Induction of Positive Cooperativity by Amino Acid Replacements within the C-terminal Domain of Penicillium chrysogenum ATP Sulfurylase*

ATP sulfurylase from Penicillium chrysogenum is an allosteric enzyme in which Cys-509 is critical for maintaining the R state. Cys-509 is located in a C-terminal domain that is 42% identical to the conserved core of adenosine 5′-phosphosulfate (adenylylsulfate) (APS) kinase. This domain is believed to provide the binding site for the allosteric effector, 3′-phosphoadenosine 5′-phosphosulfate (PAPS). Replacement of Cys-509 with either Tyr or Ser destabilizes the R state, resulting in an enzyme that is intrinsically cooperative at pH 8 in the absence of PAPS. The kinetics of C509Y resemble those of the wild type enzyme in which Cys-509 has been covalently modified. The kinetics of C509S resemble those of the wild type enzyme in the presence of PAPS. It is likely that the negative charge on the Cys-509 side chain helps to stabilize the R state. Treatment of the enzyme with a low level of trypsin results in cleavage at Lys-527, a residue that lies in a region analogous to a PAPS motif-containing mobile loop of true APS kinase. Both mutant enzymes were cleaved more rapidly than the wild type enzyme, suggesting that movement of the mobile loop occurs during the R to T transition.

ATP sulfurylase from the filamentous fungus Penicillium chrysogenum is an oligomer composed of six identical 64-kDa subunits (573 residues). Each subunit possesses three free SH (cysteinyl) groups, 2 of which only one (designated SH-1) can be modified by sulfhydryl-reactive reagents such as DTNB and NEM under nondenaturing conditions (1). Complete modification of SH-1 (six per hexamer) changes the initial velocity kinetics at pH 8 from normal-hyperbolic (Hill coefficient, n H ϭ 1) to sigmoidal (n H approximately 2) with a concomitant increase in the [S] 0.5 values for MgATP and SO 4 2Ϫ (or MoO 4 2Ϫ ); V max app at a fixed subsaturating cosubstrate level is reduced (2). A number of experimental approaches, including protection against chemical inactivation by reversibly bound ligands (2), direct binding measurements (3), and single turnover isotope trapping (3), established that the sigmoidal curves reflected true cooperative binding as opposed to a kinetically based phenomenon.
The dramatic effect of in vitro modification of SH-1 suggested several possible scenarios, including that modification induces a conformational state in the enzyme that is normally induced in vivo by a reversibly bound allosteric effector. The effector was subsequently shown to be PAPS (4). Further experiments established that the enzyme from several other fungi behaved identically to the P. chrysogenum enzyme, whereas ATP sulfurylases from rat liver (5), spinach leaf (6), cabbage leaf (7), yeast (4), and the Riftia bacterial symbiont (8) did not respond in the same way to Cys modification or to PAPS. The cumulative results indicated that (a) fungal ATP sulfurylase possesses an allosteric PAPS binding site that is not present in the enzyme from other sources and (b) SH-1 is either in the region of, or in communication with, the PAPS binding site. Fungal sulfurylase was subsequently shown to possess a C-terminal region (approximately residues 396 -539) that is 42% identical to the conserved core of APS kinase (9 -11), a protein with a high affinity for PAPS. SH-1 is Cys-509, which is located in the APS kinase-like C-terminal domain, a few residues upstream from a putative PAPS motif (12). It is likely that residues 396 -540 of P. chrysogenum ATP sulfurylase evolved from true APS kinase and that this region provides the allosteric binding site for PAPS. In effect, the C-terminal region of fungal ATP sulfurylase is a regulatory subunit that happens to be covalently linked to the catalytic subunit. 3 Our preliminary hypothesis (in terms of the concerted transition model) was that covalent modification of Cys-509 promotes the same R to T allosteric transition (13,14) as does PAPS binding.
The inhibition of P. chrysogenum ATP sulfurylase by PAPS may be the way that fungi prevent PAPS accumulation to toxic levels. Another consideration is that in fungi, PAPS is a major branch point metabolite of sulfate assimilation. One branch leads to cysteine and other reduced sulfur compounds; the other branch to choline-O-sulfate, a sulfur storage compound and/or osmoprotectant (15)(16)(17)(18). Thus the inhibition may be part of a more extensive sequential feedback process. In contrast, yeasts and most bacteria do not form large quantities of sulfate esters, whereas plants (and some bacteria) preferentially use APS (rather than PAPS) as the substrate for the reductive assimilation of sulfate. In other words, PAPS is not at a branch point in these other organisms.
The objective of the present study was to establish the role of Cys-509 in stabilizing the R state. To this end, we investigated the kinetic consequences of replacing Cys-509 with either tyrosine or serine.

MATERIALS AND METHODS
Introducing Mutations-Mutations in codon 509 were made by PCR amplification of the C-terminal 221 base pairs of the fungal ATP sulfurylase gene (codons 506 -573). This sequence begins with an indigenous XhoI site 3 base pairs upstream from codon 509 and ends after the stop codon with an engineered XbaI site. Each PCR used a cloned cDNA copy of the native gene as the template, the C-terminal coding primer PcATS308 (5Ј-GGTCTAGATCTTACTGACGCTCCAGGAAACCC-3Ј), and an upstream primer containing the XhoI site and the desired mutation. Upstream primers with their respective produced mutations were as follows: PcATS315 (C059S), 5Ј-TCCCCTCGAGCACTCTGAGC-AGTCCG-3Ј; PcATS317 (C509Y), 5Ј-TCCCCTCGAGCACTACGAGCA-GTCCG-3Ј. All PCRs were carried out using the DNA polymerase Pfu (Stratagene). The resulting 221-base pair DNAs were subcloned as XhoI-XbaI fragments into a pBluescript KS(ϩ) plasmid containing a cDNA clone of fungal ATP sulfurylase in which the wild type C-terminal 221 base pairs had been removed. All cloned PCR fragments were sequenced to ensure that the desired mutations were introduced.
Sequenced ATP sulfurylase genes were cloned as NdeI-BglII fragments into the Novagen pET23a(ϩ) plasmid and introduced into Escherichia coli strain BL21(DE3) for protein expression.
Protein Expression and Purification-About 0.2 ml of an 8-h culture was used to inoculate two 3-liter Fernbach flasks each containing 1000 ml of LB ampicillin medium. The cultures were grown aerobically at 37°C for 8 -10 h and then transferred to 15°C. Upon transfer to 15°C, 1 g of ␣-lactose was added per liter of culture to induce protein expression. After 8 -10 h at 15°C, the cells were harvested by centrifugation at 12,000 ϫ g for 10 min. Approximately 4 -8 ml of packed cells was obtained. The cells were then resuspended in about 50 ml of chilled 40 mM Tris-Cl, pH 8.0, and lysed in a single pass through a Watts Fluidair Microfluidizer (model B12-04DJC M3). All subsequent steps were carried out at 4°C. Cell debris and unbroken cells were removed by centrifuging at 16,000 ϫ g for 10 min. The supernatant fluid was applied to a blue dextran (19) column (2.5 ϫ 10 cm) that had been equilibrated with 40 mM Tris-Cl, pH 8.0. The column was then washed with the same buffer at 6 ml/min until the effluent had an A 280 nm of 0.005 or less. Protein was eluted with a linear gradient of NaCl (0 -0.7 M) in 40 mM Tris-Cl, pH 8.0 (total volume 500 ml) at a flow rate of 2 ml per min. 7-ml fractions were collected, and their A 280 nm and ATP sulfurylase activity were measured. Fractions containing enzyme activity (coincident with the major protein peak) were pooled (total volume approximately 85 ml), dialyzed against 40 mM Tris-Cl, pH 8.0, and then applied to a DEAE-cellulose column (2.5 ϫ 10 cm) equilibrated in the same buffer. After a brief wash, protein was eluted at 1 ml per min with a linear gradient of NaCl (0 -0.4 M) in 40 mM Tris-Cl, pH 8.0 (total volume, 400 ml). Seven fractions containing ATP sulfurylase activity (total volume 49 ml) were pooled, divided into 1-ml aliquots, and stored frozen. A typical preparation yielded about 25 mg of pure enzyme. The A 280 nm /A 260 nm ratio of the enzymes ranged from 1.91 (for C509Y) to 2.01 (for C509S). SDS gel electrophoresis indicated that all the enzymes were at least 95% pure. The absence of Cys-509 in the mutant enzymes was confirmed by demonstrating their lack of reactivity with DTNB in the absence of SDS (1).
Chemicals and Coupling Enzymes-Most biochemicals, buffers, column media, and coupling enzymes were obtained from Sigma. PAPS was prepared as described previously (20). Concentrations of stock solutions were established by enzymatic analysis using Nuclease P1 coupled to ATP sulfurylase, hexokinase, and glucose-6-phosphate dehydrogenase in the presence of excess PP i , MgCl 2 , NADP ϩ , and 1 mM glucose.
Protein Assays-ATP sulfurylase concentrations were determined from the relationship: conc mg ϫ ml Ϫ1 ϭ A 280 nm /0.871 (21). (In theory, this results in a 3% error in the assumed concentration of C509Y.) Enzyme Assays-ATP sulfurylase activity was characterized by the continuous, coupled spectrophotometric molybdolysis assay (22) in the presence of NADH, P-enolpyruvate, KCl, excess adenylate kinase, inorganic pyrophosphatase, sulfate-free pyruvate kinase ϩ lactate dehydrogenase, and approximately 0.5 g (0.02 unit) of pure P. chrysogenum APS kinase (10,22,23). The stoichiometry of the assay is 2 mol of NADH oxidized per mol of AMP formed. In addition to providing good sensitivity, this assay has the advantage in that both primary substrates, MgATP and MoO 4 2Ϫ , are continuously regenerated. The APS kinase serves to remove traces of APS formed from contaminating inorganic sulfate during the preincubation period (20). (APS is a potent product inhibitor of the enzyme, whereas the small increment of PAPS formed is innocuous.) Unless indicated otherwise, all assays were conducted at 30°C, in 50 mM Tris-Cl, pH 8.0. The total MgCl 2 present was always 5 mM greater than that of the total ATP. The specific activities of the wild type, C509S, and C509Y forms of the enzyme freshly purified from the E. coli expression system and assayed at 5 mM total ATP, 10 mM total Mg 2ϩ (as MgCl 2 ), and 10 mM MoO 4 2Ϫ were, in order, 20, 17, and 14.5 units ϫ mg of protein Ϫ1 . 1 unit is the amount of enzyme that catalyzes the formation of 1 mol of primary product in 1 min.
Data Analysis-For each experimental velocity curve, the V max value and the Hill coefficient, n H , were determined by fitting the plotted v versus [substrate] data to the Hill equation: Hill coefficients were also determined as the slope of the Hill plot, in the region corresponding to 50% saturation (i.e. where log [v/(V max Ϫ v)] ϭ 0) or over the range corresponding to 10 -90% saturation (14). Curve-fits were obtained using DeltaGraph 4.05c (Macintosh) with all points weighted equally. The n H of a single plot determined by the three methods generally agreed to within 0.1. The n H of replicate curves obtained at different times generally agreed to within Ͻ0.15. Although the Hill coefficient was useful for comparing the sigmoidicity of different velocity curves, ultimately, differences in n H need to be related to the complete velocity equation for an allosteric bireactant enzyme (see "Appendix").

Kinetic Properties of Cys-509 3
Tyr- Fig. 1 shows the velocity curves of the C509Y mutant enzyme under standard assay conditions. The most striking feature of the curves is that they are sigmoidal in the absence of PAPS. In fact, the increase in n H with increasing concentrations of the fixed cosubstrate is the same trend displayed by the wild type enzyme after cova-lent modification of Cys-509 (data not shown). 4 Up to this point, the results suggested that cooperative behavior is induced by either (a) increasing the bulk of the side chain at position 509 or (b) eliminating the negative charge (R-S Ϫ ) at this position. It was thought that replacing Cys-509 with the slightly smaller and uncharged Ser might help to distinguish between these two possibilities.
Kinetic Properties of Cys-509 3 Ser- Fig. 2 shows the veloc- 4 The native enzyme modified with NEM at Cys-509 yielded the following data: 2Ϫ ] curves are also sigmoidal, but n H approaches unity as the concentration of MgATP approaches saturation. This trend is consistent with the preferential binding of MgATP to free E of the R state. That is, as the fixed [MgATP] approaches saturation, the enzyme is driven far toward the R state, which binds MoO 4 2Ϫ in a normal hyperbolic manner. At 5 mM MgATP, the K m for MoO 4 2Ϫ is 0.1 mM, which is the same as that of the noncooperative wild type enzyme. In terms of Equation 9 (Appendix), L app for C509S at saturating MgATP (equivalent to Lc) must be very small, implying that c is less than unity. The sigmoidicity of the v versus MoO 4 2Ϫ plot at subsaturating MgATP can be attributed, at least in part, to the synergism between MgATP and MoO 4 2Ϫ . That is, even if K ibT ϭ K ibR (e ϭ 1), and K mbT ϭ K mbR (j ϭ 1), the v versus [B] plots can be sigmoidal at subsaturating [A] if (a) substrate A binds preferentially to the R state (c Ͻ 1), and (b) the substrates bind to the R state synergistically (f Ͻ 1). The last condition seems highly likely given that the R state should closely resemble the noncooperative wild type enzyme where the K m value for each substrate is smaller than the corresponding K i value (1).
The bireactant kinetics of C509S are similar to those of the wild type enzyme in the presence of PAPS. 5 Comparing the above results with those of the C509Y enzyme leads to the conclusions that either (a) substituting a Tyr residue for Cys-509 drives the enzyme much further toward the T state than does substituting a Ser at this position or (b) the T state induced by substituting Tyr at position 509 is structurally different from that induced by substituting Ser (see "Discussion"). In either case, the results show that cooperative behavior is a not simply a result of increasing the bulk of the residue at position 509. Either the negative charge on the side chain of Cys-509 plays a critical role in stabilizing the R state, or the side chain size is extremely important and any change will favor a shift to the T state.
Effect of a Competitive Inhibitor-Activation by a competitive inhibitor at low 6 competitive substrate concentrations is a hallmark of true cooperative binding. As shown in Fig. 3, inorganic thiosulfate, an inhibitor competitive with SO 4 2Ϫ or MoO 4 2Ϫ (24), does exactly that. Activation by S 2 O 3 2Ϫ is also seen with the wild type enzyme after chemical modification of Cys-509 (2), or in the presence of PAPS (4,20). Note that the experimental level of the noncompetitive cosubstrate (MgATP) influences the effect of the competitive inhibitor. That is, the activation is eliminated by an MgATP concentration that is too low in the case of C509Y, or too high in the case of C509S. These opposite effects are consistent with the different effects of MgATP binding on the cooperativity of the two mutant enzymes as illustrated in Figs. 1b and 2b.
Kinetics at Lower pH-The side chain of a Ser residue is not much smaller than that of a Cys residue, but unlike Ser, a substantial fraction of the Cys side chain may be ionized at the standard assay pH of 8.0. The observation that C509S is intrinsically cooperative raised the possibility that the charge on residue 509 plays a major role in stabilizing the R state. If the side chain of Cys-509 behaves normally (i.e. has a pK a of 8.0 -8.5), decreasing the assay pH from 8.0 to (e.g.) 6.5 would decrease the fraction of the residue in the Cys-S Ϫ form significantly. It was of interest then to determine whether protonating the Cys anion of the wild type enzyme had the same effect as substituting Ser for Cys. As shown in Table I, decreasing the pH did indeed induce sigmoidal v versus 5 The wild type enzyme yielded the following data at 50  6 Exactly how "low" the competitive substrate must be to demonstrate activation is best established by trial and error. For a simple unireactant system where S and I bind exclusively to the R state, the peak velocity occurs at ϭ Thus as the fixed [S] is increased, the peak moves closer to the vertical axis and eventually disappears.  [MoO 4 2Ϫ ] curves. Lowering the pH also decreased V max , app and increased the [S] 0.5 . However, the wild type enzyme at pH 6.5 did not mimic C509S: First, the velocity curve remained sigmoidal at 5 mM MgATP (n H ϭ 2.1). Second, the enzyme at pH 6.5 was activated by S 2 O 3 2Ϫ only at high concentrations of MgATP (data not shown). In these respects, the enzyme behaved like C509Y rather than C509S. Surprisingly, the n H of C509S also increased as the assay pH was decreased (n H was 1.8 at pH 8.0 and 2.3 at pH 6.5). Consequently, we cannot conclude that the sigmoidicity induced in the wild type enzyme was solely a response to protonating Cys-509. Considering the pH range studied, it is likely that protonating one or more His residues can contribute to an R to T transition. Several His residues are located in the C-terminal domain, including one adjacent to Cys-509 (His-508). His has been shown to be essential for ATP sulfurylase activity (5,9,25,26), a role that may account in part for the decrease in V max , app as the pH was decreased. (A decrease in the fraction of the total ATP in the MgATP form may also have contributed to the decrease in V max , app and increase in [S] 0.5 as the pH was decreased.) The experiments described in Table I were conducted in MES-Tris buffers in which the MES concentration increased as the pH was decreased. However, MES per se was not responsible for the sigmoidicity as evidenced by the hyperbolic velocity curves obtained in 0.05M MES (plus Tris to pH 8).
Effect of PAPS on C509S-It was of interest to determine whether PAPS had an additional effect on a mutant enzyme, or whether the mutation transformed the enzyme completely to the T state. As shown in Fig. 4, the n H value of C509S increased further as the concentration of PAPS was increased. At 240 M [PAPS], the n H of the v versus [MgATP] plot was nearly 3. Thus the Cys to Ser mutation promoted only a partial shift toward the T state allowing the R to T equilibrium to be driven further toward the T state or back toward the R state by the appropriate ligand. In this respect, C509S resembles a typical allosteric enzyme. The apparent n H limit of 3 (instead of 6) is very likely a consequence of the nonexclusive binding of PAPS and/or substrates. However, the possibility that the enzyme behaves in an alternating "half-of-the-sites" manner cannot be immediately discarded. The effect of PAPS on V max, app indicates that either (a) the catalytic activity of the T state is much less than that of the R state, or (b) substrate binding to the T state is not highly synergistic, or (c) both conditions apply. In contrast to the results shown in Fig. 4 Susceptibility of the C-terminal Domain to Proteolysis-As shown in Fig. 5, treatment of wild type P. chrysogenum ATP sulfurylase with a low concentration of trypsin results in an initial rapid cleavage producing a well-defined product. Sequence analysis of the products revealed that the primary site of cleavage was at Lys-527, a residue that lies in a region analogous to the PAPS motif-containing mobile loop of true APS kinase and close to the analogous "quick trypsin" site of that enzyme (which is Arg-158) (11). In some incubations, cleavage at a second "quick trypsin" site of ATP sulfurylase (Arg-488) could be detected before the pattern was obscured by further proteolysis. MgATP, APS, or PAPS protected the wild type and C509S against proteolysis. C509Y was not protected. The pattern for the wild type enzyme in the presence of PAPS is shown in the second row of Fig. 5. Both mutant enzymes were cleaved much more rapidly than the wild type enzyme, suggesting that the mobile loop/PAPS motif region is more accessible in the T state than in the R state. (The pattern for C509S is shown in the third row of Fig. 5.) Considering the sequence homology of the two enzymes and the similar locations of the primary "quick trypsin" sites ( Fig. 6), it is likely that true APS kinase and the C-terminal domain of ATP sulfurylase have similar structures. 2Ϫ ] curve becomes hyperbolic at saturating MgATP. 7 These kinetics indicate that MgATP has a higher affinity for the free E form of the R state compared with its affinity for free E of the T state, but that cosubstrate MoO 4 2Ϫ binds more or less equally well to free E of both states. Stated alternatively, MgATP alone can trigger the T to R transition of C509S. The kinetic effects of substituting Ser at position 509 are the same as those promoted by the reversible binding of PAPS to the wild type enzyme.
At first glance, there appears to be two different classes of kinetic response to alterations at position 509. The simplest explanation for the different kinetics is that there is a single T state, but different alterations in the region of Cys-509 cause a different extent of R to T transition, i.e. result in different base level values of the allosteric constant, L (13). The consequence of the difference is best appreciated by examining a plot of n H versus log L. If the T state has catalytic activity (even very low compared with the R state), the plot is bell-shaped with limits of 1.0 (14,27). The effect of increasing the concentration of a ligand on n H depends on which side of the maximum the enzyme is poised in the absence of ligands, i.e. whether the base level L is larger or smaller than the L at the maximum n H . Thus a decrease in the apparent L value (as would occur when the fixed concentration of a cooperatively bound cosubstrate is increased) could result in an increase or a decrease in n H . Whatever the effect of the fixed substrate concentration on n H , an increase in the apparent L (as would occur when the concentration of the allosteric inhibitor is increased) will have the opposite effect. If this explanation is applicable, the different [S] 0.5 values of the two mutant enzymes and the effects of changing [MgATP] or [PAPS] on n H mean that covalently modifying or protonating the wild type enzyme, or replacing Cys-509 with Tyr drives the enzyme further toward the T state than does PAPS binding or replacement of Cys-509 with Ser.
Another possible cause of the two classes of kinetics is that there are two types of T states. One type is produced by substituting Tyr for Cys at position 509, or by covalently modifying Cys-509 of the wild type enzyme, or by decreasing the pH below 8. The second type is formed when Cys-509 is replaced by Ser or when the wild type enzyme binds PAPS. In this scenario, the T to R transition of C509Y would be driven mainly by the formation of the R state ternary E⅐MgATP⅐MoO 4 2Ϫ complex. Compared with the wild type enzyme, the mutant enzymes have lower specific activities at saturating MgATP and MoO 4 2Ϫ (wild type Ͼ C509S Ͼ C509Y). If the V maxR values of the mutant enzymes are the same as that of the wild type enzyme, then their lower specific activities can be attributed to different base level L values, nonexclusive substrate binding, and a low activity T state (see "Appendix," Equation 12. For example, the molybdolysis V max of C509S (17 units ϫ mg of protein Ϫ1 ) is about 85% that of the wild type enzyme, suggesting that about 15% of the enzyme remains trapped in the very low activity T state at saturating substrate levels.
The dramatic change in kinetic properties resulting from the substitution of Tyr or Ser for Cys-509 confirms the key role of this position in holding the enzyme in the R state. As shown in Fig. 6, the residue analogous to Cys-509 in true APS kinase is Ala-145, which is located just before a mobile loop (residues 149 -169) containing a putative PAPS motif (12). This loop is believed to serve as a hinged element ("ATP lid") that immobilizes and protects bound MgATP in APS kinase (11). Ala-145 (and by inference, Cys-509) is located within a short helix at the N-terminal end of the loop. Although the C-terminal domain of ATP sulfurylase probably does not bind MgATP (because of alterations to the P-loop; see Ref. 10), a similar motion of the analogous mobile element may play a role in the R to T transition-a suggestion consistent with the observations that (a) the primary "quick trypsin" site resides within the PAPS motif of the mobile loop and (b) that site is more accessible in the mutant enzymes (which exist primarily in the T state) than in the wild type enzyme (which exists almost entirely in the R state). If a movement of the loop does occur as part of the allosteric transition, one can understand why covalent modifi-7 A number of years ago, Pettigrew and Frieden (30) warned that "the assumption that effects of the second substrate upon kinetic behavior may be ignored as long as it is at a saturating concentration may be invalid and lead to incorrect predictions. . . . " The experimental effects of the nonvaried substrate on cooperativity presented in this present report (Figs. 1 and 2) confirm that warning. cation or amino acid substitution within the small helix (hinge?) might alter the allosteric equilibrium. The facile dissociation and reassociation of subunits is another physical characteristic of APS kinase (28) that may have been recruited by ATP sulfurylase as part of the allosteric transition. Indeed, preliminary x-ray diffraction studies indicate that P. chrysogenum ATP sulfurylase has a dimer-of-triads structure, which is partially stabilized by interactions of C-terminal domains across the triad interface.

Kinetic Behavior of a Bireactant Cooperative Enzyme
The principles of the concerted transition (symmetry) model for cooperative enzymes (13,27) can be extended to multireactant enzymes provided that rapid equilibrium conditions prevail (or are assumed) for the substrate binding steps and the allosteric transition (29). Compared with unireactant systems, the requirement that both substrates bind to the enzyme before any catalytic activity occurs adds an additional layer of complexity. For example, one or both of the substrates might bind cooperatively to the free enzyme, but neither substrate might bind cooperatively to the binary enzyme⅐cosubstrate complex. Conversely, only one or both of the substrates might bind cooperatively to the enzyme⅐cosubstrate complex, but neither might bind cooperatively to the free enzyme. Also, the binding of one substrate at the catalytic site may promote or may hinder the binding of the other substrate. This heterotrophic interaction can also affect the properties of the velocity curves. Because of these possibilities, the Hill coefficient for the varied substrate might increase, decrease, or remain the same as the concentration of the nonvaried substrate is increased.
The velocity equation for bireactant ATP sulfurylase in the presence of substrates A (MgATP) and B (MoO 4 2Ϫ ), which add in a rapid equilibrium random fashion, is shown below. The equation takes into account that X (PAPS), the allosteric effector, binds to the catalytic site as an inhibitor competitive with both MgATP and MoO 4 2Ϫ , as well as to the allosteric site (20).
K xT is expected to be Ͻ K xR (i.e. m Ͼ1). As X approaches saturation, LЈ approaches a limit of L(K xR /K xT ) n ϭ Lm n . The sigmoidicity of the v versus [B] plot at saturating A depends on several factors: (a) the nonexclusive binding coefficient for the interaction of B with the EA form of the T and R states (K mbR /K mbT ϭ j), (b) the magnitude of g, and most importantly, (c) the magnitude of the apparent allosteric constant, L app , which equals LЈc n . It can be seen that if c is small (because substrate A binds preferentially to the free form of the R state), L app might be small even if LЈ is substantial. In this case, the velocity curve at saturating [A] will be hyperbolic (even though the plot may be sigmoidal at subsaturating [A]). It is possible to express c in terms of some other coefficients: c ϭ ep/j ϭ hp/f. The latter relationship reveals that L app at saturating [A] depends on the relative strengths of the active site A/B interactions of the two states as well as on p. For example, if the binding of one substrate to the free E form of the R state increases the affinity for the other substrate (f Ͻ 1), and this synergism is greater than that which occurs at the T state active site (f Ͻ h), the c n factor could be a large number and consequently, L app could be large yielding a sigmoidal velocity curve at saturating [A] even if LЈ is not very large and p ϭ 1. Similarly, if binding of one substrate to the free E form of the R state has no effect on the binding of the other (f ϭ 1), but the binding of one substrate to the free E form of the T state hinders the binding of the other (h Ͼ 1), again f will be Ͻh and a sigmoidal curve could result (30).
If g Յ 1, the velocity given by Equations 9 or 10 is a V max app (for saturating A at a subsaturating level of B). But if g Ͼ 1 and K mbR Ͻ K mbT (i.e. the state with the higher catalytic activity has the lower affinity for B), the v versus [B] curve might pass through a maximum and then decrease to a lower limit as [B] approaches saturation.
The equation for v versus [A] at saturating B is symmetrical to that shown for saturating A. When both substrates are saturating, the limiting velocity in the absence of X is given by: v limit ϭ V maxR ͑1 ϩ gL app ͒ ͑1 ϩ L app ͒ ϭ V maxR ͑1 ϩ gLc n j n ͒ ͑1 ϩ Lc n j n ͒ (Eq. 12) If g ϭ 1, the limiting velocity at saturating A and B will be independent of LЈ, c, and j, i.e. v limit ϭ V maxR . But if the T state is less catalytically active than the R state (i.e. g Ͻ 1), v limit can be Ͻ V maxR .