional expression levels for D1 and D2 are described by,

1

2

Fig. 1.

Schematic diagram showing the molecular interactions in a K. lactis wild-type stain. Here, K_i (I = 1–4) represents dissociation constants for respective interactions, K represents distribution coefficient for KlGal1p shuttling and K_d represents the binding of KlGal4p protein to the DNA. D1 and D2 represent genes with one and two binding sites, respectively

[D1-KlGal4p₂] represents the interaction of dimer KlGal4p with DNA for genes with one binding site, while [D1_t] is the total operator concentration of DNA with one binding site for KlGal4p. The expression of genes with two binding sites occurs when either one or both of the two binding sites are bound by Gal4p dimer that is [D2-KlGal4p₂] and/or [D2-KlGal4p₂-KlGal4p₂]. The above equations assume that no other DNA complexes contribute to transcription. [D2_t] is the total available operator concentration of genes with two binding sites for KlGal4p. The development of the dynamic model is based on unsteady molar balances written for all the species in the network (see Fig. 1) and is detailed in supplementary material. The fractional protein expression, quantified by f_1p and f_2p−, is related to the fractional transcriptional expression in a non-linear fashion as shown below,

3

4

where 0.7 represents the co-response coefficient, which was obtained by fitting the predicted steady state expression level for proteins with two binding sites to experimental values (Pannala et al. 2010). The above expressions also assume that the dynamics of transcription are fast relative to the time-scales for cell division and growth. The above equations capture the inefficiencies of the translational process, as all the mRNA that is transcribed is not converted to protein. It should be noted that for S. cerevisiae a value of 0.5 was set for the exponent in Eq. 3 and 4 to capture the inefficiencies in the translational process (Ruhela et al. 2004).

Since, the gene KlGAL4 has one binding site for its own protein KlGal4p; the KlGal4p concentration is therefore a function of f_1p. Further, the presence of glucose turns off the GAL system by repressing the synthesis of KlGal4p, which has been modeled by a Hill equation as follows,

5

k_g, K_i, and η_g represent synthesis rate constant of KlGal4p, inhibitory constant on glucose and Hill coefficient, respectively. The synthesis of the other three regulatory proteins, KlGal1p and KlGal80p and Lac12p depends on the autoregulation of genes with two binding sites (Rubio-Texeira 2005). Therefore,

6

7

8

R_KlGal1p, R_KlGal80p, R_Lac12p, and k_t1, k_t8, k_t12 represent the synthesis rate constants of KlGal1p, KlGal80p and Lac12p and the respective translational kinetic constants.

The model accounts for the transport of extracellular galactose through the cytoplasmic membrane, which is controlled by Lac12p (the first term in Eq. 9 below) as well as Lac12p independent diffusion mechanism (second term) as shown below:

9

The last two terms represents the consumption and dilution due to growth on galactose. The model is connected to growth on glucose and galactose. The overall growth rate can be written as:

10

Since excess glycerol was used relative to galactose concentration, μ_Gly represent growth rate on glycerol and was assumed independent of glycerol concentration, while μ_Gal and μ_Glu denote growth rates on galactose and glucose, respectively and are dependent on the concentration of the respective substrates in the medium as follows,

11

12

The galactose, glucose, and biomass in the medium have been modeled as follows (13)

13

14

15

The activation of KlGal1p by intracellular galactose (Gal_int) is modeled by assuming a molecular interaction between them with a forward rate constant (k₅) and an equilibrium dissociation constant K₅ to form an activated [KlGal1p-Gal_int] complex.

16

The activated [KlGal1p-Gal_int] then enters into the nucleus and interacts with monomer and dimer forms of KlGal80p to relieve the inhibition on activator KlGal4p as shown in Fig. 1. The translation of galactose permease (Lac12p) produced by genes with multiple binding sites (D₂) can be described by,

17

where k_t12, represents synthesis rate constant.

The complete model consists of 25 differential equations and three algebraic equations, which were solved by MATLAB 7.6 of Math Works Inc. USA. The complete set of model equations are presented in supplementary materials section. The equilibrium dissociation constants were taken from steady-state model (Pannala et al. 2010). The kinetic parameters and distribution coefficient for KlGal1p (K) were fitted to match the steady-state and dynamic experimental data with galactose. The specific growth and half saturation constants were obtained from experimental data. The model has 36 parameters, out of which 27 parameters correspond to reported equilibrium data (such as binding constants between proteins and between proteins and DNA) or experimental data (such as maximum growth rate, yield coefficient) obtained through independent experiments carried out specifically to estimate the parameter. Therefore, only 9 parameters were obtained by fitting parameters to the dynamic protein expression data. All the parameter values are given in Table S1 in supplementary materials.

Sensitivity of bistable behavior to model parameters

It has been experimentally demonstrated that the GAL system of S. cerevisiae shows different steady state expression levels when grown under identical galactose concentrations depending on the preculturing conditions (Acar et al. 2005). In particular, when precultured on galactose, the yeast S. cerevisiae shows higher expression levels than when precultured in an NINR medium such as glycerol or raffinose for a given galactose substrate. To quantify the above bistable behavior, we simulated the GAL system of K. lactis for the two preculturing conditions namely, on galactose and glycerol. The cells were subsequently grown under various galactose concentrations and the fractional protein expression for genes with two binding sites, f_2p (galactose, preculture medium) obtained. The maximum difference between the fractional protein expressions between the two preculturing conditions was used to quantify the degree of bistability,

18

Thus, δ = 0 indicates the absence of bistability while δ > 0 indicates a bistable behavior. δ = 1 implies that the cells do not express when precultured on one medium and show complete expression in the other.

It is known that bistable behavior occurs in nonlinear systems which consist of both positive and negative feedback effects. In case of K. lactis, the negative regulation is due to KlGal80p while Lac12p, KlGal1p and KlGal4p positive regulate the GAL system. Then, we have performed a parametric sensitivity analysis where δ was obtained by perturbing the synthesis rate constants of each of the four proteins described above, individually. Further, a global sensitivity analysis was also performed wherein all the parameters were perturbed simultaneously. A sensitivity coefficient defined as

19

was evaluated for the global sensitivity analysis.

Experimental protocol

Strain

K. lactis GAL80 mutant and wild type strains used in this study were JA6D801 and JA6, respectively (Zenke et al. 1993). The strain was stored in 20% glycerol at −20°C in micro-centrifuge tubes. The cells were precultured in a YPD medium (Yeast extract 10 g/l, peptone 20 g/l, and Dextrose 20 g/l) and streaked out on to the agar plates. A single colony was picked out from agar plate to re-inoculate the YPD broth grown in a shake flask until it reached the exponential phase. Slants were prepared using cultures grown in the shake flask and stored for experimental use. In each experiment, inoculum was prepared by a loopful of culture from the slant.

Medium for preculture

A cotton stoppered 500 ml Borosil^© flask containing 100 ml working volume of composition 10 g/l Yeast extract, 20 g/l Peptone and 20 g/l Dextrose/30 g/l Glycerol was used. The pH was adjusted to 5.5 by adding 1 M HCl. The cells were grown in a shake flask at 30°C on a rotary shaker at 240 rpm till optical density (OD₆₀₀) reached to 1.0–1.5 OD₆₀₀. Subsequently, the experimental flask was inoculated with 10% (w/v) cell mass of OD₆₀₀ equal to one.

Experimental procedures

Steady state experiments on glucose and galactose were carried out independently in a fed batch mode. Initially K. lactis strain was grown in a shake flask of composition similar to the preculture medium until the OD₆₀₀ attained a value between 0.8 and 1.0 in a rotary shaker at 30°C and 240 rpm. After this, experiment was carried out in a fed-batch mode by the addition of glucose/galactose at regular intervals while measuring the concentration of glucose/galactose in the flask. For studies on K. lactis GAL80 mutant strain, different average steady-state glucose concentrations (0–57 mM) were maintained (±10%) in the flask using two standard glucose solutions of concentrations 10 to 50-fold of the required concentration. The protein concentrations of β-galactosidase were measured for different average steady state concentration of glucose. For studies on K. lactis wild type strain, different batch experiments were performed using different galactose concentrations (0.002–0.44 M) with glycerol as the background media and the fractional β-galactosidase expression was measured dynamically. The maximum protein expression was noted for cells grown in a 3% glycerol medium without glucose/galactose for a mutant strain lacking KlGAL80. The data is provided as the fraction of the maximum value of the β-galactosidase expression. The data obtained from these experiments were tabulated as steady-state fractional protein (β-galactosidase) expressed at different average steady-state glucose/galactose concentrations. All the steady-state and batch experiments were carried out with 3% glycerol as the background medium.

Substrate and enzyme activity measurements

Glucose and galactose were measured using HPLC, using Lachrom L-7490 HPLC system and Biorad Aminex HPX-87H column attached with guard column in series. β-galactosidase activity was measured by taking 2 OD₆₀₀ cells for each measurement and stored in breaking buffer immediately at −20°C for later extraction. The yeast cells were lysed by addition of glass beads (0.5 mm) and activity of β-galactosidase was measured by the method of crude extracts as reported in Adams et al. (Rose and Botstein 1983; Adams et al. 1997). All the experiments were carried out in triplicate and the deviations in the protein expression data are shown by error bars in the results. The fluctuations in the average steady-state concentration of glucose in the fed-batch experiments were within the acceptable limits.

Results

To validate the dynamic model, experiments were performed with the wild-type and the mutant strain lacking KlGAL80 at different galactose concentrations with glycerol as the background media and the time course of β-galactosidase activity was measured. Note that the β-galactosidase activity represents the protein expression from a KlGAL gene with two binding sites for KlGal4p, and its measurement was therefore used to quantify f_2p. Firstly, the steady-state data corresponding to fractional protein expression for genes with two binding sites in a mutant strain lacking KlGAL80 was compared with model predictions at different glucose concentrations. In such a mutant strain lacking KlGAL80, the absence of repressor KlGal80p eliminates all interaction with activator KlGal4p and also with KlGal1p, thus making the expression of the GAL genes constitutive in absence of glucose. Thus, the KlGAL switch responds only to changes in KlGal4p concentration, the synthesis of which is inhibited by glucose as modeled in Eq. 5. The mutant strain was simulated by setting initial condition of Gal80p as well as its synthesis rate constant to zero. Although in literature, equilibrium model was used to obtain steady state profiles for the mutant strain and compared with experimental values, we present here the comparison of the steady state profiles obtained from the dynamic model with the reported experimental values (Pannala et al. 2010).

The squares in Fig. 2a show the experimental data for fractional protein expression for genes with two binding sites in cells containing glycerol (0.32 M) as the background medium and at different glucose concentrations, while the solid line corresponds to model predictions. It is noted from the figure that at low glucose concentrations, the KlGAL genes show the maximum expression. All the subsequent results presented in this study have been normalized with respect to this maximum constitutive expression. It is also observed from Fig. 2a that glucose does not repress the KlGAL genes completely, as a 26% expression was observed even at high glucose concentration (solid line). The steady state profiles obtained from the dynamic model compares well with that of the prediction from the model based on equilibrium considerations for the molecular mechanisms as reported by Pannala et al. (2010). Figure 2a also shows the model predictions of a wild-type system at different steady-state glucose concentrations (dashed line) under a high galactose (0.5 M) background. It should be noted that previous studies do not characterize the effect of glucose on the steady state expression of GAL genes in a wild-type strain. Here, the presence of the repressor protein KlGal80p makes glucose repress the KlGAL genes at high glucose concentrations. The circles show the experimental data. It can be noted that at high galactose and low glucose concentration, the wild-type expression corresponds to 35% of the mutant strain lacking KlGAL80. The dynamic model was also able to predict the steady state expression profile for the wild-type strain at various galactose concentrations (Fig. 2b). As indicated before, the maximum expression observed at high galactose concentration was only 35% of the maximum. The observation suggests that either the repressor protein KlGal80p concentration is very high in the nucleus or the inducer protein KlGal1p is limiting in its function to sequester the repressor protein.

Fig. 2.

a steady-state protein expression levels for genes with two binding sites (f_2p) with varying steady-state glucose concentrations (Pannala et al. 2010). Solid line and squares represents model predictions and experimental validation, respectively for a K. lactis strain lacking gene KlGAL80. Dashed line and circles represent model predictions and experimental validation, respectively for K. lactis wild-type strain. b steady-state protein expression levels for genes with two binding sites (f_2p) with varying galactose concentrations. Solid line represents dynamic model predictions, while circles represent corresponding experimental validation. Model predictions for dynamic performance of the GAL system. c Fractional protein expressions of genes with two binding sites (f_2p) in a wild-type strain for three galactose concentrations, namely 0.44 M (solid line), 0.16 M (dashed line), and 0.02 M (dotted line) and symbols show the corresponding experimental validation. d Fractional protein expressions of genes with two binding sites (f_2p) (solid line) in a mutant strain lacking KlGAL80 in a glycerol media (30 g/l). Circles show the corresponding experimental data on glycerol for genes with two binding sites. The dashed line shows the variation of total KlGal4p concentration. e Fractional protein expressions of genes with two binding sites (f_2p) in a mutant strain lacking KlGAL80 in a mixed medium of glucose and glycerol. The dashed line shows the model predictions with experimental validation (circles) for glucose and glycerol concentrations of 0.027 and 0.32 M, respectively. The solid line shows the model predictions with experimental validation (squares) for glucose and glycerol concentrations of 0.1 and 0.32 M, respectively

Having validated the steady-state predictions of the dynamic model, we now validate the dynamic model predictions. Figure 2c shows the comparison between the dynamic predictions of fractional protein expression of genes with two binding sites with experimentally obtained dynamic protein expression levels for K. lactis wild-type precultured on glycerol for three different galactose concentrations namely, 0.44 M (model: solid line; experiment: circles), 0.16 M (model: dashed line; experiment: squares) and 0.02 M (model: dotted line; experiment: diamond). At t = 0, the expression level is about 2.5%, which is observed in a glycerol medium grown until 10 h. Upon exposing the cells to a galactose concentration of 0.44 M (solid line), the genes fully express themselves in about 20 h. When exposed to 0.16 M galactose concentration the switch responds similar to that observed for previous case with a small decrease in the final steady-state expression values. Further, for a low galactose concentration of 0.02 M the system reaches the steady-state in about 10 h. Figure 2d shows the comparison of model predictions and experimental protein expressions for a mutant strain of K. lactis lacking KlGAL80 in a glycerol medium. Here, the cells were precultured in a glycerol medium till exponential phase (optical density, OD₆₀₀, between 0.8 and 1.0). At t = 0, the cells were transferred to a fresh medium containing glycerol, where the initial fractional protein expression was 20%. Since, repressor KlGal80p was absent, the switch expresses to its maximum expression levels (solid line) as the total KlGal4p concentration increases due to autoregulation (see Fig. 2d, dashed line). It can be seen from the Fig. 2d that the model predictions for a KlGAL80 mutant strain matches well with the experimental data. Further, the dynamic model was simulated for a KlGAL80 mutant strain to find the effect of glucose on the response of the GAL system. Here, the model was simulated for a medium containing both glucose and glycerol. Figure 2e shows experimental and model predictions for a glucose concentration of 0.027 M, with 0.32 M glycerol in the background. As seen from the figure, the protein expression remains at a basal level for 6 h due to repression by glucose. Once glucose is completely consumed, the switch expresses to its maximum levels (dashed line). A similar behavior was observed for a glucose concentration of 0.1 M (solid line). Here, the protein expression remains at its basal level for 10 h, until the presence of glucose in the media. Thus the model was not only able to predict the wild-type behavior for growth on galactose and glucose individually but also the mutant behavior for growth on glucose and galactose as well as mixed substrates, thereby capturing the entire range of system behaviors.

The validated dynamic model of the KlGAL system was further used to obtain insights into the regulatory design of the system. The KlGAL system in K. lactis contains four feedback loops that regulate the genes KlGAL4, KlGAL1, KlGAL80, and LAC12. Of these, regulation of gene KlGAL80 forms a negative feedback on the KlGAL system, while the regulation of the remaining genes act as positive feedback loops. We used the dynamic model to study the effect of these feedback loops on the steady-state performance of the KlGAL system. We begin the analysis by eliminating the autoregulation of the transcriptional activator KlGal4p in the model thereby making the expression of its gene constitutive by choosing the value for the synthesis rate constant k_g in Eq. 5 appropriately to reflect the constitutive synthesis rate. The maximum synthesis rate of KlGal4p is achieved when f_1p is set equal to unity in Eq. 5. The dashed line in Fig. 3a shows the response of KlGAL genes to the constitutive expression of KlGal4p and compared with the response of the wild-type (solid line). In this case, the observed maximum expression levels were higher than the wild-type due to the higher synthesis rate of KlGal4p. Similarly constitutive basal expression levels of K. lactis can be simulated by setting f_1p equal to unity and choosing a small value for rate constant k_g. On reducing the value of k_g by 16-fold, the corresponding response of the system is shown by the dotted line in Fig. 3a. It is seen that the KlGAL gene response shows a twofold reduction relative to the wild-type at high galactose concentrations. Thus, the results indicate that the autoregulation of KlGAL4 plays a major role in the operation of the KlGAL switch to produce the maximum induction levels.

Fig. 3.

a Effect of autoregulation of gene KlGAL4 on the steady-state performance of the GAL genes with two binding sites (f_2p) with varying galactose concentrations. b Effect of autoregulation of gene KlGAL4 on the dynamic performance of the GAL genes with two binding sites (f_2p) for galactose concentration of 0.4 M. In both figures a & b, dashed line shows the response of a KlGal4p constitutively expressed strain with the value of synthesis rate constant equal to wild-type. The dotted line shows the response of a constitutively expressed KlGal4p strain with synthesis rate reduced by 16-fold. Solid line represents the wild-type behavior. c Effect of autoregulation of KlGAL1and KlGAL80 on the steady-state performance of the GAL switch with varying galactose concentrations. d Effect of autoregulation of KlGAL1, KlGAL80, and LAC12 on the dynamic performance of the GAL system for galactose concentration of 0.4 M Here in both figures c & d, the dashed line shows the response of a KlGal1p constitutively expressed strain with synthesis rate constant made equal to the wild-type level. The dotted line shows the response when both KlGal1p and KlGal80p were constitutively expressed to their wild-type induced levels. The dash-dotted line shows the response when KlGal80p alone constitutively expressed at wild-type levels. The thin and thick solid line figure d shows the dynamic response when Lac12p expressed constitutively at wild-type levels and wild-type response, respectively. e Predictions of the dynamic model for steady-state protein expressions for genes with two binding sites (f_2p) with varying steady-state galactose concentrations for a LAC12 not autoregulated strain. The solid lines shows the response of the switch when Lac12p constitutively expressed and the synthesis rate constant equal to wild-type (the first solid line from top) and when synthesis rate decreased fourfold (second solid line). Dotted line and dash-dotted line represent when Lac12p synthesis rate constant value decreased by tenfold and 100-fold, respectively of the wild-type. The dashed line shows the response of a LAC12 deletion strain

In order to study the effect of KlGal4p autoregulation on the dynamic expression of the KlGAL system, the model was simulated assuming that the cells were precultured on glycerol and grown on a 0.4 M galactose medium. The solid line in Fig. 3b shows the fractional protein expression for genes with two binding sites for a wild-type. The cell reaches an expression level of 35% in 20 h and sustains the level until about 60 h, at which time the galactose in the medium is completely utilized. Thus the expression levels drop to a new steady-state corresponding to the preculturing in the glycerol medium (identical to initial condition at t = 0). The dashed line indicates the expression levels for a cell when KlGal4p is constitutively expressed using a synthesis rate constant identical to that in the wild-type. Here, the expression levels rise to about 40% and are maintained until about 60 h after which it drops to expression levels observed in NINR medium. The higher expression levels relative to wild-type are consistent with steady-state results discussed above. When the constitutive expression of KlGal4p is reduced by 16-fold using k_g = 7.5 h⁻¹, the expression levels are not maintained at steady-state. The continued reduction in the expression levels after reaching a maximum is due to inadequate intracellular galactose needed for KlGal1p activation.

The dashed line in Fig. 3c shows the fractional protein expression of genes with two binding sites (f_2p) when autoregulation of KlGAL1 is removed and expressed constitutively with a rate constant same as in the wild-type. Here, since the concentration of the inducer KlGal1p is very high, it sequesters the repressor KlGal80p from the activator-DNA complex thereby relieving repression at a lower galactose concentrations compared to wild-type (solid line). In the case when autoregulation of KlGAL80 alone is removed and expressed constitutively at its maximum expression levels using the rate constant identical to that in wild-type, the KlGAL switch completely shut off (dash dotted line in Fig. 3c). This is due to the limited availability of KlGal1p whose synthesis is autoregulated, which cannot overcome the repression by the high constitutive levels of KlGal80p. However, the switch can be turned on by reducing the constitutive KlGal80p concentration levels. For the case when both KlGal1p and KlGal80p are constitutively expressed to their maximum levels, the model predicts that the switch is induced to its maximum protein expression levels at higher galactose concentration relative to the wild-type (dotted line in Fig. 3c). The ultrasensitive behavior is evidenced by the fact that a Hill equation representation of the stimulus–response relationship yields a Hill coefficient value of 7. Here, the unregulated KlGal1p requires the high galactose concentrations to sequester the abundant repressor protein. In such a mutant strain although the response is ultrasensitive, the organism does not show growth up to 0.4 M of galactose concentration. Thus, it is noted that for the induction of the switch on galactose either both, KlGal1p and KlGal80p, have to be autoregulated or both should be expressed constitutively.

The dynamic performance for the various mutants discussed above is shown in Fig. 3d. The dashed line shows the performance of the KlGAL system when KlGal1p alone is not autoregulated and expressed constitutively at maximum induced wild-type levels. Here, the cells show a rapid response due to the large amounts of KlGal1p available for induction and reaches a new steady-state which is maintained until galactose is depleted completely at about 60 h. The dash-dotted line in Fig. 3d shows the response when KlGAL80 alone was not autoregulated. Here, the regulated amount of KlGal1p is insufficient to sequester the high concentration of KlGal80p leading to the failure of the system in response to galactose. The dotted line in the Fig. 3d shows the performance of the system when both KlGal1p and KlGal80p are not autoregulated and expressed constitutively at maximum induced wild-type levels. Here, the system shows a delay due to the time required for the KlGal1p to sequester the excessive KlGal80p. The thin solid line in Fig. 3d shows the response of the system when permease Lac12p was expressed constitutively at wild-type levels. Here, the system responds at a faster rate compared to that of wild-type case (thick solid line) due to the large amount of permease available even at t = 0 h.

Since galactose is transported into the cytoplasm both by a Lac12p facilitated transport mechanism (Lac12p) and by a diffusion mechanism as shown in Eq. 9; it is of interest to ascertain the role of the feedback loop implemented through regulation of Lac12p. The dashed line in Fig. 3e shows the fractional protein expression of genes with two binding sites for a mutant strain lacking LAC12. In this case, galactose is transported only through diffusion mechanism; the system shows a graded response with varying galactose concentrations giving subsensitive response with a Hill coefficient value of 0.8. Further, at the other extreme, when permease Lac12p is expressed constitutively in silico to its maximum expression levels using a synthesis rate constant as in the wild-type case, the system shows the wild-type expression levels as shown by top most solid curve with a Hill coefficient value of 1.25 in Fig. 3e. At intermediate constitutive synthesis rates of Lac12p, the GAL system shows a graded response for the decreased synthesis rate constant values (lower solid line, k_t12 = 125 g⁻¹ dm³ h⁻¹; dotted line, k_t12 = 50 g⁻¹ dm³ h⁻¹ and dash-dotted line, k_t12 = 5 g⁻¹ dm³ h⁻¹). Thus, the presence of the positive feedback brought about by Lac12p is critical for the observed wild-type response at various galactose concentrations.

It has been experimentally observed that the GAL system of S. cerevisiae shows a bistable behavior when exposed to different preculturing conditions (Acar et al. 2005). To verify if such a phenotype exists for the K. lactis KlGAL system, we simulated the dynamic model for two different preculturing conditions, that is, glycerol and galactose and subsequently grown on galactose. In the case of preculturing on galactose, the wild type model was simulated for a high galactose concentration for 28 h and the end points were taken as the initial condition for the subsequent growth on galactose. Our results indicate that, unlike as in S. cerevisiae, here the wild-type strain does not exhibit bi-stable behavior as shown in Fig. 4a. Experiments were performed with cells precultured on glycerol and galactose and subsequently grown on galactose. The experimental results confirmed that the steady state expression was the same at various galactose concentrations in both the cases indicating absence of bi-stable response (results not shown). On constitutive expression of KlGal80p using a synthesis rate constant lowered by 14-fold relative to the wild-type, the model predicts a bi-stable response (see Fig. 4b) indicating that a weak negative feedback through the constitutive expression of KlGal80p and a strong positive feedback by KlGal1p is essential for a bi-stable response. This fact is corroborated by observing that upon elimination of any of the positive feedback loops (through KlGal4p, KlGal1p and Lac12p) the bi-stable behavior vanishes as was the case with the wild-type (see Fig. 4a) (Vinod et al. 2008).

Fig. 4.

Effect of preculturing on the steady-state performance of the GAL system for genes with two binding sites (f_2p) when precultured on glycerol (dashed line) and galactose (solid line) and subsequently transferred to a galactose medium. a Wild-type response. bKlGAL80 not autoregulated strain

The above analysis indicates that while the wild-type strain does not show bistable behavior, a strain lacking KlGal80p feedback with a low synthesis rate for KlGal80p does show bistability. In order to quantify the role of parameters in the manifestation of bistable behavior, a parametric sensitivity study was performed by evaluating the metric ‘δ’ (see Eq. 18) for parameters perturbed from their nominal values one at a time. Figure 5a shows the variation of δ at different values of the KlGal4p synthesis rate constant (k_g) for the wild-type strain (solid line) and for the strain with KlGal80p expressed constitutively (dashed line). It can be seen that the wild-type strain does not show a significant bistable behavior for all values of k_g considered whereas the mutant strain shows bistable behavior at higher values of k_g including at the nominal value of k_g=126 g⁻¹ dm³ h⁻¹.

Fig. 5.

Parametric sensitivity of the bistable behavior for the wild-type strain (solid line) and a mutant strain wherein KlGal80p is constitutively expressed (dashed line). The ordinates correspond to the metric δ, which represents the maximum separation between the fractional protein expressions (f_2p) of K. lactis when precultured on galactose and when precultured on glycerol. Effect of a rate constant for the synthesis of KlGal4p. b Rate constant for the synthesis of Lac12p. c Rate constant for the synthesis of KlGal1p. d Rate constant for the synthesis of KlGal80p. Global analysis to study the sensitivity to parameters k₃, k₄, k_g, k_t8 and k_t1 for e wild-type and f the mutant. Parameter 1—k₃; 2—k₄; 3—k_g; 4—k_t8; 5—k_t1

Figure 5b, c and d show the variation of δ for different values of the synthesis rate constant of Lac12p, KlGal1p and KlGal80p respectively. It is clear that the synthesis rate constant for Lac12p does not influence the extent of bistability while the rate constants of KlGal1p and KlGal80p significantly affect the bistable behavior. Enhancing the KlGal1p (positive regulator) synthesis rate constant while decreasing the KlGal80p synthesis rate constant (negative regulator) induces bistable behavior. Bistable behavior is also observed in the mutant if the half saturation constant K₀ in the growth expression is enhanced (see supplementary material). A random perturbation in all other model parameters except for k_g, k_t12, k_t8, k_t1 and K₀ did not alter the bistable behavior in the wild-type or the mutant (see supplementary material). Thus, only synthesis rate constants of KlGal1p and KlGal80p influence the bistable behavior for the wild-type. In case of the mutant, the bistable behavior is altered by k_g and K₀ in addition to synthesis rate constants of KlGal1p and KlGal80p.To rank the relative importance of the parameters rate constants for the synthesis of KlGal4p, KlGal80p and KlGal1p, a global sensitivity analysis was performed. Figure 5e and f shows the sensitivity coefficient with standard deviation for the five parameters obtained by simulating the model with 500 random realizations of the 5 parameters while maintaining all other parameters at their nominal values. The results indicate that in both the wild-type as well as the mutant strain, bistable behavior is most sensitive to the synthesis rate constant of KlGal4p when the mean of sensitivity is used for ranking the parameter importance.

Comparative study with GAL system of S. cerevisiae

A similar model development for the GAL system of S. cerevisiae has been reported in the literature (Ruhela et al. 2004). Since the two species of yeast are related evolutionarily with similar regulatory components, it is of interest to compare the steady-state and dynamic performance of the GAL system of the two organisms. The dynamic modeling strategy discussed above was used to compare the performance of GAL systems in both, mutant (lacking gene GAL80) and wild type strains of S. cerevisiae and K. lactis. Experimental studies have reported that the wild-type GAL system in S. cerevisiae shows bistable behavior at intermediate galactose concentrations (Acar et al. 2005). Further, it is known that such short term memory of GAL system in S. cerevisiae was due to the presence of positive feedback loop of Gal3p. Here, the K. lactis dynamic model used to simulate such response by preculturing on galactose and glycerol. The system shows no bistability for any galactose concentration (Fig. 4a). A similar study performed on GAL system of S. cerevisiae shows a bi-stable behavior for intermediate galactose concentrations (Acar et al. 2005). It has been shown in this case that the positive feedback loop provided by Gal3p is responsible for the observed bistability. In K. lactis, since Gal3p is absent and KlGal1p functions as the inducer, the system seems to have lost the short term memory.

The GAL system in both species functions in a coordinated way with inherent feedback loops. Both species have identical repressor proteins (Gal80p and KlGal80p) which share 70% identical residues. However, the gene producing KlGal80p in K. lactis contains two binding sites in its promoter for activator KlGal4p and is confined to the nucleus. Whereas, the S. cerevisiae repressor gene contains only one binding site in its promoter for Gal4p and is a nucleocytoplasmic protein. A similar analogy was observed for inducer proteins KlGal1p and Gal3p with KlGAL1 gene contains two binding sites and KlGal1p is nucleocytoplasmic protein, whereas, Gal3p is cytoplasmic and GAL3 contains one binding site for activator Gal4p. It is therefore of interest compare the performance of the GAL systems of both species to analyze how these changes in the structure affect the performance. In the case when both regulatory proteins KlGal1p and KlGal80p were not autoregulated, the KlGAL gene response in K. lactis required higher galactose concentrations to express compared to wild-type case due to the large amount of unregulated Gal80p concentration present in the nucleus (dotted line in Fig. 3c). A similar response was observed in S. cerevisiae (result not shown). When GAL80 alone was not autoregulated the GAL system switches off in both species indicating the importance of GAL80 autoregulation (dash-dotted line in Fig. 3c) (Ruhela et al. 2004).

Further, the dynamic model can be simulated to determine temporal relevance of each protein for a given galactose concentration. Figure 6a and b shows the comparison of fractional protein expression of genes with two binding sites (f_2p) and total protein concentrations with time for KlGAL system of K. lactis (solid lines) and S. cerevisiae (dashed lines). Figure 6a shows the dynamic comparison of fractional protein expression of genes with two binding sites (f_2p). Here, the cells were precultured in a glycerol medium and exposed to a high galactose concentration (0.44 M for K. lactis and 0.44 M for S. cerevisiae) at t = 0. As seen from the figure the expression levels reached maximum after about 20 h in both species but the maximum level of expression is different. K. lactis requires high galactose concentration (0.44 M) to express at maximum level of 35%, while S. cerevisiae needs only 0.1 M to reach its maximum expression levels of 82% (Verma et al. 2003). The expression levels drop once galactose is consumed completely after about 60 h in K. lactis, whereas, in S. cerevisiae the expression levels drop after about 35 h. Since the GAL gene expression is due to the interplay of the regulatory proteins, it is of interest to see how concentration of these protein varies with time for a given steady-state galactose concentration. Figure 5b shows the total nuclear concentration of the KlGal80p (solid line) and S. cerevisiae (dashed line) for a steady-state galactose concentration of 0.4 M. The high increase in nuclear concentrations of KlGal80p from 37 nM at t = 0 to 420 nM after complete induction in K. lactis makes the system express moderately compared to that in S. cerevisiae, where the nuclear Gal80p concentrations vary between 0 and 2.2 nM (the dashed line in Fig. 6b is scaled by a factor 10 for clarity of representation).

Fig. 6.

Dynamic performance of GAL system in S. cerevisiae and K. lactis for a high galactose concentration of 0.4 M. a Fractional protein expression of genes with two binding sites (f_2p) with galactose provided in batch mode. b Total nuclear concentration of Gal80p in K. lactis and in S. cerevisiae. Here, the dashed line for S. cerevisiae is scaled by factor 10 for clarity. c Steady-state total nuclear concentrations of KlGal1p and Gal80p in K. lactis and S. cerevisiae, respectively with varying galactose concentrations. In all of the cases above dashed line represents S. cerevisiae and solid line represents K. lactis

Figure 6c shows the steady-state total nuclear concentrations for KlGal1p and Gal80p with varying galactose concentrations in K. lactis and S. cerevisiae, respectively. As seen from the figure, the steady-state total nuclear Gal80p concentration is very high at low galactose concentrations and drop relatively to a small value as the concentration of galactose increased (dashed line) resulting in shuttling of Gal80p to the cytoplasm. On the other hand, the nuclear concentration of KlGal1p is zero at low galactose concentrations and increases to a high value for increased galactose concentrations (solid line).

In silico re-engineering of GAL system

The developed dynamic models for both yeast species have been re-engineered in silico to interchange the nucleocytoplasmic shuttling of regulatory proteins. In the dynamic model of the re-engineered K. lactis KlGAL system, the inducer protein (KlGal1p) is made to reside in the cytoplasm while the repressor protein (KlGal80p) shuttles between the nucleus and the cytoplasm, thus mimicking the design prevailing in S. cerevisiae. Here, the distribution coefficient (K) is defined as the ratio of KlGal80p in the cytoplasm to the nucleus. Figure 7 shows the response of fractional protein expression for two binding site genes for these different scenarios. The modification in shuttling of regulatory proteins in KlGAL system of K. lactis makes the fractional protein expression of genes with two binding sites express to about 20% for a distribution coefficient value of 0.4, which is also used in S. cerevisiae model (solid line, Fig. 7a). However, an increase in the shuttling coefficient to K = 2.4 makes the re-engineered GAL switch behave like S. cerevisiae GAL system with expression levels reaching about 78% (dashed line). In this case, it was observed that the re-engineered system requires larger time (60 h) to reach the maximum expression levels than in the wild-type S. cerevisiaeGAL system. The corresponding steady-state performance the GAL system for varying steady-state galactose concentration was shown in Fig. 7b for genes with two binding site (f_2p). Here, for increased distribution coefficient (K = 2.4) (dashed line, Fig. 7b), the expression levels were increased even at low galactose concentrations due to the higher quantity of KlGal80p that shuttles into the cytoplasm.

Fig. 7.

In silico reengineering of GAL system in S. cerevisiae and K. lactis by interchanging the compartmentalization of regulatory proteins. K. lactis GALsystem: repressor KlGal80p made to translocate to the nucleus while KlGal1p confines to the cytoplasm. a Dynamic performance of altered K. lactis GAL system response for genes with two binding sites for distribution coefficient values of K = 0.4 (solid line) and K = 2.4 (dashed line) b Steady-state performance of K. lactis GAL system response for genes with two binding sites for distribution coefficient values of K = 0.4 (solid line) and K = 2.4 with varying galactose concentrations. S. cerevisiae GAL system: Repressor Gal80p made confined to the nucleus while Gal3p translocates to the nucleus in GAL system of S. cerevisiae. c Dynamic performance of altered S. cerevisiae GAL system response for genes with two binding sites for a unchanged parameter system (solid line) and for a change in dissociation constant, K₃ = 1×10⁻¹⁰ (dashed line). d Steady-state performance of altered S. cerevisiae GAL system response for genes with two binding sites for a unchanged parameter system (solid line) and for a change in dissociation constant, K₃ = 1×10⁻¹⁰ with varying galactose concentrations

A similar study on GAL system of S. cerevisiae is performed by making the inducer Gal3p shuttle between the nucleus and the cytoplasm and Gal80p confined to the nucleus. In such a re-engineered system, the response was switched off for a K value of 8.0, which is also used in K. lactis model (solid line, Fig. 7c) and the system response was unchanged by changing distribution coefficient value. However, the system was observed to be sensitive to the reduced affinity for [Gal80p-Gal4p] complex. The nominal S. cerevisiae system has a dissociation constant value for Gal80p–Gal4p interaction of K₃ = 1×10⁻¹³, by increasing K3 value to K₃ = 1×10⁻¹⁰, the GAL system performance was observed similar to that of K. lactis KlGAL system (dashed line, Fig. 7c). Further, the corresponding model simulations for steady-state response of genes with two binding sites are shown in Fig. 7d. As seen from the figure, the system shows no response when parameters were not changed from the original system for any galactose concentrations (solid line). However, by increasing the dissociation constant for [Gal80p–Gal4p] complex, the GAL gene response was observed similar to K. lactis (dashed line, Fig. 7d).

Recent experimental studies on S. cerevisiae GAL system have indicated that the inducer protein Gal3p can also shuttle into the nucleus and interact with the repressor protein Gal80p to relieve inhibition on activator protein Gal4p (Wightman et al. 2008). To mimic the experimental findings, we re-engineered the GAL system in S. cerevisiae to include the nucelocytoplasmic shuttling of both repressor (Gal80p) and inducer (Gal3p) proteins. Figure 8a shows the model predictions for the re-engineered system. The distribution coefficient of Gal80p was similar to the original model (K = 0.4), while the distribution coefficient for Gal3p was regressed to match the experimental data (Verma et al. 2003). Solid line in Fig. 8a shows that the model predictions were able to predict the experimental steady-state data on varying galactose concentrations for a Gal3p distribution coefficient value of 3.2 (here, the distribution coefficient for Gal3p is defined as the ratio of activated Gal3p in the cytoplasm to the nucleus), while the distribution coefficient for Gal80p was kept unchanged as in the original model. Here, the observed total nuclear Gal3p concentration of 0.05% at high galactose concentration indicates only a small portion of the total Gal3p shuttles into the nucleus. The system out-performs the nominal system when distribution coefficient for Gal3p was decreased to 0.12 (10% of total Gal3p shuttles into the nucleus) as shown by dashed line in Fig. 7a. Subsequently a similar study was performed on KlGAL system of K. lactis to include the nucleocytoplasmic shuttling of both repressor and bifunctional protein. The model predictions show that the K. lactis KlGAL system also shows fractional protein expressions under conditions of both KlGal1p and KlGal80p shuttling for a KlGal80p distribution coefficient value of 0.012 (solid line in Fig. 8b) and the KlGal1p distribution coefficient was kept similar to the original unchanged model. Here, the distribution coefficient for KlGal80p is defined as the ratio of KlGal80p in the cytoplasm to the nucleus. The KlGAL system shows the observed experimental behavior with 10% of the total KlGal80p shuttling into the cytoplasm. The fractional protein expressions can be increased by increasing the distribution coefficient value to 1.4 as show in by dashed line in Fig. 8b. The analysis shows that the GAL system in both organisms can perform under conditions of shuttling of both proteins as reported experimentally for S. cerevisiae case but with an appropriate value of distribution coefficient. However, a similar situation of KlGal80p shuttling has not been reported experimentally for the K. lactis KlGAL system (Anders et al. 2006).

Fig. 8.

In silico re-engineering of GAL system in S. cerevisiae and K. lactis for both regulatory proteins Gal3p/Gal1p and Gal80p shuttle across nuclear membrane. a Re-engineered GAL system for S. cerevisiae to include shuttling of Gal3p to nucleus. The solid line shows the experimental validation for Gal3p distribution coefficient of 3.2 and dashed line shows the response of the system for a decreased Gal3p distribution coefficient of 0.12. b Re-engineered GAL system for K. lactis to include shuttling of KlGal80p to cytoplasm. The solid line shows the experimental validation for KlGal80p distribution coefficient of 0.012 and dashed line shows the response of the system for an increased KlGal80p distribution coefficient of 1.4

Discussion

A dynamic modeling strategy is used here to understand the complex interactions in the KlGAL system of K. lactis and is subsequently compared its performance to that of S. cerevisiae. The performance of the KlGAL system in K. lactis is dependent on the interplay of its regulatory proteins and their relative concentrations. The maximum expression levels observed in wild type strain after induction with galactose (see Fig. 2b) are very low (only 35%) compared to that of a mutant strain lacking KlGAL80 expressed under no glucose or in a NINR medium (see Fig. 2a). The lowered expression levels in wild-type strain can be explained in two ways. Since, in K. lactis the repressor protein KlGal80p is nuclear, the proximity for interaction with activator KlGal4p is greater and it forms a competition between KlGal1p and KlGal4p to interact with repressor. Further, the protein KlGal1p is a bifunctional protein which has both galactokinase and inducer activity. This leads to a decisive conflict in the organism: what fraction of the KlGal1p must be refrained for inducer function. A steady-state model analysis revealed that, only 10% of the total KlGal1p is used for inducer function leading to a lowered expression levels observed in K. lactis. In case of S. cerevisiae, the species resolved this issue by undergoing a whole genome duplication to create a new regulatory protein Gal3p which has only inducer activity. In addition, the inducer protein in S. cerevisiae sequesters Gal80p into the cytoplasm leading to a small concentration of repressor in the vicinity of the activator. Further, in the presence of glucose, the KlGAL system of K. lactis is not completely repressed (see Fig. 2a) due to the autoregulation of gene KlGAL4, whereas in S. cerevisiae which is not autoregulated shows complete repression of KlGAL genes (Ruhela et al. 2004).

The regulatory proteins Gal80p and Gal3p/Gal1p in the GAL system are autoregulated by their respective genes. However, the number of binding sites in their promoter regions varies from S. cerevisiae to K. lactis. Both genes GAL80 and GAL3 in S. cerevisiae are controlled by a single binding site, whereas in K. lactis, both KlGAL80 and KlGAL1 are controlled by genes with two binding sites. It is interesting to see how these changes in the structure of the GAL system reflect in the steady-state response. The dynamic model predictions for steady-state protein expression levels shows that when autoregulation of both genes is removed, the response of the GAL system in both the species are repressed completely at low galactose concentrations due to higher repressor concentrations. However, when repressor gene alone is not autoregulated, both species respond similarly. Here, the unregulated repressor is in a large enough concentrations in both the species to keep the system under repressed conditions. The result indicates that, in both species the repressor gene must be autoregulated along with the inducer gene with the same number of binding sites in their promoter regions for activator to make the system function normally. Further, in both species, the synthesis of transporter proteins (Gal2p/Lac12p) are autoregulated by their respective genes with two binding sites for activator in their promoter regions. Elimination of regulation of the transporter gene suggests that the GAL system response can be tuned in both organisms. The system response shows a graded response when Lac12p is expressed constitutively to a low value (see Fig. 3e), indicating the importance of the positive feedback responsible for the switch like response observed in both organisms in addition to other mechanisms. However, the graded response observed for K. lactis was not as steep as it was observed for S. cerevisiae case (Hawkins and Smolke 2006).

The dynamic model can be used to analyze the effect of preculturing on steady-state response of the GAL gene expression. The K. lactisKlGAL system does not show bistable behavior for different preculturing conditions. However, the system shows bistability for a strain where KlGAL80 is not autoregulated (Fig. 4b). In the case of wild type K. lactis system, the negative feedback by KlGal80p is much stronger both due to its nuclear localization and stronger control by multiple binding sites for KlGal4p leading to a loss of bistability. In case of S. cerevisiae, the GAL system shows bistability, which is due to the presence of positive feedback by inducer Gal3p (see Fig. 4a). This is consistent with the experimental observation that the GAL3 is responsible for the short term memory observed in S. cerevisiae (Kundu and Peterson 2010). Parametric sensitivity analysis indicated that the synthesis rate constants for KlGal1p and Klgal80p, imparting positive and negative feedbacks, respectively, are the dominant parameters influencing bistability (Vinod et al. 2008).

Further, the dynamic model provides the opportunity to compare how autoregulation of all these regulatory proteins affects the dynamic performance of the GAL system in both organisms. Since, synthesis of activator protein KlGal4p is autoregulated in K. lactis, the removal of autoregulation and a constitutive expression with a reduced synthesis rate here makes the response drop at a faster rate than observed for wild-type system (see dotted line in Fig. 3b) due to insufficient amount of activator concentration. When both regulatory proteins KlGal80p and KlGal1p are independently expressed, the system responds with an initial lag both in K. lactis (see Fig. 3d), and in case of S. cerevisiae (Ruhela et al. 2004). The lag observed here is due to the time required for the Gal3p to sequester the excessive Gal80p from the nucleus in case of S. cerevisiae and due to the high concentrations of KlGal80p in the nucleus in case of K. lactis. In this case where both regulatory proteins are not autoregulated, the system shows ultrasensitive behavior, either fully expressed or fully repressed in both of the organisms. In the case when synthesis of inducer alone is not autoregulated, both systems show rapid response due to high constitutive concentrations of inducer. However, the maximum expressions observed in both species were similar to their wild-type response. The analysis shows that the autoregulation of regulatory proteins is crucial for the nominal response for both the systems. The temporal comparison of total concentrations of individual regulatory proteins in K. lactis and S. cerevisiae suggests that even though K. lactis has higher basal protein concentrations (Fig. 6b), the time required to reach the maximum is longer (Fig. 6a) due to a large increase in the nuclear concentration of KlGal80p with time (see Fig. 6b). In case of S. cerevisiae the opposite is observed leading to higher expression levels due to moderate increase in the total concentration of Gal80p (Fig. 6b). However, the relative total concentrations are very low in case of S. cerevisiae compared to that of K. lactis. Further, in silico re-engineering study shows that, interchange of nucleocytoplasmic shuttling of regulatory proteins in K. lactis was able to show response with an increased distribution coefficient, where as a similar effect was not observed for S. cerevisiae system due to high affinity between the Gal80p and Gal4p proteins, indicating the differences in affinities for regulatory proteins in two systems.

Recent studies indicate that in addition to the nucleocytoplasmic shuttling of Gal80p, the inducer Gal3p also shuttles to the nucleus (Wightman et al. 2008). To study the effect of nucleocytoplasmic transport of Gal3p on the response of GAL switch, the S. cerevisiae model was re-engineered to include the transport of Gal3p. The analysis estimated the distribution coefficient for the nucleocytoplasmic transport of Gal3p to be 3.2, which indicates that only 0.05% of the total Gal3p will reside in the nucleus. Thus, although Gal3p shuttles to the nucleus, the shuttling of Gal80p is the key mechanism for the operation of the switch. A similar analysis with K. lactis indicated that the shuttling of KlGal80p into the cytoplasm, although feasible, is not a key mechanism that influences the performances of the KlGAL switch.

In summary, the developed dynamic model predicts the steady-state behavior of the KlGAL system for various scenarios establishing the importance of a particular mechanism involved in the operation of the switch. The analysis predicts the importance of various inherent systems-level properties such as autoregulation of regulatory proteins, bistability and sensitivity arising out of the molecular interactions. The dynamic model can be used to compare the performance of two homologous yeast species to evaluate the role of regulation and compartmentalization of proteins on the phenotypic response. Further, the comparative studies revealed that the K. lactis KlGAL system operates with higher basal level concentrations of regulatory proteins compared to S. cerevisiae. The in silico re-engineering study shows that the differences in affinities for regulatory protein interactions also responsible for the observed phenotypic responses. Thus, though the GAL system in yeast species K. lactis and S. cerevisiae share similarities in some of the molecular components, the interactions among them varied considerably due to evolutionary pressures, giving a different system response. The presence of a dedicated inducer due to genome duplication in S. cerevisiae resulted in a highly sensitive to galactose. Whereas, in K. lactis the bifunctional inducer, KlGal1p and the autoregulation of KlGal4p yielded higher basal levels of regulatory proteins in response to galactose. However, it would be interesting to study the response of the KlGAL system to lactose since the lactose medium constitutes a niche environment for K. lactis.