Báo cáo khoa học: Experimental and steady-state analysis of the GAL regulatory system in Kluyveromyces lactis docx

cerevisiae are as follows: a the autoregulation of transcriptional activator KlGal4p; b the dual role of KlGal1p as a metabolizing enzyme as well as a galactose-sensing protein; c the sh

regulatory system in Kluyveromyces lactis

Venkat R Pannala, Sharad Bhartiya and Kareenhalli V Venkatesh

Department of Chemical Engineering, Indian Institute of Technology, Bombay, Mumbai, India

Introduction

Galactose metabolism in microorganisms occurs

through a well-conserved metabolic pathway which is

tightly regulated For example, both Saccharomyces

cerevisiae and Kluyveromyces lactis utilize galactose as

an alternative carbon and energy source in the absence

of glucose in the environment The uptake of galactose

is governed by the well-known Leloir pathway using

enzymes produced via the GAL switch [1] When

galac-tose is the sole carbon source, the induction and

tran-scription of GAL genes occur via the interplay between

three regulatory proteins, namely Gal4p, Gal80p and Gal3p⁄ Gal1p [2–5] The activator protein (Gal4p) binds to the upstream activator sequence (UASG) of each gene for transcription to proceed The transcrip-tion process is inhibited by a repressor protein Gal80p which binds to the C-terminal activation domain of Gal4p However, in the presence of galactose, this repression is relieved by the inducer protein Gal3p⁄ Gal1p In contrast, glucose represses the ability of galactose to activate the GAL system by multiple

Keywords

galactose; GAL system; Kluyveromyces

lactis; Saccharomyces cerevisiae;

steady-state model

Correspondence

S Bhartiya ⁄ K V Venkatesh, Department of

Chemical Engineering, Indian Institute of

Technology, Bombay, Powai,

Mumbai-400076, India

Fax: 91 22 25726895

Tel: 91 22 25767225

E-mail: venks@che.iitb.ac.in

(Received 10 December 2009, revised

7 May 2010, accepted 12 May 2010)

doi:10.1111/j.1742-4658.2010.07708.x

The galactose uptake mechanism in yeast is a well-studied regulatory net-work The regulatory players in the galactose regulatory mechanism (GAL system) are conserved in Saccharomyces cerevisiae and Kluyveromyces lactis, but the molecular mechanisms that occur as a result of the molecular interactions between them are different The key differences in the GAL system of K lactis relative to that of S cerevisiae are: (a) the autoregula-tion of KlGAL4; (b) the dual role of KlGal1p as a metabolizing enzyme as well as a galactose-sensing protein; (c) the shuttling of KlGal1p between nucleus and cytoplasm; and (d) the nuclear confinement of KlGal80p

A steady-state model was used to elucidate the roles of these molecular mechanisms in the transcriptional response of the GAL system The steady-state results were validated experimentally using measurements of b-galac-tosidase to represent the expression for genes having two binding sites The results showed that the autoregulation of the synthesis of activator KlGal4p is responsible for the leaky expression of GAL genes, even at high glucose concentrations Furthermore, GAL gene expression in K lactis shows low expression levels because of the limiting function of the bifunc-tional protein KlGal1p towards the induction process in order to cope with the need for the metabolism of lactose⁄ galactose The steady-state model of the GAL system of K lactis provides an opportunity to compare with the design prevailing in S cerevisiae The comparison indicates that the exis-tence of a protein, Gal3p, dedicated to the sensing of galactose in S cerevi-siae as a result of genome duplication has resulted in a system which metabolizes galactose efficiently

Abbreviations

NINR, noninducing, nonrepressing; UAS, upstream activator sequence; URS, upstream repressor sequence; YPD, yeast–peptone–dextrose.

mechanisms, and thus terminates the activation of

GAL genes [6–8] Although the regulatory players are

conserved in various organisms, the molecular

mecha-nisms that occur as a result of the interactions between

them are different For example, in K lactis, the

syn-thesis of the transcriptional activator protein KlGal4p

is autoregulated, but its expression is inhibited by

glu-cose [9–11], whereas, in S cerevisiae, ScGal4p synthesis

is not autoregulated, but its gene expression and

activ-ity are repressed and inhibited by glucose [10,12]

Although the GAL system of S cerevisiae has been

well characterized, a similar degree of quantification

for the GAL system of K lactis is absent in the

literature

The GAL system in K lactis contains two

regula-tory genes (LAC9 or KlGAL4 and KlGAL80), a

bifunctional gene KlGAL1 and four structural genes

(LAC12, LAC4, KlGAL7 and KlGAL10) The GAL

switch is found in three regulatory states in response

to the availability of various carbon sources In the

presence of a noninducing, nonrepressing (NINR)

medium, such as glycerol or raffinose, the GAL switch

is in a noninduced state Under such a condition,

KlGal4p activity is inhibited by the binding of

KlGal80p protein to the C-terminal activation domain

of KlGal4p In this state, the GAL genes are poised

for induction as they are not subjected to carbon

catabolite repression In the presence of lactose⁄

galac-tose medium, the GAL switch is in an induced state

The enzyme permease (Lac12p) transports lactose⁄

galactose into the cytoplasm, which, in combination

with ATP, activate 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

repres-sor protein KlGal80p to form a stable tetrameric

com-plex (KlGal1p–KlGal80p2–KlGal1p), thereby relieving

the inhibition of KlGal80p on KlGal4p [13] Further,

the regulatory proteins KlGal4p, KlGal80p and

KlGal1p are under the GAL promoter, and thus their

synthesis is dependent on the status of the GAL

switch, which in turn is a function of the

concentra-tions of these regulatory proteins This autocatalytic

effect caused by the feedbacks of the regulatory

pro-teins on the switching of the GAL genes is termed

‘autoregulation’ Although KlGal4p and KlGal1p,

as activators, constitute positive feedback loops,

KlGal80p, as an inhibitor, imparts a negative

feed-back Autoregulation, as a molecular mechanism, is

known to yield system level properties, such as signal

amplification and ultrasensitivity [14] In the presence

of glucose, the GAL switch is in a repressed state In

S cerevisiae, glucose represses GAL genes via a

specific repressor protein Mig1p, which binds to the upstream repressor sequences (URSG) present in GAL genes [7] However, in the case of K lactis, the repres-sion of KLGAL4 is independent of Mig1p, as KlGAL4 has no URSG in its promoter for Mig1p, but glucose indirectly represses the GAL system by a Mig1p bind-ing site in the KlGAL1 gene [8,15] Although KlGal4p has no Mig1p binding site for its gene promoter, its activity is inhibited directly in the presence of glucose

It has been shown experimentally that glucose affects the ability of KlGAL4 to activate the transcription of GAL genes [16,17] The activator Gal4p in yeast con-tains at least three inhibitory domains in its central region between the activator domains, which become active in the presence of glucose, but, however, are independent of the repressor Mig1p [10]

In all of the above three states, the concentration of the activator KlGal4p plays a vital role in the induc-tion mechanism of the GAL system The KlGAL4 gene contains a UASG in its own promoter for the binding

of KlGal4p, resulting in an autoregulatory circuit which causes a two- to five-fold increase in KlGal4p concentration in the presence of lactose⁄ galactose This increase is essential for the maximal growth rate on lactose and has probably evolved to give the organism

a selective advantage in its natural habitat [9] How-ever, to maintain the repressed state of KlGAL4-controlled genes in a glucose-containing medium, the KlGal4p concentration must be held below a certain threshold concentration [11] Although experimental studies of the K lactis GAL system have determined the regulatory components, uncertainties exist in the way in which these components interact with each other and their compartmentalization Until recently,

it was believed that the K lactis GAL system operated

in a similar manner to the S cerevisiae GAL system, where the repressor ScGal80p shuttles between the nucleus and the cytoplasm [4,18] However, it was later shown that, in K lactis, it is the bifunctional protein KlGal1p that shuttles between the nucleus and the cytoplasm [13] The key differences in the GAL systems

of K lactis and S cerevisiae are as follows: (a) the autoregulation of transcriptional activator KlGal4p; (b) the dual role of KlGal1p as a metabolizing enzyme

as well as a galactose-sensing protein; (c) the shuttling

of KlGal1p between nucleus and cytoplasm; (d) the nuclear confinement of KlGal80p; and (e) the fact that KlGAL4 is the only gene in the GAL system with one binding site, with the remaining genes having two binding sites

Although S cerevisiae and K lactis utilize similar molecular components in the GAL network, the archi-tecture in the organisms differs substantially

Further-more, the parameter values also play a role in the

performance of the GAL system in the two yeasts It

should be noted that K lactis utilizes the GAL

net-work to metabolize mainly lactose, whereas S

cerevi-siae uses it to metabolize melibiose and galactose

This evolutionary fact also plays a role in the

perfor-mance of the two networks Given the above

differ-ences in the two GAL networks, it is of interest to

compare the steady-state performances of the

net-works in S cerevisiae and K lactis in response to

galactose and glucose

We used a steady-state modeling approach to

quan-tify the underlying molecular mechanism for the GAL

system of K lactis and to obtain a systems’ level

understanding of its behavior The steady-state model

for the GAL system of K lactis was validated

experi-mentally by obtaining steady-state protein expression

levels in a wild-type strain and in a mutant strain

lack-ing gene KlGAL80 The steady-state model was then

used to delineate the importance of the autoregulation

of regulatory proteins and parametric sensitivity

Sub-sequently, we considered a KlGAL80 mutant strain of

K lactisto determine the importance of the

autoregu-lation of activator KlGal4p and glucose repression

The K lactis GAL system model developed in this

work has been validated experimentally As the

sys-tems’ level properties, such as ultrasensitivity and

memory, arising out of the various molecular

mecha-nisms in S cerevisiae have been well elucidated [19], it

was of interest to compare the steady-state

perfor-mance of K lactis with that of S cerevisiae Such a

comparison yields the significance of the various

molecular interactions in the two networks with similar

molecular components The results showed that the

autoregulation of the activator protein Gal4p in

K lactisis responsible for the leaky expression of GAL

genes, even at high glucose concentration The

com-parison indicates that the existence of a protein Gal3p

in S cerevisiae, dedicated for the sensing of galactose,

arising as a result of genome duplication has resulted

in a system which metabolizes galactose efficiently We

begin by describing the key features of the model

developed for the wild-type strain of K lactis, the

detailed equations for which are provided in

Support-ing information

Model development

All molecular interactions in the K lactis GAL system

that have been included in the steady-state model are

shown schematically in Fig 1 D1 in Fig 1 represents

the gene LAC9⁄ KlGAL4, with one binding site in its

promoter for KlGal4p, whereas the other genes

(LAC12, LAC4, KlGAL7, KlGAL10 and KlGAL1), which have two or more binding sites, are shown as D2 The activator KlGal4p dimerizes with a dissocia-tion constant K1 and subsequently binds to the opera-tor site of the gene KlGAL4 (D1) with a dissociation constant Kd:

½KlGal4p þ ½KlGal4p ¢

K1 ½KlGal4p2 ð1Þ

½D1 þ ½KlGal4p2 ¢

Kd ½D1  KlGal4p2 ð2Þ For genes with two binding sites (D2), dimer Gal4p binds to the first site with a dissociation constant of

Kd, followed by binding to the second site with a dis-sociation constant of Kd⁄ m, where the factor m (>1) quantifies the cooperative effect of binding of KlGal4p

to the second binding site [3]:

½D2 þ ½KlGal4p2 ¢

Kd ½D2  KlGal4p2 ð3Þ

½D2  KlGal4p2 þ ½KlGal4p2 ¢

Kd m

½D2  KlGal4p2 KlGal4p2

ð4Þ

In the absence of galactose, the repressor protein KlGal80p dimerizes with a dissociation constant K2 and binds with DNA-bound KlGal4p to inhibit the transcriptional process For example, KlGal80p2 interaction with D1–KlGal4p2 can be written as follows:

½KlGal80p2 þ ½D1  KlGal4p2 ¢

K3

½D1  KlGal4p2 KlGal80p2

ð5Þ

Similarly, the remaining interactions of KlGal80p2 with DNA–KlGal4p2 complexes can be written (see Supporting information for details)

In the presence of galactose and ATP, the inducer KlGal1p is activated, which is ultimately responsible for relieving the repression of the GAL system by KlGal80p The activation of the inducer KlGal1p can

be quantified using a steady-state saturation function given by [18]:

½KlGal1pt ¼ ½KlGal1pt Gal

Ksþ Gal

ð6Þ

where ½KlGal1pt represents total activated KlGal1p and [KlGal1p]trepresents total KlGal1p concentration

Ksrepresents the half-saturation constant for the acti-vation of KlGal1p by galactose (Gal) The activated

KlGal1p shuttles into the nucleus with a distribution

coefficient K (see Fig 1) and is defined as the ratio of

activated KlGal1p in the cytoplasm to the nucleus:

K¼½KlGal1p

 c

The monomeric form of activated KlGal1p in the

nucleus interacts with the monomeric form of the

repressor KlGal80p with a dissociation constant of K4

as shown in Fig 1

½KlGal1pnþ ½KlGal80p ¢

K4 ½KlGal1pn KlGal80p ð8Þ The monomeric form of the activated KlGal1p is known to interact with KlGal80p2 with a positive co-operativity, resulting in a reduction in the dissociation constant by two (i.e K4⁄ 2) [13]:

0

4

0

80

Galactose

Nucleus

Cytoplasm

80

12

ATP 1

K

K4

UASG D2

0

GAL genes

4 80

80

K1

D1

GAL genes

UASG

Kd

K2 K3

K3

K4

Galactose

Nucleus

Cytoplasm

80

12

ATP 1

K

UASG D2

0

GAL genes

4

K1

D1

GAL genes

UASG

Kd

Galactose

A

B

Fig 1 (A) Schematic diagram showing the molecular interactions in a Kluyveromyces lactis wild-type strain (B) GAL system in a K lactis strain lacking GAL80 Here, Ki(i = 1–4) represents the dissociation constant for the respective interactions, K represents the distribution coefficient for KlGal1p shuttling and Kd represents the binding of KlGal4p protein to the DNA ‘m’ represents the degree of cooperativity D1 and D2 represent genes with one and two binding sites, respectively.

½KlGal1pnþ ½KlGal80p2 ¢

K4 2

½KlGal1p

n KlGal80p2 ð9Þ Furthermore, two monomers of activated KlGal1p

can also interact with the dimer KlGal80p to form

a heterotetrameric complex ½KlGal1p

n KlGal80p2 KlGal1p

n with a negative cooperativity, which results

in an increase in the dissociation constant by two (i.e

2K4) [13]:

½KlGal1pn KlGal80p2 þ ½KlGal1pn¢

2K4

½KlGal1pn KlGal80p2 KlGal1pn

ð10Þ

The net result of all of these interactions relieves the

inhibition of repression on activator KlGal4p, which

allows the transcription to proceed The complete

detailed equations for all interactions are given in

Sup-porting information

Based on the mechanisms shown above, we can

obtain the fractional protein expressions for genes with

one binding site and two binding sites by applying

equilibrium and mass balance equations Thus, we

define the fractional transcriptional expressions f1 and

f2as the ratio of mRNA that is transcribed in response

to an input stimulus to the maximum capacity of

mRNA that could be transcribed by the system for

genes with one and two binding sites, respectively The

fractional transcriptional expressions for genes with

one binding site (D1) and two binding sites (D2) are

given as follows:

f1¼½D1  KlGal4p2

D1t

ð11Þ

f2¼½D2  KlGal4p2 þ ½D2  KlGal4p2 KlGal4p2

D2t

ð12Þ

where D1t and D2t are the total operator

concentra-tions of genes with one and two binding sites,

respectively As shown in Fig 1, [D1–KlGal4p2],

[D2–KlGal4p2] and [D2–KlGal4p2–KlGal4p2] represent

the concentrations of the complexes formed as a result

of the interactions between the genes (D1 and D2) and

KlGal4p2 It should be noted that, in the definition of

f2 [Eqn (12)], it is assumed that the transcriptional

capacity of a D2–KlGal4p2complex is equal to that of

a D2–KlGal4p2–KlGal4p2 complex However, the

co-operativity in binding to the second site [parameter m

in Eqn (4)] ensures that the complex D2–KlGal4p2–

KlGal4p2 dominates the gene expression quantified by

f2 The fractional protein expression fip, that is the

ratio of protein Pi synthesized for a given

transcrip-tional expression to the maximum expression possible

Pmax, is related to the fractional transcriptional expres-sion as follows [18,20]:

fip¼ Pi

Pmax

¼ fn

i; for i¼ 1; 2 ð13Þ

where n is the co-response coefficient and is defined as the ratio of the log-fold change in protein expression

to the log-fold change in mRNA expression [21] In prokaryotes, the typical value of n is close to unity, indicating that the translational process is quite effi-cient It has been shown through microarray experi-ments that n has a value in the range 0.5–0.75 for protein expression from genes in S cerevisiae [22] Spe-cifically, the GAL genes in S cerevisiae show an aver-age co-response coefficient of around 0.7 [18] In this work, we have assumed a value of 0.7 as the corre-sponding coefficient in K lactis As the gene KlGAL4 with one binding site is autoregulated; the total KlGal4p concentration (KlGal4pt) is therefore a func-tion of f1p Further, the autoregulation of KlGAL4 makes it imperative that a basal amount of KlGal4pt0, necessary to activate the switch from a completely repressed state (i.e f1p= 0), exists Thus, the total KlGal4pt concentration is dependent on f1p and is modeled as follows [14]:

½KlGal4pt ¼ ½KlGal4pt0 1 þ f 1p q

ð14Þ

where q represents the fold-change in [KlGal4pt] from

a noninduced state to a completely induced state cor-responding to f1p= 1 Experiments have indicated a two- to five-fold change in KlGal4p concentration on induction [9], and we have assumed a value of five for the parameter q [KlGal4pt0] represents the basal KlGal4ptconcentration in the noninduced state

As KlGal80p and KlGal1p are autoregulated with two binding sites for KlGal4p, their individual total concentrations can be related to the status of the switch through f2p[see Eqn (13)] as given below:

½KlGal1pt¼ f2p½KlGal1pmaxand½KlGal80pt

The model equations are obtained assuming that all molecular interactions (as shown in Fig 1) are at equilibrium and using total molar balances for the components together with the constraint imposed by Eqn (15) All component concentrations are based on

a cell volume of 23 fL [13] The model consists of 23 concentrations of various complexes, together with the two transcriptional expressions (f1 and f2) and two corresponding protein expressions (f1p and f2p)

These 27 variables are determined by 27 algebraic

equations (see detailed model development in

Sup-porting information) The mass balance equations are

then solved by the ‘fsolve’ routine of MATLABª to

obtain the response of the GAL system as the

frac-tional protein expression of genes with one (f1p) and

two (f2p) binding sites Experiments were performed

on glucose and galactose as substrates to measure the

fractional b-galactosidase expression from the gene

LAC4 to quantify (f2p) and validate the developed

model The equilibrium dissociation constants,

co-operativity factor (m) and half-saturation constants

were obtained by fitting the steady-state protein

expressions measured experimentally at various

steady-state glucose and galactose concentrations

Parameter optimization was performed using the

opti-mization toolbox of MATLAB 7.5 of Math Works

Inc., MA, USA The parameter values are

summa-rized in Table 1

Results

Steady-state model response for the wild-type

strain of K lactis

Experiments were performed at different galactose

concentrations with glycerol as the background

medium and the steady-state b-galactosidase activity was measured It should be noted that the b-galacto-sidase activity represents the protein expression from

a GAL gene with two binding sites for KlGal4p, and its measurement was used to quantify f2p The dynamic profile of b-galactosidase expression for three different galactose concentrations is shown in Fig 2A The activity of b-galactosidase reached a steady value after approximately 12 h The steady-state value was obtained by averaging over the last three time points from the individual fed-batch exper-iment The steady-state values of the b-galactosidase activity of cells grown at different galactose concen-trations (0.002–0.44 m) are shown by squares in Fig 2B These steady-state points represent the means of three independent experiments at each galactose concentration The steady-state b-galactosi-dase activities are represented by the fractional protein expressions by normalizing with a maximum b-galactosidase activity observed in a mutant

K lactis strain lacking KlGAL80 The steady-state model was simulated to validate the protein expres-sion profiles with respect to galactose The full line

in Fig 2B shows the simulated fractional expression

of proteins for genes with two binding sites (f2p) which are also responsible for the synthesis of b-galactosidase The steady-state experimental data were used to estimate the model parameters, as indi-cated in Table 1 (see model development section in Supporting information for details) The fitted bind-ing constants were of a similar order of magnitude

as those reported for Gal4p binding to GAL genes in

S cerevisiae [20] It should be noted that the model

is able to predict the experimental steady-state response (full line in Fig 2B) The broken line depicts the model prediction of fractional protein expression corresponding to genes with one binding site It is clear from Fig 2B that genes with one binding site show a leaky expression of 9% of the maximum, even in the absence of galactose How-ever, the protein expression corresponding to genes with two binding sites is tightly regulated by the GAL switch, with basal expression levels of only 2% Furthermore, as shown in Fig 2B, the maximum expression in the wild-type strain in the presence of high galactose concentration is only 37% and 35% for one and two binding sites, respectively, relative

to the maximum possible expression when D2 is completely bound by KlGal4p2 [see Eqn (12)] This maximum value can be achieved by a strain lacking repressor KlGal80p The steady-state GAL response curves for one and two binding site genes (see Fig 2B) can be represented by the Hill equation:

Table 1 Parameter values used in the steady-state model.

Parametera

Kluyveromyces

Saccharomyces cerevisiae

[KlGal4p]t0 6.95 n M [13]b

[KlGal4p]t 32.6 n M Calculated 5.47 n M

KlGal80max 170–340 n M [13] b 1000 n M

a The parameter values reported were based on the K lactis cell

volume (23 fL).bThe parameter values reported in the reference

were based on the K lactis nucleus volume (2 fL) c The reported

parameter values are from [18,20].

f1p¼ ðGalÞ

1:12 Gal

ð Þ1:12þ 0:07ð Þ1:12

!

 0:375 ð16Þ

f2p¼ ðGalÞ

1:25 Gal

ð Þ1:25þ 0:1ð Þ1:25

!

The values of the Hill coefficients are close to unity

for genes with one and two binding sites, indicating a

typical Michaelis–Menten response It should be

noted that the half-saturation constants were 0.07

and 0.1 m for genes with one and two binding sites,

respectively

Figure 2C shows the variation of total KlGal1p (full

line), activated KlGal1p in the nucleus (broken line)

and total KlGal80p (dotted line) at different galactose

concentrations It is observed that total KlGal1p

changes from 777 to 11 000 nm when the medium

changes from NINR to a high galactose concentration

Of the total KlGal1p, 0.11% exists in the activated

state at low galactose concentrations, whereas 99% of

total KlGal1p is activated at high galactose concentra-tions Thus, it should be noted that, although KlGalpt shows a 14-fold change in its concentration on maxi-mal induction, the corresponding fold change in acti-vated KlGal1p is very high (approximately 13 000) Similarly, KlGal80p changes from 24 to 342 nm on induction The variation in these total regulatory pro-tein concentrations is caused by autoregulation The basal level of KlGal80p protein was sufficient for the system to exist in a repressed state in the absence of galactose Activated KlGal1p in the nucleus would be absent in NINR medium and its concentration corre-sponds to 1190 nm in the maximally induced state, representing a 10th of the total KlGal1p concentration Thus, the ratio of activated KlGal1p in the nucleus to total KlGal80p is 3.5, which is in the range of the three- to six-fold ratio observed in Anders et al [13] Furthermore, in the K lactis GAL system, the synthe-sis of activator protein KlGal4p is also autoregulated

by having one binding site in its gene promoter region

As a result, the total KlGal4p concentration changes from 10.0 to 20 nm (see Fig 2D), which is necessary

10 –2

10 0

10 2

10 4

10 6

Galactose ( M )

10 12 14 16 18 20

Galactose ( M )

10 −4 10 −3 10 −2 10 −1 10 0 10 1 0

0.1 0.2 0.3 0.4

Galactose ( M )

0 0.05 0.1 0.15 0.2 0.25 0.3

Time (h)

ηH = 1.12

ηH = 1.25

ηH = 1.12

Fig 2 (A) Time course of fractional b-galactosidase expression in a typical fed-batch experiment to obtain steady-state expression values for f2p in a Kluyveromyces lactis wild-type strain Diamonds, squares and circles represent experiments with galactose concentrations of 0.022, 0.077 and 0.16 M , respectively (B) Steady-state fractional protein expression with varying galactose concentrations for the K lactis wild-type strain The full line represents the predicted fractional protein expression for genes with two binding sites (f2p), and the broken line represents the expression levels for genes with one binding site (f1p) Experimental data for the expression of genes with two binding sites (f2p) are shown by filled squares (C) Model predictions of total KlGal80p, KlGal1p and nuclear activated KlGal1p concentrations with varying galactose concentration in a K lactis wild-type strain The full line represents total KlGal1p, the dotted line represents total KlGal80p and the broken line represents activated KlGal1p in the nucleus (D) Model prediction of total KlGal4p concentration with varying galactose concentra-tions in a K lactis wild-type strain.

for the GAL system to express at its protein expression

levels in the induced state

It is of interest to elicit the influence of the

nucleocy-toplasmic shuttling of KlGal1p on the behavior of the

switch The steady-state model is simulated by varying

the value of the distribution coefficient above and

below its nominal value (K = 8) On halving the value

of K from eight to four, a greater amount of the

indu-cer KlGal1p is available in the nucleus, which results

in an ultrasensitive response of protein expression

cor-responding to genes with two binding sites, together

with a decrease in the threshold value (broken line in

Fig 3A) The sensitivity as measured by the Hill

coef-ficient is 2.4, a nearly two-fold increase over the

wild-type sensitivity However, doubling the value of the

shuttling constant to 16 shuts off the expression

because of a lack of the inducer in the nucleus (dotted

line in Fig 3A) Thus, the distribution coefficient is a

key parameter in the operation of the GAL switch

The steady-state model has been evaluated for

regu-latory designs of the GAL system It is of interest to

ascertain the role of autoregulation in the synthesis of

activator protein KlGal4p in K lactis as the synthesis

of the corresponding activator in S cerevisiae is not

autoregulated Figure 3B shows that, on constitutive

expression of KlGal4p at a value corresponding to the

uninduced concentration of KlGal4p in the wild-type,

the system response shows a two-fold reduction in expression levels (broken line) This reduction in gene expression is a result of insufficient concentration of the activator, as autoregulation of KlGAL4 in the wild-type increases the availability of KlGal4p by

two-to five-fold [9,15] However, when KlGAL4 is

constitu-10 −4 10 −3 10 −2 10 −1 10 0 10 1

10 −4 10 −3 10 −2 10 −1 10 0 10 1

0 0.2 0.4 0.6 0.8 1

f2p

0 0.1 0.2 0.3 0.4

f2p

0 0.1 0.2 0.3 0.4

f2p

A

B

C

Fig 3 (A) Effect of the distribution coefficient K on the GAL

switch: fractional protein expression of genes with two binding

sites (f2p) for three different K values Broken line, K = 4; full line,

nominal K = 8; dotted line, K = 16 (B) Effect of autoregulation of

KlGal4p: comparison of model prediction between the wild-type

(full line) and the strain lacking autoregulation of KlGal4p (broken

line) The constitutive expression of KlGal4p was maintained at its

basal level of 6.95 n M (C) Fractional protein expression for two

binding site genes for the following conditions (a) KlGAL80 alone

was not autoregulated (dashed–dotted line) and expressed

constitu-tively to its maximum value The regulated bifunctional protein

KlGal1p was not sufficient to interact with excessive repressor,

leading to the complete repression of the GAL system (b) Both

KlGAL80 and KlGAL1 were autoregulated, representing the

wild-type strain (solid line) (c) Both KlGAL80 and KlGAL1 were not

autoregulated (dotted line) and constitutively expressed to the

maximum expression achieved under induced conditions As both

regulatory proteins were in excess and the KlGal1p concentration in

the nucleus was three- to six-fold higher than the repressor

KlGal80p concentration, the switch is able to function normally,

yielding protein expression levels similar to those of the wild-type.

(d) KlGAL1 was not autoregulated and was constitutively expressed

to its maximum concentration (broken line) In this case, the

auto-regulation of the repressor KlGAL80 results in a low KlGal80p

con-centration, leading to the activation of the switch at low galactose

concentrations.

tively expressed at 20 nm, which corresponds to a

KlGal4p concentration at the induced level, the

frac-tional protein expression is similar to that of the

wild-type response Model simulations suggest that, in this

case, the excess KlGal4p binds to the free basal

KlGal80p, and thus the fractional protein expression

remains similar to the wild-type expression (results not

shown) The steady-state model was further simulated

to determine the effect of autoregulation of KlGAL1

and KlGAL80 Figure 3C shows the response when the

synthesis of both regulatory proteins was not

autoreg-ulated (dotted line), and they were expressed

constitu-tively at their maximum concentration, which

corresponds to the maximally induced concentration in

the wild-type strain It should be noted that the

sensitivity of the response of such a mutant strain to

galactose is higher than the sensitivity observed in the

wild-type response (see Fig 3C, full line) However,

when the synthesis of the repressor KlGAL80 alone is

not autoregulated and is constitutively expressed at

wild-type levels (340 nm), the regulated amount of

KlGal1p is insufficient to interact with the high levels

of KlGal80p in the nucleus, leading to the inhibition

of the GAL switch and thereby reducing expression

levels to zero (broken–dotted line in Fig 3C) When

KlGAL80 is autoregulated and KlGAL1 is expressed

constitutively, the GAL switch is induced at a lower

galactose concentration and shows wild-type

expres-sion levels at a high galactose concentration (broken

line in Fig 3C) Thus, it is observed that, for the GAL

system to function normally, the autoregulation of

KlGAL80is essential if KlGAL1 is autoregulated

Steady-state model response for a K lactis

mutant strain lacking GAL80

The steady-state model for the wild-type strain can be

validated by predicting the behavior of a mutant strain

lacking the repressor gene KlGAL80 The expression of

GAL genes of such a mutant is independent of

galac-tose concentration However, glucose represses the

transcriptional activator KlGal4p, thereby inhibiting

the expression of GAL genes To evaluate the effect of

glucose on GAL gene expression, experiments were

performed in a fed-batch mode operated at different

average glucose concentrations The fractional protein

expressions were measured as the steady-state

b-galac-tosidase concentration relative to the maximum

b-galactosidase concentration obtained in glycerol

medium A typical experimental run that aimed to

maintain a constant glucose concentration of 57 ±

4 mm is shown in Fig 4A The expression of LAC4,

the gene for b-galactosidase expression with two

binding sites for KlGal4p, is also shown in Fig 4A The cells were grown in glycerol medium until the absorbance at 600 nm (A600) attained a value between 0.8 and 1 before the addition of glucose, where the ini-tial protein expression (i.e at t = 0) was 48% of the maximum value The enzyme profile indicates that glucose represses protein expression and reaches a steady-state value of about 28% of the maximum about 6 h after glucose addition Similar experiments were performed to obtain steady-state protein expres-sions at different average glucose concentrations in the range 0–57 mm

In order to predict the response of the mutant strain lacking KlGal80p, all interactions pertaining to KlGal80p were eliminated in the wild-type model This subsystem is shown in Fig 1B Although it is known that glucose inhibits the synthesis of KlGal4p, the mechanism of repression is not clearly understood Equation (14), which represents the effect of autoregu-lation on KlGAL4 expression, is modified to reflect the inhibition by glucose using a Hill equation:

½KlGal4pt ¼ ½KlGal4pt0 1 þ f1p q  K

gg i

Kgg

i þ Glcgg

!!

ð18Þ

It should be noted that, in the absence of KlGal80p, GAL gene expression is negatively dependent only on glucose Ki represents the inhibitory constant on glu-cose and gg represents the Hill coefficient Equations (S-39)–(S-52) in Supporting information were solved

to relate the fractional protein expression to varying glucose concentrations The steady-state protein expressions at different glucose concentrations were obtained and are shown by the squares in Fig 4B The experimental data were used to identify the half-saturation constant Ki and the Hill coefficient gg in Eqn (18), which were estimated to be 1.13 mm and 1.3, respectively Except for Kiand gg, all other model parameters used to predict the mutant behavior are identical to those of the wild-type (see Table 1) Fig-ure 4B shows a comparison between the experimental data and model simulations It can be seen that the protein expressions are leaky for GAL genes with one and two binding sites (18% and 28%, respectively), even at high glucose concentrations (> 104lm), thus indicating partial repression However, the maximum expression in the absence of glucose demonstrated that genes with one binding site could express only 73% of the maximum, whereas genes with two binding sites could express completely (see Fig 4B) This implies that the concentration of the activator KlGal4pt is limiting, even in the absence of glucose The inhibitory

effect of glucose on the profiles of protein expression

for one and two binding sites was quantified using a

Hill equation, accommodating the leaky expression, as

follows:

f1p¼ 0:18 þ ½K1p

1:67

½K1p1:67þ ½Glc1:67

!

 0:55 ð19Þ

f2p¼ 0:28 þ ½K2p

2

½K2p2þ ½Glc2

!

 0:7 ð20Þ

where K1p and K2p are the half-saturation constants

for genes with one and two binding sites, whose values

were estimated to be 0.82 and 1.33 mm, respectively

The values of the Hill coefficients indicate that the

inhibitory response is ultrasensitive

The steady-state model of the K lactis mutant strain

lacking KlGAL80 was further used to evaluate the

fractional transcriptional (fi, i = 1, 2) and protein

expressions (fip, i = 1, 2) for genes with one and two binding sites at different total KlGal4p (KlGal4pt) concentrations in the absence of glucose Total KlGal4p was varied by independently changing KlGal4pt0 and setting the glucose concentration to zero in Eqn (18) [or Eqn (S-49) in Supporting infor-mation] Figure 4C shows the fractional transcriptio-nal expression at various KlGal4pt concentrations obtained by the solution of Eqns (S-39)–(S-52) in Supporting information It can be observed from Fig 4C that the transcriptional responses were ultrasen-sitive for genes with both one and two binding sites, with Hill coefficients of 1.89 and 3.19, respectively The genes with two binding sites were more sensitive than those with one binding site as a result of the effect of cooperativity The half-saturation constants (K0.5) were determined to be 0.024 and 0.012 lm for genes with one and two binding sites, respectively This implied that the expression of genes with one binding site required

a larger amount of total KlGal4p concentration,

0 0.1 0.2 0.3 0.4 0.5 0.6

Time (h)

10 0 −4 10 −3 10 −2 10 −1 10 0 10 1 0.2

0.4 0.6 0.8 1

KlGal4p t (μM )

10 0 −4 10 −3 10 −2 10 −1 10 0 10 1 0.2

0.4 0.6 0.8 1

KlGal4p t (μM )

f1p

f2p

0 0.2 0.4 0.6 0.8 1

Glucose (μM )

f1p

f2p

ηH = 3.19

ηH = 1.89

ηH = 1.64

ηH = 2.57

ηH = 2.04

ηH = 1.67

Fig 4 (A) Time course of fractional b-galactosidase expression in a mutant strain lacking KlGAL80 A typical fed-batch operation aimed at maintaining an average steady-state glucose concentration of 57 m M (full line) and precultured on glycerol (30 gÆL–1) for 12–16 h until

A600= 0.8–1.0 was achieved Triangles represent glucose concentration, circles represent fractional protein expression as measured by b-galactosidase expression and broken lines represent glucose concentrations (within ±10%) (B) Steady-state response of Kluyveromy-ces lactis mutant strain lacking GAL80 Comparison of the experimental data with the model prediction for different average steady-state glucose concentrations Full and broken lines represent model predictions for genes with one (f1p) and two (f2p) binding sites, respectively, and circles with error bars represent the experimental data of fractional b-galactosidase expression (C) Model predictions for fractional tran-scriptional expression of genes with one (full line, f1) and two (broken line, f2) binding sites for varying KlGal4pt concentration in a K lactis mutant strain lacking KlGAL80 (D) Model predictions for fractional protein expression of genes with one (full line, f1p) and two (broken line,

f2p) binding sites for varying KlGal4ptconcentration in a K lactis mutant strain lacking KlGAL80.