ATP sulfurylase from Penicillium chrysogenum. Molecular basis of the sigmoidal velocity curves induced by sulfhydryl group modification.

ATP sulfurylase from Penicillium chrysogenum is a noncooperative homooligomer containing three free sulfhydryl groups per subunit. Under nondenaturing conditions, one SH group per subunit was modified by 5,5'-dithiobis-(2-nitrobenzoate), or N-ethylmaleimide. Modification had only a small effect on kcat, but markedly increased the [S]0.5 values for the substrates, MgATP and SO4(2-). MgATP and adenosine-5'-phosphosulfate protected against modification. The SH-modified enzyme displayed sigmoidal velocity curves for both substrates with Hill coefficients (nH) of 2. Fluorosulfonate (FSO3-) and other dead-end inhibitors competitive with SO4(2-) activated the SH-modified enzyme at low SO4(2-) concentration. In order to determine whether the sigmoidicity resulted from true cooperative binding (as opposed to a kinetically based mechanism), the shapes of the binding curves were established from the degree of protection provided by a ligand against phenylglyoxal-dependent irreversible inactivation under noncatalytic conditions. Under standard conditions (0.05 M Na-N-(2-hydroxyethyl)piperazine-N'-3-propanesulfonic acid buffer, pH 8, 30 degrees C, and 3mM phenylglyoxal) the native enzyme was inactivated with a k of 2.67 +/- 0.25 X 10-3 s-1, whereas k for the SH-modified enzyme was 5.44 +/- 0.27 X 10-3 s-1. The increased sensitivity of the modified enzyme resulted from increased reactivity of ligand-protectable groups. Both the native and the SH-modified enzyme displayed hyperbolic plots of delta k (i.e. protection) versus [MgATP], or [FSO3-], or [S2O3(2-]) in the absence of coligand (nH = 0.98 +/- 0.06). The plots of delta k versus [ligand] for the native enzyme were also hyperbolic in the presence of a fixed concentration of coligand. However, in the presence of a fixed [FSO3-] or [S2O3(2-]), the delta k versus [MgATP] plot for the SH-modified enzyme was sigmoidal, as was the plot of delta k versus [FSO3-] or [S2O3(2-]) in the presence of a fixed [MgATP]. The nH values were 1.92 +/- 0.09. The results indicate that substrates (or analogs) bind hyperbolically to unoccupied SH-modified subunits, but in a subunit-cooperative fashion to form a ternary complex.

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$ T o whom correspondence and reprint requests should be addressed. 2.7.7.4) catalyzes the first reaction in the assimilation of inorganic sulfate: MgATP + SO:-MgPPi + APS.' The enzyme from Penicillium chrysogenum is a homooligomer with a subunit M, of about 69,000. Each subunit contains three free sulfhydryl groups, one of which can be readily modified under nondenaturing conditions. Tweedie and Segel (1) and later, Farley et al. (2) reported that chemical modification of this SH group had no effect on catalytic activity. However, in these earlier studies, activity was measured at near-saturating substrate concentrations. More recent studies disclosed that sulfhydryl modification markedly affected enzyme activity at subsaturating substrate concentrations (3). The experiments reported in this present paper were designed to characterize the kinetic consequences of SH group modification.

MATERIALS AND METHODS
Enzyme Purification and Assays-The purification of ATP sulfurylase and APS kinase, the assay methods (3-lo), and the general procedures used to characterize the kinetics of inactivation in the presence and absence of protective ligands (11-12) have been described previously.
Freshly prepared, homogeneous ATP sulfurylase was used in experiments where an accurate knowledge of active site concentration was required (e.g. Fig. 1). The specific activity of the homogeneous enzyme is 21 f 3 units X mg protein" in the molybdolysis assay and 8 f 1 units X mg protein" in the APS synthesis assay. Aged preparations with slightly decreased specific activities were used in some of the kinetics and inactivation experiments.
Protein concentration was determined from the absorbances (1-cm cuvette) at 278 nm (5), 280 and 260 nm and 280 and 235 nm (14). A typical stock solution was calculated to contain respectively, 0.97 mg X ml-', 0.96 mg X ml-', and 0.99 mg X ml-' by the above methods. bated with 150 p~ NEM in 0.05 M Na-MOPS, pH 7.0. After 1 h Prernodification with NEM-The enzyme (13 p~ sites) was incuresidual NEM was removed and the enzyme transferred to 0.05 M Na-EPPS, pH 8.0, by repeated washing on a Centricon@ membrane filter.
Inactivation by Phenylglyoral-The native or NEM-modified enzyme (0.5 PM sites unless otherwise indicated) was preincubated for various periods in 0.05 M Na-EPPS buffer (pH 8.0, 30 "C) containing 3 mM phenylglyoxal, the protective ligands, and (unless otherwise indicated) 5 mM excess M$+. The incubation volume was 0.22 ml. Periodically, a 20-p1 sample was withdrawn and the residual activity measured at 15 mM MgATP, 5 mM excess M$', and 30 mM SO:in a continuous spectrophotometric assay coupled to APS kinase, pyruvate kinase, and lactate dehydrogenase (8). Inactivation rate constants (kapp) were determined from the slopes of log % remaining activity versus time plots. At least three time points were used to The abbreviations used are: APS, adenosine 5'-phosphosulfate (5'-adenylylsulfate); SDS, sodium dodecyl sulfate; DTNB, 5,5'-dithiobis-(2-nitrobenzoate); pCMB, p-chloromercuribenzoate; A-485, acetamidomaleimidylstilbene disulfonic acid NEM, N-ethylmaleimide; MOPS, 3-(N-morpholino)propanesulfonic acid EPPS, N-(2-hydroxyethyl)piperazine-N'-3-propanesulfonic acid MES 2-(N-mor-pho1ino)ethanesulfonic acid. 16279 generate the linear semilog plot. In the absence of phenylglyoxal, no inactivation was evident over the experimental incubation periods (<30 min). In sequential quadruplicate measurements made over a 5h period with the same solution of phenylglyoxal, k,, varied by less than +4% from the mean. The variance in daily replicates using a freshly prepared phenylglyoxal solution each time was greater: kep, for the native enzyme averaged 2.7 X s-' with a maximum deviation of k0.3 X s-'; kapp for the NEM-modified enzyme was 5.4 X s-l with a maximum deviation of +0.4 X s-'. The variations affect Ak,.x,,, and kli,,,it but have no effect on the determination of [L]o.5 and nH (see below).
Data Analysis-Inactivation protection data were analyzed by plots of Ak uersus [L] and l/Ak uersus l/ [L] where Ak is the difference between k,, in the absence of the varied ligand, L, and k.,, in the presence of the varied ligand. Ak was obtained at five or more different concentrations of L. Ak,,,aI,BPP was obtained by extrapolating the l/Ak uersus 1/[L] plot to the vertical axis. The limiting inactivation constant (klImlt) representing the kap, at a saturating concentration of varied ligand can be calculated from kep, in the absence of the varied ligand and Akmax.app Neither Akmar.8pp nor kl,,,, are true constants but rather, depend on the concentrations of any nonvaried protective ligands present and the particular combination of varied and nonvaried ligands examined. [L]O.S, the concentration of varied ligand yielding 0.5 Akmax,app (i.e. half-maximal protection) at any nonvaried ligand concentration (including zero) was obtained by extrapolating linear reciprocal plots to the horizontal axis. If the primary plot was sigmoidal, [LIo5 was obtained as the varied ligand concentration required to double the vertical axis intercept of the concave-up reciprocal plot. The Hill coefficient, n H , was obtained from the slope of the log [Ak/ (Akmex,a,, -Ak)] uersus log [L] plot.

RESULTS AND CONCLUSIONS
Sulfhydryl Group Modification under Nondenaturing and Denaturing Conditions-Under nondenaturing conditions, one free SH group per subunit of A T P sulfurylase is modified by DTNB. This group is designated SH-1. Upon addition of 0.01% (w/v) SDS, two additional SH groups become accessible t o D T N B (Fig. 1A). Higher concentrations of SDS or 2 M guanidine HC1 increase the rate of modification but do not alter the end point. Thus, we can conclude that the P. chrysogenum ATP sulfurylase contains three SH groups per subunit, two of which (SH-2 and SH-3) are buried and inaccessible to DTNB under nondenaturing conditions. The three SH groups can be further differentiated with pCMB. Under nondenaturing conditions, pCMB almost instantaneously modifies SH-1 and then reacts more slowly with SH-2. The third SH group becomes accessible only after the addition of 0.01% SDS (Fig. 1B).
In other experiments, the enzyme was modified with NEM or A-485 in the absence of SDS. After removal of the unreacted reagent by repeated washings through a membrane filter, the modified enzyme was treated with DTNB. No reaction occurred until 0.01% SDS was added. Then, the formation of thionitrobenzoate equivalent to 2 mol of enzyme sites was observed. Thus, NEM and A-485, like DTNB, modify only SH-1 under nondenaturing conditions.
T h e SH-1-modified enzyme eluted from a TSK-4000 gel filtration column at the same retention time as the native enzyme. Thus, modification had no effect on the quaternary structure.
Relationship between SH-1 Modification and Enzyme Actiu-&- Fig.  2 shows the effect of DTNB treatment under nondenaturing conditions on the residual activity of ATP sulfurylase. T h e decision as to whether modification of the SH group has a significant effect on enzyme activity and the nature of that effect depends on the postmodification assay conditions. When both substrates in the assay mixture were near saturating, DTNB had very little effect.
(V,,, was reduced to about 80% of the control value.) When only one substrate was subsaturating, DTNB appeared to effect a partial inactivation. When both substrates were sufficiently The incubation mixtures contained 128 pg X ml" ATP sulfurylase (1.86 ~L M sites) in 50 mM Na-EPPS buffer, pH 8.0, 30 "C. An extinction coefficient of 1.42 X lo4 M-' X cm" was used to calculate the concentration of thionitrobenzoate formed (15). At zero time, the recorder pen was reset to the base line to correct for the absorbance of the added DTNB. E, reaction with pCMB (30 p~) .
The reaction was started by mixing equal volumes of enzyme (0.37 mg X ml-'; Az55 = 0.137) and pCMB (60 PM; AZb5 = 0.137) solutions. Both solutions were prepared with 50 mM Na-EPPS buffer, pH 8.0. A A.4255 of 7500 M-' X cm" was used to calculate the concentration of mercaptide formed (16). Measurements were made on a Gilford model 250 recording spectrophotometer with the chart recorder set to 0.1-absorbance units full scale.
subsaturating, DTNB appeared to act as a classical modifierinactivating agent (activity + zero as t + . . ). The results are consistent with an effect of modification on the K,,, value of each substrate with little effect on k,,,. In the absence of DTNB, no loss of activity was observed in any of the substrate concentration sets.
The semilog plot for "inactivation" or modification by DTNB appeared to be linear when the half-life ( tl,J was about 2 min or less. If the reaction rate was decreased by decreasing the DTNB concentration and/or omitting M$' , the semilog plots displayed a lag. The cause of the lag is unknown. One possible explanation (other than experimental error) is that subunit modification is partially cooperative.' Whatever the cause, it is obvious from Fig. 3 that the loss of enzyme activity paralleled modification of SH-1. The result suggests that modification of a subunit causes a decrease in activity of only that subunit. However, we cannot exclude the alternative explanation that modification of any one subunit causes a partial but equal loss of activity in all associated subunits.
'Another explanation that was considered is that DTNB binds slowly to the enzyme prior to modification of SH-1. However, when the initial slopes of the semi-log plots were used to calculate k.,,, the replot of l/kaPp uersus l/[DTNB] was linear extrapolating to the origin. Thus, there is no evidence for the formation of an E.DTNB complex. The enzyme (0.58 p~ sites) was preincubated at 30 "C for the times shown with 20 PM DTNB and 5 mM Mg2f in 0.04 M Tris-C1 buffer, pH 8.0. Remaining enzyme activity was measured by the APS kinase-pyruvate kinase-lactate dehydrogenase coupled spectrophotometric method (8) under the assay conditions shown.

Protection against SH-1 Modification by Reversibly Bound
Ligands-SH-1 is not required for catalysis and is not essential for substrate binding. Yet a reciprocal relationship exists between SH-1 modification and MgATP binding. Modification appears to have increased the [SIoa for MgATP (verified in a later section) and, as shown in Fig. 4, MgATP binding protected the SH group against modification by DTNB. Note that in the presence of high MgATP, the lag in the semi-log modification plot is quite obvious. As a check on the above results, enzyme activity after different modification times was measured at low substrate concentrations. (The carryover of MgATP into the assay medium was negligible.) The plots were quite similar to those shown in Fig The enzyme (2 p~ sites) was incubated at 30 "C with 20 p~ DTNB in 0.04 M Tris-C1 buffer, pH 8.0, in the absence of M e . The modification reaction was followed by continuously monitoring the A412 of the solution. Remaining SH groups were calculated from A , -A,,, where A , was taken as the ,4412 after which the rate of absorbance increase was indistinguishable from the drift plus DTNB hydrolysis rate. Remaining enzyme activity was measured at 1 mM MgATP, 0.6 mM SO:-, and 5 mM M$+ at the times shown. A, semilog plots. B, correlation plot. The line represents the theoretical 1:1 correlation between SH groups modified and activity lost. than 19-fold and 14-fold to 3.8 mM and 11.5 mM for MgATP and sulfate, respectively. Hill plots (Fig. 5 C ) were linear with slopes (i.e. Hill coefficients, nH) of 1 for the native enzyme and 2 for the modified enzyme.
The experiment depicted in Fig. 5B was conducted at a near-saturating level of the fixed cosubstrate. At 1 mM MgATP, the Vm,,,a,, and [SI,,, for SO:were reduced to 1.5 units X mg protein" and 2.3 mM, respectively, but n H was still 2. At 5 mM SO:-, the V, , , and [SIo., for MgATP were reduced to 2.9 units X mg protein" and 1.1 mM; n H remained 2.
Treatment of the DTNB-modified enzyme with 10 mM NaCN (after removal of the unreacted DTNB) resulted in the stoichiometric release of thionitrobenzoate (1 mol/mol of subunit; data not shown). The remodified enzyme (presumably cyanylated at each SH-1) displayed the same sigmoidal kinetics as that of the original DTNB-modified form. The enzyme modified with NEM, or tetranitromethane, or A-485 also displayed sigmoidal kinetics with respect to both substrates; nH was 2 in all cases. Thus, the sigmoidal kinetics can be attributed solely to the covalent modification of SH-1. The chemical nature or size of the substituent seems to be unim- The same effect was observed with ClO;, ClO;, NO;, FPOi-, and S @ - (Table I). Moreover, the relative analog concentrations required for maximum activation were in the same order as the limiting K, values of the compounds as dead-end inhibitors of the unmodified enzyme (e.g. the K, values for FSO; and S20zare 3.4 and 360 p~, respectively) (8).
In the presence of 25 mM MgATP, 5 mM excess M$+, and 350 p~ FSO;, the v versus [SO:-] plot for the modified enzyme was hyperbolic ( nH = 1). The Kmapp for SO:was increased to about 50 mM, but V,,, remained about 7 units X mg protein-'.
Thus, FSO; behaved as a dead-end inhibitor that competes with and mimics a substrate that binds cooperatively (p. 387 of Ref. 28).
Chemical Inactivation Kinetics of the Native and SH-modified Enzymes-Sigmoidal velocity curves and activation by competitive inhibitors are characteristics of positively COOPerative ligand binding. However, there are a number of purely kinetic phenomena that can yield the same qualitative patterns (see "Discussion"). Consequently, it was necessary to determine whether MgATP and SO:-(or suitable analogs) displayed cooperative binding under equilibrium, nonturnover conditions. In lieu of direct binding measurements, which were impractical because of the high [S]os values, we attempted to characterize the equilibrium interaction of ligands  -] was maintained at 40 mM. When [SO:-] was varied, [MgATP] was maintained at 20 mM. The enzyme concentration in the assay ranged from 0.13 to 0.25 pg X ml". Inset, reciprocal plot of primary data. Vmax is 9 units X mg protein-'. B, u versus [SI for the SH-modified enzyme. The SH group was modified by incubating the enzyme (128 pg X ml-'; 1.86 p~ in subunit or active sites) with 30 p~ DTNB at pH 8.0, 30 "C for 12 min. The solution was then diluted 5-fold in ice-cold 50 mM Na-EPPS buffer, pH 8.0. The assay conditions were the same as those described in A except 50 mM SO:-was used when MgATP was varied. The enzyme concentration in the assay ranged from 0.25 to 0.5 pg X m1-I. Inset, reciprocal plot of primary data. Vmax is 7.8 units X mg protein-'. C, Hill plots of data shown in A and B.
with the enzyme by analyzing the protection provided by a ligand against chemical inactivation by phenylglyoxal (an arginine-targeted reagent). The major objective was to determine whether the ligand concentration dependence of protection was hyperbolic or sigmoidal (see Appendix 1). Preliminary experiments showed that phenylglyoxal did not attack SH-1 (3) nor release thionitrobenzoate from enzyme previously modified with DTNB. However, to insure stability of the modification, these experiments were conducted with the NEM-modified enzyme. Residual enzyme activity was measured at 15 mM MgATP and 30 mM SO:-. Thus, a decrease in

Activation of DTNB-modified ATP sulfurylase by sulfate analogs
Activity was measured at 15 mM MgATP, 5 mM NazS04, 5 mM excess MgCl,, and varying concentrations of analog at pH 8.0, 30 "C. The control rates (taken as 100) were 1.20-1.5 units X mg protein". enzyme activity reflected true inactivation. The maximum carryover of phenylglyoxal (60 p~) had no effect on the assay. The semi-log inactivation plots were linear for the native and for the NEM-modified enzyme, both in the absence of added ligands and in the presence of a single ligand, or combinations which did not promote catalytic activity. In most cases, protection by bound ligands was partial. That is, inactivation proceeded at a measurable rate even at a saturating concentration of a protective ligand. FSO; in the absence of MgATP was the exception. Partial protection was not a hindrance to analysis because the difference between k,,, in the absence of the varied protector and k,,, at a saturating concentration of that protector ( Akmax,app) was large enough to analyze by plots of Ak uersus [ligand] and the corresponding reciprocal and Hill plots. This procedure has been used successfully to examine the interaction of an enzyme with a single ligand (10, 17-24) and with multiple ligands (12,25,26). Some of the results are summarized in Table I1 and described below.
( a ) The SH-modified enzyme was more susceptible than the native enzyme to inactivation by phenylglyoxal. In the absence of ligands, k, the first order rate constant for inactivation of the native enzyme was 2.67 f 0.25 x lo-" s-' while k for the SH-modified enzyme was double at 5.44 & 0.27 X lo-" s-' (means k standard deviations for 10 and 11 measurements, respectively). For any single protective ligand (first five rows of Table II), the AkmaX.8PP for the SH-modified enzyme was 1.9 k 0.3 times that for the native enzyme (mean k maximum range). Thus, the increased susceptibility of the SH-modified enzyme to phenylglyoxal resulted mainly from an increase in the reactivity of one or more ligand-protectable groups.
( b ) None of the Ak uersus [ligand] plots for the native enzyme displayed an inflection. Log-log Hill plots of Ak/ (Akmax.8PP -Ak) uersus [L] were linear with slopes of 0.98 k 0.06 (mean f standard deviation). In the absence of a coligand, the plots of Ak uersus [   Low MgATP was 0.34 mM with the native enzyme, and 0.68 mM with the NEM-modified enzyme. Fig. 7 shows the plotted-results for this experiment.
uersus [SI plots for both substrates to become sigmoidal with nH values of 2. There are two basic causes of sigmoidal velocity curves. The first is positive cooperativity in substrate binding, an equilibrium process that (theoretically) can be observed in the absence of substrate turnover. Equilibrium cooperativity requires the interaction of two or more subunits (or sites) and can be described in terms of the concerted symmetry model A second cause of sigmoidal velocity curves is the "V-type" substrate activation system in which the catalytic activity of occupied sites increases progressively as vacant sites are filled (p. 382 of Ref. 28). Substrate binding is noncooperative. A requirement for two or more sites to be filled before any catalytic activity occurs is a limiting case of this mechanism. Other explanations for sigmoidal responses are strictly kinetic in nature and have nothing to do with subunit interactions. These mechanisms involve a substrate-dependent shift in the overall reaction flux from a slower to a faster limb of a random pathway. Examples of current interest include ( a ) a shift from one route to the central complex (e.g. E + EA + EAB) to a more rapid route ( E + E B + EAB) in a steady state random AB mechanism (32, 33, p. 460 of Ref. 28), ( b ) a mechanism involving substrate-dependent product release from a ternary E . S . P complex (34), and (c) the mnemonical enzyme mechanism (35-38) and a similar mechanism involving two or more slowly interconverting enzyme conformations which provide two or more kinetically distinct paths for product generation MgATP and SO;bind randomly to native ATP sulfurylase (9).3 Thus, it is easy to imagine that SH modification could significantly alter certain rate constants and set up the conditions for two kinetically unequal paths to the central complex. However, this model was unacceptable for three reasons. First, the steady state random AB mechanism provides for sigmoidal behavior only for the substrate initiating the faster route. Second, the mechanism predicts partial substrate inhibition when the substrate initiating the slower path is varied. Both MgATP and SO:produced sigmoidal velocity curves at >[S]o.5 of the fixed cosubstrate (Fig. 5) and in neither plot was substrate inhibition observed. Third, the random mechanism does not provide for activation by a dead-end competitive inhibitor. The substrate-dependent product release mechanism assumes that product release from an abortive ternary E-product-substrate complex is faster than release from the normal binary E-product complex. As applied to a monomer of SHmodified ATP sulfurylase, this mechanism would require the formation of unlikely ternary complexes (e.g. E.APS. MgATP). However, an alternating site mechanism (41) in curves. But if S H modification partially uncouples the interacting subunits, two kinetically distinct paths of APS release would be generated, slow and site-independent at low substrate levels changing to faster and alternating site at higher substrate levels. This mechanism can also accommodate activation by nonreactive substrate analogs. Thus, this model cannot be disregarded on the basis of the experimental kinetic data.
In its simplest form, the mnemonical enzyme model assumes that the free enzyme can exist in two slowly interconverting forms: El (with a low substrate affinity) and Ell (with a high substrate affinity) of which only El[ is regenerated at the conclusion of a catalytic cycle. Addition of substrate A to either form yields the same E,,A species. Sigmoidicity results from a shift in the flux from El + EIIA + ElrAB + EII + products to EII + EllA + EllAB + Ell + products as [A] is increased. Low concentrations of a dead-end inhibitor, I, could activate the reaction at low substrate if I, like A, induces the Ell conformation which then persists long enough to bind A after I dissociates. On the basis of kinetics alone, the mnemonical enzyme mechanism was a viable possibility for SHmodified ATP sulfurylase. The same intermediates could be involved in the reaction catalyzed by the native enzyme, but E 1 and Ell would have to be in rapid equilibrium to yield hyperbolic velocity curves. In other words, we would have to postulate that the effect of S H modification is to slow the interconversion of the two free enzyme species.
Because two kinetically based mechanisms yielding sigmoidal velocity curves could not be eliminated, we determined the equilibrium binding curves for MgATP, S,Oz-, and FSO; (the latter two are nonreactive sulfate analogs). The binding curves were established from the protection provided by a varied ligand against phenylglyoxal-dependent inactivation. Both the native and the SH-modified enzyme displayed hyperbolic plots of Ak versus [ligand] in the absence of a coligand. For the native enzyme, the Ak plots also were hyperbolic in the presence of a fixed concentration of coligand. But the SH-modified enzyme displayed sigmoidal plots of Ak versus [FSO;] or [SzOi-] in the presence of MgATP and sigmoidal plots of Ak versus [MgATP] in the presence of FSO; or SzOf-. The nH values were 1.8-2.0. The sigmoidicity is not a result of synergistic protection by the two ligands. It can be shown that if MgATP and a sulfate analog bind noncooperatively to their respective subsites, the plots of Ak versus [ligand] will be hyperbolic as long as only one ligand is varied at a constant concentration of the coligand (Appendix 1). Even if the binding of one molecule of ligand protects multiple subunits (42), the Ak versus [ligand] plots will not be sigmoidal (Appendix 2). The cumulative results support positively cooperative ligand binding as the cause of the sigmoidal velocity curves. However the cooperativity is evident only in the formation of the ternary complex, i.e. both FSO, (or S,Oif-) and MgATP bind hyperbolically to the free SH-modified enxyme, but cooperatively to the appropriate binary complex. The nH of 2 could reflect weak cooperativity between all subunits of the oligomer or strong cooperativity restricted to interacting pairs of subunits.
Several important questions remain to be answered including: ( a ) is there any regulatory significance to the sigmoidal response of the SH-modified enzyme? Or, to phrase it differently: Does SH modification occur in vivo and if so, what is the modifying agent? Clearly, a reversible modification of SH-1 in vivo would modulate enzyme activity over a wide range at the normal cellular level of ATP. One can easily envision a process whereby the availability of NADPH controls the native/modified ATP sulfurylase ratio through the interme-diacy of some sulfhydryl/disulfide agent, e.g. glutathione.
(NADPH is needed a t a 4:l ratio for each molecule of SO:reduced to HzS for cysteine biosynthesis). A decrease in the cellular level of NADPH would result in an increase in the level of oxidized glutathione (GSSG) which might "turn off" ATP sulfurylase by GSSG-enzyme S H interchange. Another possibility is that SH modification is a negative feedback process that reduces the activity of the SO:assimilation pathway when the cells have sufficient reserves of reduced organic sulfur. Glutathione and S-adenosylmethionine are potential effectors for this process. (The latter might serve as an SH-methylating agent.) S H modification may also be a mechanism for deactivating ATP sulfurylase when the cellular ATP falls below the apparently essential level of -1 mM (43). It is also possible that in vitro S H modification induces the same conformational change in the enzyme that is normally triggered in vivo by a reversibly bound effector or perhaps by phosphorylation or adenylation (etc.). Because ATP sulfurylase is the first enzyme in a branched biosynthetic pathway, these possibilities are worthy of further consideration.
If SH modification has no physiological role and does not occur in vivo, then a different question becomes important: ( b ) is there any relationship between the sigmoidal response of the SH-modified enzyme and the mechanism of the native enzyme? To put it another way, does the mechanism of the native enzyme involve subunit interactions which are kinetically invisible (i.e. nH = 1) but which become evident when the enzyme is forced into an unnatural state?
Finally, it has also occurred to us that the sigmoidal response may be an accident of SH modification with no significance to either metabolic regulation or the mechanism of the native enzyme. But even in this case, the phenomenon is relevant to considerations of protein evolution because it demonstrates how easy it is to convert a hyperbolically responding enzyme to one that displays positive binding cooperativity.

1) Kinetics of Enzyme Inactivation in the Presence of Two Partially Protective Ligands that Form a Catalytically Inactive Ternary Complex
Scheme 1 shows the general model for chemical inactivation of a noncooperative enzyme by reagent I in the presence of two reversibly bound ligands that add randomly to form a catalytically inactive ternary complex. Thus, for ATP sulfurylase, A could be MgATP while X would be FSO,. Alternatively, if A is a nonreactive MgATP analog, X could be SO," or MOO:-. KA and Kx are the ligand dissociation constants of A and X from their respective binary complexes. The symbols CVKA and aKx are the respective ligand dissociation constants of the ternary complexes. In the presence of a large excess of reagent I, the modification of free E proceeds with a pseudo first order rate constant kl[I], which can be designated simply as k. The reactions of I with the ligand-occupied species are expressed in terms of k, e.g. E A is modified with a rate constant kz[I] indicated as pk. The model makes no assumption about the number or location of I-sensitive groups present, only that modification of any one of them is sufficient to inactivate an active site. For example, there could be a single I target group. Ligand A, when bound to the enzyme reduces the rate of modification but does not prevent the reaction. Similarly, bound X alone partially protects against modification, while A and X together protect to a greater extent but not completely. There could also be (e.g.) three different I target groups essential for activity, one of which can be completely or partially shielded by bound A, another by bound X, while the third is equally accessible to I in all enzyme species. A bound ligand may wholly or partially protect one target group while inducing a conformational change in the enzyme that increases the reactivity of another target group. The different possibilities only alter the physical meanings of k, pk, etc. but have no effect on the final equation. Scheme 1 assumes that if the enzyme is oligomeric, modification of one subunit has no effect on the rate of modification of another subunit. It is also assumed that the rate of inactivation is much slower than the rate of ligand dissociation so that the various active enzyme species remain at equilibrium throughout the modification period.
The rate of inactivation is given by: where  (1 -6). A successful analysis requires that Akmax,spp be large enough to provide measurable Ak values as the ligand concentration is varied. KXapp is given by: This appears to be the situation for ATP sulfurylase when X is a monovalent oxyanion such as FSO;, ClO;, etc (8). The same enzyme distribution and Kapp expressions hold if binding is compulsory ordered (A before X). In this case, the a factor can be omitted as there is only one mode of X binding. If the subunits are not independently modified, the semilog plots of activity versus time will be nonlinear, and the above scheme and equations will not be valid. If the subunits are independently modified, but X binds cooperatively, the semi-log plots at each [X] will be linear, but the replot of Ak versus [X] will be sigmoidal.
In inactivation protection studies (as in kinetics studies), the concentration of free ligand, e.g. [A], can be assumed to be equal to the added concentration, [A],, as long as no depletion occurs upon binding. In general, this requires that the concentration of enzyme sites, [Elt, be no greater than 0.1 K~app.

2) Protection of Multiple Subunits (Sites) by a Single Bound Ligand
Consider a homodimer that binds two molecules of ligand A in a noncooperative fashion. Suppose that the occupancy of either subunit is sufficient to protect both subunits completely. Thus, the only species susceptible to attack by inactivating agent, I, is free El. If k is the first order rate constant for modification of a subunit, the rate of inactivation is given by: where [E], is the total concentration of subunits (proportional to enzyme activity) and [Ez], is the total concentration of dimer. If KA is the intrinsic A dissociation constant, the rate of activity loss in the presence of A is given by: or Equation (10) can be integrated to the usual form:

Thus the semilog plot at any [A] is linear.
Ak can be defined as kk,,,. The effect of varied [A] can 8. then be written as 9.

(14)
In general, if n subunits are completely protected by the 20.
binding of a single molecule of A, the equation is:

KA J
A plot of Ak uersus [A] will rise more steeply than normal but will not be sigmoidal. Half-maximal protection will occur at an [AIoa that is less than KA4 The reciprocal plot is nonlinear, decreasing in slope as 1/[A] decreases and intersecting the vertical axis at l/Akmax. As 1/[A] increases, the plot approaches a linear asymptote with a slope of K,/nAk,.,. The Hill plot will be nonlinear (concave up) with an average slope >1 at the point corresponding to or between the points corresponding to [AIo., and [A],,. However, even for a hexamer, this slope will be d . 4 . If a nonprotectable target group is present, or if the binding of A to one subunit only partially protects the single target group on all subunits, Ak,., will equal k(1p) (where @k is the limiting rate constant). The general properties of the plots will be the same as those described above.