A kinetic model of the branch-point between the methionine
and threonine biosynthesis pathways in
Arabidopsis thaliana
Gilles Curien, Ste
´
phane Ravanel and Renaud Dumas
Laboratoire de Physiologie Cellulaire Ve
´
ge
´
tale DRDC/CEA-Grenoble, France
This work proposes a model of the metabolic branch-point
between the methionine and threonine biosynthesis path-
ways in Arabidopsis thaliana which involves kinetic compe-
tition for phosphohomoserine between the allosteric enzyme
threonine synthase and the two-substrate enzyme cysta-
thionine c-synthase. Threonine synthase is activated by
S-adenosylmethionine and inhibited by AMP. Cystathio-
nine c-synthase condenses phosphohomoserine to cysteine
via a ping-pong mechanism. Reactions are irreversible and
inhibited by inorganic phosphate. The modelling procedure
included an examination of the kinetic links, the determin-
ation of the operating conditions in chloroplasts and the
establishment of a computer model using the enzyme rate
equations. To test the model, the branch-point was recon-
stituted with purified enzymes. The computer model showed
a partial agreement with the in vitro results. The model was
subsequently improved and was then found consistent with
flux partition in vitro and in vivo. Under near physiological
conditions, S-adenosylmethionine, but not AMP, modulates
the partition of a steady-state flux of phosphohomoserine.

flux in the systems studied previously have not been
considered.
The present paper proposes a computer model of the
branch-point between the methionine and threonine
biosynthesis pathways in Arabidopsis thaliana (Fig. 1). The
computer model was validated in vitro andusedtoexamine
the branch-point kinetics in detail and to obtain insights into
the kinetic controls of methionine and threonine synthesis in
plants.
The branch-point between the methionine and threo-
nine biosynthesis pathways (Fig. 1) involves a two-substrate
enzyme (cystathionine c-synthase, CGS) and an allosteric
enzyme (threonine synthase, TS). These enzymes compete
kinetically for their common substrate, phosphohomoserine
(Phser), in chloroplasts [9–11]. CGS catalyses the formation
of cystathionine, the precursor of methionine, by condensa-
tion of Phser and cysteine. The reaction follows a ping-pong
mechanism [12]. In the competing branch, TS catalyses the
formation of threonine from Phser. In plants, TS is sti-
mulated in vitro by S-adenosylmethionine (AdoMet) in an
allosteric manner [10,13–16]. AdoMet is a direct derivative
Correspondence to G. Curien, Laboratoire de Physiologie Cellulaire
Ve
´
ge
´
tale DRDC/CEA-Grenoble, 17 rue des Martyrs,
38054 Grenoble Cedex 9, France.
Fax:+33438785091,Tel.:+33438782364,
E-mail:

activation) and AMP (inhibition) and the concentration
ranges exhibiting this effect are unknown. We also ignore
how cysteine, the second substrate for CGS, modulates
Phser distribution and to what extent changes in the
concentration of the inhibitor P
i
alters the Phser flux
partition. Due to the numerous interactions in the system, a
mathematical model of the branch-point could be instru-
mental in finding answers to these questions. Such a model
could be built without any assumptions as detailed enzyme
rate equations and kinetic parameters are known.
In this paper we first describe the procedure followed to
build a mathematical model of the branch-point. The model
was then validated in vitro. For this purpose, the branch-
point was reconstituted with purified enzymes and partition
of a constant flux of Phser was measured as a function of the
concentration of AdoMet under conditions as close as
possible to those thought to prevail in vivo in the chloroplast
of an illuminated leaf cell. The model was subsequently
improved and used to calculate the sensitivity of the fluxes
to the different input variables using the framework of
metabolic control analysis. The computer model was finally
used to examine the consequences of TS allosteric activa-
tion, P
i
inhibition and CGS ping-pong mechanism on the
branch-point properties. The analysis provides insights into
the mechanisms of control of methionine and threonine
syntheses in plants.

in vitro [16,17]; (e) P
i
inhibits the activity of both CGS and
TS [12,17]; (f) the enzymatic products cystathionine and
threonine do not inhibit the activities of CGS [9,12] and TS
[13,16] and (g) finally and importantly, Phser is not an
allosteric effector of upstream enzymatic activity. Indeed,
the concentration of Phser was shown to vary to a large
extent (20-fold increase) in transgenic plants with reduced
levels of CGS [23]. Therefore, the concentration of Phser
Fig. 1. Phser branch-point in the aspartate-derived amino acid biosyn-
thetic pathway in plants. In plants and microorganisms, aspartate
serves as a precursor for the synthesis of lysine, methionine and thre-
onine. Threonine is a precursor for isoleucine synthesis and methionine
is a direct precursor of S-adenosylmethionine (AdoMet). In plants, the
branching between the methionine and threonine biosynthesis path-
ways occurs at the level of phosphohomoserine (Phser) and involves
cystathionine c-synthase (CGS) and threonine synthase (TS). CGS is a
two-substrate enzyme that catalyses the condensation of Phser and
cysteine. The production of the aspartate-derived amino acid in plants
is thought to be controlled by numerous allosteric controls identified
in vitro and represented in the figure as dotted lines. The dashed square
indicates the limits of the Phser branch-point system analysed in the
present paper. In microorganisms branching between the methionine
and threonine biosynthesis pathways occurs at the level of homoserine
and involves different enzymes and different allosteric patterns [8].
4616 G. Curien et al. (Eur. J. Biochem. 270) Ó FEBS 2003
depends exclusively on the flux of Phser and on CGS and TS
activity. As a consequence it is possible to model the branch-
point kinetics if one knows the CGS and TS rate equations,

,thatis0.7l
M
(on a 52-kDa monomer mass
basis). Such data are lacking for TS, however, the ratio
[CGS]/[TS] can be calculated as follows: ELISA assays were
carried out using rabbit antibodies raised against the
recombinant proteins [12,14] and purified proteins as
standards. We measured that an extract of soluble proteins
from Arabidopsis contains 1500 ng TS and 210 ng CGS per
mg protein (data not shown), corresponding to a [CGS]/
[TS] ratio of about 1/7. Thus, [TS] is approximately 5 l
M
in
the chloroplast stroma (7 · 0.7 l
M
). The value of the flux of
Phser in vivo is unknown for Arabidopsis and thus data from
Lemna [30] were used. In this plant, cystathionine and
threonine flux rates are about 1 and 7.9 nmol per frond per
doubling time, respectively. As Phser has no other fate in
plant than the synthesis of cystathionine and threonine [31],
Phser flux rate is about 8.9 nmol per frond per doubling
time. With a doubling time of 41 h [30], a mean frond
cellular volume of 0.509 lL [32] and assuming that Phser is
restricted to the chloroplast (9.5% of cellular volume [33]),
where it is produced and used, a value of 1 l
M
Æs
)1
can be

app
catCGS
¼
k
catCGS
1 þ
K
Cys
mCGS
Â
Cys
Ã

ð2Þ
K
app
mCGS
¼
K
Phser
mCGS
1 þ
K
Cys
mCGS
Â
Cys
Ã

Á 1 þ

k
appCys
catCGS
Á½CGSÁ½Cys
K
appCys
mCGS
þ½Cys
ð4Þ
Expressed in this form, apparent kinetic parameters k
appCys
catCGS
and K
appCys
mCGS
are defined as functions of [Phser] and [P
i
]by
Eqn (5) and Eqn (6), respectively:
k
appCys
catCGS
¼
k
catCGS
1 þ
K
Phser
mCGS
Â

P
i
Ã
K
P
i
iCGS

ð6Þ
TS catalytic rate depends hyperbolically on the concen-
tration of Phser at any concentration of AdoMet [15]
(Eqn 7).
m
Thr
¼
½TSÁk
app
catTS
Á½Phser
K
app
mTS
þ½Phser
ð7Þ
Where, [TS] is TS monomer concentration, k
app
catTS
is the TS
apparent catalytic constant and K
app

½AdoMet
2
K
1
K
2
0
@
1
A
ð8Þ
K
app
mTS
¼
250 Á
1þ
½AdoMet
0:5
1þ
½AdoMet
1:1
1 þ
½AdoMet
2
140
0
B
@
1

iTS
is
the TS inhibition constant for P
i
. K
Pi
iTS
is independent of the
concentration of AdoMet (G. Curien and R. Dumas,
unpublished results). Numerical values in the expression of
K
app
mTS
(expressed in l
M
) correspond to groups of kinetic
constants explaining the effect of AdoMet when present at
Ó FEBS 2003 An Arabidopsis phosphohomoserine branch-point model (Eur. J. Biochem. 270) 4617
low concentrations (< 2 l
M
[15]). Values of the kinetic
parameters for CGS and TS are summarized in Table 1.
The mechanism of inhibition of TS by AMP is unclear,
and some kinetic parameters are lacking. However, as will
be shown below (Results), the AMP effect on partition is
negligible under physiological conditions and for this reason
the inhibition was not taken into account in the present
model.
A simple mathematical procedure was developed to
simulate the steady-state of a two-enzyme branch-point [2].

and TS Michaelis–Menten equations (Eqns 1 and 7)
yielding the following quadratic equation (Eqn 11).
½Phser
2
ðJ
Phser
À k
app
catCGS
À k
app
catTS
Þ
þðK
app
mCGS
ðJ
Phser
À k
app
catTS
Þ
þ K
app
mTS
ðJ
Phser
À k
app
catCGS

purified threonine deaminase and commercial lactate dehy-
drogenase. Threonine deaminase transforms threonine into
oxobutyrate that is further reduced by lactate dehydroge-
nase in the presence of NADH. Cystathionine flux was
measured with cystathionine b-lyase and lactate dehydro-
genase. Cystathionine b-lyase transforms cystathionine into
homocysteine and pyruvate. Pyruvate is reduced by lactate
dehydrogenase in the presence of NADH. The achievement
of the steady-states can be followed with a spectrophoto-
meter (decrease in absorbance at 340 nm). Steady-state
fluxes can be determined in the two branches in independent
reactions containing either threonine deaminase or cysta-
thionine b-lyase mixed with homoserine kinase, CGS, TS
and lactate dehydrogenase.
Experiments were carried out in a thermoregulated quartz
cuvette (30 °C) and in a total volume of 150 lL. Twenty
microlitres of protein mix (0.15 l
M
homoserine kinase,
0.7 l
M
CG, 5 l
M
TS, 2 l
M
lactate dehydrogenase, and 2 l
M
threonine deaminase or 0.7 l
M
cystathionine b-lyase) were

), this
reaction contributed significantly to the production of
pyruvate under our conditions, where the concentrations of
cysteine and cystathionine b-lyase are high. Thus, a correc-
tion had to be made to obtain the actual flux of cystathionine.
The side reaction of cystathionine b-lyase exhibited first-
order kinetic behaviour with respect to cysteine concentra-
tion under our conditions (not shown). The rate was
calculated with the following relation, v ¼ k.[Cystathionine
b-lyase] [Cys] with k ¼ 2.2 10
)4
l
M
)1
Æs
)1
. The concentration
of cysteine at each time point was estimated to be equal to the
initial concentration of cysteine minus the concentration of
NAD
+
at time, t. A small error is made in this calculation as
a consequence of the time delay in the enzymatic chain.
Subtraction of the rate of the cystathionine b-lyase side
reaction from the total rate of NADH oxidation yielded the
actual rate of cystathionine production.
Results
Modelling procedure
In order to model the branch-point between the methionine
and threonine biosynthesis pathways in Arabidopsis the

2500 l
M
K
1
K
2
73 l
M
2
K
iCGS
Pi
2000 l
M
K
iTS
Pi
1000 l
M
4618 G. Curien et al. (Eur. J. Biochem. 270) Ó FEBS 2003
Secondly, as the model aimed to describe a physiological
situation, we characterized the in vivo operating conditions
of the system in terms of input flux, enzyme concentrations
and external metabolite concentrations (AdoMet, cysteine,
P
i
, AMP). We chose to consider the metabolic state of an
illuminated chloroplast leaf cell as many data were available
for this state in Arabidopsis or other plants that can be
considered equivalent. We also determined the in vivo

coupled to lactate dehydrogenase. Under these conditions,
CGS and TS were operating in vitro at physiological
concentration, with Phser concentration set by the system
and in the presence of the reaction products, neighboring
enzymes and salts (K
+
and Mg
2+
). Phser flux had to be
set at one third of its estimated value in the chloroplast of
an illuminated leaf cell to minimize substrate consump-
tion. In addition, the concentration of cysteine was set at
250 l
M
rather than 15 l
M
(physiological concentration).
Indeed, it was difficult to achieve a constant concentration
of cysteine. However, as will be detailed later, CGS
velocity was saturated by cysteine in these conditions and
J
cystathionine
was not affected by the consumption of
cysteine. The time courses of the reactions in the presence
of 20 l
M
AdoMet are displayed in Fig. 2A, showing that
the fluxes reached a steady-state in about 600 s. Results in
Fig. 2A confirmed that CGS was saturated by cysteine
throughout the time course of the reactions, otherwise

Phser flux, 0.3 l
M
Æs
)1
;AdoMet,20l
M
; cysteine, initial concentration,
250 l
M
;P
i
,10m
M
;CGS,0.7l
M
;TS,5l
M
. The rate of NADH oxi-
dation at each time point was calculated from the absorbance time
curves (A
340
)withaDt of 20 s. (B) Steady-state flux of cystathionine
(m) and threonine (d) in the reconstituted branch-point as a function
of the concentration of AdoMet. Experimental conditions were as in
(A). The total flux (h) is the sum of the fluxes of cystathionine and
threonine at steady-state. The experimental points were fitted to Hill
equations. The thick curves are flux values calculated with the com-
puter model using CGS and TS mechanistic equations. Input variables
were set at the value they have in the experiment. (C) The experimental
results in (B) were compared with the predictions using the improved

increasing as the concentration of AdoMet was
increased. Half changes in J
cystathionine
and J
Thr
are
obtained for a concentration in AdoMet of about
15 l
M
, i.e. for a value close to the estimated cellular
concentration.
In order to determine whether the properties of isolated
CGS and TS, as defined by their mechanistic equations
(Eqns 1–9, Materials and methods), could explain the
observed behaviour in Fig. 2B, the computer model
described in the Materials and methods was used to
calculate J
cystathionine
and J
Thr
as a function of the concen-
tration of AdoMet with the remaining input variables set at
the experimental values used to obtain Fig. 2B. As shown in
Fig. 2B, the experimental fluxes depend on the concentra-
tion of AdoMet in a manner similar to that predicted by the
computer model. [The small bumps in the theoretical curves
barely discernable at low AdoMet concentration originate
from the complex dependence of TS K
m
for Phser on

AdoMet binding curve was about three and only about two
for the enzyme–substrate/AdoMet binding curve. As a
consequence, a new equation had to be derived for AdoMet
binding to TS under the present conditions where the
enzyme-substrate complex concentration was low. For this
purpose, it was first observed that, when TS operates at the
branch-point, the calculated concentration of Phser ranged
from 1000 l
M
(no AdoMet) to 5 l
M
(100 l
M
AdoMet)
(Fig. 4C). Under these conditions we observed graphically
(not shown) that TS catalytic rate at the branch-point is
approximately first-order with respect to Phser concentra-
tion at any AdoMet concentration. So the complicated
mathematical expression of TS velocity (Eqns 7–9) could be
simplified to a linear equation for Phser concentration
(Eqn 12).
m
Thr
¼½TS
k
TS
1 þ
½P
i


TS
(Eqn 13).
k
TS
¼ 5:4 Â 10
À5
þ
6:210
À3
½AdoMet
2:9
32
2:9
þ½AdoMet
2:9
ð13Þ
When the branch-point behaviour was simulated with Eqns
(12 and 13) instead of the TS mechanistic equations
(Eqns 7–9) the computer model was in much better
agreement with the experimental results (Fig. 2C). These
results confirm that TS velocity is first-order with respect to
Phser concentration. Moreover the agreement indicates that
the branch-point behaviour is fully explained by the
individual enzyme’s kinetic properties. More complex
phenomena such as protein–protein interactions, need not
be invoked to explain the behaviour of the system in
response to changes in AdoMet concentration.
AMP inhibition does not affect partition
As a kinetic mechanism for the inhibition of TS activity by
AMP is unclear, and kinetic parameters are lacking, it was

represent 11% and 89% of the flux of Phser,
respectively. The numerical model using the simplified TS
equation (Fig. 2C) or the in vitro model give a value of 20–
30% for J
cystathionine
(and 70–80% for J
Thr
)at20l
M
AdoMet. Considering that flux partition is highly sensitive
to the concentrations of AdoMet and of the competing
enzyme concentrations (see later) and thus to small errors in
the estimation of their physiological values, the consistency
is satisfying. The in vitro and numerical models are
consistent with J
Thr
being larger than J
cystathionine
in the
metabolic condition of a leaf cell. Also, a Phser concentra-
tion of about 80 l
M
in A. thaliana leaf chloroplast can be
derived from the measurements in planta, in good agreement
with the model which predicts a value of about 128 l
M
.The
Phser content in A. thaliana leaves is about 6.6 nmolÆg
)1
fresh weight [23]. The concentration was calculated assu-

operating point in quantitative terms, the results in Fig. 3
were used to calculate the flux response coefficients as
defined in the framework of metabolic control analysis
[35–40]. The results are displayed in Table 3. The changes
in flux and their sensitivities are explained by variations in
the concentration of Phser. For this reason, the concen-
tration of Phser calculated for each of the situations
analysed are indicated in Fig. 4.
From the results in Table 3 one can verify that the
summation relationship [35] between control coefficients is
satisfied in the three enzyme system, thus, showing an
internal consistency of the model. Indeed
R
Jcystathionine
CGS
þ R
Jcystathionine
TS
þ R
Jcystathionine
JPhser
¼ 1
(R
Jcystathionine
JPhser
is the homoserine kinase control coefficient
over cystathionine flux). The same relation is obtained
for J
Thr
.

Cys 15 l
M
0.18 )0.03
P
i
10 m
M
0.06 )0.007
[CGS] 0.7 l
M
0.89 )0.1
[TS] 5 l
M
)0.7 0.11
J
Phser
1 l
M
Æs
)1
0.81 1.03
4622 G. Curien et al. (Eur. J. Biochem. 270) Ó FEBS 2003
Next, we analysed the sensitivity of the flux of cystathi-
onine and threonine to P
i
, cysteine, AdoMet, CGS and TS
concentrations as well as to Phser input flux in the three
enzyme system.
Sensitivity to P
i

(Fig. 4A) is due to the competitive
nature of the inhibition.
Sensitivity to cysteine. An advantage of the computer
model is the possibility to vary the concentration of cysteine
around the estimated physiological concentration (15 l
M
).
This was not possible in the experiments used for Fig. 2B
(see above). Table 3 indicates that the flux response
coefficients for the cystathionine and threonine fluxes at
15 l
M
cysteine are low (0.18 and )0.03, respectively). Also,
Fig. 3B shows that when the concentration of cysteine is
increased above 15 l
M
, the fluxes are modified only slightly.
This result indicates that the partition experimentally
determined in Fig. 2B at 20 l
M
AdoMet would not have
been different if cysteine concentration had been set at
15 l
M
instead of 250 l
M
. Figure 3B also explains why
cysteine consumption left J
cystathionine
unaffected in the

more sensitive to AdoMet than J
Thr
for AdoMet at 20 l
M
.
These calculations highlight an asymmetry in the branch-
point. J
Thr
and J
cystathionine
are not equivalent with respect to
changes in the concentration of AdoMet.
Sensitivity to the concentration of CGS and TS. In the
model, an increase or a decrease in the concentration of one
of the branch-point enzymes promotes an increase or a
decrease in the flux in the corresponding branch and a
quantitatively equivalent but opposite change in the flux in
the other branch (Fig. 3D,E). However, as observed for
AdoMet, and as a consequence of the flux imbalance, an
asymmetry in the response is observed. As indicated in
Table 3, J
Thr
presents a low sensitivity to changes in the
concentration of the enzymes (for TS % 5 l
M
and
CGS % 0.7 l
M
). By contrast, J
cystathionine

Figure 4F indicates that the Phser steady-state concentra-
tion depends in a quasi-linear manner on J
Phser
.Usinga
larger scale for the abscissa (not shown) would reveal an
upward curvature. Indeed, [Phser]
steady-state
increases hyper-
bolically and reaches infinity as J
Phser
gets closer to the sum
of CGS and TS maximal catalytic rates. In the next part this
response of the system to J
Phser
will be related to the enzyme
individual properties, but the important point here is the
following: Fig. 3F indicates that, as J
Phser
is increased and
the concentration of Phser increases (Fig. 4F), the outflows
are modified in the same sense and to a similar extent. The
model thus predicts that changes in Phser flux in the range
0–2 l
M
Æs
)1
taking place with no changes in the other input
variables, would not modify partition. In other words,
changes of the output fluxes are coordinated in these
conditions. Note that as the simulations indicate that

Phser concentrations under physiological conditions. These
two features explain the response of the system to the
modifications of the flux of Phser as indicated in Fig. 3F.
Consequences of CGS ping-pong kinetic mechanism
on the branch-point kinetic properties
As CGS follows a ping-pong mechanism, its specificity
constant for Phser, in marked difference with a sequential
mechanism, does not depend on the second substrate
(cysteine) concentration (Eqns 2 and 3). Therefore, as the
concentration of cysteine is increased, CGS velocity curve
Ó FEBS 2003 An Arabidopsis phosphohomoserine branch-point model (Eur. J. Biochem. 270) 4623
for low concentrations of Phser is not modified and thus
remains similar to the TS velocity curve as indicated in
Fig. 5.
Another property of the ping-pong mechanism is the
hyperbolic dependence of the apparent K
m
for one substrate
on the concentration of the other substrate (Eqns 3 and 6).
This explains why the flux of cystathionine is saturated for
low concentrations of cysteine (Fig. 3B). Indeed, as the
concentration of Phser is low in the physiological conditions
considered, the K
m
for cysteine is low. For example, at
80 l
M
Phser the apparent K
m
for cysteine is 2.5 l

K
m
for Phser and decreases the apparent K
m
for cysteine
(Eqns 3 and 6). Therefore, in the physiological context
considered, CGS operates in the first-order range with
respect to Phser (Fig. 5), but is virtually saturated by
cysteine in the same range of concentration (Fig. 6).
Time-constant of the branch-point system
Physiological changes in the concentration of P
i
do not
modify the partition (Fig. 3A). However, the presence of P
i
considerably affects the dynamics of the system. Indeed, in
the presence of 10 m
M
P
i
, the model indicates that the
catalytic rates of CGS and TS are divided by a factor of 6
and 11, respectively, compared to a situation without P
i
.
One can therefore calculate that the time constant [41] of the
branch-point system (s) is about 20 times higher in the
presence of 10 m
M
P

that the allosteric interaction had a function in the control of
Phser partition in vivo. However, no experimental results,
whether in vivo or in complete systems in vitro, supported
this assumption [31]. As TS activity is inhibited by AMP
in vitro some authors denied a physiological importance for
the allosteric activation of TS by AdoMet [16]. In addition
to this controversy, the quantitative influences of the
inhibitor phosphate and cysteine (CGS second substrate)
on the branch-point kinetics have never been considered.
In order to solve these questions we established a
computer model of the branch-point and validated it
in vitro. A satisfying but imperfect agreement of the
predictions with the experimental results lead us to improve
the model with a simplification of the TS mechanistic
equation. The improved version of the numerical model was
in a very good agreement with the in vitro results and
consistent with threonine and cystathionine syntheses
in vivo. Our results show that although AMP is an inhibitor
of TS in vitro [16,17], this general metabolite has no effect on
the partition of the flux of Phser in the branch-point when
present at a physiological concentration. This result thus
Fig. 6. CGS velocities calculated as a function of cysteine concentration.
P
i
concentration is 10 m
M
and Phser concentration is as indicated. The
dotted vertical line indicates the physiological operating condition (leaf
chloroplast).
Fig. 5. Comparison of the kinetic efficiencies of CGS and TS. CGS and

catTS
¼ 3.02 s
)1
. The dotted vertical line indicates the physiolo-
gical operating condition (leaf chloroplast).
4624 G. Curien et al. (Eur. J. Biochem. 270) Ó FEBS 2003
strongly suggests that TS allosteric activation by AdoMet is
physiologically significant. Our results validate the qualit-
ative model in Fig. 1 and strongly suggest that there is
indeed a single allosteric control at the Phser branch-point
in plants. The concentration of AdoMet determines the
partition of flux between the cystathionine and threonine
synthesis pathways. However, the model shows that, as a
consequence of an imbalance in the partition of Phser flux
(threonine flux is much more important than cystathionine
flux), the cystathionine flux (but not threonine flux) is highly
sensitive to changes in AdoMet concentration. The interac-
tion of AdoMet with TS is therefore consistent with
AdoMet being part of a negative feedback mechanism for
methionine synthesis, as an increase in AdoMet concentra-
tion decreases cystathionine flux in a highly sensitive
manner. Nevertheless, a definitive answer concerning the
function of the allosteric activation of TS can still not be
given. Indeed, in the three-enzyme system of the present
study (in vitro and in the computer model) homoserine
kinase is not inhibited by its product [22] and therefore
necessarily controls the overall flux (J
cystathionine
+ J
Thr

experiments [31] failed to distinguish between the two
scenarios, a computer model taking into account the
properties of the enzymes upstream the Phser branch-point
is required to solve this question definitively.
An issue of interest with respect to flux partition at a
branch-point concerns the relative degree of dependence of
the diverging pathways. The model shows that cystathio-
nine flux is sensitive to threonine flux but that the reverse is
not true. Therefore, the model suggests that threonine flux is
relatively independent of what happens on the cystathionine
side. The Phser branch-point combines the divergence of
two fluxes (fluxes of cystathionine and threonine) with the
convergence of two fluxes (fluxes of Phser and cysteine).
Interestingly, the properties of CGS are such that the flux of
cystathionine and, as a consequence the flux of threonine,
present a low sensitivity to the CGS second substrate
cysteine. According to the model, a large increase in the
concentration of cysteine, to sustain a larger demand for
glutathione for example, may occur without major effects
on the fluxes of cystathionine and threonine. CGS proper-
ties thus confer independence between the cysteine and the
cystathionine/threonine fluxes. The nature of the kinetic
mechanism of CGS (a ping-pong mechanism) is particularly
favourable to such an effect. For a sequential mechanism
(ternary complex mechanism) the apparent K
m
for one
substrate does not stringently depend on the concentration
of the second substrate. The same performance with a two-
substrate enzyme following a sequential mechanism would

substrate isocitrate whereas the competing enzyme (isocitrate
lyase) exhibits first-order kinetics for this substrate concen-
tration. This organization allows the isocitrate branch-point
to operate as a switch. Upon growth on acetate, the flux of
isocitrate increases and isocitrate dehydrogenase is inhibited
by phosphorylation. The flux through isocitrate lyase thus
increases 300-fold, switching on the glyoxylate shunt. The
Phser branch-point with its two enzymes operating in the
first-order range with respect to the common substrate
concentration cannot display such a switch property, but
instead allow flux coordination. Outflows may increase to a
similar extent as Phser flux increases. Such a change in the
input flux with the other variables left unchanged may
correspond to an increase in carbon supply in vivo (upon
increase in light intensity for example).
The extent to which the Phser branch-point can serve as a
model for the other two-partner branch-points is hard to
establish. It would be necessary to determine the physiol-
ogical operating conditions and obtain kinetic data of
physiological significance before a valid comparison is
possible. However, one can hypothesize that the enzyme
kinetic properties in the other two-partner branch-points of
Ó FEBS 2003 An Arabidopsis phosphohomoserine branch-point model (Eur. J. Biochem. 270) 4625
the aspartate-derived amino-acids pathway and aromatic
amino-acids pathway in plant and in microorganisms are
such that flux coordination could also be obtained. The
distribution of the carbon skeleton toward the various end-
products would not be affected when supply increases or
decreases in these conditions. If this is true then, as shown
here for TS, limited in vitro kinetic characterization of the

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