Kinetic Study of Yeast Hexokinase

Transcription

1 European J. Biochem. 5 (1968) Kinetic Study of Yeast Hexokinase 1. Steady-State Kinetics G. NOAT, J. RCARD, M. BOREL, and C. GOT Laboratoire de Physiologie cellulaire vkgktale associk au C. N. R. S., Facult6 des Sciences, Marseille (Received December l4,1967/march 5, 1968) Thirty-one different models corresponding to all plausible mechanisms of glucose phosphorylation conditioned by yeast hexokinase have been analysed. Comparison of these models with the results given by kinetic study of the enzyme has enabled us to prove that the catalysis corresponds to an ordered mechanism in which hexokinase binds first glucose and then the chelate MgATP2-. The latter substrate is not able, to any great extent, to form directly the first complex with the phosphotransferase. The ionic species Mg2+ and ATP4- have only a negligible affinity for the enzyme, or the enzyme-glucose complex. Glucose-6-phosphate and ADP appear in the medium following the decomposition of the enzyme-glucose-magnesium-atp complex. This decomposition is also controlled by an ordered mechanism, MgADP- being formed first, and glucose-6-phosphate afterwards. MgADP- is able not only to fix itself on the enzyme-glucose-6-phosphate complex but also on the enzyme-glucose complex. This mechanism is in contradiction with that of Fromm. On the other hand it agrees with that postulated but not proved by Hammes and Kochavi. The rate constant values in the proposed mechanism have been calculated. They are different from those calculated by Hammes and Kochavi. Recent kinetic studies of hexokinases have led to contradictory results. Even though some workers in this field [l-31 admit that the catalysis is mediated through an enzyme-phosphate complex, it seems that this conception is not widely accepted, at least as far as yeast hexokinase is concerned. Most authors now agree that glucose phosphorylation involves a complex of the enzyme-glucose-magnesium-atp type. However, the mechanism of the catalysis still remains very much a matter of controversy. Hammes and Kochavi [4-61 reached the conclusion that yeast hexokinase binds glucose first, and then the chelate magnesium-atp. On the other hand, Toews [7] claims that the enzyme, from another source it is true, fixes MgATP2- before hexose. n both cases the mechanism of the glucose phosphorylation would be an ordered one ( Bi Bi Mechanism in Cleland s terminology [S]). Fromm and his colleagues [9, lo], on the contrary, consider they have shown, with yeast hexokinase, the existence of a rapid equilibrium random mechanism among all the possible enzymesubstrate complexes. Enzyme could then bind glucose and magnesium-atp in either order. n fact, to be able to assert that a model is valid, one has not only to prove that the experimental Enzyme. Hexokinase or ATP: ~-hexose-b-phosphotransferase (EC ). results agree with the model, but also that they disagree with all the other apparently plausible models. This latter condition does not seem to have always been entirely satisfied, at least as far as the kinetic study of hexokinase is concerned. Thus, for example, Hammes [4,5] concluded from his results the existence of an ordered mechanism, and that, a few years later, Ottolenghi [ill showed that these same results could also be interpreted by a rapid equilibrium random mechanism of the type proposed by Fromm [9,10]. The study of the phosphotransferase catalytic mechanism is also complicated by the existence of chelation complexes between the adenine-nucleotides and the metal activators. Although numerous results make one think that these complexes constitute the true substrates of these enzymes, others [12] reach an opposite conclusion or, sometimes, a conclusion half way between the two [13]. n the case of yeast hexokinase, it has been generally assumed [6,iO,l] that MgATP2- chelate is the true substrate, but, as far as we know, no experimental proof has been presented in support of that assertion. We have therefore considered it of importance to carry out again, in great detail, the kinetic study of yeast hexokinase, taking into account the critical remarks that have been made.

2 56 Kinetics of Yeast Hexokinase. 1. European J. Biochem. METHODS Hexokinase was prepared from baker's yeast in accordance with the method of Darrow and Colowick [14] (specific activity about 600 Colowick units/mg [14]). n some experiments the crystalline enzyme was purchased from Boehringer Laboratories. t was kept, after elimination of traces of ammonium sulphate, in a tetramethylammonium 0.1 M chloride solution. Adenosine &phosphate and adenosine triphosphate (sodium salts from Nutritional Biochemical Corporation Laboratories) were purified by being passed over a Sephadex A 25 column, then precipitated as barium salts. The metal wasthen eliminated by passing over Dowex 50 resin. The concentration of nucleotide was determined spectrophotometrically using the coefficients of molecular extinction given by Bock[l5]. The ph of the solutions was Table 1. Mechanisms involving the formation of an enzyme-phosphate complex n the mechanisms of Tables 1, 2, 3, 6 and 7, E represents the enzyme, E' the enzyme-phosphate complex, G the glucose, M the magnesium, A the ATP, MA the chelate MgATP2-, G'the glucose-6-phosphate, A' the ADP and MA' the cheate MgADP- - ~ ~ M and A substrates MA substrate

3 Vol.6, No.1, 1968 G. NOAT, J. RCARD, M. BOREL, and C. GOT 57 brought to 8 with tetramethylammonium hydroxide (Merck). Glucose-6-phosphate and fructose-6-phosphate (barium salts supplied by Nutritional Biochemical Corporation or Calbiochem Laboratories) were purified by several successive ethanol precipitations. After elimination of the metal by passing over Dowex 50 the concentrations were determined by measuring the reduction of NADP in the presence of an excess of glucose-6-phosphate dehydrogenase and of phospho-hexosisomerase (in the case of fructose-6-phosphate). Tetramethylammonium chloride (Fluka), used to keep the ionic strength constant, was recrystallized twice in isopropyl alcohol. Hexoses and magnesium chloride (Fluka) were used without any further purification. The value of the stability constant of themgatp2- complex was determined with the aid of the Burton method [ 161 under conditions identical to those used for the measurements of phosphorylation rates. These rates were estimated by continuous titration of the H+ ions set free in the medium. The apparatus was a Metrohm titrator used as a ph-stat. Control of the ph (ph 8.5), verified with the aid of an accessory recorder, was effected to 0.01 of a ph unit. The base used was tetramethylammonium hydroxide (about 10-3 N). The volume of the base injected was always negligible in comparison with the total volume of the medium. The ionic strength was fixed at 0.3 (tetramethylammonium chloride), the temperature at 30 & 0.1". The measurements were done in nitrogen atmosphere. The enzyme concentration in the medium, varying with the experiments, was about 1 nm. RESULTS AND DSCUSSON The catalytic mechanism of glucose phosphorylation can apparently be explained by various types of different models. Tables 1 and 2 show the possible models for ordered mechanisms using either the formation of an enzyme-phosphate complex (E', Table 1) or that of a quaternary complex enzyme-glucosemagnesium-atp (EGMA, Table 2). Table 3 shows the possible random mechanisms. n the case of each of these three types of mechanisms, it may be supposed that the "free" ions Mg2+ and ATP4- are the "true" substrates of the enzyme (mechanisms 1 * * 11, , ), or that the chelate MgATP2- binds the enzyme and that free ionic species do not possess this ability ( , 22, 23, and 31). At a ph of 8.5 all the ATP is in ATP4- form. The value of the apparent stability constant of MgATP2- chelate (K = [MgATP2-] / [Mg2++l [ATP4-]) determined under the same experimental conditions used Table 2. Ordered mechanisms involving the forrnatio n of an enzyme-glucose-magnesium-atp complex Mand A substrates k, [M k, [A1 16 E - EM - EMA G1 EGMA k.: E + G'+ M + A' k, k k4 E + G'+ M + A' 9 E EG A EGMA k4 +G+ M +A' MA substrate

4 58 Kinetics of Yeast Hexokinase. 1. European J. Biochern. Table 3. Random mechanisms involving the formation of an enzyme-glucose-magnesium-atp complex Mond A substrates K 24 E EMA 2 EGMA k E tg'+m+a' K 25 E EGA A EGMA k E t G'+M+A' K 26 E EGM EGMA k E +G'+MtA' K +y EGM q 28 E & EM EGMA k, E + G+ M + A' K +y EMA$ 29 E& EA EGMA k E + Go+ M + A' MA substrate yeg% 31 E EGMA k E + G'r MA' for measuring the reaction rates is 7 x lo4 M-l. This value is in complete agreement with the most recent determinations [22]. The knowledge of this constant enables the calculation of the concentrations of the various species in solution, MgATP2-, Mg2+, and ATPd-. The Lineweaver-Burk plots thus obtained are represented in Fig. 1. The secondary plots are shown in Fig.2. These results are compatible with the expression : equivalent to : n these equations [Elo represents the total concentration of hexokinase, [G, [MA], [M, [A] the respective concentrations of glucose, MgATP2-, Mg2+, and ATP4-, v the initial rate of the reaction (in steadystate or in rapid equilibrium conditions), pl and pl' the Dalziel coefficients [ 171. The steady-state treatment of the mechanisms 1-23 and the equilibrium

5 Vol. 5, No. 1, 1968 G. NOAT, J. RCARD, P.BOREL, and C. GOT A T 15 l/lglucosel (mm ) 5 40 C D _i ) zo ioe 1/[ATP4 l irnm- ) 1/[Mq2+1 (rnm- ) Fig. 1. Primary plots of glucose phosphorylation. (A) Plot of reciprocal of initial velocity versus reciprocal of concentration of glucose. The concentrations of the MgATP2- complex were respectively: 15 pm (X); 31 pm (0); 62 pm (A); 125pM (0); 750 pm (v). The concentration of the free metal was maintained at 0.1 mm. (B) Plot of reciprocal of initial velocity versus reciprocal of concentration of MgATP2- complex. The glucose concentrations were respectively: 0.05 mm (0); mm (A); 0.25 mm ( x); 0.5 mm (0). The rate measurements were taken in respect of all the combinations of four concentrations (20, 50, 100, and 200 pm) of the free metal (Mg2+) and of the free ATP (ATP4-). Under these conditions, the apparent Michaelis constant of the MgATP2- complex did not depend upon the free concentrations used. (C) Plot of reciprocal of initial velocity versus reciprocal of concentration of free ATP (ATP4-). The glucose concentration was 0.25 mm. The concentrations of free magnesium (Mg2+) were respectively: 20 pm (0); 50 pm (A); 100 pm (0); 200 pm (A). (D) Plot of reciprocal of initial velocity versus reciprocal of concentration of free magnesium (Mg2+). The concentration of glucose was 0.25 mm. The concentrations of free ATP were respectively: 20 pm (0); 50 pm (A); 100 pm (0); 200 pm (a). The plots C and D are symmetrical in comparison with the free concentrations of ATP and magnesium. n all experiments reported in this paper the initial reaction velocity was expressed for an enzyme concentration of 2 nm (determined by assuming a molecular weight of 96,000 and a maximum specific activity of 700 units per milligram according to tho Darrow method [14]) treatment1 of the models give rise to the fourteen equation of Table 4. These coefficients are defined in Tables5A and 5B. f one compares equations (1 a) and (1 b) with those of Table 4, it may be observed that three models (22,23,31) directly verify the experimental results, and the same applies to models 16, 18, 20, 21, and 30 provided that coefficients q ~ q3, ~, rp5, and q6 are small. All these models imply that the catalysis is mediated through This is iustified as no inhibition of the reaction rate is observed it high concentrations of glucose, MgATP2-, Mg2+, or ATP4-. a quaternary complex of the enzyme-glucosemagnesium-atp type. n the mechanisms 22, 23, and 31, the MgATP2- chelate is a true substrate, the free species Mg2+ and ATP4- having only a negligible affinity for hexokinase. n models 16, 18, 20, 21, and 30, on the contrary, the free ionic species rather than the chelate fix themselves on the enzyme. Although the first hypothesis is more likely, it is unreasonable to eliminate the second without having first shown that it does not match the reality. This demonstration can be done easily. n fact, the apparent affinity of the hexokinase for the glucose

6 60 Kinetics of Yeast Hexokinase. 1. European J. Biochem. A B t LO 1/[MaATP2? OR l/lgwcose (mm- ) VMg ATP2-l OR l/[glucose (m M- ) C D l/[mgztl (mm ) Fig.2. Secondary plots of glucose phosphorylation. (A) A, the slopes of l/v = f (l/[g]) plots versus reciprocal of concentration of MgATP2- complex; 0, the slopes of l/v = f [MgATP2-]) plots versus reciprocal of concentration of glucose. (B) 0, the intercepts of l/v = f (l/[g]) plots versu8 reciprocal of concentration of MgATP2- complex; A, the intercepts of l/v = f (1/[MgATP2-]) plots versus reciprocal of concentration of glucose. (C) The slopes of l/v = f (l/[atp4-]) plots versus reciprocal of concentration of free magnesium (Mg2+).(D) The slopes of l/v = f (1/[Mg2+]) plots versus reciprocal of concentration of free ATP (ATP4-) A B l/[glucose (mm- ) Fig.3. (A) Participation of free magnesium and ATP in glucose phosphorylation. 0, plot of reciprocal of initial velocity versus reciprocal of total concentration of magnesium ([Mgl~). The total concentration of ATP was fixed at 0.25 mm, that of glucose at 1 mm. A, plot of reciprocal of initial velocity versus reciprocal of total concentration of ATP ([ATP?). The total magnesium concentration wa6 fixed at 0.25 mm, that of glucose at 1 mm. (B) Plot of reciprocal of initzal velocity versus reciprocal of the glucose concentration. The total concentrations of magnesium and ATP were reversed in each of the straight lines obtained: 0, [ATPT = 1 mm, [M~]T = 0.5 mm; +, [ATPT = 0.5 mm, [Mgl~ = 1 mm; A, [ATPT = 1 mm, [Mgl~ = 2 mm; X, [ATPT = 2 mm, [Mgl~ = 1 mm. The constancy of the apparent Michaelis constant, in Fig.3A and 3B, does not remain noticeable if the ratio of the total concentrations of magnesium and ATP is very different from the optimum ratio, which is about 2.5 in the present experimental conditions >

7 Vol. 5, No. 1, 1968 G. NOAT, J. RCARD, M. BOREL, and C. GOT 61 Mechanisms Equa ti o n s remains unchanged when the concentrations of ATP and magnesium are reversed (Fig. 3). n this way, the concentration of free ionic species varies, and the concentration of the chelate remains constant. As the rate of the reaction remains unchanged, one must conclude that MgATP2- is a true substrate, and that Mg2 and ATP4- have no affinity, or a very small one, for the enzyme. Therefore mechanisms 16, 18, 20, 21, and 30 do not fit the experimental results. This interpretation is identical to that of Hammes and Kochavi [4], but these authors did not produce the experimental proof for it. t is possible to determine which one of the mechanisms, 22, 23, or 31 corresponds to the reality in studying the phosphorylation of various hexoses. n the three cases in fact, the position of the intersection point of the Lineweaver-Burk plots, is determined by the expression i/[mgatp2-] = - p71/y,. n the mechanism

8 62 Kinetics of Yeast Hexokinase. 1. European J. Biochem. Table 5A and B. Definition of DalzieE's coefficients of Table 4 Table 5A 23, this value is equal to - k2k3/c-1 (k2 + C,) and consequently must depend on the nature of the hexose. n the mechanisms 22 and 31, it corresponds to respectively - k,/k-, and - KMA, both of these values being independent of the nature of the hexose. The plots of Fig.4 prove that the first case applies. The only mechanism compatible with these results is therefore mechanism 23. This conclusion is in agreement with that of Hammes and Kochavi [4], but does not agree with that of Fromm [9]. The interpretation proposed is confirmed, in addition, by the study of the simultaneous phosphorylation of two hexoses. n this way, mechanisms 22, 23, and 31, can be replaced by models 22', 23', and 31' (Table 6). The corresponding rate equations provide linear Lineweaver-Burk plots ( /v plotted against l/[mgatp2-]) in the case of models 22' and 31', and non-linear plots in the case of mechanism 23'. The results of Fig.4 prove the second possibility.

9 ' - Vol. 5, No. 1, 1068 G. NOAT, J. RCARD, M. BOREL, and C. GOT 63 Table 5B $1-1 k2-1 kl 1 21 ' 1 1 % ~ - 1 kl t -_ 1 - KG i 1 k KG K', 1 k KG Ki k KGKH Ki 26 + i l k 2a k k KL 29 ' - 1 k 1 - k Kb - k KM KL 1 t 1 k; k KL 1 : k K KLA The facts which have been discussed permit us to establish the sequence of events that precede the formation of the enzyme-glucose-magnesium-atp complex. Similarly, one may determine the succession of events following the formation of this complex. Only two types of mechanisms, in agreement with the facts already discussed, can be used to explain the formation of glucose-&phosphate and that of ADP from the enzyme-glucose-magnesium-atp complex. They are represented in Table 7A. n this same table the rate equations corresponding to mechanism 23 associated with each of these two models, are expressed. These models, and the equations which result from them, clearly show that if scheme 23a is valid, MgADP- must be competitive with regard to glucose and non-competitive with regard to MgATP2-. n the same way, glucose-6-phosphate must be non-competitive with regard to glucose

10 64 G. NOAT, J. RCARD, 11. BOREL, and C. GOT: Kinetics of Yeast Hexokinase.. lb T" European J. Biochem. 15 Fig.4. Plots of reciprocal of initial phosphorylation rates of various hexoses versus the reciprocal of the concentration of the MgATP2- complex. (A) Phosphorylation of fructose. The fructose concentrations were respectively: 0.1 mm (0) ; 0.25 mm (0); 0.5 mm (A); 1 mm (+); and 2.5 mm ( x ). (B) Phosphorylation of mannose. The mannose concentrations were respect,ively: mm (0); 0.05 mm (0); 0.1 mm (v); 0.25 mm (A) and 0.5 mm (+). (C) Simultaneous phosphorylation of glucose and fructose. The concentrations used were respectively: glucose = 0.5mM (0 and +); fructose = 2.5mM (A and +) Table 6. Mechanisms of the phosphorylatiwh of two hexoses G and G,, and the corresponding rate equutions EG2 MA k2, E G; + MA' 32' EG, MA kl, E + G; + MA'

11 Table 7 A. Mechanisms of the forrnation and decomposition of the enz~~me-glucose-wiu~nesium-atp covnplex with MgADP- at the beginning of the reaction [Elo , [MA'] [MA'] - 9, +A [G [MA] "MA] + [cl + [G [MA] with glucose-6-phosphate at the beginning of the reaction -..- EGMA' with MgADP' at the beginning of the reaction [El, G7 all [MA'] -=do V [G [MA] [Gl[MA] [G [MA1 [Gl[MAl with glucose-6-phosphate at the beginning a1 the reaction k, [G k [MA] k 23 b E - EG & EGMA 2 EG' E T k-2 'k_3tma1 rn with MgADP- at the beginning of the reaction wilh glucose-6-phosphote at the beginning of the reaction [Elo [G'1 0, G'l - = $ [G [MA1 - - V [G 1 [G + + [MA1 + EGMA' with MgADP-at the beginning OF the reaction with glucose-6-phosphate at the beginning of the reactton cchanisrns 1 Table 7B. Definition of Dalziel's coefficients of Table?'A o1 $ a /i.tl+ k3 4 5 European J. Biochem., Vol. 5

12 66 Kinetics of Yeast Hexokinase. 1. Ellropean J. Biochern. A C VLGLUCOSE (rnm- ) LO D E lmqadp-l.(mm) Fig.5. nhibition of the phosphorylation rate by the products of the reaction. (A) Plot of reciprocal of initial velocity (glucose phosphorylation) versus reciprocal of glucose concentration in the absence and presence of glucose-6-phosphate. The glucose-6-phosphate concentrations were: 0 (0); 10 mm (0); 20 mm (A); 40 mm (+).. The MgATP2- complex concentration was mm, that of the free magnesium was 0.2 mm. (B) Plot of reciprocal of nitial velocity (fructose phosphorylation) versus reciprocal of fructose concentration in the absence and presence of fructose-6-phosphate. The fructose-6-phosphate concentrations were: 0 (0); mm (A); 0.75 mm (A); 1.5 mm (0); 3.75 mm (+). The MgATP2- complex concentration was 0.25 mm, that of free magnesium was 0.2 mm. (C) Plot of reciprocal of initial velocity (glucose phosphorylation) versus reciprocal of MgATP2- concentration in the absence and presence of glucose-6-phosphate. The glucose-6-phosphate concentrations correspond to those of Fig.5A with symbols 0 and reversed. The glucose concentration was mm. (D) Plot of reciprocal of initial velocity (glucose phosphorylation) versus reciprocal of glucose concentration in the absence and presence of MgADP-. The MgADP- complex concentrations were respectively: 0 (A), 2.25 mm (0); 4.65 mm (A); 9.5 mm (+). The MgATP2- complex concentration was 0.1 mm and that of the free magnesium 0.2 mm. The free ADP (ADP3-) concentration was less than of the total ADP concentration. (E) Plot of reciprocal of initial velocity (glucose phosphorylation) versus reciprocal of MgATP2- in the absence and presence of MgADP-. The MgADP- complex Concentrations were respectively 0 (A); 2.25 mm (A); 4.65 mm (0) and 9.5 mm (+). The glucose concentration was 0.2 mm. (F) Tlie intercepts of l/v = f (l/[g]) plots (Fig.5D) versus the concentration of MgADP-. The MgATP2- complex concentrations were respectively 0.1 mm (0); 0.2 mm (+) and 0.5 mm (A) and MgATP2-. On the other hand, in the case of model 23 b, glucose-6-phosphate must be competitive with regard to glucose, and non-competitive with regard to MgATPZ-, whereas MgADP- must be noncompetitive with regard to both glucose and MgATP2-. The results in Fig. 5 show that model 23 a must be rejected and that model 23b is not entirely satisfactory. n fact, one may observe in plots 5D and 5E, that the straights lines do not intersect at the same point (left of the ordinates). n addition, the secondary plots 5F and 5 C are not linear. Their curvature increases with the concentration of MgADP-. These results prove that the inhibition caused by MgADP- is due to its fixation onto both the enzyme-glucose-6-phosphate complex and onto the enzyme-glucose complex ( dead-end complex [24]). Since glucose-6-phosphate is competitive with regard to glucose (Fig.B), the model 23a is not satisfactory. Only mechanism 23 b is thus able to fit all our experimental results. t is identical to the one proposed by Hammes and Kochavi [4-61. However, these authors did not produce a proof [ill, and their

13 Vo1.5, So.1, 1068 (1. NOAT, J. RWAR), M. BOREL, and C. GOT [MgADP-.(mM) W a 1501 p loo( ( E F 1500 / [GLUCOSE-6-PHOSPHATE.(mM), [GLUCOSE-6-PHOSPHATEJ(mM) [GLUCOSE-6-PHOSPHATElh M) Fig.5. nhibition of the phosphorylation rate by the products of the reaction: secondary plots. (A) The slopes of l/v=f (l/[g]) plots versus the concentration of MgADP-. The MgATP2- concentrations were: 0.1 mm (0); 0.2 mm (A); 0.5 mm (0); 1 mm (A).(B) The intercepts of l/v = f (1/[MgATP2-]) plots versus tho concentration of MgADP-. The glucose concentrations were: 0.1 mm (0); 0.2 mm (A); 0.5 mm (0); 1 mm (+). (C) The slopes of l/v = f (l/[mgatp2-]) plots versus the concentration of MgADP-. The glucose concentrations were 0.1 mm (0); 0.2 mm (0); 0.5 mm (A); mm (+).(D) Thc slopes of l/v = f (l/[g]) plots versus the concentration of glucose-6-phosphate. The MgATP2- concentrations were: 0.05 mm (0); 0.1 mm (a); 0.2 mm (0); 0.5 mm (A). (E) The intercepts of l/v = f (l/[mgatp2-]) plots versus the concentration of glucose-&phosphate. The glucose concentrations were: 0.05 mm (0); 0.1 mm (A); 0.2 mm (0); 0.5 mm (A). (F) The slopes of l/v = f ( i/[mgatp2-]) plots versus the Concentration of glucose-6-phosphate. The glucose concentrations were 0.05 mm (0); 0.1 mm (A); 0.2 mm (0); 0.5 mm (A) b results could also be interpreted by entirely different mechanisms (mechanisms 16, 18, 20, 21, 22, 23, 30, and 31, Table 4). We consider we have provided this proof. The interpretation presented is actually in agreement with the results of Cohn [18]. On the other hand, model 23b is in contradiction with that of Fromm and his colleagues. t seems to us important now to seek the reasons for these contradictions. Fromm has in particular studied the inhibition of hexokinase by ADP and adenine. He remarks that these substances are competitive inhibitors of ATP. These observations should exclude an ordered mechanism. The results obtained in the present work (Fig.5) are very different from those of Fromm [19]. There seems to be at least one reason for this. t is easy to calculate from his data [9] that, in any given experiment, the ionic strength of the reaction mixture is very small and not constant. But 5* for low ionic strengths, the stability constant of complexes MgATP2- and MgADP- decreases considerably with increase in (Fig.6). t follows that when the concentration of MgATP2- varies, the concentration of MgADP- (Fig. 6) also necessarily varies. This provokes a systematic deformation of the Lineweaver-Burk plots. The results of Fig. 7 show, in fact, that with ionic strengths similar to those used by Fromm [9], adenosine diphosphate seems, at least in some cases, to be a competitive inhibitor of adenosine triphosphate. One only has to diminish the variation of ionic strength of the medium by adding an electrolyte, to see that this competitive aspect is illusory (Fig. 7). Thus, the kinetic results presented by Fromm cannot be considered as arguments in favour of a random mechanism [31j. The cp coefficients corresponding to model 23b can be calculated. The values of these coefficients are

14 68 Kinetics of Yeast Hexokinase.. European J. Biocliem.. + i 15 Fig. 6. Variation of the stability constant of the MgATP2- (8) and MgADP- (A) complexes versus the ionic strength of the reactive medium. The results were obtained by means of the Burton method [17] in the presence of 0.03 M triethanolamine buffer, ph 8.5. The ionic strength was adjusted with tetramethylammonium chloride in their calculations, have used a value (lo4 M-) of the stability constant of MgATP2- which is now known to be lower than the real value [21,22]. The difference between these two values is sufficient to disturb the results of the kinetic study. n Fig.8, secondary plots similar to those of Fig.2 are shown, but determined by choosing, as Hammes andkochavi have done, a value of the stability constant equal to lo4 M-l. These plots, in contrast to those of Fig.2, do not intersect at the same point, which would, at first sight, lead one to suppose thatrthe terms in q/[m], v/[a], v/[g] [A], and p/[g] [M exist in the rate equation, and consequently that the "free" ionic species should be able to fix themselves on the enzyme. t is easy to show that this interpretation is unsatisfactory and is only due to the choice of a wrong value of the stability constant. n fact, the experimental points of the secondary plots do not fall on one straight line, as provided for by models 22, 23, and 31, or on several straight lines, as provided for in model 30, but on a curve. Only in the case of a stability constant value of 7 x lo4 M-l, is th' is curve transformed into a straight line. A kinetic analysis of the experimental results thus allows the finding 7-6- A 7-6- B /LMg ATP2-1hM-'l /[MgATP2~l.(mM-') Fig.7. nfluence of the ionic strength on the inhibition of the reaction by ADP. The ADP concentrations were respectively: 0, (+), 1 mm (0) and 2 mm (0). The glucose concentration was 0.5 mm. The magnesium was introduced into the reactive medlum, in a constant ratio of concentrations with the nucleotides (respectively 2.5 and 1 with respect to ATP and ADP, Fromm [9]). The concentration of tetramethylammonium chloride was 0.05 M (Fig.7A), 0.3 M (Fig.7B). n the case of Fig.7A the ionic strength of the reactive medium was not constant but was of the same magnitude as that usually used by Fromm ( ) given in Table 8. Calculation of the rate constants of the value determined directly by the Burton necessitates knowing the equilibrium constant of the method [16]. reaction. A good estimation of this constant [20], The study of the rate of exchange at equilibrium under our experimental conditions, seems to be 320. between ATP and ADP and between glucose and The values of the eight velocity constants of the glucose-6-phosphate, according to Boyer's method mechanism can then be calculated and are given in [23], had led Fromm [lo] to conclude the existence Table 8. These results are comparable to those of of a rapid equilibrium random mechanism. As shown Hammes and Kochavi [a-61 but with notable dif- by Cleland [24], the results of Fromm [lo] are ferences (Table 8). These differences seem to be due not in agreement with such a mechanism. Moreover at least in part to the fact that Hammes and Kochavi, these results were obtained at ph 6.5, a condition

15 Val. 5, No., 1968 G. NOAT, J. RCARD, M. BOREL, and C. GOT 69 Table 8. Values of the Dalziel s coefficients and of the velocity constants for the model 23b Ualziel s encfticicnts Velocity constant5 (Noat et al. results) Velocity constants (Harnrnes el az. results) po = 4.0~ sec k, = 8.3 x lo6 M-l sec-l k, = 3.7 x lo6 M-l sec-l p1 = 1.2 x M see k-, = 1.9 x lo3 sec-1 k-, = 1.5 x lo3 sec-l pa = 1.9 x lo- M sec p7 = 4.35 x 10-l1 M2 sec k, = 6.5 x 1U6 M-l sec-l k-, = 1.0 x lo3 sec-l k, = 4 x lo6 M-l see-l k-, = 6.5 x 10, sec-l p9 = 3 x M sec k, = 4.35 x lo3 sec-l pll = 7.8 x M scc k-, = 5.65 x lo6 M-l sec-l pl, = 8.2 x sec k, = 5.9 x lo3 sec-l k4 = 103sec-1 pl, = 5.5 x 10-5 SCc k-, = 4 x lo5 M-l seer1 cpls = 0.22 sec plo = 3.7 x M-1 sec k K5 = 5 = 1.1 x 10 M-l k-5 k-5 k, = 3 x lo3 see-l k-, = 2 x lo6 M-l sec-l k-, = lo5 M-l sec-l k K, = = 3.3 x 10, Mpl /[ATP4-l.(mM- ) /[ATP4-14mM- ) C /[Mg ATP*-.lmM- ) /[ MgATP ~1~ nm~ Fig.8. nfluence of the magnitude of the stability constant of the MgATP2- complex on the kinetic results. (A) The intercepts of the l/v = f (l/[g]) plots versus reciprocal of the concentration of free ATP (ATP4-). The free magnesium concentrations were respectively: 0.02 mm (0); 0.05 mm (0); 0.1 mm (A); 0.2 mm (A). The total concentrations of ATP and metal were simultaneously increased in a ratio determined by the value of the stability constant of the MgATP2- complex supposed equal to lo4 M-l. (B) The slopes of the primary plots l/v = f (l/[g]) versus the reciprocal of the concentration of free ATP. The experimental conditions are those of Fig.8A. (C and D) The intercepts (C) and slopes (D) of the primary plots l/v = f (l/[g]) versus the concentration of the Mg ATP2- complex. The stability constant is fixed at a lo4 M-l value (0). The curves obtained become straight lines (+) if the complex concentrations calculated from a valuc of the stability constant equal to 7 x lo4 M-l

16 70 G. NOAT, J. RCARD, M. BOREL, and c. GOT: Cinetics of Yeast Hexokinase. 1. Xiiropcsn J. Uiochem. very different from that in which we worked. Further, the analysis of the equations presented by Boyer [23], using values of velocity constants that we worked out, shows that the ADP and ATP concentrations used by Fromm [lo] are insufficient to allow the observation of a decrease in the exchange rate. As with the kinetic studies [9,10,20], the application [lo] of Boyer s method [23] to the study of hexokinase has not, therefore, lent support for a random mechanism. t is possible that the ordered model, which seems to us justified by our results, is too simplified, and may not represent all the types of interaction that can exist between hexokinase, the reactants, and the reaction products. Nevertheless, it seems to us that it represents the fundamental model of the enzyme action. The senior author (J. R.) is pleased to acknowledge with thanks fruitful discussions and constructive criticisms of Drs. G. N. Cohen, M. Lazdunski, J. Yon, and Prof. R. Wurmser. Thanks are also due to Mrs. Grossman for carefully reading the manuscript. REFERENCES 1. Agren, G., and Engstrom,L., Acta Chem. Scand. 10 (1956) Fromm, H. J., and Zewe, V., J. Biol. Chem. 237 (1962) Hanson, T. L., and Fromm, H. J., J. Biol. Chem. 240 (1965) Hammes, G. G., and Kochavi, D., J. Am. Chem. Soc. 84 (1962) Harnmes, G. G., and Kochavi, D., J. Am. Chem. Soc. 84 (1962) Hammes. G. G.. and Kochavi. D.. J. Am. Chem. SOC., * 84 (1962) Toews. C. J.. Biochern. J. 100 (1966) Cleland, 14. W., Biochinz. Biophys. Acta, 67 (1963) Fromm, H. J., and Zewe, V., J. Biol. Chem. 237 (1962) Fromm, H. J., Silverstein, E., and Boyer, P. D., J. Biol. Chem. 239 (1964) Ottolenghi, P., Cornpt. Rend. Trac. Lab. Carlsberg, 34 (1964) Raaflaud, J., and Leupin,., Helv. Chim. Acta, 39 (1956) Morrison, J. F., O Sullivan, W. J., and Ogston, A. G., Biochirn. Biophys. Acta, 52 (1961) Darrow, R. A., and Colowick, S. P., Methods in Enzymology (edited by S. P. Colowick, and N. 0. Kaplan). Academic Press, Xew York 1961, Vol. V, p Bock, R. M., Ling, N. S., Morel], S. A., and Lipton, 8. H., Arch. Biochem. Biophys. 62 (1956) Burton, <., Biochem. J. 71 (1959) Dalziel, K., Acta Chem. Scand. 11 (1957) Cohn, M., Biochemistry, 2 (1963) Zewe, V., Promm, H. J., and Fabiano, R., J. Biol. Chena. 239 (1964) Robbins, E. A., and Boyer, P. D., J. Biol. Chern. 224 (1957) Bock,R.M., The Enzymes (edited by P. D. Boyer, H. Lardy, and K. Myrback). Academic Press, New York 1961, Vol. 2, p O Sullivan, W. J., and Perrin, D. D., Biochemistry, 3 (1964) Boyer, P. D., Arch. Biochem. Biophys. 82 (1959) Cleland, W. W., Ann. Reo. Biochem. 36 (1967) 77. G. Noat, J. Ricard, f. Borel, and C. Got Laboratoire de Physiologie v6ghtale de la Facult6 des Sciences Traverse de la Barasse, F-13 Marseille-13, France