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. The computer model indicates a high sensitivity of cysta- thionine flux to enzyme and S-adenosylmethionine concen- trations. Cystathionine flux is sensitive to modulation of threonine flux whereas the reverse is not true. The cysta- thionine c-synthase kinetic mechanism favours a low sensi- tivity of the fluxes to cysteine. Though sensitivity to inorganic phosphate is low, its concentration conditions the dynamics of the system. Threonine synthase and cystathio- nine c-synthase display similar kinetic efficiencies in the metabolic context considered and are first-order for the phosphohomoserine substrate. Under these conditions out- flows are coordinated. Keywords: allosteric activation; branch-point; kinetic com- petition; ping-pong; sensitivity coefficient. Metabolic branch-points display a very large diversity in terms of the number of the enzymes involved, the kinetic mechanisms of the competing enzymes and the number as well as the nature of the allosteric controls. Whether such diversity in the organization of the branch-points reflects differences in the branch-point kinetics is not well known. Indeed, detailed models that take into account the individ- ual enzyme kinetic properties in their metabolic context are scarce. Flux partition at the dividing point of several pathways has been studied both theoretically [1–3] and experimentally [2,4–7]. Some studies used the framework of metabolic control analysis for this purpose [6,7]. However, the allosteric controls of the branch-point enzymes are not taken into account in these experimental studies. Also the occurrence of branch-point two-substrate enzymes and the consequence of their kinetic mechanisms for the partition of 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: gcurien@cea.fr Abbreviations: AdoMet, S-adenosylmethionine; CGS, cystathionine c-synthase; Phser, phosphohomoserine; TS, threonine synthase. Enzymes:cystathioninec-synthase (EC 4.2.99.9; Swiss Prot entry P55217); cystathionine b-lyase (EC 4.4.1.8; Swiss Prot entry P53780); homoserine kinase (EC 2.7.1.39; Swiss Prot entry Q8L7R2); threonine deaminase (EC 4.2.1.16; Swiss Prot entry Q9ZSS6); threonine synthase (EC 4.2.99.2; Swiss Prot entry Q9S7B5); lactate dehydrogenase (EC 1.1.1.27, Swiss Prot entry P13491). Note: The mathematical model described here has been submitted to the Online Cellular Systems Modelling Database and can be accessed at http://jjj.biochem.sun.ac.za/database/curien/index.html free of charge. (Received 2 September 2003, accepted 23 September 2003) Eur. J. Biochem. 270, 4615–4627 (2003) Ó FEBS 2003 doi:10.1046/j.1432-1033.2003.03851.x of methionine (Fig. 1) and can be considered as the end- product of the pathway. AdoMet binding to TS increases the enzyme’s catalytic constant and decreases the Michaelis– Menten constant for the Phser substrate [15]. CGS and TS activities are inhibited by inorganic phosphate (P i ), a by- product of the reaction [12,17]. TS activity is inhibited by AMP in vitro [16,17] and AMP competes with AdoMet for its binding site on the enzyme [16]. Although the individual properties of CGS and TS are known in detail and equation rates are available [12,15], the equivalent data for when CGS and TS compete for their common substrate in a metabolic context remain to be determined. For example, the effect on branch-point partition of TS activity modifiers, AdoMet (allosteric 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. The mathematical model described here has been submitted to the Online Cellular Systems Modelling Data- base and can be accessed at http://jjj.biochem.sun.ac.za/ database/curien/index.html free of charge. Materials and methods Chemicals ATP, Hepes, homoserine, NADH, AdoMet, lactate dehy- drogenase (Rabbit Muscle type IV) were from Sigma. Cysteine was from Fluka. Phser was prepared according to [14] and AdoMet was purified as reported in [15]. Proteins Arabidopsis CGS, TS, cystathionine b-lyase and threonine deaminase were purified to homogeneity as described previously [12,15,18,19]. Mature Arabidopsis homoserine kinase devoid of its transit peptide sequence was cloned, overexpressed in Escherichia coli and purified to homogen- eity for the present work (G. Curien and R. Dumas, unpublished results). Purified protein concentration was determined by absorbance measurements at 205 nm [20]. Protein concentrations are expressed on a monomer basis. Modelling procedure Figure 1 maps all the kinetic links identified from previous studies carried out in vitro on the enzymes of the aspartate- derived amino acid pathway in plant. This map indicates that (a) homoserine kinase, which provides Phser, catalyses an irreversible reaction [21] and is not inhibited by its product Phser in planta [22]; (b) CGS and TS catalyse irreversible reactions [9,13]; (c) CGS activity depends on the concentration of Phser and cysteine and is not subject to allosteric control in the plant [12]; (d) TS activity is stimulated by AdoMet [10,13–15] and inhibited by AMP 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, Phser flux rates and the concentrations of AdoMet, cysteine, P i and the two enzymes in a metabolic context. To determine the values of the input variables, we considered the metabolic state of an illuminated plant leaf cell chloroplast. Some data were already available from previous studies and these were completed with data from the present work. Assuming a homogeneous distribution in Arabidopsis leaf cells, concentrations of about 20 l M for AdoMet (averaged from [24] and [25]), and about 15 l M for cysteine [26] can be calculated. The concentration of P i in the spinach chloroplast stroma was shown to be about 10 m M [27]. We assumed a similar concentration for Arabidopsis. The concentration of CGS in the chloroplast can be estimated as follows: CGS represents 1/11000 of the soluble proteins in the spinach chloroplast [28], the soluble protein content in the chloroplast is about 400 mgÆmL )1 [29], the content of CGS monomer is thus approximately 36 lgÆmL )1 ,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 calculated for the flux of Phser. Modelling of the Phser branch-point at steady-state The rate equations of CGS and TS published in [12] and [15] required to model the branch-point kinetics are expressed here as hyperbolic functions of Phser concentration. These forms are equivalent to those previously published but they suit our modelling purpose better (see later). The CGS rate equation is defined by Eqn (1): m cystathionine ¼ k app catCGS Á½CGSÁ½Phser K app mCGS þ½Phser ð1Þ Where, [CGS] is the CGS monomer concentration, k app catCGS is the apparent catalytic constant for CGS (Eqn 2) and K app mCGS is the apparent Michaelis–Menten constant for CGS with respect to Phser (Eqn 3). k app catCGS ¼ k catCGS 1 þ K Cys mCGS  Cys à  ð2Þ K app mCGS ¼ K Phser mCGS 1 þ K Cys mCGS  Cys à  Á 1 þ ½P i  K P i iCGS ! ð3Þ Where, [P i ] is the concentration of P i .P i competitively inhibits Phser binding to CGS [12,17] and K Pi iCGS in Eqn (3) is the CGS inhibition constant for P i . An equivalent mathematical form of the CGS rate equation can also be derived (Eqn 4) and will be used in the Discussion. In this equation, the enzyme velocity is expressed as a function of [Cys] instead of [Phser]. m cystathionine ¼ 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  Phser à  Á 1 þ ½P i  K P i iCGS  ð5Þ K appCys mCGS ¼ k Cys mCGS 1 þ K Phser mCGS  Phser à  Á 1 þ  P i à 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 mTS is the apparent Michaelis–Menten constant for TS with respect to Phser. k app catTS and K app mTS are complex functions depending on the concentration of AdoMet [15] as defined by Eqn (8) and Eqn (9), respectively. k app catTS ¼ k noAdoMet catTS þ k AdoMet catTS Á ½AdoMet 2 K 1 K 2 1 þ 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 C A Á 1 þ ½P i  K Pi iTS ! ð9Þ Where, k noAdoMet catTS and k AdoMet catTS are the TS catalytic constant in the absence and presence of a saturating concentration of AdoMet, respectively. K 1 K 2 is the product of the binding constants for the association of the first and the second molecule of AdoMet with the TS dimer. P i competitively inhibits Phser binding to TS [17]. K Pi 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]. Three conditions allowed us to use this procedure for the simulation of the Phser branch-point kinetics. First, the enzymes homoserine kinase, CGS and TS catalyse irrevers- ible reactions. Second, Phser flux is an external variable (Phser concentration does not determine Phser flux, see above) and third, Phser substrate saturation curves for CGS and TS are hyperbolic (Eqns 1 and 7). The mathematical treatment of LaPorte et al. [2] is reproduced here for the Phser branch-point. When the branch-point is in steady-state, the flux of Phser (J Phser ) is equal to the sum of the flux of cystathionine (J cystathionine ) and the flux of threonine (J Thr ) (Eqn 10). J Phser ¼ J cystathionine þ J Thr ð10Þ J cystathionine and J Thr in Eqn (10) can be replaced by CGS 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 ÞÞ½Phser þðJ Phser K app mCGS K app mTS Þ¼0 ð11Þ Solving Eqn (11) yields an expression for [Phser] steady-state that can be introduced back into Eqns (1 and 7) yielding expressions for the output fluxes at steady-state. Such calculations, based on the integration of independent kinetic data, are authorized because the initial velocity measure- ments of purified CGS and TS were carried out under similar physicochemical conditions (30 °C, pH 7.5–8). The simulations were carried out with KALEIDAGRAPH (Abelbeck Software, Reading, PA, USA). A series of constant or changing values were generated for the different input variables and the calculations were done using the appropriate equations. Reconstitution of the branch-point A constant flux of Phser was obtained with purified homoserine kinase in the presence of saturating concentra- tions of ATP and homoserine. Two different coupling systems were used in order to measure threonine and cystathionine flux. Threonine flux was measured using 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 added to a 120-lL solution containing: 50 m M Hepes KOH (pH 8.0), 10 m M KP i (pH 8.0), 2 m ML -homoserine, 200 l M NADH, 250 l ML -cysteine and 0–100 l M AdoMet (final concentrations). The reaction was started by addition of ATP-Mg (10 lL, final concentration 2 m M ATP, 10 m M Mg-Acetate). In the absence of threonine deaminase or cystathionine b-lyase, the rate of NADH oxidation was undetectable. Background NADH oxidation was negligible in the presence of threonine deaminase when homoserine or ATP were omitted. However, cystathionine b-lyase was shown to catalyse the degradation of cysteine into pyruvate. Though certainly a minor quantitative contribution in vivo where the concentration of cysteine is low (15 l M ), 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 following procedure was used. Firstly, the kinetic links inside the branch-point and between the branch-point system and the rest of the pathway were identified explicitly. We used some of our previous results concerning CGS and TS enzymes as well as other works for this purpose (Fig. 1 and Materials and methods). Table 1. CGS and TS kinetic parameters. CGS kinetic parameters TS kinetic parameters k catCGS 30 s )1 k catTS noAdoMet 0.42 s )1 K mCGS Cys 460 l M k catTS AdoMet 3.5 s )1 K mCGS Phser 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 concentration of CGS and TS in A. thaliana.Details concerning the sources of the information and the calcula- tions can be found in Methods. Results are shown in Table 2. Thirdly, the rate equations of CGS and TS [12,15] were used to create a computer model of the steady-state in the branch-point. The mathematical procedure published pre- viously for the study of the isocitrate branch-point in E. coli [2] was adapted to model the Phser branch-point kinetics (see Materials and methods). Finally, prior to its use for the examination of branch-point kinetics, the model was validated in vitro. Validation of the computer model The model was derived from initial velocity measurements carried out with low enzyme concentrations and high substrate concentrations, that is, under conditions exactly opposite to those found in the physiological situation. In order to estimate the validity of the computer model, the branch-point was reconstituted with purified enzymes and allowed to reach a steady-state, under conditions as close as possible to those thought to occur in vivo.Phserwas delivered in flux by the ÔupstreamÕ enzyme (homo- serine kinase). The fluxes of cystathionine and threonine (J cystathionine and J Thr ) were measured with the enzymes that occur downstream of CGS and TS, namely cystathi- onine b-lyase and threonine deaminase, respectively, 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 Table 2. Estimated values of the input variables in a leaf cell chloroplast. The values of the input variables were derived as indicated in Materials and methods from measurements carried out on illuminated photo- synthetic leaf tissue. Input variable J Phser (l M Æs )1 ) Concentration (l M ) Concentration (m M )[P i ] [CGS] [TS] [AdoMet] [Cys] 1 0.7 5 20 15 10 Fig. 2. Phser branch-point kinetic behaviour in vitro. (A) establishment of the steady-state. The flux of cystathionine (lower curve) was measured with cystathionine b-lyase and lactate dehydrogenase and threonine flux (upper curve) was measured with threonine deaminase and lactate dehydrogenase. The flux of Phser was generated with homoserine kinase in conditions where substrates were saturating. 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 version of the numerical model (bold curves; details in the text). Ó FEBS 2003 An Arabidopsis phosphohomoserine branch-point model (Eur. J. Biochem. 270) 4619 steady-state fluxes could not have been obtained. The experiment was carried out for different AdoMet concen- trations and outflow values measured at steady-state were plotted as a function of AdoMet concentration (Fig. 2B). J cystathionine and J Thr summed to a constant value, thus confirming that steady-state had been reached. (For [AdoMet] < 5 l M , the time constant of the system was high and steady-state may not be entirely reached.) Figure 2B shows that J cystathionine and J Thr are strongly dependent on the AdoMet concentration, in the range 0–100 l M . The fluxes showed a sigmoidal dependence on the concentration of AdoMet with J cystathionine decreasing and J Thr 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 at low concentration (Eqn 9). This effect is either too subtle to be detected in the present experiments or irrelevant to the present experimental conditions.] However, despite good agreement, the model was not entirely satisfying. Indeed, when experimental and predicted curves are fitted with Hill equations, the Hill number thus obtained is much higher in the first case (n H ¼ 2.7) than in the second (1.8). Improvement of the computer model We anticipated that the discrepancy between the computer model and the experimental data originated from an inadequacy of the TS mechanistic equation. This equation correctly describes the interaction between TS and AdoMet in the presence of high concentrations of Phser [15]. However, the model indicates that when TS operates at the branch-point, Phser concentration is low ([Phser] << K app mTS ). Moreover, the presence of P i prevents the binding of Phser on the enzyme and contributes to a decrease in the concentration of the enzyme-substrate complex. Under these conditions, AdoMet binds on the enzyme which is virtually free of substrate. We showed previously [15] that a synergy exists between Phser and AdoMet for their binding to TS. The Hill number calculated for the free enzyme/ 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  K P i iTS  ½Phserð12Þ where, k TS is TS apparent specificity constant for Phser (k app catTS =K app mTS ). k TS is a function of the concentration of AdoMet that can be determined experimentally. In order to obtain this function, TS velocity (TS alone) was measured as a function of the concentration of AdoMet in the physicochemical environment of the experiments of Fig. 2. Threonine deaminase and lactate dehydrogenase were used as the coupling system and TS activity was measured in the presence of a low concentration of Phser (500 l M ). The experimental results (not shown) were fitted to a Hill equation thus giving the following empirical equation for k TS (Eqn 13). k TS ¼ 5:4  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 of special interest to use the in vitro system to test the effect of AMP on the partition of the flux of Phser under physiological conditions. The partition was measured in the conditions of Fig. 2B in the presence of 20 l M AdoMet and a physiological concentration of AMP (100 l M [34]). Under these conditions, we observed that the partition was the same whether AMP was present or not (result not shown) indicating that AMP was efficiently displaced in these conditions. [Measurements of TS initial catalytic rate showed that the binding of AMP to TS is efficiently displaced by AdoMet and P i (G. Curien and R. Dumas, unpublished observations)]. Our results suggest that the presence of AMP in vivo does not have any quantitative consequence on the partition of the flux of Phser, at least under the physiological operating conditions defined in Table 2. As a consequence, the inhibitory effect is not taken into account in the model. 4620 G. Curien et al. (Eur. J. Biochem. 270) Ó FEBS 2003 Consistency with data collected in planta Measurements in planta [32] indicated that J cystathionine and J Thr 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- ming that Phser is restricted to the chloroplast (60 lLÆmg )1 chlorophyll [33] and 1.3 mg chlorophyll per gram fresh weight [34]). Together, these data indicate that the model of the Phser branch-point is relevant to at least one metabolic situation and therefore provides a realistic, detailed descrip- tion of the branch-point between the methionine and threonine biosynthesis pathways. In the following the model is used to investigate the sensitivity of the two-enzyme system to the different input variables and to explain the behaviour of the branch-point in terms of the kinetic properties of CGS and TS. Sensitivity analysis In a first analysis, fluxes of cystathionine and threonine (Fig. 3) were calculated as a function of each input variable. The fixed input variables were set at their physiological values (Table 2). Although the curves in Fig. 3 are displayed for a large range of the changing Fig. 3. Calculated fluxes in the vicinity of the physiological operating point. The steady-state fluxes were calculated with the improved version of the computer model in which the TS equation was the simplified empirical equation (Eqn 12). All input variables but one (indicated beneath the graphs abscissa) were set at their values in an illuminated leaf cell chloroplast (Table 2). The dotted lines in the graphs indicate the value of the changing input variable in the physiological context considered. The flux response coefficients were calculated from these curves and are indicated in Table 3. Ó FEBS 2003 An Arabidopsis phosphohomoserine branch-point model (Eur. J. Biochem. 270) 4621 input variables, the analysis has to be limited to the vicinity of the physiological operating point, especially when a high sensitivity to the changing variable is predicted. Indeed, the values of the input variables in vivo for a metabolic context that is very different from the one indicated in Table 2 are unknown. In order to describe the sensitivity of the system at the physiological 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 . Fig. 4. Calculated Phser concentration for changing input variables. Phser concentrations corresponding to the steady-state conditions calculated in Fig. 3 are plotted as a function of the changing input variable with the other input variables set at their physiological values. The dotted lines in the graphs indicate the value of the changing input variable in the physiological context considered. Table 3. Flux response coefficients. The values of the flux response coefficients (R J i I ¼ (DJ/J)/(DI/I)) where J stands for flux and I for input variable) were calculated using the curves in Fig. 3 for the estimated physiological environment of the Phser branch-point in Arabidopsis leaf chloroplast. R J I ¼ a means that a 1% change in I around a given value promotes an a percent change in flux J. A negative value means that input variable and flux vary in opposite directions. Input variable (I) Input variable physiological value (illuminated leaf cell) R I Jcystathionine R JThr I AdoMet 20 l M )1.55 0.25 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 . The sensitivity of the system to P i was considered because the concentration of P i in the chloroplast is high and variable (from 5 to 30 m M depending on the physiological state of the cell [27]). The calculations indicate that the flux response coefficients for P i are very low (Table 3). Figure 3A also shows that J cystathionine and J Thr are virtually unmodified despite important changes in the concentration of P i . Indeed, K iP i values for CGS and TS are similar and lower than the physiological concentration of P i . Note that the linear dependence of Phser concentration on the concentration of 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 experiments described in Fig. 2B. This response of the system to cysteine will be related to the kinetic mechanism of CGS later. Sensitivity to AdoMet. Figure 3C indicates that the con- centration of AdoMet determines Phser flux partition in a much more sensitive manner than do cysteine and P i .At 20 l M AdoMet, J Thr is larger than J cystathionine in accordance with the in vivo situation (see above). Therefore, although AdoMet-mediated changes in J Thr promote quantitatively equivalent opposite changes in J cystathionine , relative changes (flux response coefficient), are larger for J cystathionine than for J Thr (Table 3). In the model, J cystathionine is about six times 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 is about six times more sensitive in the same conditions. Sensitivity to J Phser . Individual output fluxes are expected to present a different sensitivity on J Phser depending on the absolute and relative degree of saturation of CGS and TS by the common substrate Phser. Figure 3F indicates that the flux of threonine depends in a quasi-linear manner on J Phser whereas the flux of cystathionine displays a slight downward curvatureforthesamerangeofJ Phser values. When a larger range for J Phser is considered (not shown) the curve for threonine flux displays an upward curvature. Accordingly, the sensitivity of J Thr is slightly higher than unity (1.03, Table 3), and the sensitivity of J cystathionine is lower (R J cystathionine J Phser ¼ 0.8) for the physiological state considered. 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 partition is not a sensitive function of the flux of Phser, small errors in the estimation of its in vivo value would not change the conclusions. Also partition measured in Fig. 2 with Phser flux set at 0.3 l M Æs )1 would not be different at 1 l M Æs )1 . Comparison of CGS and TS kinetic efficiencies under physiological operating conditions In order to detail the characteristics of the branch-point in terms of the individual enzyme properties, the kinetic efficiencies of CGS and TS (v/[E]) were calculated for the physiological context considered (Table 2). Results in Fig. 5 show that, under these conditions, using either the mech- anistic or the simplified rate equations for TS (details in Fig. legends), the saturation curves of CGS and TS by Phser are very similar in the concentration range investigated. The concentration of Phser in the stroma is about 80 l M (see above). Under these conditions, the model suggests that CGS and TS have similar kinetic efficiencies in the in vivo context. Moreover, both enzymes (and not only TS as indicated previously) operate in the first-order range for 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 M . Thus, at 15 l M cysteine (6 · K m ), CGS velocity is virtually maximal (Fig. 6). Though a similar relation exists for the apparent K m for Phser and cysteine concentration (Eqn 3), the situation is not symmetrical from a quantitative point of view for two reasons: firstly, the maximal K m for cysteine is lower than for Phser (K Cys mCGS ¼ 460 l M and K Phser mCGS ¼ 2500 l M , Table 1); Secondly, this difference is amplified in the presence of P i which increases the apparent 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 i (102 s) than in its absence (4.8 s) [In the physiological operating condition considered, CGS and TS are first-order with respect to their common substrate (Fig. 5). Thus, the time constant of the branch-point (s)is defined by the following equation: s ¼ 1 k CGS Á½CGSþk TS Á½TS where, k CGS and k TS are CGS and TS specificity constants. Considering that following a perturbation the steady-state is reached after approximately 5· s [41], methionine and threonine metabolisms are rather slow, with the kinetic controls potentially operating in a time scale of at least 10 min]. Discussion Prior to the present study, the only model available for the branch-point between the methionine and threonine bio- synthesis pathways in the plant was the qualitative model shown in Fig. 1. The allosteric interaction of TS with AdoMet was observed in vitro with the enzyme isolated from the other enzymes of the system [10,13–16], suggesting 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 TS velocities as a function of Phser concentration. v/[CGS] (thin line) was calculated using Eqns (1–3). v/[TS] was calculated using either the mechanistic equation (Eqns 7–9), thick line, or TS empirical simplified equation (Eqn 12), thick dotted line. For the calculations [cys- teine] ¼ 15 l M , [AdoMet] ¼ 20 l M and [P i ] ¼ 10 m M .Underthese conditions, K app mCGS ¼ 474 l M , k app catCGS ¼ 0.95 s )1 , K app mTS ¼ 1526 l M and k app 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 [...]... 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 4626 G Curien et al (Eur J Biochem 270) 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. .. decrease via the inhibition of AdoMet/lysine-sensitive aspartate kinase by AdoMet In the second more frequently proposed scenario, AdoMet mediates an indirect negative feedback for the synthesis of methionine, via the activation of TS by AdoMet, followed by the inhibition of bifunctional aspartate kinase-homoserine dehydrogenase by threonine In this case, it is implicitly assumed that the interaction of. .. cystathionine and threonine to AdoMet may thus be modified when the branch-point is embedded in the aspartate system Two scenarios were previously proposed [31]: in the first, the activating interaction of AdoMet with TS may attenuate the changes in the flux of threonine due to a modification of the level of AdoMet Indeed, upon an increase in the level of AdoMet, TS is activated but Phser flux may simultaneously... exon coding region of cystathionine gamma-synthase gene is necessary and sufficient for downregulation of its own mRNA accumulation in transgenic Arabidopsis thaliana Plant Cell Physiol 42, 1174–1180 46 Hacham, Y., Avraham, T & Amir, R (2002) The N-terminal region of Arabidopsis cystathionine gamma-synthase plays an important regulatory role in methionine metabolism Plant Physiol 128, 454–462 47 Chiba, Y.,... special interest to simplify the characterization of branchpoints where the enzyme activities are controlled by numerous allosteric interactions Acknowledgements ´ We wish to thank Marie-Christine Butikofer and Valerie Verne for the ELISA assays We thank Pr Roland Douce and Dr Michel Matringe and Mickaela Hoffman for critical reading of the manuscript Special ¨ thanks to Maighread Gallagher for the correction... 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 properties thus confer independence between the cysteine and the cystathionine /threonine fluxes The nature... localisation of aspartate kinase and the enzymes of threonine and methionine biosynthesis in green leaves Plant Physiol 71, 780– 784 Ó FEBS 2003 12 Ravanel, S., Gakiere, B., Job, D & Douce, R (1998) Cystathionine gamma-synthase from Arabidopsis thaliana: purification and biochemical characterization of the recombinant enzyme overexpressed in Escherichia coli Biochem J 331, 639–648 13 Giovanelli, J., Veluthambi,... 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... 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 interaction of AdoMet with TS is therefore consistent with AdoMet being part of a negative feedback... 2003 An Arabidopsis phosphohomoserine branch-point model (Eur J Biochem 270) 4625 strongly suggests that TS allosteric activation by AdoMet is physiologically significant Our results validate the qualitative 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 . A kinetic model of the branch-point between the methionine and threonine biosynthesis pathways in Arabidopsis thaliana Gilles Curien, Ste ´ phane Ravanel. 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