Regulation of Stromal Sedoheptulose 1,7-Bisphosphatase Activity by pH and Mg2+ Concentration*

A scheme is proposed for the regulation of stromal sedoheptulose 1,7-bisphosphatase activity which en-larges upon a previously elaborated mechanism (Wood- row, I. E., and Walker, D. A. (1983) Biochim. Biophys. Acta 722, 508-516). The latter involves oxidized (in- active) and reduced (active) enzyme forms. Both the free enzymes and the enzyme-substrate complexes undergo slow oxidation/reduction. This study exam-ines the behavior of the system under pH and M 8 + concentration regimes that are likely to occur in the chloroplast stroma. The control of enzyme activity by pH can be described in terms of each free enzyme and enzyme-substrate complex existing in protonated and nonprotonated forms. The molecular dissociation constants for each protonation reaction were calculated from kinetic data. Mg“+ concentration changes modu-late these constants. Under conditions that are likely to obtain in the stroma in the dark, the model predicts that approximately 99.1% of the enzyme will be in the inactive forms. Such inactivation is important since it would prevent the reductive pentose phosphate path- way from operating in darkness. Upon illumination the stromal pH

roplasts caused an inhibition of CO, fixation and an increase in both the fructose 1,6-bisphosphate and sedoheptulose 1,?bisphosphate pool sizes (Hiller and Bassham, 1965;Pedersen et al., 1966;Purczeld et al., 1978;Enser and Heber, 1980;Flugge et al., 1980). The rise in these metabolite levels and the concomitant decline in the carbon flux was interpreted to mean that the activities of fructose bisphosphatase and sedoheptulose bisphosphatase are sensitive to pH changes in the 7-8 range and that, under conditions of declining pH, these enzymes play a significant role in limiting the rate of CO, fixation. The transfer of protons across the thylakoid membrane is believed to be electrically compensated for by a countertransfer of MgZ+ ions (Dilley and Vernon, 1965;Barber et al., 1974;Hind et al., 1974;Krause, 1974;Krause, 1977). Since the chloroplast envelope is relatively impermeable to MgZ+ (Pfluger, 1973;Gimmler et al., 1975), this transfer results in an increase in the stromal MgZ+ concentration (Hind et al., 1974;Chow et al., 1976). Portis et al. (1977) lowered the stromal MgZ' concentration of illuminated chloroplasts using a divalent ionophore. This effected a decline in the carbon flux and an increase in the sedoheptulose 1,7-bisphosphate and fructose 1,6-bisphosphate levels which were suggested to indicate that the bisphosphatases limited the carbon flux under conditions of declining M$+ concentration.
In the present report we enlarge upon a previously proposed model for the regulation of sedoheptulose 1,7-bisphosphatase (Woodrow and Walker, 1983) to include the role of stromal pH and MgZ' concentration changes. This unified view of the relationship between enzyme kinetic parameters, the redox state of ferredoxin, and the stromal H+, Mp", and sedoheptulose 1,7-bisphosphate concentrations allows predictions to be made concerning the degree of activation of sedoheptulose 1,7-bisphosphatase under specific conditions. It is probable that enzyme activity in the chloroplast is, under most conditions, related to the light intensity since the latter controls all the factors which regulate sedoheptulose 1,7-bisphosphatase activity. In the extreme case (darkness), it is estimated that less than 1% of the total enzyme is in the active form. Inactivation of sedoheptulose 1,7-bisphosphatase in darkness, therefore, accounts for the cessation of CO, fixation by ribulose 1,5-bisphosphate carboxylase.

Miterials
Wheat (Triticum aestioum L. cv . ) and Hepes (c".) buffers. The dotted section represents the activities corrected for the inhibition observed in the presence of Hepes.

Methods
Preparation of Sedoheptulose 1,7-Bisphosphutase-Sedoheptulose 1,7-bisphosphatase was purified by the procedure outlined by Woodrow and Walker (1982). This preparation was loaded onto a column (2 cm2 X 6 cm) of hydroxylapatite previously equilibrated with 50 mM Na acetate, pH 5.8, and 2 mM 8-mercaptoethanol. Protein was eluted in a linear gradient of 0-300 mM &PO4. Active fractions were combined and concentrated in an Amicon ultrafiltration cell fitted with a PM-10 membrane. The enzyme was estimated to be about 90% pure by sodium dodecyl sulfate-polyacrylamide gel electrophoresis and had a final specific activity of 42 units mg" protein (bovine serum albumin standard). Enzyme was stored in 20% glycerol and 50 mM Tricine-NaOH' (pH 8.0) in liquid nitrogen. Protein was determined by the procedure of Lowry et al. (1951).
Determination of Sedoheptulose 1,7-Bisphosphatase Activity-Enzyme activity was measured at 20 "C using a continuous spectrophotometric assay which couples the formation of sedoheptulose 7phosphate to the oxidation of NADH (Woodrow and Walker, 1982). The reaction was followed at 340 nm using a Pye-Unicam SP-1800 spectrophotometer. The standard reaction mixture contained, in a final volume of 1 ml: 50 mM buffer; 10 mM MgCl,; 20 mM KCI; 0.1 mM A T P 1 mM phosphoenolpyruvate; 0.15 mM NADH; 20 mM dithiothreitol; 0.1 mM sedoheptulose 1,7-bisphosphate; 2 units of pyruvate kinase; 2 units of lactate dehydrogenase; 0.5 unit of 6phosphofructokinase; and sedoheptulose bisphosphatase solution. The latter was normally used to initiate the reaction. Calcium was not added to the reaction mixture although it may increase the rate of enzyme activation (Wolosiuk et al., 1982). The activation kinetics did not vary, under standard conditions, throughout the experiments. Two buffers were used in the experiments: Tricine (pH 7.7-8.4) and Hepes (pH 7.25-7.8). The reaction velocities were standardized around those obtained with Tricine buffer (Fig. 1).
Analysis of Reaction Progress Curves--Reaction progress curves (product formation with time) were analyzed by plotting log ( V f -Vob) versm time, where V, is the final steady state reaction velocity and V,,, the instantaneous rate of product formation. These plots yielded the apparent rate constants for enzyme activation (Woodrow and Walker, 1983). Activation was, in all cases, described by a single first order rate constant. The contribution of the coupled enzyme system to the apparent activation kinetics was discussed in a previous study (Woodrow and Walker, 1983).
addition of tetraethylammonium bromide. The interaction between the latter, sedoheptulose 1,7-bisphosphate and Mg2+ is assumed to be negligible. The pH meter was calibrated at 20 "C using 50 mM potassium hydrogen phthalate (pH 4.0) and 50 mM sodium borate (pH 9.22). The titration was repeated at three levels of MgCl,.

RESULTS
Titration of Sedoheptulose 1,7-Bisphosphate--The titration curve of sedoheptulose 1,7-bisphosphate over the pH range 4 to 8 shows a single inflection of about pH 6.42. pK, values of the third (pK,,) and fourth (p&) dissociation constants for sedoheptulose 1,7-bisphosphoric acid at an ionic strength of 0.08 M of 6.02 and 6.82, respectively, were estimated from the pH and slope at the midpoint ( Table I) (Martell and Calvin, 1952). The separation of these values is only slightly greater than that expected for identical phosphate groups (Martell and Calvin, 1952).
The ionic species most probably present in the current experiments are related by the following equilibria. PKI PK, The stability constants of the magnesium sedoheptulose 1.7bisphosphatase complexes are given by K1, Kz, and Ka. pK,, and pK,, are pK values of the dissociation constants for the MgHZSBP and MgHSBP-species, respectively.
In the absence of Mg", the amount of sedoheptulose 1,7bisphosphate in the tetraanionic state over the pH range used in the kinetic experiments is shown in Table 11. Titrations in the presence of 2, 10, and 20 mM MgCl2 were also performed to evaluate the other equilibrium constants (Table I). Approximate values for K2 and K3 of 159 M" and 587 M-' , respectively, were calculated using the method described by O'Sullivan and Perrin (1964). The pK, values of the dissociation constants K,, and Km2 are approximately 5.43 and 6.24, respectively. Over the pH range used in the kinetic experiments and in the presence of 10 mM M$+, most of the sedoheptulose 1,7-bisphosphate occurs in the MgSBP2-form (Table 11). It is, therefore, probable that the latter is a substrate for the catalytic reaction. Nevertheless, formation of species such as Mg,SBP and Mg(SBP)z-cannot be excluded, especially at higher M e levels.
Regulation of Sedoheptulose 1,7-Bisphosphutase Actiuity-The dependence of the steady state reaction velocity ( V I ) upon the proton concentration is consistent with the simple dibasic acid model of Michaelis and Davidsohn (1911). The data were analyzed by plotting the logarithms of the kinetic constants against pH (Dixon, 1953). Fig. 3 shows a plot of log V uersus pH. V was calculated from Lineweaver-Burk plots and represents the maximum reaction velocity at given H+ and M$+ concentrations. Over the pH range likely to occur in the chloroplast stroma, the data are consistent with the occurrence of a single ionization step. The second step of the

P"
Michaelis and Davidsohn (1911) model is negligible over this pH range. Since most of the substrate exists as a single species (MgSBP2-) over this pH range, changes in apparent kinetic properties of sedoheptulose 1,7-bisphosphatase do not appear t o be due to substrate effects. The plot of log V versus pH was made using both 10 and 2 mM M$+, and molecular dissociation pK values of 7.67 and at least 8.3, respectively, were recorded for the active enzyme-substrate complex. The plot of log (V/K,) versus pH shown in Fig. 4 gives a pK value for ionization of the free active enzyme of 7.82 (10 mM M C ) .
In both graphs, the slope of the linear portions at the lower pH values is about 1. This probably indicates that one protonation is required to convert the enzyme form predominant over these pH ranges into the active form (Dixon, 1953).
The activation of sedoheptulose 1,7-bisphosphatase was studied under several H+ regimes at constant concentrations of substrate, reductant, and Mg2+ (Fig. 5). Plots of T (7-' is the apparent rate constant for enzyme activation) versus the H+ concentration yielded pK6 (Fig. 2) values of 8.49 and 8.8 for 10 mM Mg2f and 2 mM M$+, respectively. The linear relationship between 7 and the H' concentration is consistent with the models shown in Fig. 2. The Ks value represents the molecular dissociation constant for the inactive enzyme-substrate complex. Graphs of 7 versus [sedoheptulose I,?-bisphosphate]" were made at various pH values. The inverse of the abscissa intercepts of these plots were then plotted against the inverse of the H+ concentration (Fig. 6)  results is discussed in the next section.
Analysis of Sedoheptulose 1,7-Bisphsphtase Activation Kinetics-The data presented in this study indicate that enzyme species undergo protonation/deprotonation reactions which can be described by the models presented in Fig. 2. The nonprotonated reduced form is the active species. The basis of this model was deduced by Woodrow and Walker (1983) who examined the catalytic and relaxation properties of the system under various substrate and reductant regimes. These measurements were made at a constant pH, and the apparent K, and KO for substrate binding to the inactive enzyme form were functions of KT, K4, K8, and kI3, and Ks K3, and K6, respectively.
In the present analysis, the protonation/deprotonation and substrate-binding reactions are assumed to be much faster than the oxidation/reduction reactions. This is a reasonable assumption because the latter have half-times of the order of minutes (Woodrow and Walker, 1983;Woodrow et al., 1983). It is also assumed that the overall reaction is irreversible, the substrate level remains constant, and there is no product inhibition. Under these conditions, the slowest relaxation will be due to the oxidation/reduction of the enzyme and enzymesubstrate complex and can be described by a single rate constant. The relationship between the latter and the catalytic reaction velocity was derived by Frieden (1970) and is given by where ut is the reaction velocity at time t (which is relative to the change in conditions that initiates the slow relaxation), ut the final reaction velocity at t = 00, uo the initial reaction velocity, and k the apparent rate constant describing the transition to the new steady state.
If it is assumed that the concentration of reductant is much greater than that of the enzyme and that the level of reductant ( R ) and oxidant (0) remains essentially constant, then the rate constant for activation/inactivation is given by (21

?ptulose 1,7-Bisphosphatase
If enzyme activation is examined and the amount of oxidant is assumed to remain essentially zero, then the slow relaxation can be described by

As the concentration of substrate is increased and [S]kz
Equations 6 and 7 allow the determination of the molecular dissociation constants (Ks and K6) and substrate-binding constant (K3) for the inactive enzyme form.
The concentration of individual enzyme species can be described by assuming that all the steps prior to product release are at equilibrium and that the time of measurement is long compared to the time required for adjustment to equilibrium. The concentrations of the species shown in and Eo is the total enzyme concentration.

DISCUSSION
The simplest model that is consistent with the measured dependence of the apparent K,, V, , , and T values on proton concentration is shown in Fig. 2. This mechanism is based upon one previously suggested to account for the effect of reductant, oxidant, and substrate on enzyme activity (Woodrow and Walker, 1983;Woodrow et al., 1983).
These mechanisms are based on kinetic evidence and, therefore, may represent simplifications of the actual mechanisms.

Regulation of Stromal Sedoheptulose l,?-Bisphosphatase
Description of the effect of pH as a single protonation reaction is undoubtedly a simplification (Tipton and Dixon, 1980). The mechanism could also conceivably involve oxidation/ reduction of the protonated enzyme forms. In this case, activation would also be described by a single first order rate constant. However, to be consistent with the present data the rate constants for reduction of the E . H and E.S.H forms must be much smaller than kl and h. It is also possible that the protonated enzyme forms bind substrate. Although this leads to different paths by which the active enzyme-substrate complex may be formed, the interpretation will not be affected if all the steps prior to product release are close to equilibrium. If the latter is not the case, substrate binding to the protonated enzyme forms would result in extremely complicated kinetics (Laidler, 1955;Peller and Alberty, 1963;Stewart and Lee, 1967;Kaplan and Laidler, 1967). The inclusion of more than one enzyme-substrate intermediate is also a possibility. However, the number of these intermediates is unimportant in terms of describing the behavior of the system since the constants obtained from the pH dependence of V are average values weighted in favor of the predominant complex (Tipton and Dixon, 1980).
The proton concentration has a multiple role in the present model; it controls the apparent K,' and V,, values as well as the total amount of enzyme in the reduced form. Variations in pH will cause a net shift of enzyme from the active to the inactive forms or vice versa. This phenomenon is caused by the differences between pKs and p&, and pK7 and p&. The dependence of the concentration of the various enzyme species upon the proton, reductant, oxidant, and substrate concentrations is described in Equations 8-12. By altering the apparent p& and p& (and almost certainly pKs and pK7) values, M e also controls the distribution of enzyme between protonated and nonprotonated and oxidized and reduced forms (Table   111). Low levels of Mg2+ may also affect the system by reducing the proportion of substrate in the MgSBPZ-form. Effects of H+ and Mg2+ consistent with the present proposals were also observed by Laing et al. (1981) using a chloroplast extract. The pH for optimal enzyme activity was shifted by changing the M e concentration. A similar effect was observed by Minot et al. (1982) for stromal fructose 1,6-bisphosphatase. These authors also used a single protonation step to describe the effect of the H+ concentration on enzyme activation. In the chloroplast, the kinetic properties of sedoheptulose 1,7-bisphosphatase appear to be ultimately controlled by the light intensity. Both the stromal H+ and M$+ concentrations are linked to the rate of photosynthetic electron transport. And the R/O ratio, which is used to describe the relationship between the amount of reductant available for enzyme activation and the position of the equilibrium between active and inactive enzyme forms, appears to be linked to the redox state of the ferredoxin pool (Woodrow and Walker, 1983). In this way, the light intensity could control the amount of enzyme in the active form and the apparent K,,, and V , , values. It is conceivable that at nonsaturating light intensities, changes in the flux through the reductive pentose phosphate pathway may be paralleled by similar changes in sedoheptulose 1,7bisphosphatase activity. In darkness, inactivation of this enzyme is necessary to prevent futile cycling of metabolites and   would contribute to the cessation of CO, fixation. Table I11 shows the anticipated distribution of enzyme species under conditions which approximate those obtaining in the chloroplast stroma in the light and the dark. Assuming a constant O/R ratio, the pH and Mg2+ changes alone account for a 17fold reduction in the proportion of enzyme in the active form. This change is magnified by a concomitant change in the redox state, with 99.1% of the enzyme in inactive forms with an O/R ratio of 5. This represents a 60-fold inactivation of sedoheptulose 1,7-bisphosphatase in darkness.