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Synthesis of Inorganic Pyrophosphatase–Nanodiamond Conjugates Resistant to Calcium and Fluoride

Pyrophosphate arthropathy is the mineralization defect in humans caused by the deposition of microcrystals of calcium pyrophosphate dihydrate in joint tissues. As a potential therapeutic strategy for the treatment of pyrophosphate arthropathy, delivery of exogenous pyrophosphate-hydrolyzing enzymes, inorganic pyrophosphatases (PPases), to the synovial fluid has been suggested. Previously, we synthesized the conjugates of Escherichia coli PPase (Ec-PPase) with detonation synthesis nanodiamonds (NDs) as a delivery platform, obtaining the hybrid biomaterial retaining high pyrophosphate-hydrolyzing activity in vitro. However, most known PPases including Ec-PPase in the soluble form are strongly inhibited by Ca2+ ions. Because synovial fluid contains up to millimolar concentrations of soluble calcium, this inhibition might limit the in vivo application of Ec-PPase-based material in joint tissues. In this work, we proposed other bacterial PPases from Mycobacterium tuberculosis (Mt-PPase), which are resistant to the inhibition by Ca2+ ions, as an active PPi-hydrolyzing agent. We synthesized conjugates of Mt-PPase with NDs and tested their activity under various conditions. Unexpectedly, conjugates of both Ec-PPase and Mt-PPase with aminated NDs retained significant hydrolytic activity in the presence of well-known mechanism-based PPase inhibitors, fluoride or calcium. The incomplete inhibition of PPases by fluoride or calcium was found for the first time.


INTRODUCTION
The problem of treatment of calcium pyrophosphate deposition disease (CPPD disease, or pseudogout) has remained unsolved for many years. 1−3 The disease is caused by deposition of microcrystals of calcium pyrophosphate dihydrate in joint tissues. 4 Most of the symptoms of this disease are due to the immune response of neutrophils attacking calcium pyrophosphate crystals. 5−7 One of the most significant events leading to the CPPD disease is increased production of enzymes responsible for the synthesis and/or transport of P 2 O 7 4− pyrophosphate anions to the tissue matrix. Examples are overproduction of a transport protein ANKH 8 or increased activity of the pyrophosphate-producing enzymes ENPP1. 9 To date, no specific treatment for the CPPD disease has been developed. 1−3 The drugs used for this purpose have a number of serious side effects because of which they are not commonly used in clinical practice. 10 Thus, the search for and development of new strategies and highly effective, low-toxicity agents for the treatment of the CPPD disease is a significant challenge in modern rheumatology and nanomedicine. 11 Soluble inorganic pyrophosphatases (PPases, E.c. 3.6.1.1) found in all known organisms catalyze the hydrolysis of inorganic pyrophosphate into inorganic phosphate (P i ). Mammalian cells express two PPases, cytoplasmic PPA1 12 and mitochondrial PPA2, 13 encoded by different genes.
Cytoplasmic PPase is an essential house-keeping enzyme maintaining normal cell growth and division by utilizing intracellular pyrophosphate (PP i ), the byproduct of key biosynthetic reactions, for example, DNA synthesis. Human PPA1 can also dephosphorylate c-Jun N-terminal kinase JNK and is thus involved in clinically significant processes regulated by this signaling pathway, for example, neurite growth, cancer progression, and so forth. 14−16 Overexpression of PPA1 detected in tumors of various origin correlates with their malignant potential, clinicopathological parameters, and prognosis in patients. 17−20 PPase PPA2 in humans is transported to the mitochondria where it is important for maintaining the membrane potential and other mitochondrial functions. 13,21 PPases are absent in the extracellular matrix or synovial fluid where PP i -hydrolyzing activity relies on other enzymes, for example, tissue-nonspecific alkaline phosphatases, TNAPs. 22,23 Yeast PPase was earlier suggested as a potential therapeutic agent for the treatment of the CPPD disease 24 because it efficiently hydrolyzes pyrophosphate. 25 Pyrophosphate is present in excess in the articular and periarticular tissues of patients 26 and leads to the deposition of calcium pyrophosphate microcrystals. 27 However, the in vivo use of carrier-free enzymes has many drawbacks and limitations. 28 Among the possible carriers, detonation synthesis nanodiamonds (NDs) are promising agents of drug delivery into cells and tissues. 29 NDs have the ability to penetrate biological barriers, so they can be used as carriers for the targeted delivery of immobilized proteins. 30 In our previous paper, we synthesized a number of covalent and noncovalent conjugates of inorganic pyrophosphatase with NDs that retained high hydrolytic activity, implying their possible applications in the treatment of the CPPD disease. 31 It is assumed that PPase included in the heterogeneous conjugates with NDs has a number of advantages compared with the carrier-free form. Among other tissues, ND samples have been shown to penetrate the bone tissue after intratracheal instillation; therefore, they can potentially be used as carriers for the delivery of proteins (e.g., PPases) to the site of precipitation of CaPP i crystals. 32 A predicted advantage of the proposed hybrid material will be its increased resistance to degradation by matrix proteases. It is assumed that the protein molecules trapped in conjugates are less accessible to proteolytic digestion than the carrier-free enzyme. This combination of properties makes conjugates of PPases with NDs a promising new biomaterial.
Considering the known protein-phosphatase activity of human PPase, its cell growth-promoting effects, and possible involvement in key regulatory pathways, we suggested bacterial PPases devoid of these properties as the source of exogenous PPase activity of the new material. PPase from Escherichia coli (Ec-PPase) was used in our previous work as a model PPase for obtaining conjugates and testing their properties. However, some catalytic features of Ec-PPase may limit the application of its conjugates to joint tissues. In particular, calcium ions in vitro completely inhibit Ec-PPase with an inhibition constant of 2−12 μM. 33 Calcium levels outside the cell are rather high; for example, synovial fluid contains up to 2 mM Ca 2+ , 34 which is expected to completely block the activity of Ec-PPase conjugates in biological samples. Our recent preliminary data suggested that inorganic pyrophosphatase from Mycobacterium tuberculosis (Mt-PPase) binds calcium ions and other known inhibitors of PPases with a much lower affinity than Ec-PPase or other family I PPases [unpublished data]. In the present work, we immobilized Mt-PPase on NDs, evaluated the activity of the conjugates, and tested their performance at high concentrations of Ca 2+ . We also characterized the conjugates of Ec-and Mt-PPases enzymatically and physico-chemically and tested the effects of other possible constituents of biological tissues on their activity. Our in vitro tests demonstrate that the conjugates of both enzymes are stable in pH range 5−10 and retain significant PPase activity in the presence of high concentrations of calcium and fluoride.

RESULTS AND DISCUSSION
2.1. Covalent Immobilization of PPase. Earlier, we reported the preparation of E. coli PPase (Ec-PPase) covalently immobilized on ND-NH 2 and ND-NH-(CH 2 ) 6 -NH 2 retaining its high enzymatic activity. 31 However, Ec-PPase is known to be completely inhibited by Ca 2+ in vitro with a micromolar inhibition constant. 33 Thus, the reliability of this model enzyme for the proposed in vivo applications was not quite obvious because the levels of Ca 2+ in tissues may be too high for the efficient enzymatic function of Ec-PPase-based conjugates. PPase from M. tuberculosis (Mt-PPase), on the other hand, binds Ca 2+ with a significantly lower affinity than Ec-PPase [unpublished data]. It was shown 35 that Mt-PPase shares most of the basic features of family I inorganic pyrophosphatases, including the catalytic residues and mechanism. However, this enzyme has notable structural and functional properties 36 that allow Mt-PPase-based conjugates to provide some resistance to Ca 2+ inhibition expected of Ec-PPase-based conjugates. With this in mind, we prepared Mt-PPase covalently immobilized on ND-NH 2 and ND-NH-(CH 2 ) 6 -NH 2 and tested them, as well as Ec-PPase-based samples.
Taking into account the general similarity of Mt-PPase and Ec-PPase, we tested Mt-PPase immobilization using the previously developed system of Ec-PPase immobilization. 31 The enzyme was cross-linked to the amine-containing ND with glutaraldehyde with the protection of the active site by the substrate (MgPP i ), cofactor (Mg 2+ ), and inhibitor (F − ). The ratio of protein and ND concentrations, the concentration of glutaraldehyde and compounds protecting the active site, and the incubation and washing protocols were also the same as for Ec-PPase. However, because of the possible differences between Mt-PPase and Ec-PPase, it was necessary to characterize the resulting conjugates and confirm that the enzyme retained its activity.
The characteristics of the obtained samples are presented in Table 1. Mt-PPase immobilized on ND-NH-(CH 2 ) 6 -NH 2 almost completely retained the activity of soluble enzyme (95%), whereas conjugates with ND-NH 2 lost approximately 20% of the initial activity. A similar pattern was observed earlier for Ec-PPase. Compared with the Ec-PPase-based conjugates, Mt-PPase-based conjugates had a somewhat lower protein content, and the enzymatic activities of the conjugates were significantly lower because of the lower initial activity level of soluble Mt-PPase used for immobilization. The particles of Mt-PPase-based conjugates were significantly smaller than those of Ec-PPase-based conjugates. For Mt-PPase, we did not observe aggregates greater than approximately 1 μm in diameter. The Fourier-transform infrared (FTIR) results for samples of ND and Mt-PPase individually and Mt-PPase conjugated to ND-NH 2 are shown in Figure 1. The spectra of Mt-PPase and its ND conjugates of both types [ND-NH 2 and ND-NH-(CH 2 ) 6 -NH 2 ] were similar. The spectra show the preservation of key protein absorption bands during immobilization: CO, C−N stretching, and N−H bending ("amide I" band at 1600− 1700 cm −1 ); N−H deformation ("amide II" band at 1510− 1580 cm −1 ); and C−N stretching ("amide III" band at 1200− 1400 cm −1 ). 37 Thus, the successful immobilization of Mt-PPase on the surface of NDs can be confirmed.
2.2. Catalytic Parameters of Immobilized PPases. Until date, several strategies involving various detection methods have been proposed to determine PPase activity, the most recent strategy being the quantitation of Cu 2+ ions released from the Cu-PP i complex after PP i hydrolysis. 38,39 In this work, we employed the conventional strategy of spectrophotometric quantitation of P i released from PP i by PPase, which was applicable for both soluble and immobilized enzymes. PPase activity was measured in a range of conditions as the initial rate of P i release with time. The catalytic parameters of Mg-activated hydrolysis of magnesium pyrophosphate by immobilized enzymes were determined. The activity profiles versus substrate concentration are shown in Figure 2. According to the linear character of the double reciprocal plots (Figure 2, insets), Michaelis−Menten kinetics was observed for all the conjugates. The calculated K m and V max values are given in Table 2.
The pyrophosphatase activity of the conjugates was preserved. However, significant decreases in substrate affinity and the rate of hydrolysis were observed in comparison with soluble enzymes. Nevertheless, the values obtained for specific enzymatic activity were sufficiently high to suggest that these conjugates could hydrolyze inorganic pyrophosphate at concentrations expected in the synovial fluid of joints with various pathologies (5.9−20.2 μM). 40 Comparison of the catalytic parameters of Ec-PPase and Mt-PPase conjugates showed that although the Ec-PPase-based conjugates were more active, Mt-PPase-based conjugates had a higher affinity for the substrate. The two enzymes showed similar patterns when immobilized on ND-NH 2 versus ND-NH-(CH 2 ) 6 -NH 2 : conjugates with ND-NH-(CH 2 ) 6 -NH 2 were more active, but they had higher Michaelis constants than ND-NH 2 conjugates. To sum up, both enzymes, Mt-PPase and Ec-PPase, and both types of NDs are suitable for the preparation of active conjugates.
2.3. PPase Activation by Mg 2+ . PPases are metaldependent enzymes. For family I PPases, the main physiological cofactor is Mg 2+ . 41,42 Therefore, we studied the effect of Mg 2+ ions on catalysis by soluble and immobilized enzymes. The result is presented in Figure 3.
Binding of two Mg 2+ ions (at the M1 and M2 sites, which differ in affinity) is necessary for enzyme activation. Binding of only the lower-affinity Mg 2+ ion at the M2 site can be detected by PPase activity. The resulting hyperbolic profiles were approximated using eq S1, corresponding to the scheme of enzyme activation by binding of one Mg 2+ ion. The calculated parameters are presented in Table 3. A max is the maximal activity of the PPase at saturation with the cofactor, and K d is the dissociation constant of the enzyme−magnesium complex at the M2 site. At these concentrations of Mg 2+ , inhibition of PPases by the lowest-affinity Mg 2+ at the M4 site 36 was not observed.
These results show that immobilization of PPases does not significantly impair their affinity for Mg 2+ at the M2 site. Most affected is Mt-PPase immobilized on ND-NH 2 . Nevertheless, these conjugates are highly active under the conditions   (1) and ND-NH-(CH 2 ) 6 -NH 2 (2). Lines are the best fit to the Michaelis−Menten eq 1. In the insets, same data are presented in double reciprocal coordinates.  43,44 It binds reversibly to an enzyme−substrate complex and competes with the attacking nucleophile to block pyrophosphate hydrolysis. 44 Because F − ions play an important role in the processes of growth and renewal of bone and articular tissues, 45 we determined its effect on the activity of soluble and immobilized PPases in vitro. Activity profiles in the presence of F − are shown in Figure 4.
All tested PPases were fully or partially inhibited by F − . The calculated inhibition parameters (inhibition constant K i , maximal activity A 0 , and limiting activity at saturation with inhibitor A 1 = αA 0 ) are shown in Table 4. These results demonstrate that all samples of Mt-PPase, including its soluble form, retain some residual activity, approximately 10−20% of the initial value, even at the highest concentrations of F − used in the experiment (50 mM). Soluble Ec-PPase, as was reported earlier, 46 is inhibited completely by F − with an inhibition constant of 0.1 mM. However, immobilized Ec-PPase is not inhibited completely, demonstrating unusual behavior similar to that of Mt-PPases. So far, incomplete inhibition of family I PPases by the fluoride ion has not been reported. In general, the immobilized forms of both PPases are more active at high F − than the soluble forms.
2.5. PPase Inhibition by Calcium Ions. Ca 2+ is an effective inhibitor of family I PPases. 33,47 According to the publication, 34 normally, a large amount of Ca 2+ (up to 1.4 mM) is presented in synovial fluid. In the present work, we determined the activity of immobilized PPases in the presence of Ca 2+ ions. The dependencies obtained are presented in Figure 5.
All tested PPases were inhibited by Ca 2+ . According to these data, in the case of Ca 2+ inhibition, both samples of soluble PPases were completely inhibited, while all samples of immobilized PPases retained residual activity of 50% or more. This effect is most unusual and has not been reported previously. The data on immobilized enzymes were fitted to eq S2 for partial inhibition.
Unlike immobilized PPases, soluble forms showed cooperative inhibition (as reported in the paper, 33 so the data in this case were fitted to the Hill eq (S3, Supporting Information).   The calculated inhibition parameters are shown in Table 5.
Parameter α for the soluble PPases is 0, and the Hill coefficient h for the immobilized PPases is 1.
The immobilized PPases show the lower values of K i compared to the soluble enzymes. This effect is most obvious for the conjugates with ND-NH-(CH 2 ) 6 -NH 2 . However, because of incomplete inhibition, at high concentration of Ca 2+ , the activity of immobilized PPases remains high, while the activity of soluble PPases is almost completely inhibited.
2.6. pH Dependence of the Activity of Immobilized PPases. As part of a general characterization of the catalytic behavior of conjugates, the activity of immobilized PPases was determined as a function of the pH of the reaction medium ( Figure 6).
The dependencies obtained were bell-shaped with two asymmetrical shoulders. All tested samples were active in the pH range 7.2−8.3, which corresponds to the pH of most biological fluids, including synovial fluid. At alkaline pH, all samples showed nonzero levels of activity up to pH 12. For Ec-
PPase and its conjugate with ND-NH 2 , the left branch of the plot shows a rapid drop in activity at acidic pH, demonstrating the involvement of at least two protons in the observed titration of catalytically important residue(s). The data were fitted to eq S4 (Supporting Information). The parameters obtained are presented in Table 6. A 1 is the maximum activity, A 2 is the limiting level of activity in the alkaline range, K a1 and K a2 are acidity constants of the catalytic groups, and m and n are the numbers of titratable protons in the acid and alkaline pH ranges, respectively. The pH range of activity and the pK a values of the titratable groups are typical for family I PPases. 35 After protein immobilization, pH dependencies change only marginally.
2.7. Stability of the PPase Oligomer in Conjugates as a Function of pH. In a previous paper, 31 we demonstrated that Ec-PPase retained sufficient thermal stability after immobilization. In the present work, we studied the dependence of the activity of immobilized PPases on the pH of the storage medium.
The stability of PPases at different pH values is the result of pH-sensitive dissociation/association equilibrium between various oligomeric forms of the protein. 48 Family I PPases from bacteria under physiological conditions are homohexamers organized into two trimers. 49 The protein residues involved in intersubunit contacts differ considerably between species. In Ec-PPase, the intertrimeric interface is stabilized by ionic interactions while the contacts between the subunits of the same trimer are mostly hydrophobic. 49 The native hexamer dissociates into a number of oligomeric forms depending on the storage conditions, leading to loss of activity. The trimeric form of Ec-PPase retains approximately 40% of the activity of the hexamer, while the other oligomeric forms are virtually inactive. 48 Therefore, storage conditions may be important for retaining the active PPases. Immobilization of enzymes can cause significant changes in the structure of their subunit interfaces, which can be manifested in changes in the oligomeric equilibrium or affect the catalytic characteristics of individual oligomeric forms. 50 To address this problem, PPase samples were incubated for 24 h at different pH levels. Subsequently, aliquots were taken from these solutions, and the PPase activity was measured under standard conditions (pH 7.5, fixed concentrations of the cofactor and substrate). The results are presented in Figure 7.
All the obtained pH-stability profiles are bell-shaped. The data were fitted to eq S5 (Supporting Information). The obtained parameters are presented in Table 7. All samples of Ec-PPase are essentially stable over a wide pH range of 5−11. For Mt-PPase and its conjugate with ND-NH-(CH 2 ) 6 -NH 2 , the stability range is narrow (5−8 for the soluble enzyme and 6−9 for the conjugate); however, this range is much wider for its conjugate with ND-NH 2 (5−11). The analysis of pK a values of the titratable groups responsible for the transitions between the oligomeric forms (Table 7) shows that for Ec-PPase, immobilization on ND-NH-(CH 2 ) 6 -NH 2 slightly changes the   pK a values of both acidic and basic protein groups involved in stabilization of the hexamer, while immobilization on ND-NH 2 does not. The pK a values of the soluble Mt-PPase differ from those of Ec-PPase because of significant differences in the oligomeric interfaces of these two proteins. 36 Immobilization of Mt-PPase on both types of ND changes these values. The observed variations in the pK a values upon immobilization may stem from changes in the microenvironment of titrable groups involved in the oligomeric interaction. Significant alterations in the shape of the pH-stability profile observed for Mt-PPase immobilized on ND-NH 2 may be due to the increased activity of the oligomeric form prevailing at pH 10−12 (according to publication, it is a trimer). 36

CONCLUSIONS
In this work, conjugates of inorganic pyrophosphatase from M. tuberculosis (Mt-PPase) with modified nanodiamonds ND-NH 2 and ND-NH-(CH 2 ) 6 -NH 2 were synthesized using the protocol reported earlier for PPase from E. coli (Ec-PPase). 31 New Mt-PPase-based conjugates retain significant enzymatic activity toward Mg 2+ -dependent hydrolysis of MgPP i . Both Ec-PPase and Mt-PPase-based conjugates are stable and active in the wide pH range (5−10), which makes them suitable pyrophosphate-hydrolyzing agents for in vivo applications.
Predictably, Mt-PPase-based conjugates in the absence of inhibitors had lower absolute activity than Ec-PPase-based conjugates, following the lower activity of soluble Mt-PPase. Also, as expected, Mt-PPase-based conjugates had lower affinity to the known inhibitors of PPases, calcium or fluoride, than Ec-PPase-based conjugates. However, the interpolation of the inhibition profile to the higher concentrations of inhibitors shows incomplete inhibition (immobilized Mt-PPase retained up to 40% in the presence of Ca 2+ or 15% in the presence of F − ). The most unexpected result was that Ec-PPase, in the immobilized form, in contrast to the soluble form, also showed incomplete inhibition by either F − or Ca 2+ . The incomplete inhibition of Family I PPases by these ions was found for the first time. Both these ions are considered to be catalytic mechanism-based inhibitors: Ca 2+ replaces the catalytic Mg 2+ ions, and F − replaces the attacking nucleophile. The results of this study demonstrate that both PPase-based conjugates retaining some PPase activity in the presence of F − or Ca 2+ , constituents of major human tissues, have potential for the hydrolysis of t-CPPD under physiological conditions. However, their activity is yet to be demonstrated in more complex biological systems. To sum up, the PPase-based conjugates suggested here can be a step toward a solution to the challenging problem of managing CPP-related arthropathies. were stored at 4°C as suspensions with ammonium sulfate (90% saturation). Immediately before testing, the enzymes were desalted by gel filtration on a column with Sephadex G-50 Fine in 50 mM HEPES, pH 7.5, with 5 mM MgCl 2 . The concentrations of soluble proteins were determined using an Ultrospec 3000 spectrophotometer (Pharmacia Biotech, Sweden), using the mass extinction coefficients of 1.18 25 and 0.98 35 for Ec-PPase and Mt-PPase, respectively. The initial catalytic activity was about 800 U mg −1 for soluble Ec-PPase or about 300 U mg −1 for soluble Mt-PPase.
The original UDA-TAN ND obtained by the detonation synthesis method was purchased in the powdered form from the Federal State Unitary Enterprise "SKTB Tekhnolog" (St. Petersburg, Russia). Samples of aminated NDs were obtained using the procedure described previously 31 by reducing the original ND sample with hydrogen, followed by chlorination and amination with gaseous ammonia (ND-NH 2 ) or covalent modification using hexamethylenediamine [ND-NH-(CH 2 ) 6 -NH 2 ]. ND surface modification was checked at each stage of the synthesis using FTIR spectroscopy and X-ray photoelectron spectroscopy. Furthermore, hydrosols with particle sizes of 70 and 50 nm for ND-NH 2 and ND-NH-(CH 2 ) 6 -NH 2 , respectively, were prepared from aminated NDs. The concentration of hydrosols was determined by gravimetry. The concentration was 7.3 mg mL −1 for ND-NH 2 and 5.9 mg mL −1 for ND-NH-(CH 2 ) 6 -NH 2 . The particle size in hydrosols was determined by dynamic light scattering (DLS).
The chemicals were purchased from Sigma (USA), Fluka (Switzerland), Merck (Germany), and Pharmacia Fine Chemicals (Sweden) and used without further purification. Deionized water was purified to an impedance value greater than 18 MΩ cm −1 using a Milli-Q plus system (Millipore).

Covalent Immobilization of Inorganic Pyrophosphatases on NDs.
Mt-PPase and Ec-PPase covalently immobilized on ND-NH 2 and ND-NH-(CH 2 ) 6 -NH 2 were obtained according to the method described previously for the Ec-PPase procedure. 31 Briefly, a solution of PPase (1.0 mg mL −1 ) in 50 mM HEPES, pH 7.5, containing 5 mM MgCl 2 , 10 mM NaF, 100 μM Na 4 P 2 O 7 , hydrosol of aminated NDs (1 mg mL −1 ), and glutaric aldehyde CH 2 (CH 2 CHO) 2 (50 or 500 μM) was shaken for 1 h at 20°C. The solid phase and the supernatant were separated by centrifugation (14,000 rpm, 10 min). The concentration of protein in the supernatant was determined. The solid phase containing the immobilized PPase was collected and repeatedly washed with 50 mM Tris pH 7.5 and 5 mM MgCl 2 , with shaking for 10−15 min, until complete absence of protein in the supernatant. The protein content in the conjugates (mg PPase per mg ND) was determined from the data obtained on the total collected supernatant. In further experiments, to recreate the required protein concentration in the mixture, conjugates were added until the required immobilized protein amount (mg) per mixture volume (mL) was reached.
4.3. Characterization of ND-PPase Conjugates. 4.3.1. Infrared Spectroscopy with Fourier Transform. Infrared (IR) absorption spectra were measured in KBr tablets using an FTIRS Nicolet IR200 spectrometer (Thermo Scientific, USA) with a resolution of 2 cm −1 in the range of 400−4000 cm −1 . Each experiment consisted of 100 scans.
4.3.2. Dynamic Light Scattering. Determination of the particle size and ζ-potential by DLS was performed using a ZetaSizer Nano ZS ZEN 3600 (Malvern instruments, USA). The minimum volume of the investigated solution was 0.5 mL.
4.3.3. Determination of Hydrolytic Activity of PPase. The catalytic activity of PPase (Ec-PPase or Mt-PPase) was determined at 20°C as the initial rate of phosphate production from pyrophosphate. The reaction mixture contained buffer solution (50 mM Tris pH 7.5), 100 μM MgPP i as a substrate, and 5 mM Mg 2+ as a cofactor. The reaction was started by the addition of 0.2−1.5 μL of the PPase sample (either solution or hydrosol) to 25 μL of the reaction mixture to a final protein concentration of 0.1−0.4 μg·mL −1 . After 30 s, reaction was stopped by the addition of 80 μL of malachite green dye reagent containing ammonium molybdate, HCl, polyvinyl alcohol, and sodium citrate, 51 and the absorbance at 595 nm was measured using a Victor Multilabel plate reader (PerkinElmer, USA). The phosphate concentration was determined according to the P i standard curve. Specific activity of PPase was presented as U mg −1 . A value of 1 U mg −1 equals hydrolysis of 1 μmol of substrate per minute by 1 mg of the enzyme.
Raw data were approximated by the corresponding equations using SigmaPlot for Windows, version 10.0 (Systat Software Inc.).
4.3.4. Catalytic Parameters of Magnesium Pyrophosphate Hydrolysis. To determine the catalytic parameters of MgPP i hydrolysis, V max and K m , PPase activity was measured as described above, at 5 mM Mg 2+ , in a range of substrate concentrations (0−180 μM MgPP i ) and at a final protein concentration of 0.1 μg mL −1 . The dependence of activity on the concentration of MgPP i was processed by nonlinear regression according to the Michaelis−Menten equation where V is the initial rate of MgPP i hydrolysis, V max is the maximum rate of the enzymatic reaction, K m is the Michaelis constant, and S 0 is the initial concentration of the substrate.

Effect of Cofactor Metal Ions.
To study the effect of magnesium ion concentration, PPase activity was measured as described above, at 100 μM MgPP i , 0−3 mM Mg 2+ , and at a final protein concentration of 0.4 μg mL −1 . The dependency of activity on Mg 2+ concentration was processed by nonlinear regression using eq S1, 36 corresponding to Scheme S1 (Supporting Information).
4.3.6. Analysis of the Inhibition of PPases by Fluoride or Calcium Ions. To study inhibition by fluoride and calcium ions, PPase activity was measured as described above, at 100 μM MgPP i , 2 mM Mg 2+ , and a final protein concentration of 0.2−0.4 μg mL −1 . The reaction mixture additionally contained one of the inhibitors in a range of concentrations (either 0− 150 mM NaF or 0−5.5 mM CaCl 2 ). The dependency of PPase activity on F − or Ca 2+ concentrations was processed by nonlinear regression using eqs S2 or S3 (Scheme S2, Supporting Information), as described in the text. 43 4.3.7. pH Dependence of Conjugate Activity. Solutions of PPase (Ec-PPase and Mt-PPase) or hydrosols of covalently immobilized PPase (final protein concentration 0.2−0.4 μg mL −1 ) were added to the reaction mixture containing 50 mM buffer solution with pH 1.6−12.6 (HCl−KCl pH 1.6, Na citrate pH 2.6−4.6, MES-KOH pH 5.6−6.6, Tris-HCl pH 7.5−8.6, CAPSO pH 9.6, CAPS pH 10.6, or NaOH−KCl pH 11.6−12.6), 100 μM MgPP i , and 2 mM Mg 2+ , and the activity of PPase was measured as described above. The dependencies of activity on pH were processed by nonlinear regression using the eq S4 corresponding to Scheme S4 (Supporting Information). 36 4