Cystathionine β-Synthase (CBS) Domains Confer Multiple Forms of Mg2+-dependent Cooperativity to Family II Pyrophosphatases*

Background: Enzymes and transporters may contain regulatory nucleotide-binding cystathionine β-synthase domains. Results: Both substrate and adenine nucleotides bind cooperatively to four bacterial cystathionine β-synthase domain-containing pyrophosphatases. Conclusion: Cystathionine β-synthase domains internally inhibit catalysis and impart cooperativity; both effects are modulated by bound nucleotides. Significance: The observed regulatory complexity may be characteristic of cystathionine β-synthase domain-containing proteins involved in hereditary diseases. Regulated family II pyrophosphatases (CBS-PPases) contain a nucleotide-binding insert comprising a pair of cystathionine β-synthase (CBS) domains, termed a Bateman module. By binding with high affinity to the CBS domains, AMP and ADP usually inhibit the enzyme, whereas ATP activates it. Here, we demonstrate that AMP, ADP, and ATP bind in a positively cooperative manner to CBS-PPases from four bacteria: Desulfitobacterium hafniense, Clostridium novyi, Clostridium perfringens, and Eggerthella lenta. Enzyme interaction with substrate as characterized by the Michaelis constant (Km) also exhibited positive catalytic cooperativity that decreased in magnitude upon nucleotide binding. The degree of both types of cooperativity increased with increasing concentration of the cofactor Mg2+ except for the C. novyi PPase where Mg2+ produced the opposite effect on kinetic cooperativity. Further exceptions from these general rules were ADP binding to C. novyi PPase and AMP binding to E. lenta PPase, neither of which had any effect on activity. A genetically engineered deletion variant of D. hafniense PPase lacking the regulatory insert was fully active but differed from the wild-type enzyme in that it was insensitive to nucleotides and bound substrate non-cooperatively and with a smaller Km value. These results indicate that the regulatory insert acts as an internal inhibitor and confers dual positive cooperativity to CBS domain-containing PPases, making them highly sensitive regulators of the PPi level in response to the changes in cell energy status that control adenine nucleotide distribution. These regulatory features may be common among other CBS domain-containing proteins.

proteins consist of only a Bateman module (15,16). The majority of CBS domain-containing proteins form homodimers with the CBS domains participating in subunit interface interactions. Consequently, the two CBS domain pairs form a disklike structure (10). Interestingly, PPase appears to be the only Bateman module-containing protein in which a DRTGG domain intercalates the CBS domains (see Fig. 1). However, in rare cases, for example Moorella thermoacetica PPase (mtPPase), the enzyme contains only CBS domains in the regulatory part of the molecule. Typically, CBS domains bind adenine nucleotides, such as S-adenosylmethionine, AMP, ADP, and ATP, as regulatory ligands (10,(11)(12)(13)(14). Each CBS domain contains a potential binding cavity for nucleotides; however, with rare exceptions (16,17), each pair of CBS domains generally binds only one adenylate ligand. The structural and kinetic basis for regulation through CBS domains is still unknown for any protein, and CBS domain-containing PPases represent a good model enzyme for exploring this general phenomenon.
We reported previously that mtPPase (18) and the CBS domain-containing PPase of Clostridium perfringens (cpPPase) (19) are highly sensitive to micromolar concentrations of adenine nucleotides. Remarkably, AMP and ADP acted as inhibitors, whereas ATP and AP 4 A were activators. We also determined the three-dimensional structures of an isolated regulatory insert of cpPPase comprising two CBS domains and one DRTGG domain in complexes with AMP and AP 4 A (19). Rates of AMP-induced conformational transitions were much faster in cpPPase (20) than in mtPPase (21), suggesting a role for the DRTGG domain in regulatory site performance.
Here, we show that the regulatory part of the molecule, comprising two CBS domains with or without an intercalating DRTGG domain, binds adenine nucleotides cooperatively and confers catalytic cooperativity to cpPPase and three newly isolated family II PPases of Desulfitobacterium hafniense (dhPPase), Clostridium novyi (cnPPase), and Eggerthella lenta (elPPase). We found that both types of cooperativity depend on Mg 2ϩ concentration and the identity of the bound nucleotide, further expanding our understanding of the mechanisms involved in regulating cellular PP i level. These findings were corroborated by studies of a genetically engineered dhP-Pase deletion variant corresponding to the isolated catalytic part of the enzyme. CBS domain-containing PPases are thus the first known oligomeric PPases whose subunits exhibit cooperative behavior.

EXPERIMENTAL PROCEDURES
Cloning-Genomic DNA extracted from D. hafniense, C. novyi, and E. lenta (DSM numbers 10664, 14992, and 2243, respectively) was obtained from DSMZ (Deutsche Sammlung von Microorganismen und Zellkulturen GmbH). The sequences of full-length dhPPase (residues 1-544; YP_002458003), cnPPase (residues 1-548; YP_878001), and elPPase (residues 1-455; YP_003181314) were amplified by PCR and ligated into NdeI and XhoI restriction sites of the pET28bTEV plasmid (Novagen) for dhPPase and pET46 Ek/LIC plasmid (Novagen) for cnPPase and elPPase. A synthetic gene encoding the catalytic part of dhPPase (dhPPase⌬CDC) containing codons for dhPPase fragments 1-63 and 306 -544 connected by the linker ESVEAKQK was obtained from GeneArt. The linker sequence was identical to that found in the family II PPase from Desulfosporosinus acidiphilus SJ4 that most closely resembles the catalytic part of dhPPase but has no regulatory element. The gene was subcloned into the pET28bTEV plasmid using NdeI and XhoI restriction sites. The plasmid constructs thus obtained expressed dhPPase, dhPPase⌬CDC, cnPPase, elPPase, or dhCDC with a cleavable His 6 tag at their N termini. All constructs were confirmed by sequencing.
Protein Expression and Purification-Full-length dhPPase and dhPPase⌬CDC were produced in the E. coli strain BL21(DE3)-RIL (Stratagene) by cultivating at 37°C in Terrific Broth medium supplemented with 30 g/ml each of kanamycin and chloramphenicol. Gene expression was induced by incubating with 1 mM isopropyl ␤-thiogalactopyranoside for 3 h. Collected cells were suspended in lysis buffer (50 mM Tris-HCl, 500 mM NaCl, 20 mM imidazole-HCl, pH 7.8) and disrupted with an MSE 100-watt ultrasonic disintegrator. The cell lysate was applied to a 2-ml TALON Superflow gravity column (GE Healthcare), and dhPPase was eluted using a buffer containing 50 mM Tris-HCl, 500 mM NaCl, and 0.2 M imidazole-HCl (pH 7.8). Imidazole was removed from eluate fractions containing dhPPase by passing through a HiPrep 26/10 column (GE Healthcare) pre-equilibrated with buffer consisting of 50 mM Tris-HCl (pH 7.8) and 500 mM NaCl. The His 6 tag was removed by digesting overnight with tobacco etch virus (TEV) protease at 20°C as described by the manufacturer after which the mixture was passed through a TALON Superflow gravity column to remove His 6 -containing peptides from the sample. The flowthrough was further purified by size exclusion chromatography on a Superdex 200 26/60 (GE Healthcare) column pre-equilibrated with 50 mM MOPS-KOH (pH 7.2), 150 mM KCl, 0.1 mM CoCl 2 , and 20 M diethylenetriaminepentaacetate. cnPPase and elPPase were expressed and purified similarly except that the His 6 tag was not removed, and the buffer in size exclusion chromatography was 25 mM MOPS-KOH (pH 7.2), 50 mM KCl, and 0.1 mM CoCl 2 . cpPPase was expressed and purified as described previously (19). Protein solutions were stored at Ϫ40 to Ϫ80°C.
The purity of the isolated proteins was assessed by SDS-PAGE using Phast system 8 -25% gradient gels (GE Healthcare 2) except where specified otherwise. In measurements done at higher Mg 2ϩ concentrations, buffer concentration was decreased appropriately to maintain constant ionic strength. The reaction was initiated by adding enzyme, and P i accumulation due to PP i hydrolysis was continuously recorded for 2-3 min at 25°C using an automatic P i analyzer (22). The analyzer utilizes the principle of color change of methyl green in the presence of phosphomolybdate and consists of a three-channel peristaltic pump and a flow-through photometer. The pump delivers a constant flow of sample, acid molybdate, and methyl green solutions, which are successively combined and directed to the flow photometer. The sensitivity of the analyzer was varied to yield full-scale recorder values of 4 or 20 M P i using an appropriate choice of pump tubing diameters; corresponding sample consumption rates were 5 and 1 ml/min. The dead time of the analyzer (i.e. the time from feeding the sample into the analyzer to mixing with the acid molybdate solution, which quenches the enzymatic reaction) was 10 -20 s in the standard mode. The precision of initial velocity estimates for reactions yielding nonlinear time courses of P i production was increased by decreasing the dead time to 1 s using an appropriate modification of the inlet system (23). The initial velocity values obtained in replicate measurements agreed within 5-10% and were strictly proportional to enzyme concentration.
Calculations and Data Analysis-The values of the apparent dissociation constants for the various metal ion complexes used to calculate the free metal ion concentrations at pH 7.2 were as follows: MgPP i , 112 M (24); Mg 2 PP i , 2.84 mM (24); MgAMP, 10.5 mM (25); MgADP, 0.42 mM (25); and MgATP, 0.034 mM (25). The values for adenine nucleotides were derived from published values of the corresponding pH-independent constants. Nonlinear least square fits were performed using the program Scientist (Micromath).
Initial velocities of PP i hydrolysis were typically estimated graphically from the slopes of the tangents to the initial portion of hydrolysis time courses recorded with the P i analyzer. The time courses generated by truncated PPase were markedly nonlinear because of gradual inactivation of the enzyme upon dilution into the reaction medium. In this case, the initial velocities (v) were obtained by fitting the time courses to Equation 1, where k d is the rate constant for enzyme inactivation, t is time, and a is the background signal of the instrument.
The dependence of hydrolysis rate on nucleotide concentration ([N]) at fixed substrate concentration was fit to Equation 2, where A 0 and A N are activities of free and nucleotide-saturated enzyme, respectively, and K N1 and K N2 are the apparent dissociation constants for the enzyme-nucleotide complexes. Equation 2 was derived for Scheme 1, which describes successive binding of nucleotide to two regulatory sites per enzyme molecule. Here, E 2 refers to a mixture of free and substrate-bound dimeric enzyme. The activity of E 2 N is intermediate between the activities of E 2 and E 2 N 2 (i.e. activities of two subunits respond independently to nucleotide binding). Equation 2 is equally valid if N is an inhibitor or activator.
For non-cooperative binding, Equation 3 with a single K N value was used.
Notably, if Equation 2 instead of Equation 3 is applied to a non-cooperative binding reaction, the fitted values of K N1 and K N2 should differ 4-fold: K N1 ϭ K N /2 and K N2 ϭ 2K N (26). Consequently, the ratio 4K N1 /K N2 can be used to recognize cooperativity: it is greater than 1 for positive cooperativity and less than 1 for negative cooperativity. In terms of generally accepted nomenclature, K N is a "microscopic" binding constant, and K N1 and K N2 are "macroscopic" binding constants (26). The merit of using 4K N1 /K N2 instead of h to characterize cooperativity is that the former parameter is directly related to the free energy change associated with cooperativity, that is the effect of a ligand binding at one site on the binding affinity of the other site (27).
Alternatively, nucleotide binding data were fit to the Hill equation (Equation 4) to determine the Hill coefficient h.
Cooperative kinetics of substrate hydrolysis was analyzed in terms of Scheme 2, which assumes different Michaelis constants (K m1 and K m2 ) and equal k cat values for two active sites in the dimer (E 2 ); [E] 0 is total enzyme concentration. The values of K m1 , K m2 , and k cat were obtained by fitting Equation 5 to the dependence of hydrolysis rate (v) on substrate (MgPP i ) concentration at fixed Mg 2ϩ concentrations.
v ϭ k cat ͓E͔ 0 ͑1 ϩ 0.5K m2 /͓S͔͒/͑1 ϩ K m2 /͓S͔ ϩ K m1 K m2 /͓S͔ 2 ͒ (Eq. 5) As was the case for Equation 2, the ratio 4K m1 /K m2 can be used to recognize catalytic cooperativity: its value is greater than 1 for positive cooperativity and less than 1 for negative cooperativity (26). The applicability of the microscopic/macroscopic constant concept to Michaelis constants results from the formal similarity of the Michaelis-Menten equation to the equilibrium binding equation (28) despite the fact that they are not equilibrium substrate binding constants in a general case.
The dependence of K N on Mg 2ϩ (M) concentration was fit to Equation 6 derived for Scheme 3 where (K N ) 0 and (K N ) M are the limiting values of K N at zero and infinite Mg 2ϩ concentrations, and K M is the metal binding constant. Equations analogous to Equation 6 were used to analyze the Mg 2ϩ concentration dependence of K m .

Production of PPases-
The genes for CBS-PPases and the deletion variant of dhPPase (dhPPase⌬CDC; Fig. 1A) were expressed in E. coli, and the proteins were purified with a yield of ϳ10 mg of pure protein/liter of medium. Constructs were designed to encode an additional N-terminal MGSSHHHHH-HENLYFQGH sequence containing a His 6 tag to facilitate isolation by immobilized metal ion affinity chromatography. TEV protease cleaves this sequence between the Gln and Gly residues, leaving only a dipeptide extension on the protein. His 6 tag removal did not affect PPase activity but diminished the aggregation of full-size dhPPase during purification and concentration procedures. Tag removal was not performed with dhPPase⌬CDC and other PPases as it did not improve their solubility. Inactive aggregates were separated from soluble active proteins during size exclusion chromatography. The final products were at least 95% pure as estimated by SDS-PAGE.
The final purification step (Superdex 200 chromatography) was conducted in the presence of 0.1 mM Co 2ϩ to stabilize the enzymes; Co 2ϩ was also routinely added to enzyme stock solutions. The stabilizing effect of Co 2ϩ is consistent with data showing that "canonical" family II PPases contain one site that tightly binds transition metal ions (Co 2ϩ or Mn 2ϩ ) in addition to several more loosely binding sites with broader specificity that are apparently filled with Mg 2ϩ in vivo (5,29,30). All of these sites have a role in catalysis, but the tightly bound transition metal ion also has a structural role (7,8) as it does in many other metalloenzymes. The activities of CBS-PPases preincubated with 0.1 mM Co 2ϩ were somewhat higher than those incubated with Mn 2ϩ . Therefore, Co 2ϩ was routinely used as the transition metal cofactor in these studies.

Cooperativity of Substrate Hydrolysis by CBS-PPases-
The dependence of CBS-PPase activity on substrate concentration in the presence of 5 mM free Mg 2ϩ exhibited systematic deviations from simple Michaelis-Menten kinetics as illustrated in Fig. 2 for dhPPase. The Hill coefficient h, derived from this dependence using Equation 4 by setting A 0 to zero, was 1.37 Ϯ 0.02 (Fig. 2), indicating positive catalytic cooperativity. Therefore, the dependence was analyzed using Equation 5 derived for Scheme 2, which assumes different Michaelis constants (K m1 and K m2 ) for two active sites. This analysis markedly increased the quality of the fit compared with the Michaelis-Menten equation (Fig. 2) as indicated by a ϳ12-fold lower sum of the squares of residuals. The values of K m1 and K m2 were found to be 26 Ϯ 1 and 10 Ϯ 1 M, respectively; the ratio 4K m1 /K m2 (equal to 10) was thus much greater than 1, confirming positive catalytic cooperativity. Importantly, product formation curves were linear, and reaction rates were strictly proportional to enzyme concentration in all cases, ruling out the possibility that the deviation from simple kinetics seen in Fig. 2 resulted from a FIGURE 1. CBS-PPase structure. A, domain arrangement in the primary structures of wild-type dhPPase and its deletion variant. The five domains that form one subunit are shown in different colors and are labeled; short linker regions are depicted in black. DHH and DHHA2 are catalytic domains. Numbers indicate residues that start/end domains or their parts or precede/follow the deleted sequences. Residue numbering is based on the sequence of the full-length protein. For dhPPase⌬CDC, the linker sequence is shown using single letter notation. B, two views of the modeled three-dimensional structure of the cpCBS-PPase homodimers (19) in a sphere representation. Domain colors of one subunit are the same as in A; the other subunit is colored gray. The AMP molecules bound between CBS domains are shown in green.  rapid substrate-dependent change in enzyme oligomeric structure upon dilution into the assay medium.
The Hill coefficient h as well as the ratio 4K m1 /K m2 for dhPPase were similarly greater than 1 across the entire 0.05-20 mM Mg 2ϩ concentration range (Fig. 3) but decreased at low Mg 2ϩ concentrations, indicating a decrease in the degree of cooperativity. This transition resulted from changes in K m1 but not K m2 , which did not vary significantly (Fig. 3). The dependence of K m1 on Mg 2ϩ concentration obeyed Equation 6 with the parameters (K N ) 0 and (K N ) M replaced by the respective parameters (K m1 ) 0 and (K m1 ) M , the Michaelis constants at zero, and infinite Mg 2ϩ concentration. The fitted (K m1 ) 0 , (K m1 ) M , and K M values were 4.7 M, 60 M, and 0.6 mM, respectively ( Table 1). The measured value of k cat for dhPPase showed little dependence on Mg 2ϩ concentration (0.05-20 mM) and was in the range of 300 -350 s Ϫ1 .
A similar kinetic analysis was conducted with three other CBS-PPases. The results are summarized in Fig. 3 and Table 1.
With cnPPase, K m1 was virtually independent of Mg 2ϩ concentration, whereas K m2 increased at high [Mg 2ϩ ]. As a consequence, Mg 2ϩ exerted an opposite effect on cooperativity compared with dhPPase, and the Hill coefficient dropped to slightly below unity at high [Mg 2ϩ ]. With cpPPase and elPPase, both K m1 and K m2 changed with [Mg 2ϩ ] concentration but in opposite directions. Consequently, the degree of cooperativity increased with increasing [Mg 2ϩ ]. The largest effect was observed with cpPPase, which exhibited h values in the range of 1.0 -1.8 depending on Mg 2ϩ concentration.
The measured value of k cat was nearly constant over the entire [Mg 2ϩ ] range for elPPase but changed 2-fold for cnPPase and 50-fold for cpPPase (Fig. 3). For the latter enzyme, k cat depended on the second power of Mg 2ϩ concentration (see Fig.  3 legend), indicating that two metal ions are required for the transition from k cat,0 to k cat,M .
The above analyses were based on the assumption that the k cat value for E 2 S is half that for E 2 S 2 in Scheme 1. Assuming   Fig. 3 legend for details). c ND, not determined. AUGUST 15, 2014 • VOLUME 289 • NUMBER 33 zero activity for the E 2 S species increased the sum of the squared residuals by severalfold, indicating significantly worse fits. In contrast, assuming equal activities of E 2 S and E 2 S 2 decreased the quality of the fits to a lesser extent, making this case a likely alternative. However, if the ratio of the k cat values for E 2 S and E 2 S 2 was treated as an adjustable parameter, its best fit value was generally closer to 0.5 than 1.0. Importantly, the values of K m1 , K m2 , and their ratio showed essentially the same trends with the k cat ratio equal to 0.5 and 1, indicating positive cooperativity, which decreased at low [Mg 2ϩ ] in both cases. We thus conclude that Scheme 1 is the simplest scheme consistent with the data because any value of the k cat ratio greater than 0.5 implies additional negative catalytic coopera-tivity because of diminished activity of one of the active sites in the dimeric enzyme. Kinetic Behavior of dhPPase⌬CDC-Remarkably, dhPPase⌬CDC, which is devoid of the regulatory unit, demonstrated Michaelian kinetics in the presence of 5 mM Mg 2ϩ and over the entire 0.1-20 mM Mg 2ϩ concentration range as indicated by a 4K m1 / K m2 value for Scheme 2 and a Hill coefficient close to 1 (Fig. 4 and Table 1). The single microscopic K m value describing dhPPase⌬CDC kinetics showed little variation in the metal concentration range used, and its values (3.8 -5.0 M) were markedly less than ͌K m1 K m2 (the geometric mean of the two K m values) values for dhPPase (Fig. 4).

Nucleotide-regulated Soluble Pyrophosphatases
The value of k cat for dhPPase⌬CDC was 100 -120 s Ϫ1 over the 0.1-20 mM Mg 2ϩ concentration range. The somewhat lower activity of dhPPase⌬CDC compared with dhPPase may indicate that deletion of the regulatory part of the protein caused some distortions in the active site.
Cooperativity of Nucleotide Binding to dhPPase- Fig. 5 shows the concentration dependence of nucleotide effects on activity measured at fixed substrate (MgPP i ) and Mg 2ϩ concentrations. Micromolar concentrations of AMP and ADP caused inhibition in most cases, whereas ATP acted as an activator. Qualitatively similar effects of these nucleotides were reported previously for the CBS domain-containing mtPPase (18). The major new finding here is that, in most cases where the size of the effect allowed quantitative analysis, the curves were poorly described in terms of a simple 1:1 binding model (Equation 3) but obeyed Equation 2 for cooperative binding to two sites with concomitant activation or inhibition. The quality of the fit was relatively insensitive to the value of A 1/2 in Scheme 1, but better fits were generally observed with A 1/2 ϭ (A 0 ϩ A N )/2 compared with the limiting cases of A 1/2 ϭ 0 or A N . Importantly, most curves generated K N1 values greater than K N2 regardless of the A 1/2 value used and Hill coefficients greater than 1 (Table 2). Thus, nucleotide binding also exhibited positive cooperativity. In only two pairs (cpPPase/ADP and elPPase/ATP) did the analysis indicate insignificant cooperativity.  Interestingly, ADP did not affect cnPPase activity, and AMP was equally ineffective with elPPase (Fig. 5). Activity was nucleotide-insensitive in these enzyme-nucleotide pairs over the entire 0.05-20 mM Mg 2ϩ concentration range. 5 To test whether the nucleotides bound to enzyme in these cases, we performed competition experiments (Fig. 6A). In both cases, a "functionally silent" nucleotide modulated the activating effect of ATP, indicating that the former is able to bind. Moreover, although ineffective by itself, AMP synergistically enhanced the effect of ADP on elPPase, shifting the inhibition profile to lower ADP concentrations and decreasing the activity value extrapolated to infinite ADP concentration (Fig. 6B). This profile shift is explained by a 3-fold lower K N1 value for ADP in the presence of 100 M AMP (Table 2). Accordingly, AMP acted in a concentration-dependent manner to potentiate the inhibitory action of ADP measured at a constant ADP concentration (Fig.  6C). Clearly, binding of AMP to one site greatly enhanced ADP binding to the other site(s) to form a mixed enzyme-AMP-ADP complex with low activity in these conditions. The values in the last line of Table 2 suggest that AMP binding to elPPase is 5 V. A. Anashkin, unpublished observations.  highly cooperative: the first nucleotide molecule binds quite weakly, but the mean binding constant (͌K N1 K N2 ) is comparable with that of the other nucleotides. It is unlikely that the extraordinarily high values of 4K N1 /K N2 and h for AMP, which are close to their limiting values for two-site binding (27), are somehow associated with the ADP present in the system because the latter nucleotide exhibited quite low binding cooperativity with elPPase ( Table 2). The above analysis of nucleotide effects was conducted at a half-saturating substrate concentration. Because the substrate itself also binds cooperatively, the apparent nucleotide binding cooperativity may result from nucleotide effects on substrate binding. Therefore, measurements were extended to low and high substrate concentrations at which the enzyme (dhPPase) predominantly exists in the substrate-free form or as enzymesubstrate complex, respectively. As Table 2 makes clear, the cooperativity of AMP and ATP binding as characterized by 4K N1 /K N2 and h did not depend significantly on substrate concentration and showed only a moderate change in the case of ADP binding. Therefore, the observed cooperativity of nucleotide binding is not induced by bound substrate or by modulation of substrate binding. In contrast, the relative final activity at infinite nucleotide concentration (v N /v 0 ) increased with increasing substrate concentration in all cases, whereas the mean binding affinity (͌K N1 K N2 ) significantly decreased.
The Mg 2ϩ dependence of AMP, ADP, and ATP binding to dhPPase and of AMP binding to cpPPase was determined (Fig.  7). These enzymes and nucleotides were chosen because they demonstrate profound effects on activity, allowing accurate analysis of the binding curves. Although quite large, the effect of ATP on elPPase was not included in this analysis because ATP chelates Mg 2ϩ appreciably (25) at the high ATP concentrations at which this enzyme operates (Fig. 5), introducing uncertainty in free Mg 2ϩ concentration at the lower values in this range. Varying Mg 2ϩ concentration in the assay changed K N1 and K N2 values for AMP binding to dhPPase and cpPPase in opposite directions (Fig. 7). As a result, the ratio 4K N1 /K N2 , the Hill coefficient h, and hence the degree of cooperativity increased with increasing Mg 2ϩ concentration. With ATP, K N1 , but not K N2 , was Mg 2ϩ -dependent, resulting in a similar although smaller effect. With ADP, both binding constants changed in parallel without affecting 4K N1 /K N2 or h. Notably, dhPPase activity at saturating ATP concentration (470 Ϯ 10 s Ϫ1 ) was independent of [Mg 2ϩ ].
The dependences of K N1 and K N2 on Mg 2ϩ concentration ([M]) obeyed Equation 6 derived for a simple model that assumes that metal binding to a site characterized by the dissociation constant K M shifts the dissociation constant for the enzyme-nucleotide complex from (K N ) 0 to (K N ) M . The fitted values of these parameters are summarized in Table 3. Interestingly, K M values were essentially independent of the nucleotide and enzyme used and correlated well with the K M value derived from substrate hydrolysis kinetics for dhPPase (and other PPases) (Table 1). Moreover, in all cases, the K M values derived from K N2 dependence were greater than those derived from the K N1 dependence; in both cases, their ratio was not much different from 4, the value expected for non-cooperative metal binding to two identical sites.
Effects of Nucleotides on Kinetic Cooperativity- Table 4 summarizes nucleotide effects on hydrolysis kinetics measured at a Mg 2ϩ concentration of 5 mM. The general trend was that nucleotides decreased kinetic cooperativity as characterized by h val- ues. With cnPPase, which exhibited no cooperativity at this Mg 2ϩ concentration (Fig. 3), ATP conferred slightly negative cooperativity (h ϭ 0.86 Ϯ 0.02). Another general trend was that the activating nucleotide (ATP) increased k cat values up to 2-fold and decreased the mean K m value (͌K m1 K m2 ) up to 3-fold for all CBS-PPases except cpPPase in which the latter parameter increased in the presence of ATP. This means that ATP inhibits rather than activates cpPPase at low substrate concentrations.
Of the three inhibition cases documented in Table 4, one (cnPPase/AMP) resulted solely from a decrease in k cat (noncompetitive inhibition), and one (cpPPase/ADP) resulted from an increase in ͌K m1 K m2 (competitive inhibition). In the last case (elPPase/ADP), the inhibitor decreased both k cat and ͌K m1 K m2 to the same degree (uncompetitive inhibition), indicating an absence of inhibition at very low substrate concentrations. Functionally silent nucleotides (ADP with cnPPase and AMP with elPPase; see Fig. 5) did not significantly change k cat or ͌K m1 K m2 (Table 4).
Similar analyses could not be performed in the cases of the most efficient inhibitors (AMP and ADP with dhPPase and AMP with cpPPase). These pairs exhibited quite low (although finite) activities of the enzyme-nucleotide complexes, resulting in a significant relative contribution of nucleotide-free enzyme to activity even at high nucleotide concentrations.
CBS-PPase Activity as a Function of ADP:ATP Ratio-The ADP:ATP ratio is a critical determinant of cellular energy status that regulates many metabolic activities. Fig. 8 shows how the value of this parameter affected activities of the four CBS-PPases. The sum of ADP and ATP concentrations was fixed at 0.5 mM. Although this value is an order of magnitude less than that in a typical cell, this did not markedly affect the profiles because ADP and ATP concentrations exceeded the respective ͌K N1 K N2 values (Table 2) in most cases. Substrate concentration was arbitrarily fixed at 50 M. Because ATP is an activator and ADP is an inhibitor or an inert species, enzyme activity decreased with increasing ADP:ATP ratios in all cases. However, the sensitivity of CBS-PPases to this parameter varied considerably with dhPPase being the most sensitive and cnPPase being the least sensitive.

DISCUSSION
The organisms that harbor the CBS-PPases used in this study are Gram-positive anaerobic bacteria belonging to the phylum Firmicutes (D. hafniense, C. novyi, C. perfringens) or Actinobacteria (E. lenta). Three of them (C. novyi, C. perfringens, and E. lenta) are pathogenic and are found in the human intestinal tract. D. hafniense is found in soil and is capable of reductive dechlorination of chlorophenols (31). In three of these bacteria (excluding C. perfringens), PP i metabolism depends on soluble and membrane-bound PPases (32), which convert metaboli-

TABLE 3
Kinetic parameters for nucleotide inhibition derived from the dependencies of K N1 and K N2 on Mg 2؉ concentration (Fig. 7) cally inert and inhibitory PP i into usable P i . The soluble PPase converts PP i energy into heat. In contrast, membrane-bound PPases use PP i to establish an H ϩ gradient (D. hafniense) or Na ϩ gradient (C. novyi and E. lenta) and thereby mobilize PP i energy to maintain cation gradients and help cells survive under stress conditions (33). This dual utilization of PP i explains the need for regulation of soluble PPases, which has been achieved evolutionarily by the acquisition of a pair of regulatory, energysensing CBS domains. Binding of ATP, which prevails under high energy conditions, activates soluble PPases and decreases PP i levels, thereby facilitating biosynthetic reactions that are inhibited by PP i . Under low energy conditions, bound ATP is replaced by ADP and AMP, resulting in inhibition of PPase and an increase in the PP i level, which in turn slows down biosynthesis and provides substrate for membrane PPases that support the membrane H ϩ or Na ϩ gradient.
The results reported above reveal added complexity in PPase regulation: the CBS domains introduce dual positive cooperativity to the regulatory mechanism. The first level of cooperativity relates to nucleotide binding and serves to amplify the initial signal (change in adenine nucleotide distribution). Simple calculations for AMP inhibition of dhPPase ( Fig. 5) with an h value of 1.68 (Table 2) showed that a change in PPase activity from 10 to 90% of its maximal value occurs when AMP concentration changes 16-fold, whereas the same effect would require an 81-fold change in AMP level if it bound non-cooperatively. Cooperativity of nucleotide binding is not caused by bound substrate as its degree, characterized by the values of 4K N1 /K N2 and h in Table 2, does not depend (or only slightly depends) on the degree of enzyme saturation with substrate. Notably, nucleotide binding cooperativity is not uncommon among other CBS domain-containing proteins. Positive cooperativity was reported for S-adenosylmethionine binding to cystathionine ␤-synthase (34), AMP binding to IMP dehydrogenase (13), and AMP and ATP binding to AMP-activated protein kinase (13). More recently, AMP-activated protein kinase was reported to successively bind nucleotides with decreasing affinity (17,35), which suggests negative binding cooperativity.
The second level of positive cooperativity in CBS-PPases relates to enzyme interaction with substrate as characterized by the Michaelis constant (K m ). This type of behavior is called "catalytic cooperativity" to distinguish it from the more common "binding cooperativity." One should keep in mind that catalytic cooperativity may not be interpreted in terms of binding insofar as K m is not a thermodynamic binding constant in a general case and is a combination of six individual rate constants in the case of PPase (36). Therefore, a change in K m value may result from a change in any of the rate constants that describe the four catalytic steps in PPase: substrate binding, substrate hydrolysis, and sequential release of two phosphates.
Catalytic cooperativity, which further amplifies the initial signal, is observed in the absence of nucleotides, is modulated by nucleotides (Table 4), and is therefore induced by the regulatory insert itself rather than by the bound nucleotide. Consistent with this notion, removal of the insert abolished the cooperativity. The capacity of CBS domains to impart cooperativity on enzyme or transporter function has not been previously recognized. However, Labesse et al. (37) have recently reported that IMP dehydrogenase binds its substrate, IMP, with positive cooperativity; this cooperativity was abolished by mutation of a single residue in the CBS domain or binding of MgATP to the enzyme. Of note, CBS-PPases are the only cooperative enzymes among different types of oligomeric PPase enzymes.
Mg 2ϩ binding had a strong modulatory effect on both types of cooperativity, but its mode of action varied with enzyme and nucleotide. Increasing Mg 2ϩ concentration generally conferred or increased positive kinetic and nucleotide binding cooperativity (Figs. 3 and 7). However, Mg 2ϩ changed the kinetic cooperativity in cnPPase in the opposite direction (Fig. 3) and did not affect ADP binding cooperativity in dhPPase (Fig. 7). Similar values of the Mg 2ϩ binding constant, K M , derived from measurements of hydrolysis kinetics (Table 1) and nucleotide effects ( Table 3) suggest that a single site controls both cooperativity types. Notably, the structure of the AMP-bound regulatory portion of cpPPase crystallized in the presence of Mg 2ϩ contains no bound divalent metal ion (19). In contrast, canonical family II PPases, which represent the catalytic part of CBS-PPases, bind three or four Mg 2ϩ ions in the absence of substrate (5) and up to five metal ions in its presence (6). All metal ions are located in the active site, but one of them is not absolutely required for activity (6). This last activity-modulating site is thus the most likely candidate for the site that modulates cooperativity in CBS-PPases.
All K N values are reported here in terms of total nucleotide concentrations without regard to complexation with Mg 2ϩ . Based on the Mg 2ϩ binding constants (see "Experimental Procedures"), 99.8% of ATP, 98% of ADP, and 70% of AMP exist as magnesium complexes at the highest Mg 2ϩ concentration used (20 mM). Thus, it is not unlikely that nucleotide-bound Mg 2ϩ modulates enzyme-nucleotide interactions and therefore contributes to the dependences shown in Fig. 7. However, several lines of evidence rule out the possibility that Mg 2ϩ binding to nucleotides is the sole cause of the Mg 2ϩ effects on K N values. As already mentioned, two molecules of AMP bind to cpPPase as free nucleotide (19). If recalculated in terms of free AMP, K N1 and K N2 values for dhPPase and cpPPase (Fig. 7) would decrease in parallel (up to 3-fold at the highest Mg 2ϩ concentration), resulting in a minor effect on the AMP binding pattern. The crystal structures of the cpPPase fragment (19) suggest that other nucleotides form major contacts with the enzyme through their AMP moieties. Therefore, free and Mg 2ϩ -complexed ADP or ATP are likely to have equal or similar affinities for enzyme. This interpretation is consistent with similar mean K N values (͌K N1 K N2 ) for AMP, ADP, and ATP observed for dhPPase and cpPPase, which bind all three nucleotides. However, the possibility that Mg 2ϩ binding to ADP and ATP contributes to their binding patterns in Fig. 7 cannot be excluded.
The structural basis for the effects of the regulatory element on the active site and for the modulation of these effects by bound nucleotides still remains to be determined for PPase as well as for other CBS domain-containing enzymes and transporters. Our results pose further questions in this context. Because the two AMP molecules bound per dimeric regulatory fragment of cpCBS-PPase are in proximity to each other (19), one would expect negative rather than positive cooperativity in their binding. Indeed, AMP analog binding was shown to exert negative cooperativity in mtPPase (21). The reversal of nucleotide binding cooperativity in PPase observed in the present study may reflect plasticity of CBS domains and is consistent with the known variability of their amino acid sequences (10). The available crystallographic data show significant opening of the CBS domain interface in the activator (AP 4 A) complex of cpPPase compared with that in the inhibitor (AMP) complex (19). Lucas et al. (38) observed an open-to-closed conformational change in the CBS domain pair of Methanocaldococcus jannaschii protein MJ0100 upon successive binding of adenosine derivatives. Quite recently, Jeong et al. (39) reported a dramatic AMP-induced structural change in Arabidopsis thaliana protein CBSX2.
The concept of "autoinhibition" was introduced vis-à-vis CBS domains by Janosík et al. (40) to explain cystathionine ␤-synthase activation by S-adenosyl-L-methionine as well as its limited proteolysis and thermal denaturation. According to this concept, the CBS domain insert acts as an "internal inhibitor," sensitizing proteins with catalytic or transport functions to structural changes caused by nucleotide binding and permitting either activation or further inhibition. CBS domain-containing PPases provide strong support for this theory. Thus, deletion of the regulatory domains in dhPPase favorably changed its K m1 value (Table 3). A similar deletion in cystathionine ␤-synthase increased k cat but not K m (41,42). The concept of autoinhibition is also consistent with the diminished activity (1-3 orders of magnitude) of CBS domain-containing PPases compared with their close homologs lacking CBS domains (5) as well as their ability to be activated by ATP. Many mutations in the CBS domains also activate mtPPase, and some even reverse the effects of nucleotide from inhibition to activation (43), resembling the effects of mutations in cystathionine ␤-synthase (44) and AMP-dependent protein kinase (45,46).
Unlike other known CBS domain-containing proteins, dhPPase, cnPPase, and cpPPase contain a DRTGG domain insert within the CBS domain pair. The results of the present work do not shed light on the function of this extra domain in these (and most other) CBS-PPases as we did not observe any fundamental differences in the behavior of these PPases compared with that of elPPase, which has no DRTGG domain in its structure.
In summary, CBS-PPase presents a unique case, demonstrating in one protein the diverse regulatory capabilities of CBS domains as sensors of cell energy status. The regulation of this enzyme is based on a complex interplay among the effects of nucleotides, substrate, and Mg 2ϩ on binding cooperativity. Further work is clearly needed to fully elucidate this interplay and determine its importance for other CBS domain proteins.