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Sustained oscillations in a reconstituted enzyme system containing phosphofructokinase and fructose 1,6-bisphosphatase
ARCHIVES OF BIOCHEMISTRY AND BIOPHYSICS Vol. 222, No. 2, April 15, pp. 657660, 1983
COMMUNICATION Sustained Oscillations in a Reconstituted Enzyme System Containing Phosphofructokinase and Fructose 1 ,&Bisphosphatase KLAUS
ESCHRICH,’ AND
Institute
WOLFGANG SCHELLENBERGER, EBERHARD HOFMANN
of Physiological Chemistry, Karl-Afarx-University, 7010 Leipzig, Liebigstrasse 16, German Democratic Republic
Received November
29, 1982, and in revised form February
1, 1983
In a reconstituted open and homogeneous enzyme system containing phosphofructokinase, fructose 1,6-bisphosphatase, pyruvate kinase, adenylate kinase, and glucose6-phosphate isomerase sustained oscillations could experimentally be generated. The approach is based on a stirred flow-through reaction chamber. The periodic motions of the reactants are mainly caused by the antagonistic allosteric effects of the adenine nucleotides on the activities of the phosphofructokinase and fructose 1,6-bisphosphatase.
The discovery of the oscillatory glycolysis in various cells and cell-free extracts was of considerable influence on the development of dynamic conceptions about metabolic regulation (1, 2). The theoretical analysis based on simplified reaction schemes led to the view that phospbofructokinase’ owing to its allosteric properties is responsible for the generation of the glycolytic periodicities (3, 4). Hitherto, in reconstituted glycolytic enzyme systems oscillations could not be generated experimentally and the meehanism underlying the oscillating motions of the glycolytic intermediates as well as their biological function are still a matter of debate. A recent theoretical analysis suggested that oscillations may originate from a kinetic cooperation of phosphofructokinase with fructose 1,6-bisphosphatase (5). The periodic changes of the activities of the
two enzymes were considered to be of significance to the temporal organization of the fructose 6-phosphate/fructose 1,6-bisphosphate reaction cycle because of their effect in reducing the ATP-wasting cycling of the hexose phosphates. In a reconstituted homogeneous enzyme system operating under open conditions and composed of phosphofructokinase, pyruvate kinase, adenylate kinase, and glucose-6-phosphate isomerase we recently demonstrated experimentally the appearance of hysteretic behavior based on the existence of alternative stable stationary states. However, no oscillations were found to occur (6). As shown in this contribution the system attains the capability of generating sustained oscillations, if fructose 1,6-bisphosphatase is included into the reaction network. MATERIALS
’ To whom all correspondence should be addressed. ’ Abbreviations used: Substrates; Fru-6-P, fructose 6-phosphate; Fru-1,6-P,, fructose 1,6-bisphosphate; Gle-6-P, glucose 6-phosphate; P-Pyr, phosphoenolpyruvate; Enzymes; AK, adenylate kinase (EC 2.7.4.3); FbPase, fructose l,&bisphosphatase (EC 3.1.3.11); GPI, glucose-&phosphate isomerase (EC 5.3.1.9); PFK, 6-phosphofructokinase (EC 2.7.1.11); PK, pyruvate kinase (EC 2.7.1.40); V, maximum activity of the indicated enzyme in rmol/min (U).
AND
METHODS
Phosphofructokinase was prepared from Sac&aromyces eertitioe (7) and fructose l,&bisphosphatase (neutral form) from pig liver (Ch. Schubert, this institute, unpublished procedure). Pyruvate kinase, adenylate kinase (both from rabbit muscle), glucose6-phosphate isomerase (from yeast), substrates, coensymes, and buffer substances were purchased from Boehringer (Mannheim, FRG). All other chemicals were of analytical grade. 657
0003-9861/83 ‘$3.00 Copyright All rights
0 1993 by Academic Press, Inc. of reproduction in any form reserved.
658
ESCHRICH,
SCHELLENBERGER.
The kinetic analysis of the enzymes and the flow experiments were carried out at 25°C in 0.1 M imidazole/HCl buffer, pH 6.6, in the presence of 20 mM KzHPOI, 20 mM MgClz, 100 mEd KCl, 0.1 mM ethylenediaminetetraacetie acid, and 2.5 mM mercaptoethanol. Flow-through expen’ments. The kinetic interactions of the enzymes were investigated in a stirred tank reactor through which a continuous flow of substrates and enzymes was maintained. In a modification of the published procedure (8) the thermostated reactor (volume 1 ml) is fed continuously with equal rates from two reservoirs, one containing the substrates, the other containing the enzymes. The concentrations of the substrates and enzymes in the two reservoirs are twice the respective concentrations given in the legend of Fig. 2. The dynamics of the reactant concentrations in the reactor were followed in the efflux solution which contains the enzymes and reactants in the concentrations reached in the reactor. Immediately after leaving the reactor the efflux solution was continu1 M) ously mixed with 2 M HCIOl (final concentration to stop the enzyme reactions and 4-min fractions were collected. After neutralization the reactant concentrations were determined enzymatically (9). Mathematical modelling. The procedure for the analysis of the dynamics of the reaction system was described previously (8). The treatment is based on a set of differential equations governing the time evolution of the reactant concentrations. These equations take into account the enzymatic reactions and the flow processes. The enzymatic conversions are characterized by steady state rate equations derived from the kinetic investigation of the individual enzymes. For phosphofructokinase and pyruvate kinase the steady state rate laws as published (6) are used. The properties of fructose 1,6-bisphosphatase have been summarized by Horecker et al. (10) and Benkovich and DeMaine (11). The enzyme exhibits high affinity to its substrate fructose 1,6-bisphosphate and is inhibited by AMP, fructose 6-phosphate, and fructose l,&bisphosphate. The rate of fructose 1,6-bisphosphatase (v) follows quantitatively Eqs. [l]-[3], which are isomorphous with the allosteric model of Monod et al. (12): r = ‘(K
[Fru-1,6-Pzj + [Fru-1,6-Pz])
1 (1 + L)
/ (1 + [AMWKAMP.T) ’ = LO
HOFMANN
KF~-I,E-P~ the affinity
of the enzyme to its substrate. between the product and the substrate at the active site. & is the allosteric constant of the tetrameric enzyme. KA,p,T, KAMp,R,KFm-l,~pz,T,KFru-1,Gp2,R are the dissociation constants of AMP and fructose 1,6-bisphosphate to the regulatory sites of the T and the R states of the enzyme.
KFru4.Pexpresses the competition
KF~~-,,B-P~ = 1.8 W; KAMP,T = &ru-WPZ,T
40PM;
= 420 W
KAMP,R = 220lJM KFru-1.CPe.R = 930 W
According to the stoichiometric structure of the reaction network (Fig. 1) three reactant pools are distinguishable for which conservation equations hold: the total concentration of ATP, ADP, and AMP, the concentration of the hexose phosphates, and the total concentration of phosphoenolpyruvate plus pyruvate. Adenylate kinase and glucose-6-phosphate isomerase were supplied in excess compared with the other enzymes so that quasi-equilibria between the adenine nucleotides and hexose monophosphates are maintained. The time evolution of the reactants is governed by three nonlinear differential equations describing the motions of ATP, hexose monophosphates, and phosphoenolpyruvate, respectively. All other metabolites are computable from these quantities due to pool constancy and maintenance of quasi-equilibria by adeInflux
of enzymes I I
and
substrates I
\’
(1 + [Fru-6-P]/Kr,,r). K = KF~~-I,o-P~activity
45 PM
Lo = 0.1
x (1 + [FrU-1,6-P2]/KF~-~.s-Pp.T) PI
the maximum
KF~u-E-P =
PI
(1 + [AMP]/&ur,a) X (1 + [Fru-1,6-P2Y~FFlu-,.6R.R)
V designates
AND
Efflux
FIG. 1. Cooperation
r31
of the enzyme
of phosphofructokinase, fructose 1,6-bisphosphatase, pyruvate kinase, adenylate kinase, and glucose-6-phosphate isomerase in the reaction chamber.
OSCILLATIONS
IN AN ENZYME
nylate kinase and glucose-6-phosphate isomerase. Hence, the state of the system is completely determined by the experimental determination of only one reactant from each pool (6). RESULTS
AND
DISCUSSION
Figure 2 shows the results of a representative experiment. For the applied experimental conditions sustained oscillations were predicted theoretically. In order to characterize the temporal pattern of the reaction network the actual concentrations of the hexosemonophosphates, ATP and phosphoenolpyruvate were determined experimentally. The constancy of the pools and maintenance of quasi-equilibria between the hexosemonophosphates and the adenine nucleotides were regularly checked experimentally. Hence, at each moment the concentrations of AMP, ADP, fructose 1,6-bisphosphate, and pyruvate are unequivocally determined. In period I of the experiment fructose 1,6-bisphosphatase is absent. A unique and stable stationary state is approached (6). At t = 60 min fructose 1,6bisphosphatase is introduced and a constant concentration of this enzyme in the reactor is maintained in period II. The addition of fructose 1,6-bisphosphatase gives rise to oscillatory motions of the reactants. The sustained character of the periodicities is obvious from the constancy of the amplitude during three oscillatory periods. Figure 3 demonstrates a computer simulation of
SYSTEM
659
the time evolution of the reactants (Fig. 3A) and the respective variations of the actual activities of the enzymes (Fig. 3B). At the end of period I a dynamic balance in respect to all metabolites is attained. The addition of fructose l,&bisphosphatase perturbs the balance between the hexose phosphates. The increase of fructose 6-phosphate leads to an enhancement of phosphofructokinase until a new quasi-stationary level of the hexose monophosphates is attained. Due to the increased activity of phosphofructokinase the ATP balance becomes negative resulting in a decrease of ATP. At a stationary high level of ATP (period I) small diminutions of ATP lead to large relative increases of ADP and AMP (not shown) because of the maintenance of the adenylate kinase equilibrium. This enhances efficiently the activity of pyruvate kinase. In consequence a high ATP level is transitorily maintained at the expense of phosphoenolpyruvate. ATP collapses when phosphoenolpyruvate is exhausted. Then the pyruvate kinase activity is limited by the influx rate of phosphoenolpyruvate. The increased AMP level gives rise to a strong activation of phosphofructokinase and to an inhibition of fructose 1,6-bisphosphatase. These changes induce a dramatic decrease in the concentration of fructose 6-phosphate which causes a diminution of the activity of phosphofructokinase. A critical activity of the enzyme is passed at which the ATP balance becomes positive. The increase of ATP leads to further diminution of the phosphofructokinase activity as a con-
I
II
3
200
300
time (min I FIG. 2. Generation of sustained oscillations in the reconstituted enzyme system. A, [ATP]; 0, [PPyr]; 0, ([Fru-6-P] + [Glc-6-P]). Experimental conditions: concentrations of the substrates in the influx solution [ATP]rn = 3 mM, [P-Pyr] m = 6.3 mM, [Fru-6-P&n = 6 mM; flow rate: 0.025 ml/min; maximum activities of the enzymes in the reactor (U means micromole of substrate conversion per minute): VP,, = 1.1 U/ml, VP, = 7 U/ml, V,,, = 7 U/ml, VAx = 9 U/ml; period I (t < 60 min): VFbpase = 0; period II (t > 60 min): VpbFbpare = 0.2 U/ml.
ESCHRICH,
SCHELLENBERGER,
AND
HOFMANN
accelerate the increase of fructose B-phosphate. As in the beginning of period II the accumulation of fructose g-phosphate produces an enhancement of the activity of phosphofructokinase and the oscillatory cycle starts again. During the oscillations transitory balances with respect to the various reactants are reached. However, a stationary state with respect to one reactant correlates with a nonstationary state for the others. This maintains the reactions in the oscillatory state. REFERENCES
200
x)0 time
hd
FIG. 3. Computation of the periodic motions of the reactants (A) and of the actual activities of the involved enzymes (B) in the reconstituted enzyme system (conditions as in Fig. 2).
sequence of which the concentration of fructose 6phosphate starts to increase again. When ATP approaches its upper possible level, ADP and AMP decrease to very low concentrations. The low ADP reduces the pyruvate kinase activity which becomes less than the influx rate of phosphoenolpyruvate. Consequently, phosphoenolpyruvate increases. The decrease of AMP gives rise to a reactivation of fructose 1,6-bisphosphatase and a diminution of phosphofructokinase. These changes
1. HESS, B., AND BOITEUX, A. (1971) Annu. Rev. B&hem. 40, 237-258. 2. HEINRICH, R., RAPOPORT, S. M., AND RAPOPORT, T. A. (1977) Proc Biophys. Mol. BioL 32, l-82. 3. GOLDBETER, A., AND LEFEVER, R. (1972) Biophys. J 12, 1302-1305. 4. SELKOV, E. E. (1975) Eur. J. Biochem 59.151-157. 5. SELKOV, E. E. (1980) Ber. Bunsenges. Phys. Chem 84,399-402. 6. ESCHRICH, K., SCHELJZNBERGER, W., AND HOFMANN, E. (1980) Arch. Bioche-m. Biophys. 205, 114-121. 7. DIEZEL, W., B~~HME, H.-J., NISSLER, K., FREYER, R., HEILMANN, W., KOPPERSCHLAGER, G., AND HOFMANN, E. (1973) Eur. 1. B&hem. 38,479488. 8. SCHELLENBERGER, W., ESCHRICH, K., AND HOFMANN, E. (1981) in Advances in Enzyme Regulation (Weber, G., ed.), Vol. 19, pp. 257-284, Pergamon, Oxford/New York. 9. BERGMEYER, H. U. (1974) Methods of Enzymatic Analysis, Vols. I-IV, Verlag Chemie, Weinbeim. 10. HORECKER, B. L., MELLONI, E., AND PONTREMOLI, S. (1975) in Advances in Enzymology (Meister, A., ed.), Vol. 42, pp. 193-226, Wiley-Interscience, New York. 11. BENKOVIC, S. J., AND DEMAINE, M. M. (1982) Advan Enzymd 53; 45-82. 12. MONOD, J., WYMAN, J., AND CHANGEU~, J. P. (1965) J. MoL BioL 12. 88-118.
COMMUNICATION Sustained Oscillations in a Reconstituted Enzyme System Containing Phosphofructokinase and Fructose 1 ,&Bisphosphatase KLAUS
ESCHRICH,’ AND
Institute
WOLFGANG SCHELLENBERGER, EBERHARD HOFMANN
of Physiological Chemistry, Karl-Afarx-University, 7010 Leipzig, Liebigstrasse 16, German Democratic Republic
Received November
29, 1982, and in revised form February
1, 1983
In a reconstituted open and homogeneous enzyme system containing phosphofructokinase, fructose 1,6-bisphosphatase, pyruvate kinase, adenylate kinase, and glucose6-phosphate isomerase sustained oscillations could experimentally be generated. The approach is based on a stirred flow-through reaction chamber. The periodic motions of the reactants are mainly caused by the antagonistic allosteric effects of the adenine nucleotides on the activities of the phosphofructokinase and fructose 1,6-bisphosphatase.
The discovery of the oscillatory glycolysis in various cells and cell-free extracts was of considerable influence on the development of dynamic conceptions about metabolic regulation (1, 2). The theoretical analysis based on simplified reaction schemes led to the view that phospbofructokinase’ owing to its allosteric properties is responsible for the generation of the glycolytic periodicities (3, 4). Hitherto, in reconstituted glycolytic enzyme systems oscillations could not be generated experimentally and the meehanism underlying the oscillating motions of the glycolytic intermediates as well as their biological function are still a matter of debate. A recent theoretical analysis suggested that oscillations may originate from a kinetic cooperation of phosphofructokinase with fructose 1,6-bisphosphatase (5). The periodic changes of the activities of the
two enzymes were considered to be of significance to the temporal organization of the fructose 6-phosphate/fructose 1,6-bisphosphate reaction cycle because of their effect in reducing the ATP-wasting cycling of the hexose phosphates. In a reconstituted homogeneous enzyme system operating under open conditions and composed of phosphofructokinase, pyruvate kinase, adenylate kinase, and glucose-6-phosphate isomerase we recently demonstrated experimentally the appearance of hysteretic behavior based on the existence of alternative stable stationary states. However, no oscillations were found to occur (6). As shown in this contribution the system attains the capability of generating sustained oscillations, if fructose 1,6-bisphosphatase is included into the reaction network. MATERIALS
’ To whom all correspondence should be addressed. ’ Abbreviations used: Substrates; Fru-6-P, fructose 6-phosphate; Fru-1,6-P,, fructose 1,6-bisphosphate; Gle-6-P, glucose 6-phosphate; P-Pyr, phosphoenolpyruvate; Enzymes; AK, adenylate kinase (EC 2.7.4.3); FbPase, fructose l,&bisphosphatase (EC 3.1.3.11); GPI, glucose-&phosphate isomerase (EC 5.3.1.9); PFK, 6-phosphofructokinase (EC 2.7.1.11); PK, pyruvate kinase (EC 2.7.1.40); V, maximum activity of the indicated enzyme in rmol/min (U).
AND
METHODS
Phosphofructokinase was prepared from Sac&aromyces eertitioe (7) and fructose l,&bisphosphatase (neutral form) from pig liver (Ch. Schubert, this institute, unpublished procedure). Pyruvate kinase, adenylate kinase (both from rabbit muscle), glucose6-phosphate isomerase (from yeast), substrates, coensymes, and buffer substances were purchased from Boehringer (Mannheim, FRG). All other chemicals were of analytical grade. 657
0003-9861/83 ‘$3.00 Copyright All rights
0 1993 by Academic Press, Inc. of reproduction in any form reserved.
658
ESCHRICH,
SCHELLENBERGER.
The kinetic analysis of the enzymes and the flow experiments were carried out at 25°C in 0.1 M imidazole/HCl buffer, pH 6.6, in the presence of 20 mM KzHPOI, 20 mM MgClz, 100 mEd KCl, 0.1 mM ethylenediaminetetraacetie acid, and 2.5 mM mercaptoethanol. Flow-through expen’ments. The kinetic interactions of the enzymes were investigated in a stirred tank reactor through which a continuous flow of substrates and enzymes was maintained. In a modification of the published procedure (8) the thermostated reactor (volume 1 ml) is fed continuously with equal rates from two reservoirs, one containing the substrates, the other containing the enzymes. The concentrations of the substrates and enzymes in the two reservoirs are twice the respective concentrations given in the legend of Fig. 2. The dynamics of the reactant concentrations in the reactor were followed in the efflux solution which contains the enzymes and reactants in the concentrations reached in the reactor. Immediately after leaving the reactor the efflux solution was continu1 M) ously mixed with 2 M HCIOl (final concentration to stop the enzyme reactions and 4-min fractions were collected. After neutralization the reactant concentrations were determined enzymatically (9). Mathematical modelling. The procedure for the analysis of the dynamics of the reaction system was described previously (8). The treatment is based on a set of differential equations governing the time evolution of the reactant concentrations. These equations take into account the enzymatic reactions and the flow processes. The enzymatic conversions are characterized by steady state rate equations derived from the kinetic investigation of the individual enzymes. For phosphofructokinase and pyruvate kinase the steady state rate laws as published (6) are used. The properties of fructose 1,6-bisphosphatase have been summarized by Horecker et al. (10) and Benkovich and DeMaine (11). The enzyme exhibits high affinity to its substrate fructose 1,6-bisphosphate and is inhibited by AMP, fructose 6-phosphate, and fructose l,&bisphosphate. The rate of fructose 1,6-bisphosphatase (v) follows quantitatively Eqs. [l]-[3], which are isomorphous with the allosteric model of Monod et al. (12): r = ‘(K
[Fru-1,6-Pzj + [Fru-1,6-Pz])
1 (1 + L)
/ (1 + [AMWKAMP.T) ’ = LO
HOFMANN
KF~-I,E-P~ the affinity
of the enzyme to its substrate. between the product and the substrate at the active site. & is the allosteric constant of the tetrameric enzyme. KA,p,T, KAMp,R,KFm-l,~pz,T,KFru-1,Gp2,R are the dissociation constants of AMP and fructose 1,6-bisphosphate to the regulatory sites of the T and the R states of the enzyme.
KFru4.Pexpresses the competition
KF~~-,,B-P~ = 1.8 W; KAMP,T = &ru-WPZ,T
40PM;
= 420 W
KAMP,R = 220lJM KFru-1.CPe.R = 930 W
According to the stoichiometric structure of the reaction network (Fig. 1) three reactant pools are distinguishable for which conservation equations hold: the total concentration of ATP, ADP, and AMP, the concentration of the hexose phosphates, and the total concentration of phosphoenolpyruvate plus pyruvate. Adenylate kinase and glucose-6-phosphate isomerase were supplied in excess compared with the other enzymes so that quasi-equilibria between the adenine nucleotides and hexose monophosphates are maintained. The time evolution of the reactants is governed by three nonlinear differential equations describing the motions of ATP, hexose monophosphates, and phosphoenolpyruvate, respectively. All other metabolites are computable from these quantities due to pool constancy and maintenance of quasi-equilibria by adeInflux
of enzymes I I
and
substrates I
\’
(1 + [Fru-6-P]/Kr,,r). K = KF~~-I,o-P~activity
45 PM
Lo = 0.1
x (1 + [FrU-1,6-P2]/KF~-~.s-Pp.T) PI
the maximum
KF~u-E-P =
PI
(1 + [AMP]/&ur,a) X (1 + [Fru-1,6-P2Y~FFlu-,.6R.R)
V designates
AND
Efflux
FIG. 1. Cooperation
r31
of the enzyme
of phosphofructokinase, fructose 1,6-bisphosphatase, pyruvate kinase, adenylate kinase, and glucose-6-phosphate isomerase in the reaction chamber.
OSCILLATIONS
IN AN ENZYME
nylate kinase and glucose-6-phosphate isomerase. Hence, the state of the system is completely determined by the experimental determination of only one reactant from each pool (6). RESULTS
AND
DISCUSSION
Figure 2 shows the results of a representative experiment. For the applied experimental conditions sustained oscillations were predicted theoretically. In order to characterize the temporal pattern of the reaction network the actual concentrations of the hexosemonophosphates, ATP and phosphoenolpyruvate were determined experimentally. The constancy of the pools and maintenance of quasi-equilibria between the hexosemonophosphates and the adenine nucleotides were regularly checked experimentally. Hence, at each moment the concentrations of AMP, ADP, fructose 1,6-bisphosphate, and pyruvate are unequivocally determined. In period I of the experiment fructose 1,6-bisphosphatase is absent. A unique and stable stationary state is approached (6). At t = 60 min fructose 1,6bisphosphatase is introduced and a constant concentration of this enzyme in the reactor is maintained in period II. The addition of fructose 1,6-bisphosphatase gives rise to oscillatory motions of the reactants. The sustained character of the periodicities is obvious from the constancy of the amplitude during three oscillatory periods. Figure 3 demonstrates a computer simulation of
SYSTEM
659
the time evolution of the reactants (Fig. 3A) and the respective variations of the actual activities of the enzymes (Fig. 3B). At the end of period I a dynamic balance in respect to all metabolites is attained. The addition of fructose l,&bisphosphatase perturbs the balance between the hexose phosphates. The increase of fructose 6-phosphate leads to an enhancement of phosphofructokinase until a new quasi-stationary level of the hexose monophosphates is attained. Due to the increased activity of phosphofructokinase the ATP balance becomes negative resulting in a decrease of ATP. At a stationary high level of ATP (period I) small diminutions of ATP lead to large relative increases of ADP and AMP (not shown) because of the maintenance of the adenylate kinase equilibrium. This enhances efficiently the activity of pyruvate kinase. In consequence a high ATP level is transitorily maintained at the expense of phosphoenolpyruvate. ATP collapses when phosphoenolpyruvate is exhausted. Then the pyruvate kinase activity is limited by the influx rate of phosphoenolpyruvate. The increased AMP level gives rise to a strong activation of phosphofructokinase and to an inhibition of fructose 1,6-bisphosphatase. These changes induce a dramatic decrease in the concentration of fructose 6-phosphate which causes a diminution of the activity of phosphofructokinase. A critical activity of the enzyme is passed at which the ATP balance becomes positive. The increase of ATP leads to further diminution of the phosphofructokinase activity as a con-
I
II
3
200
300
time (min I FIG. 2. Generation of sustained oscillations in the reconstituted enzyme system. A, [ATP]; 0, [PPyr]; 0, ([Fru-6-P] + [Glc-6-P]). Experimental conditions: concentrations of the substrates in the influx solution [ATP]rn = 3 mM, [P-Pyr] m = 6.3 mM, [Fru-6-P&n = 6 mM; flow rate: 0.025 ml/min; maximum activities of the enzymes in the reactor (U means micromole of substrate conversion per minute): VP,, = 1.1 U/ml, VP, = 7 U/ml, V,,, = 7 U/ml, VAx = 9 U/ml; period I (t < 60 min): VFbpase = 0; period II (t > 60 min): VpbFbpare = 0.2 U/ml.
ESCHRICH,
SCHELLENBERGER,
AND
HOFMANN
accelerate the increase of fructose B-phosphate. As in the beginning of period II the accumulation of fructose g-phosphate produces an enhancement of the activity of phosphofructokinase and the oscillatory cycle starts again. During the oscillations transitory balances with respect to the various reactants are reached. However, a stationary state with respect to one reactant correlates with a nonstationary state for the others. This maintains the reactions in the oscillatory state. REFERENCES
200
x)0 time
hd
FIG. 3. Computation of the periodic motions of the reactants (A) and of the actual activities of the involved enzymes (B) in the reconstituted enzyme system (conditions as in Fig. 2).
sequence of which the concentration of fructose 6phosphate starts to increase again. When ATP approaches its upper possible level, ADP and AMP decrease to very low concentrations. The low ADP reduces the pyruvate kinase activity which becomes less than the influx rate of phosphoenolpyruvate. Consequently, phosphoenolpyruvate increases. The decrease of AMP gives rise to a reactivation of fructose 1,6-bisphosphatase and a diminution of phosphofructokinase. These changes
1. HESS, B., AND BOITEUX, A. (1971) Annu. Rev. B&hem. 40, 237-258. 2. HEINRICH, R., RAPOPORT, S. M., AND RAPOPORT, T. A. (1977) Proc Biophys. Mol. BioL 32, l-82. 3. GOLDBETER, A., AND LEFEVER, R. (1972) Biophys. J 12, 1302-1305. 4. SELKOV, E. E. (1975) Eur. J. Biochem 59.151-157. 5. SELKOV, E. E. (1980) Ber. Bunsenges. Phys. Chem 84,399-402. 6. ESCHRICH, K., SCHELJZNBERGER, W., AND HOFMANN, E. (1980) Arch. Bioche-m. Biophys. 205, 114-121. 7. DIEZEL, W., B~~HME, H.-J., NISSLER, K., FREYER, R., HEILMANN, W., KOPPERSCHLAGER, G., AND HOFMANN, E. (1973) Eur. 1. B&hem. 38,479488. 8. SCHELLENBERGER, W., ESCHRICH, K., AND HOFMANN, E. (1981) in Advances in Enzyme Regulation (Weber, G., ed.), Vol. 19, pp. 257-284, Pergamon, Oxford/New York. 9. BERGMEYER, H. U. (1974) Methods of Enzymatic Analysis, Vols. I-IV, Verlag Chemie, Weinbeim. 10. HORECKER, B. L., MELLONI, E., AND PONTREMOLI, S. (1975) in Advances in Enzymology (Meister, A., ed.), Vol. 42, pp. 193-226, Wiley-Interscience, New York. 11. BENKOVIC, S. J., AND DEMAINE, M. M. (1982) Advan Enzymd 53; 45-82. 12. MONOD, J., WYMAN, J., AND CHANGEU~, J. P. (1965) J. MoL BioL 12. 88-118.