Good-Practice Non-Radioactive Assays of Inorganic Pyrophosphatase Activities

Review Good-Practice Non-Radioactive Assays of Inorganic Pyrophosphatase Activities

Alexander A. Baykov 1,*, Viktor A. Anashkin 1 and Anssi M. Malinen 2,*

1 Belozersky Institute of Physico-Chemical Biology, Lomonosov Moscow State University, 119899 Moscow, Russia; [email protected] 2 Department of Life Technologies, University of Turku, FIN-20014 Turku, Finland * Correspondence: [email protected] (A.A.B.); ansmal@utu.ﬁ (A.M.M.)

Abstract: Inorganic pyrophosphatase (PPase) is a ubiquitous enzyme that converts pyrophosphate

(PPi) to phosphate and, in this way, controls numerous biosynthetic reactions that produce PPi as a byproduct. PPase activity is generally assayed by measuring the product of the hydrolysis

reaction, phosphate. This reaction is reversible, allowing PPi synthesis measurements and making PPase an excellent model enzyme for the study of phosphoanhydride bond formation. Here we summarize our long-time experience in measuring PPase activity and overview three types of the

assay that are found most useful for (a) low-substrate continuous monitoring of PPi hydrolysis, (b) continuous and ﬁxed-time measurements of PPi synthesis, and (c) high-throughput procedure for screening purposes. The assays are based on the color reactions between phosphomolybdic acid and triphenylmethane dyes or use a coupled ATP sulfurylase/luciferase enzyme assay. We also provide procedures to estimate initial velocity from the product formation curve and calculate the assay medium’s composition, whose components are involved in multiple equilibria. Keywords: pyrophosphate assay; phosphate assay; malachite green; methyl green; luciferase; ATP Citation: Baykov, A.A.; Anashkin, sulfurylase; initial velocity; pyrophosphate complexes V.A.; Malinen, A.M. Good-Practice Non-Radioactive Assays of Inorganic Pyrophosphatase Activities. Molecules 2021, 26, 2356. https:// 1. Introduction doi.org/10.3390/molecules26082356 Inorganic pyrophosphatase (inorganic diphosphatase; EC 3.6.1.1; PPase) is a constitu-

Academic Editor: Marko Golicnikˆ tive, highly specific enzyme that converts pyrophosphate (PPi), a byproduct and regulator of numerous biosynthetic reactions [1], into a metabolizable phosphate. Ubiquitous soluble Received: 6 April 2021 PPases dissipate PPi energy as heat, whereas less common membrane-bound PPases use + + Accepted: 16 April 2021 the energy to transport H or Na across lipid membranes [2,3]. Both PPase types can also Published: 18 April 2021 catalyze the reverse reaction of PPi synthesis from Pi, and this activity of membrane-bound PPases is also considered physiologically important [4,5]. Soluble PPases are additionally Publisher’s Note: MDPI stays neutral divided into two nonhomologous families—family I, known for nearly a hundred years with regard to jurisdictional claims in and found in all kingdoms of life, and family II found in 1998 in prokaryotes [6,7]. Several published maps and institutional affil- nonspecific phosphatases also exhibit PPase-like activity [8–10]. iations. Although the primary structures of the three groups of specific PPases are completely different, their mechanisms and active sites reveal close similarity, making these enzymes remarkable examples of convergent evolution. All PPases are Mg2+-dependent enzymes, but family II PPases additionally require a transition metal ion (Mn2+ or Co2+) for maximal Copyright: © 2021 by the authors. activity [11]. In total, three to four metal ions per active site are required for PPi conver- Licensee MDPI, Basel, Switzerland. sion [7]. These metal ions, coordinated by numerous protein carboxylates and substrate This article is an open access article phosphates, play key roles in catalysis. PPi hydrolysis involves a direct attack of an ac- distributed under the terms and tivated water molecule on a phosphorus atom and a stepwise release of two phosphate 4 −1 conditions of the Creative Commons molecules. The value of kcat for soluble PPases reaches 10 s for PPi hydrolysis and 2 −1 Attribution (CC BY) license (https:// 10 s for PPi synthesis [3,4,11]. Km values for most PPases with PPi as substrate lie in the creativecommons.org/licenses/by/ micromolar range. 4.0/).

Molecules 2021, 26, 2356. https://doi.org/10.3390/molecules26082356 https://www.mdpi.com/journal/molecules Molecules 2021, 26, x FOR PEER REVIEW 6 of 13

both ATP sulfurylase and PPase need Mg2+ as a cofactor. The synthesized PPi is continuously converted into ATP at such a high rate that the steady-state PPi level is not inhibitory for PPase and luciferase activities. This is ensured by maintaining high ATP sulfurylase concentration, such that its doubling does not increase the measured rate of ATP accumulation. In the second assay version, the PPase reaction mix contains ATP sulfurylase/APS, which continuously converts the formed PPi into ATP, whose concentration is determined at fixed time points with luciferase/luciferin in a separate tube. Importantly, PPase does not hydrolyze ATP in the presence of Mg2+. Both assay versions combine the high sensitivity of the luciferase ATP determination with the possibility to accumulate detectable amounts of ATP while keeping the steady-state concentration of PPi at a sub-equilibrium, non-inhibitory level. ATP sulfurylase and luciferase act thus as amplifiers of the PPi-generated signal and allow the measurement of the initial velocities of PPi synthesis from Pi.

Table 2. Assays measuring PPi formation.

Assay Type and Procedure Comments PPi synthesis (continuous) [34] ATP sulfurylase is from BioLabs (UK). Its con- Assay mixture contains calculated amounts of potassium phosphate and MgCl2, 0.7 centration should be sufficiently high so that U/mL ATP-sulfurylase, 10 µM APS, 5 µL of luciferin/luciferase solution (Sigma ATP its doubling does not change the measured assay mix, catalog no. FLAAM, reconstituted with 5 mL of water), 1 mM dithio- rate of ATP accumulation. The luminescence- threitol, 0.8 mg/mL bovine serum albumin and 0.1 M MOPS–KOH buffer in a total versus-time dependencies are slightly curved volume of 0.2 mL. The reaction is initiated by adding PPase, and the time-course of because of the slow inactivation of luciferase luminescence is followed with a luminometer (e. g., LKB model 1250). After the PPi- in the reaction medium. generated signal stabilizes, 2 µL of 10 µM ATP are added for internal calibration. PPi synthesis (fixed-time) [35] Assay mixture contains calculated amounts of potassium phosphate and MgCl2, 0.7 U/mL ATP-sulfurylase, 10 µM APS, and 0.1 M MOPS–KOH buffer in a total volume of 100 µL. The reaction is initiated by adding PPase and carried out for 10 min. Ali- quots (15 µL) are withdrawn at various times, quenched with 15 µL of 1 M trifluoro- Crystalline phosphoric acid (Fluka) is freed acetic acid, incubated for 4 min at room temperature, and neutralized with 15 µL of from PPi contamination as described in the 1.5 M Tris. The ATP formed is quantitated by adding 10 µL of the mixture to 200 µL text. of 0.2 M Tris-HCl buffer, pH 8.0 containing 6 µL of the luciferin/luciferase solution (Sigma ATP assay mix, catalog No. FLAAAM, reconstituted with 5 mL of water) and measuring the luminescence. After the signal stabilizes, 2 µL of 10 µM ATP are added for internal calibration. Enzyme-bound PPi formation [36] 2+ PPase (typically 20–100 µM) is Moleculespreequilibrated2021, 26, with 2356 Pi and Mg under appropriate 2 of 13 conditions in a 50 µL volume and quenched with 10 µL of 5 M trifluoroacetic acid. Determined PPi content refers to the sum of After several minutes, precipitated protein is removed by centrifugation, a 10 µL ali- enzyme-bound and medium PPi. The latter is quot of the supernatant is added to 0.2 mL of the PPi assay cocktail (0.2 M Tris-HCl, measured similarly but using a 100 times pH 8.0, 0.4 U/mL ATP sulfurylase, 10 µM APS, 6 µL of the luciferase/luciferinPPase is solu- generally assayed by measuring phosphate, the product of PPi hydrolysis. lower enzyme concentration and subtracted. tion, 1 mM dithiothreitol, 0.8 mg bovine serum albumin, 30 µM DependingEGTA), and the on lu- the task, PPase activity is assayed at sub-Km PPi concentrations (in mecha- minescence is recorded. After the signal stabilizes, 2 µL of 10 µMnistic PPi are studies) added orfor a saturating PPi concentration (in high-throughput screening procedures). internal calibration. The former assay is more demanding concerning sensitivity because of the low Km value, especially with family I and membrane PPases. Sensitivity is also the limiting factor in PPi The third version of thesynthesis PPi assay studies accesses because the equilibrium the equilibrium of the PPPPii  2Pii reactionis largely shifted to the right. Here, in the active site of PPase. Thiswe summarizeinformation our is required experience to inestimate sensitive the PPase rate constants activity measurements for in both directions individual steps of PPase catalysisand present [37,38]. protocols This equilibrium suitable for is high-throughputmarkedly shifted screeningto the left and mechanistic studies. by comparing the equilibrium in solution—up to 20% of enzyme-bound Pi is converted to PPi [37,38]. To assay, the enzyme-bound2. Continuous PP Low-Substratei, the enzyme (20–100 Assay µM) of PP isi -Hydrolyzingincubated with Activity Pi and Mg2+, inactivated by trifluoroaceticThe low acid value to ofrelease the Michaelis enzyme-bound constant PP ofi into PPases solution, makes it necessary to use highly and an aliquot is taken to assaysensitive PPi using assays the in kineticcoupled studies ATP sulfurylase/luciferase conducted at sub-Km substrateproce- concentrations. The assay dure. currently used in our labs combines two approaches to achieve high sensitivity: first, it measures the formation of the intensively colored complex of 12-molibdophosphoric acid with a triphenylmethane dye, methyl green, and, second, it is continuous. The PPase reaction mixture and two-color reagents are continuously pumped off by a peristaltic pump and mixed, and the absorbance of the resulting solution is measured at 620 or 660 nm in a flow photometer. Even though the background absorbance is relatively high, it is automatically subtracted in this continuous assay mode, allowing the precise recording of much smaller changes in absorbance (Pi concentration) compared to a fixed-time assay. The principal advantage of the methyl green dye in this application is its low tendency to deposit on the optical cuvette [12]. The phosphate analyzer consists of three main parts: a four-channel peristaltic pump, flow photometer, and paper recorder (Figure1A). Alternatively, the photometer’s output can be directed to a computer, which calculates initial velocity from the absorbance time- course. However, we found that the manual procedure, using paper recordings, is less sensitive to signal fluctuations and provides more accurate data. We have used a four- channel Gilson Minipuls pump equipped with Tygon tubings. Three pump channels are used to deliver a sample, acid/molybdate, and dye/Triton X-305 solutions. Their initial mixing occurs in tubing T-joints and is completed in a mixing device consisting of a glass tube of 1.3 mm inner diameter with 12–15 bubbles of 3.5 mm inner diameter. The fourth pump channel eliminates any air bubbles from the final mixed solution before it is directed to the flow photometer. To prevent excessive air from entering the flow system, the pump is stopped when the sample inlet tubing is transferred between the samples and water. To ensure that the color reaction proceeds to completion, the time intervals between the two mixing events and between the second mixing event and entry to the photometer cuvette should be adjusted to 12 and 32 s, respectively, by using connecting tubings of appropriate diameter and length. The small nonlinearity of the calibration plot at low phosphate content is eliminated by adding a small amount of phosphate to the stock acid/molybdate solution. We have been using ISCO UA-5 and 229 flow photometers. These instruments are no longer produced but can be replaced by any flow photometer operating at 620–660 nm wavelengths and a flow rate of approximately 10 mL/min. Alternatively, one can use a standard spectrophotometer with a flow cuvette, such as a Helma model 178-010-10-40 (10 mm pathlength, 80 µL internal volume). Three setups of the phosphate analyzer were found useful for standard, high-sensitivity, and low dead-time measurements (Figure1A–C). A five-fold increase in sensitivity was achieved in version B by interchanging the sample and molybdate tubings on the pump (Figure1B). As the response is linear up to approximately 0.5 absorbance unit, the photometer sensitivity is adjusted to 0.5 absorbance unit per recorder scale in the standard mode (version A) and down to 0.1 unit in the high-sensitivity mode (version B). These settings correspond to approximately 100 and 4 µMPi, respectively, per recorder scale. As each PPi molecule yields 2 molecules of Pi, this sensitivity is sufficient for a reliable measurement of initial velocities at PPi concentrations down to 0.5 µM (see AppendixA for further details). PPase concentration in the assay is typically in the pM range when activity is determined Molecules 2021, 26, x FOR PEER REVIEW 3 of 13

further details). PPase concentration in the assay is typically in the pM range when activity is determined at saturating substrate concentrations and optimal pH and temperature values. We have successfully used the phosphate analyzer to determine PPase reaction kinetics over a broad temperature range (reaction mixture temperature 20–60 °C). The dead-time between withdrawing the sample and mixing it with acid/molybdate Molecules 2021, 26, 2356is 10 s in the standard mode but can be decreased to 1 s by shifting the first mixing point 3 of 13 to the pump inlet (Figure 1C). In this version, the sample is withdrawn from the reaction vessel at a rate of 1.2 mL/min due to differences in the two lowest pump tubes' flow rates. This setup helps monitor reactions demonstrating nonlinear progress curves because of enzyme activationat saturating or inact substrateivation during concentrations the reaction. and optimalReagent pH concentrations and temperature were values. ad- We have successfully used the phosphate analyzer to determine PPase reaction kinetics over a broad justed in versions B and C as indicated in Table 1 to ensure the same optimal◦ final concentrations in thetemperature photometer range cuvette. (reaction mixture temperature 20–60 C).

Figure 1. The phosphateFigure 1. The analyzer phosphate is used analyzer to assay is PPaseused to activity assay inPPase a continuous activity in way. a continuous (A) Flow diagramway. (A) forFlow the phosphate analyzer in standarddiagram mode; for the (B )phosphate Tubing connections analyzer in on standard the pump mode; in the ( high-sensitivityB) Tubing connections mode; (onC) tubingthe pump connections in the in the low dead-timehigh mode.-sensitivity Numbers mode; on the (C pump) tubing refer connections to flow rate in the in mL/minlow dead (before-time mode. the slash) Numbers and tubing on the diameterpump in mm refer to flow rate in mL/min (before the slash) and tubing diameter in mm (panel A) or flow rate in (panel A) or flow rate in mL/min (panels B and C). (D) Actual Pi accumulation recordings in setup A with photometer mL/min (panels B and C). (D) Actual Pi accumulation recordings in setup A with photometer sen- sensitivity of 1 absorbance unit per recorder scale. The calibration data shown at the beginning of the recording was sitivity of 1 absorbance unit per recorder scale. The calibration data shown at the beginning of the obtained by adding 0–200 µMPi to the reaction buffer. (E) Actual Pi accumulation recordings in setup B with photometer recording was obtained by adding 0–200 µM Pi to the reaction buffer. (E) Actual Pi accumulation µ sensitivity of 0.1recordings absorbance in setup unit B per with recorder photometer scale. sensitivity The assay of mixture 0.1 absorbance of 40 mL unit volume per recorder contained scale. 140 TheM PPi, 5 mM −1 MgCl2, 50 mMassay MOPS–KOH, mixture of pH 40 7.2, mL and volume 0.03 nMcontainedStreptococcus 140 µM gordonii PPi, 5 mMPPase MgCl with2, a50 specific mM MOPS activity–KOH, of 480 pH s 7.2,.( F) Actual recordings of Pandi accumulation 0.03 nM Streptococcus in the setup gordonii C for ratPPase liver with PPase a specific in the presenceactivity of (a) 480 or absences-1. (F) Actual (b) of recordings slow-binding of inhibitor (10 mM fluoride).Pi accumulation The arrow marks in the thesetup moment C for rat of liver enzyme PPase addition. in the presence Part of the (a) figure or absence was taken(b) of withslow- permissionbinding from references [13]inhibitor (panels A(10 and mM D) fluoride and [14)]. (panelsThe arrow C and marks F). the moment of enzyme addition. Part of the figure was taken with permission from references 13 (panels A and D) and 14 (panels C and F). The dead-time between withdrawing the sample and mixing it with acid/molybdate is 10 s in the standard mode but can be decreased to 1 s by shifting the first mixing point to the pump inlet (Figure1C). In this version, the sample is withdrawn from the reaction vessel at a rate of 1.2 mL/min due to differences in the two lowest pump tubes’ flow rates. This setup helps monitor reactions demonstrating nonlinear progress curves because of enzyme activation or inactivation during the reaction. Reagent concentrations were adjusted in versions B and C as indicated in Table1 to ensure the same optimal final concentrations in the photometer cuvette.

Molecules 2021, 26, 2356 4 of 13

Table 1. Assays measuring PPi hydrolysis. Instrument setups for the continuous assay versions A–C are shown in Figure1A–C.

Assay Type and Procedure Comments Continuous, version A [13] Stock dye solution contains 80 mg/L methyl green and 3.4 g/L Methyl green and Triton X-305 are from Sigma-Aldrich, Triton X-305. Stock acid/molybdate solution contains 0.55 M ammonium molybdate from Fisher Scientific. Phosphate-free H SO (32 mL concentrated H SO per 1 L final solution 1), 2 4 2 4 sulfuric acid (1.83 g/cm3) is used. When switching to a new 12 g/L ammonium molybdate, and 2 µMP . The mixing ratio i batch of Triton X-305, its concentration may need adjustment to sample: acid/molybdate:dye is 1.5:7:2. Washing solution: 0.1 M ensure linearity of the calibration plot and low baseline drift NaOH and 2 g/L Triton X-305. The enzymatic reaction is because of dye deposition on the photometer cuvette. performed in a thermostated vessel with magnetic stirring at 10–60 ◦C; the reaction volume is typically 5 mL. Continuous, version B [13] Stock dye solution contains 86 mg/L methyl green and 3.7 g/L Triton X-305. Stock acid/molybdate solution contains 1.8 M Acid-resistant Iso-Versinic tubing is preferable on the pump for H SO (105 mL concentrated H SO per 1 L final solution), 2 4 2 4 the acid/molybdate solution in this case. 39 g/L ammonium molybdate, and 7 µMPi. The mixing ratio sample:acid/molybdate:dye is 7:2.3:2. The PPase reaction volume is typically 25–40 mL. Continuous, version C [14] Stock dye solution contains 30 mg/L methyl green and 1.3 g/L Triton X-305. Stock acid/molybdate solution contains 1.0 M H2SO4 (59 mL concentrated H2SO4 per 1 L final solution), 22 g/L ammonium molybdate, and 4 µMPi. The mixing ratio sample: acid/molybdate:dye is 1.2:3.2:4.4. Fixed-time [15,16] Stock dye/molybdate solution (stable for months in a refrigerator): 115 mg of malachite green are dissolved in 100 mL Malachite green is from Sigma-Aldrich, Tween-20 from Ferak of 2.5 M H SO , followed by 1.4 g of ammonium molybdate. 2 4 Berlin. Tween-20 (0.05%, w/w) can be added instead to the On the day of use, 0.25 mL of 10% Tween-20 (w/w) is added per PPase assay mixture, which typically contains 0.05 M Tris-HCl 10 mL of the dye/molybdate solution. The PPase reaction is or another buffer, 0.05 mM PP , and 5 mM MgCl . performed in a total volume of 0.2 mL in 96-well plates and i 2 terminated by adding 0.05 mL of the color reagent. Absorbance at 630 nm is measured after 10 min. 1 Note: dilution of sulfuric acid generates much heat, which may cause boiling/spilling. It is advised to add the acid slowly to water in a Duran/Pyrex glass beaker in a fume hood.

The continuous Pi assay is robust and tolerates the presence of many biochemical compounds, including magnesium ions at high concentrations (up to 40 mM). In contrast, 2+ Mg interferes with the Pi assay based on 12-molibdophosphoric acid reduction [17]. Nevertheless, it is wise to calibrate the instrument by measuring phosphate standard against background each time when a new component is added to the sample assayed, especially when working in the high-sensitivity mode (version B). Importantly, PPi at high concentrations was found to suppress the Pi signal (by 25% for 1.5 mM PPi) in this mode. This should be taken into consideration in measurements of PPase activity at a variable substrate concentration. The effect is proportional to PPi concentration and likely results from the competitive formation of 12-molibdopyrophosphoric acid, detected by Raman spectroscopy [18]. Other known continuous assays of PPase activity monitor, depending on pH, uptake or release of hydrogen ions during PPi conversion to Pi [19,20] or monitor PPi concentration using synthetic PPi sensors [21–25]. These assays are less sensitive and less convenient in that the signal is not proportional to the degree of conversion. Substances that modulate PPase activity will interfere with any assay. Among them, Tris and other amine buffers were found to dramatically increase the Michaelis constant for family I and membrane PPases [26–28]. Accordingly, zwitterionic buffers, such as Tes, Mops, and HEPES, are preferable for work at sub-Km substrate concentrations. Tetramethy- Molecules 2021, 26, x FOR PEER REVIEW 6 of 13

Molecules 2021, 26, 2356 5 of 13 both ATP sulfurylase and PPase need Mg2+ as a cofactor. The synthesized PPi is continuously converted into ATP at such a high rate that the steady-state PPi level is not inhibitory for PPase and luciferase activities. This is ensured by maintaining high ATP sulfurylase lammoniumconcentration, hydroxide was such found that to its be doubling useful as thedoes second not increase component the measured of the zwitterionic rate of ATP accumu- + + + Molecules 2021, 26, x FOR PEER REVIEWbuffers in experimentslation. In the measuring second assay K and version, Na effectsthe PPase on Kreaction-dependent mix contains membrane ATP PPase. sulfurylase/APS,5 of 13

However, somewhich batches continuously of this strongly converts basic the formed compound PPi suppliedinto ATP, in whose glass concentration containers were is determined found to nonspecificallyat fixed time inactivatepoints with this luciferase/luciferin enzyme when used in asa separate a buffer componenttube. Importantly, instead PPase does of KOH. not hydrolyze ATP in the presence of Mg2+. Both assay versions combine the high sensi- 3. Sensitive Fixed-Time Assay of PPi-Hydrolyzing Activity tivity of the luciferase ATP determination with the possibility to accumulate detectable 3. SensitiveFixed-time Fixed-Time assays Assay measuring of PP the-Hydrolyzing product Pi Activityare perhaps most suitable for high- amounts of ATP while keepingi the steady-state concentration of PPi at a sub-equilibrium, throughput screening of compound libraries for the effects on PPase activity. Most pub- Fixed-timenon-inhibitory assays measuring level. ATP the sulfurylase product P andi are luciferase perhaps act most thus suitable as amplifiers for high- of the PPi-gen- lished procedures determine Pi as reduced 12-molybdophosphoric acid [29] and perform throughputerated screening signal of compoundand allow the libraries measurem for theent effectsof the initial on PPase velocities activity. of MostPPi synthesis pub- from Pi. –5 –4 lishedwell with procedures 10 –10 determine M Pi concentrations. Pi as reduced Although 12-molybdophosphoric this sensitivity suffices acid [29 ]for and most perform appli- −5 −4 wellcations, with the 10 identification–10 MPTablei concentrations.of 2. samples Assays measuring with Although low PPPPasei formation. this activity sensitivity or assays suffices performed for most at ap-low plications,PPi concentrations the identification (<10 µM) of would samples require with a low more PPase sensitive activity Pi orassay, assays such performed as the assay at Assay Type and Procedure Comments lowbased PPi onconcentrations the shift of m (<10alachiteµM) wouldgreen spectrum require a moreupon sensitive binding Ptoi assay, 12-molybdophosphoric such as the assay PPi synthesis (continuous) [34] basedacid. onHowever, the shift low of malachitedye solubility, green leading spectrum to its upon precipitation, bindingATP to sulfurylasewas 12-molybdophosphoric a serious is from drawback BioLabs of(UK). Its con- Assay mixture contains calculated amounts of potassium phosphate and MgCl2, 0.7 acid.the original However, malachite low dye g solubility,reen-based leading procedure to its [30 precipitation,] and its centrationmany was later a should serious variants. be drawback sufficiently of high so that U/mL ATP-sulfurylase, 10 µM APS, 5 µL of luciferin/luciferase solution (Sigma ATP the originalA solution malachite to this green-based problem procedurewas finding [30 that] and increased its manyits doubling lateracid variants. concentration does not change (2.5 the Mmeasured assay mix, catalog no. FLAAM, reconstituted with 5 mL of water), 1 mM dithio- H2SOA4 solution) in stock to dye this solution problem wassurprisingly finding that increases increased dye acid solubilityrate concentration of ATP and accumulation. stability(2.5 M [ H15 The].SO This luminescence-) threitol, 0.8 mg/mL bovine serum albumin and 0.1 M MOPS–KOH buffer in a total 2 4 in stock dye solution surprisingly increases dye solubility andversus-time stability dependencies [15]. This finding are slightly curved volume of 0.2 mL. Thefinding reaction allowed is initiated the by formulati adding PPase,on of anda single the time-course stable color of reagent that stops the enzymatic allowedreaction the and formulation produces a of green a single-blue stable color color (630 reagentnm), whose thatbecause stopsintensity theof the enzymaticis slowproportional inactivation reaction to ofP i luciferase luminescence is followed with a luminometer (e. g., LKB model 1250). After the PPi- in the reaction medium. generated signal stabilizes,andconcentration. produces 2 µL of 10 a green-blue TheµM ATPcolor are reagent color added (630 isfor made nm),internal whosedaily calibration. by intensity adding is the proportional nonionic detergent to Pi concentra- Tween- tion. The color reagent is made daily by adding the nonionic detergent Tween-20 (color 20 (colorPP stabilizeri synthesis )(fixed-time) to the stock [35] dye/molybdate solution (Table 1). The signal produced by stabilizer) to the stock dye/molybdate solution (Table1). The signal produced by 2 µM Assay mixture contains2 µM calculated Pi (corresponding amounts of potassium to 1 µM PP phosphatei hydrolyzed and MgCl) is 0.152, 0.7 absorbance units in a 1 cm cuvette. U/mL ATP-sulfurylase,PThei (corresponding 10 assayµM APS, can and be to0. performed1 1Mµ MOPS–KOHM PP i inhydrolyzed) a 96buffer-well in platea is total 0.15 (volumeFigure absorbance 2) and units quantified in a 1 cm with cuvette. a plate of 100 µL. The reactionThereader is assay initiated. can by be addi performedng PPase in and a 96-well carried plateout for (Figure 10 min.2 )Ali- and quantified with a plate reader. quots (15 µL) are withdrawn at various times, quenched with 15 µL of 1 M trifluoro- Crystalline phosphoric acid (Fluka) is freed acetic acid, incubated for 4 min at room temperature, and neutralized with 15 µL of from PPi contamination as described in the 1.5 M Tris. The ATP formed is quantitated by adding 10 µL of the mixture to 200 µL text. of 0.2 M Tris-HCl buffer, pH 8.0 containing 6 µL of the luciferin/luciferase solution (Sigma ATP assay mix, catalog No. FLAAAM, reconstituted with 5 mL of water) and measuring the luminescence. After the signal stabilizes, 2 µL of 10 µM ATP are added for internal calibration. Enzyme-bound PPi formation [36] PPase (typically 20–100 µM) is preequilibrated with Pi and Mg2+ under appropriate conditions in a 50 µL volume and quenched with 10 µL of 5 M trifluoroacetic acid. Determined PPi content refers to the sum of After several minutes, precipitated protein is removed by centrifugation, a 10 µL ali- Figure 2. PPase assay using the malachite green procedure. Twoenzyme-bound bottom rows show and mediuma duplicate PP i. The latter is quot of the supernatantFigure is added 2. PPase to 0.2 assay mL usingof the thePPi malachiteassay cocktail green (0.2 procedure. M Tris-HCl, Two bottom rows show a duplicate series of phosphate dilutions from 0 µM (left) to 10 µM (right). Twomeasured top rows similarly show typicalbut using results a 100 times pH 8.0, 0.4 U/mL ATPseries sulfurylase, of phosphate 10 µM dilutions APS, 6 fromµL of 0 theµM luciferase/luciferin (left) to 10 µM (right). solu- Two top rows show typical results of of a duplicate screening test of a library of potential inhibitors oflower Escherichia enzyme coli concentration PPase. The yellow and subtracted. tion, 1 mM dithiothreitol,a duplicate 0.8 mg screening bovine serum test of aalbumin, libraryof 30 potential µM EGTA), inhibitors and the of lu-Escherichia coli PPase. The yellow color color indicates strong inhibition, dark green color—no inhibition. minescence is recorded.indicates After strong the signal inhibition, stabilizes, dark 2 greenµL of color—no10 µM PPi inhibition.are added for internal calibration. i 4.4. Continuous Continuous and and Fixed-Time Fixed-Time Assays Assays of of PP PPi-Synthesizing-Synthesizing Activity Activity Like any catalyst, PPase accelerates the attainment of thermodynamic equilibrium Like any catalyst,The third PPase version accelerates of the the PP attainmenti assay accesses of thermodynamic the equilibrium equilibrium of the PPii  2Pi reaction PPi  2Pi in both directions. Although the equilibrium is shifted to the0 right (∆G0 = −20– 2Pi in both directions.in the active Although site of the PPase. equilibrium This information is shifted to is the required right (∆ Gto estimate= −20–25 the kJ/mol) rate constants, for 25 kJ/mol), it allows the formation of measurable amounts of PPi under physiological con- it allows theindividual formation steps of measurable of PPase catalysis amounts [37,38]. of PPi under This equilibrium physiological is markedly conditions. shifted For to the left ditions. For instance, the concentration of PPi at equilibrium with 10 mM Pi (pH◦ 7, 25 °C, instance, theby concentration comparing the of equilibrium PPi at equilibrium in solution—up with 10 to mM 20%P ofi (pHenzyme-bound 7, 25 C, 1 P mMi is converted to 1 mM2+ Mg2+) is approximately 1 µM [31], which is below the detection limits of most ana- Mg ) is approximatelyPPi [37,38]. To 1 µassay,M[31 the], which enzyme-bound is below the PP detectioni, the enzyme limits (20–100 of most µM) analytical is incubated with Pi lytical methods for2+ PPi determination. However, micromolar sensitivity has been claimed methods forand PP iMgdetermination., inactivated However, by trifluoroacetic micromolar acid sensitivityto release hasenzyme-bound been claimed PP fori into solution, for several assays based on fluorogenic and electrochemical PPi sensors [21–25]. Some of several assaysand based an aliquot on fluorogenic is taken andto assay electrochemical PPi using the PP icoupledsensors [ATP21–25 sulfurylase/luciferase]. Some of them proce- arethem commercially are commerciallydure. available. available. However, However, they are they of limited are of limited use in measurements use in measurements of initial of initial velocities of PPi synthesis, which require that PPi concentration in the medium does velocities of PPi synthesis, which require that PPi concentration in the medium does not exceednot exceed 10% of10% the of equilibrium the equilibrium concentration concentration to prevent to prevent product product inhibition. inhibition. ThisThis problem problem is is elegantly elegantly obviated obviated in in the the coupled-enzyme coupled-enzyme luminescent luminescent procedure procedure of of NyrNyrénén and and Lundin Lundin [ 32[32],], which which later later became became a a core core element element of of “pyrosequencing”, “pyrosequencing”, a a well- well- establishedestablished DNA DNA sequencingsequencing methodmethod [[33].33]. In In their their procedure, procedure, PP PPi iisis converted converted to to ATP ATP by reaction with adenosine-5′-0phosphosulfate (APS), catalyzed by ATP sulfurylase (E.C. by reaction with adenosine-5 -phosphosulfate (APS), catalyzed by ATP sulfurylase (E.C. 2.7.7.4), and the ATP formed is detected with a firefly luciferase/luciferin system. This method is used in three versions in PPase studies (Table 2 and Figure 3). In the first version, all components of the detection system, including ATP sulfurylase, luciferase, APS, and luciferin, are added to the PPase assay mix, and PPi formation is recorded continuously. This became possible because neither APS nor luciferin affects PPase activity, and

Molecules 2021, 26, 2356 6 of 13

2.7.7.4), and the ATP formed is detected with a firefly luciferase/luciferin system. This method is used in three versions in PPase studies (Table2 and Figure3). In the first version, all components of the detection system, including ATP sulfurylase, luciferase, APS, and luciferin, are added to the PPase assay mix, and PPi formation is recorded continuously. This became possible because neither APS nor luciferin affects PPase activity, and both ATP sul- 2+ furylase and PPase need Mg as a cofactor. The synthesized PPi is continuously converted into ATP at such a high rate that the steady-state PPi level is not inhibitory for PPase and luciferase activities. This is ensured by maintaining high ATP sulfurylase concentration, such that its doubling does not increase the measured rate of ATP accumulation. In the second assay version, the PPase reaction mix contains ATP sulfurylase/APS, which continuously converts the formed PPi into ATP, whose concentration is determined at fixed time points with luciferase/luciferin in a separate tube. Importantly, PPase does not hydrolyze ATP in the presence of Mg2+. Both assay versions combine the high sensitivity of the luciferase ATP determination with the possibility to accumulate detectable amounts of ATP while keeping the steady-state concentration of PPi at a sub-equilibrium, non-inhibitory level. ATP sulfurylase and luciferase act thus as amplifiers of the PPi-generated signal and allow the measurement of the initial velocities of PPi synthesis from Pi.

Table 2. Assays measuring PPi formation.

Assay Type and Procedure Comments

PPi synthesis (continuous) [34] Assay mixture contains calculated amounts of potassium phosphate and MgCl , 0.7 U/mL ATP-sulfurylase, 10 µM APS, 2 ATP sulfurylase is from BioLabs (UK). Its concentration should 5 µL of luciferin/luciferase solution (Sigma ATP assay mix, be sufﬁciently high so that its doubling does not change the catalog no. FLAAM, reconstituted with 5 mL of water), 1 mM measured rate of ATP accumulation. dithiothreitol, 0.8 mg/mL bovine serum albumin and 0.1 M The luminescence-versus-time dependencies are slightly curved MOPS–KOH buffer in a total volume of 0.2 mL. The reaction is because of the slow inactivation of luciferase in the initiated by adding PPase, and the time-course of luminescence reaction medium. is followed with a luminometer (e.g., LKB model 1250). After the PPi-generated signal stabilizes, 2 µL of 10 µM ATP are added for internal calibration.

PPi synthesis (ﬁxed-time) [35] Assay mixture contains calculated amounts of potassium phosphate and MgCl2, 0.7 U/mL ATP-sulfurylase, 10 µM APS, and 0.1 M MOPS–KOH buffer in a total volume of 100 µL. The reaction is initiated by adding PPase and carried out for 10 min. Aliquots (15 µL) are withdrawn at various times, quenched with 15 µL of 1 M triﬂuoroacetic acid, incubated for 4 min at room Crystalline phosphoric acid (Fluka) is freed from PPi temperature, and neutralized with 15 µL of 1.5 M Tris. The ATP contamination as described in the text. formed is quantitated by adding 10 µL of the mixture to 200 µL of 0.2 M Tris-HCl buffer, pH 8.0 containing 6 µL of the luciferin/luciferase solution (Sigma ATP assay mix, catalog No. FLAAAM, reconstituted with 5 mL of water) and measuring the luminescence. After the signal stabilizes, 2 µL of 10 µM ATP are added for internal calibration.

Enzyme-bound PPi formation [36] 2+ PPase (typically 20–100 µM) is preequilibrated with Pi and Mg under appropriate conditions in a 50 µL volume and quenched with 10 µL of 5 M triﬂuoroacetic acid. After several minutes, precipitated protein is removed by centrifugation, a 10 µL Determined PPi content refers to the sum of enzyme-bound and aliquot of the supernatant is added to 0.2 mL of the PPi assay medium PPi. The latter is measured similarly but using a cocktail (0.2 M Tris-HCl, pH 8.0, 0.4 U/mL ATP sulfurylase, 100 times lower enzyme concentration and subtracted. 10 µM APS, 6 µL of the luciferase/luciferin solution, 1 mM dithiothreitol, 0.8 mg bovine serum albumin, 30 µM EGTA), and the luminescence is recorded. After the signal stabilizes, 2 µL of 10 µM PPi are added for internal calibration. Molecules 2021, 26, x FOR PEER REVIEW 6 of 13

Table 2. Assays measuring PPi formation. Molecules 2021,, 26,, 2356x FOR PEER REVIEW 7 of 13 Assay Type and Procedure Comments PPi synthesis (continuous) [34] ATP sulfurylase is from BioLabs (UK). Its con- Assay mixture contains calculated amounts of potassium phosphate and MgCl2, 0.7 centration should be sufficiently high so that U/mL ATP-sulfurylase, 10 µM APS, 5 µL of luciferin/luciferase solution (Sigma ATP its doubling does not change the measured assay mix, catalog no. FLAAM, reconstituted with 5 mL of water), 1 mM dithio- rate of ATP accumulation. The luminescence- threitol, 0.8 mg/mL bovine serum albumin and 0.1 M MOPS–KOH buffer in a total versus-time dependencies are slightly curved volume of 0.2 mL. The reaction is initiated by adding PPase, and the time-course of because of the slow inactivation of luciferase luminescence is followed with a luminometer (e. g., LKB model 1250). After the PPi- in the reaction medium. generated signal stabilizes, 2 µL of 10 µM ATP are added for internal calibration. PPi synthesis (fixed-time) [35] Assay mixture contains calculated amounts of potassium phosphate and MgCl2, 0.7 U/mL ATP-sulfurylase, 10 µM APS, and 0.1 M MOPS–KOH buffer in a total volume of 100 µL. The reaction is initiated by adding PPase and carried out for 10 min. Ali- quots (15 µL) are withdrawn at various times, quenched with 15 µL of 1 M trifluoro- Crystalline phosphoric acid (Fluka) is freed acetic acid, incubated for 4 min at room temperature, and neutralized with 15 µL of from PPi contamination as described in the 1.5 M Tris. The ATP formed is quantitated by adding 10 µL of the mixture to 200 µL text. of 0.2 M Tris-HCl buffer, pH 8.0 containing 6 µL of the luciferin/luciferase solution (Sigma ATP assay mix, catalog No. FLAAAM, reconstituted with 5 mL of water) and measuring the luminescence. After the signal stabilizes, 2 µL of 10 µM ATP are added for internal calibration. Enzyme-bound PPi formation [36] 2+ PPase (typically 20–100 µM) is preequilibratedFigure 3. Schematics with Pi ofand the Mg assays under toto measuremeasure appropriate PPase-catalyzedPPase -catalyzed PP PPi isynthesis. synthesis. ( A(A)) A A continuous continuous assay conditions in a 50 µL volume andassayof quenched the of medium the with medium PP 10i synthesis;µL PP ofi synthesis;5 M (trifluoroaceticB) fixed-time (B) fixed assay -acid.time ofassay the mediumof the medium PPi synthesis; PPi synthesis; (C) determination (C) determi- of Determined PPi content refers to the sum of nation of enzyme-bound PPi. The assayed PPase is added to all far-left tubes. Three other major After several minutes, precipitatedenzyme-bound protein is removed PPi. The by assayedcentrifugation, PPase isa added10 µL ali- to all far-left tubes. Three other major components enzyme-bound and medium PPi. The latter is quot of the supernatant is added componentsto 0.2 mL of theare PPshowni assay as cocktail colored (0.2spots. M TheTris-HCl, principal analytes transferred between the tubes are are shown as colored spots. The principal analytes transferredmeasured betweensimilarly the but tubes using are a indicated100 times above indicated above the arrows. The blue star refers to the luminescence signal. (D) Actual PPi accu- pH 8.0, 0.4 U/mL ATP sulfurylase,the 10 arrows.µM APS, The 6 µL blue of starthe refersluciferase/luciferin to the luminescence solu- signal. (D) Actual PP accumulation recordings mulation recordings in the assay version A for baker’slower yeast enzyme PPase concentrationin the ipresence and of subtracted.slow-binding tion, 1 mM dithiothreitol, 0.8 mg bovinein the assay serum version albumin, A for30 µM baker’s EGTA), yeast and PPase the lu- in the presence of slow-binding inhibitor (fluoride; inhibitor (fluoride; its concentrations in mM are indicated on the curves). Panel D was taken with minescence is recorded. After the signal stabilizes, 2 µL of 10 µM PPi are added for permissionits concentrations from reference in mM are[34] indicated. on the curves). Panel D was taken with permission from internal calibration. reference [34]. Several comments on the assay procedure are appropriate. First, phosphoric acid and TheThe third third version version of the PP i assay accesses the equilibrium of the PPPPii  2Pi reactionreaction its salts are often contaminated with PPi, leading to high background luminescence. A inin the the active active site site of of PPase. PPase. This This information information is is required required to to estimate estimate the the rate rate constants constants for for low-PPi potassium phosphate can be prepared in the following way: phosphoric acid is individualindividual steps steps of of PPase PPase catalysis catalysis [37,38]. [37,38]. This This equilibrium equilibrium is is markedly markedly shifted shifted to to the the left left diluted to 0.2 M with water, boiled for 3 h, and neutralized with KOH [39]. Second, low byby comparing comparing the the equilibrium equilibrium in in solu solution—uption—up to 20% of enzyme-bound P i isis converted converted to to but significant background luminescence results from APS being a poor substratei for lu- PPPPii [37,38].[37,38]. To To assay, assay, the the enzyme-bound enzyme-bound PP i,, the the enzyme enzyme (20–100 (20–100 µM)µM) is incubated with P i ciferase.2+ Third, as Pi is added in high concentrations, care should be taken to ensure the andand Mg , ,inactivated inactivated byby trifluoroacetictrifluoroacetic acid acid to to release release enzyme-bound enzyme-bound PP iPPintoi into solution, solution, and assay mixture's desired pH. It is not enough to adjust to this value the pH of the stock Pi andan aliquot an aliquot is taken is taken to assay to assay PPi using PPi using the coupled the coupled ATP sulfurylase/luciferaseATP sulfurylase/luciferase procedure. proce- solution because the formation of the MgHPO4 complex from H2PO4- upon mixing stock dure.Several comments on the assay procedure are appropriate. First, phosphoric acid Pi and Mg2+ solutions would cause acidification of the medium (by 0.10 pH unit with 50 and its salts are often contaminated with PPi, leading to high background luminescence. mM Pi, 5 mM Mg2+ in 0.1 M MOPS–KOH buffer, pH 7.2). This effect is compensated by A low-PPi potassium phosphate can be prepared in the following way: phosphoric acid addingis diluted an toappropriate 0.2 M with amount water, of boiled KOH for to the 3 h, assay and neutralizedmixture. An with Excel KOH subroutine [39]. Second, to cal- 2+ + culatelow but this significant amount, backgroundwhich depends luminescence on Pi, Mg results, and fromH concentrations APS being a poorand reaction substrate vol- for ume, is available (Supplementary Material). Alternatively, one can adjust the pH of the luciferase. Third, as Pi is added in high concentrations, care should be taken to ensure the stock Pi solution used at each Mg2+ concentration to the value (above the desired assay assay mixture’s desired pH. It is not enough to adjust to this value the pH of the stock pH) determined in a trial titration. − Pi solution because the formation of the MgHPO4 complex from H2PO4 upon mixing 2+ stockA P i differentand Mg coupledsolutions-enzyme would assaycause acidification with similar of characte the mediumristics (by has 0.10 been pH described unit with 2+i [40].50 mM In this Pi, 5 assay, mM Mg PP isin converted 0.1 M MOPS–KOH to adenosine buffer, 5’-triphosphate pH 7.2). This (ATP effect) by ispyruvate compensated phos- phateby adding dikinase an appropriate in the presence amount of its of substrates, KOH to the pyruvate assay mixture. phosphate An and Excel AMP. subroutine The ATP to 2+ + formedcalculate is thissimilarly amount, determined which depends by the onfirefly Pi, Mglucifera, andse reaction. H concentrations The detection and limit reaction for PPvolume,i is approximately is available (Supplementary 10–8 M. The use Material). of this assay Alternatively, in PPase studies one can has adjust not the yet pH been of there- 2+ ported.stock P i solution used at each Mg concentration to the value (above the desired assay pH) determined in a trial titration. 5. IonicA different Equilibria coupled-enzyme in the Assay Media assaywith similar characteristics has been described [40]. In thisMagnesium, assay, PPi is the converted essential tocofactor adenosine of PPases, 5’-triphosphate has a dual (ATP) role in by catalysis pyruvate—it phosphate activates thedikinase enzyme in the and presence substrates of its by substrates, forming complexes pyruvate phosphate with both. and Because AMP. The the ATPenzyme formed can senseis similarly only the determined actual substrate by the species firefly luciferasein the medium reaction., but Thenot total detection substrate limit concentra- for PPi is −8 tion,approximately the magnesium 10 M. complexes The use ofof thisthe substrates assay in PPase PPi and studies Pi are has named not yet “true been substrates reported..” A meaningful analysis of enzyme kinetics with the Michaelis–Menten equation should be

Molecules 2021, 26, 2356 8 of 13

5. Ionic Equilibria in the Assay Media Molecules 2021, 26, x FOR PEER REVIEW 8 of 13 Magnesium, the essential cofactor of PPases, has a dual role in catalysis—it activates Molecules 2021, 26, x FOR PEER REVIEW the enzyme and substrates by forming complexes with both. Because8 of the 13 enzyme can

sense only the actual substrate species in the medium, but not total substrate concentra- donetion, thein terms magnesium of these complexestrue substrates. of the Furthermore, substrates PP thei and substrate Pi are named–concentration “true substrates.” depend- done in termsenciesA of meaningful these of trueenzyme substrates. analysis activity of Furthermore, enzymeshould be kinetics measured the withsubstrate theat a Michaelis–Mentenfixed–concentration free Mg2+ depend-ion equation concentrat shouldion be- be encies of enzymecausedone activity init, termsnot theshould of total these bemagnesium true measured substrates. concentration, at a Furthermore,fixed free determines Mg the2+ ion substrate–concentration concentrat the fractionion of be- the metal dependen--com- 2+ cause it, not theplexedcies total of enzymeenzymemagnesium activityand, concentration, hence, should its activity. be measured determines at athe ﬁxed fraction free Mgof theion metal concentration-com- because plexed enzymeit, and, notPyrophosphoric the hence, total its magnesium activity. acid undergoes concentration, a four determines-step dissociation, the fraction of which of the metal-complexedonly the last two enzyme and, hence, its activity. Pyrophosphoricsteps with acid the undergoes pKa3 of 6.38 a fourand -pstepKa4 ofdissociation, 9.11 should of be which considered only the in enzymelast two studies. Mag- Pyrophosphoric acid undergoes a four-step dissociation,2- of which only the last- two steps with thenesium pKa3 of forms6.38 and four p Kcomplexesa4 of 9.11 should with three be considered PPi species: in enzymeMgP2O7 studies., Mg2P2 OMag-7, MgHP2O7 , and steps with the pK of 6.38 and pK of 9.11 should be considered in enzyme studies. Mag- MgH2P2O7 (Schemea3 1). Furthermore,i a4 alkali metal2 72 ions,- 2often2 7 present2 in7 -the assay medium, nesium forms four complexes with three PP species: MgP O , Mg P O , MgHP2− O , and − nesium forms four complexes with3- three PP2i- species: MgP22-O7 , Mg+ 2P2O+7, MgHP2O7 MgH2P2O7 (Schemeform additional 1). Furthermore, complexes: alkali MP metal2O7 ions,, M2P often2O7 , andpresent MHP in2 Othe7 assay(M = K medium, or Na ) . At fixed pH and MgH2P2O7 (Scheme1). Furthermore, alkali metal ions, often present in the assay form additionaland complexes: alkali metal MP ion2O 7concentrations,3-, M2P2O72-, and the MHP complexation2O72- (M = K +in or this Na +system). At fixed can pH be described by medium, form additional complexes: MP O 3−,M P O 2− and MHP O 2− (M = K+ or and alkali metalsimple ion Schemeconcentrations, 2, in which the eachcomplexation species is in the2 this 7sum system of2 all2 candifferently7 be described protonated2 by7 individual Na+). At ﬁxed pH and alkali metal ion concentrations, the complexation in this system simple Schemespecies 2, in which of the eachsame species magnesium:PP is the sumi stoichiometry. of all differently protonated individual can be described by simple Scheme2, in which each species is the sum of all differently species of the same magnesium:PPi stoichiometry. protonated individual species of the same magnesium:PPi stoichiometry.

Scheme 1. Complex formation between PPi, H+, Mg2+, K+, and Na+ ions under physiological condi- + 2+ + + Scheme 1. Complex formation between PPi,H , Mg ,K and Na ions under physiological conditions. The number Scheme 1. Complextions. formationThe number between above PPor ibeside, H+, Mg arrows2+, K+, andrefers Na to+ ionsthe minus under logarithm physiological of the condi- respective dissocia- above or beside arrows refers to the minus logarithm of the respective dissociation constant [41]. tions. The numbertion aboveconstant or beside[41]. arrows refers to the minus logarithm of the respective dissociation constant [41].

Scheme 2. A simplified description of complexation between PPi and Mg2+2+ at fixed pH and alkali Scheme 2. A simplified description of complexation between PPi and Mg at fixed pH and alkali metal ion concentrations. 2+ Scheme 2. A simplifiedmetal ion description concentrations. of complexation between PPi and Mg at fixed pH and alkali metal ion concentrations. TheThe values of Kmpp andand KKm2ppm2pp cancan be be calculated calculated at at each each pH pH value value and and alkali metal + The valuesconcentrationconcentration of Kmpp and from from Km2pp the can dissociation be calculated constants at each of pH the value individual and alkali PPii complexes metal with H ,, 2+2+ + + + + concentrationMgMg from, ,KK the, and dissociationand Na Na (tabulated(tabulated constants in ina previousof a the previous individual publication publication PPi [41]complexes [)41. Knowing]). Knowing with the H +values, the values of Kmpp of Mg2+, K+, andand KNampp+ K (tabulatedm2ppand allowsKm2pp in allowscalculating a previous calculating the publication total the magnesium total [41] magnesium). Knowing and PP andi concentrationsthe PP valuesi concentrations of K neededmpp needed to main- to 2+ 2+ and Km2pp allowstainmaintain calculating the required the required the concentrations total concentrations magnesium of MgPPand of PP MgPPi ior concentrations Mgi or2PP Mgi complex2PPi neededcomplex and to free and main- Mg free. Mg This .algo- This tain the requiredrithmalgorithm concentrations was wasembedded embedded of inMgPP an in Excel ani or Excel Mg subroutine2 subroutinePPi complex that that calculatesand calculates free Mg the the2+ composition. compositionThis algo- of of the the assay assay rithm was embeddedmediummedium in at 25an25 ◦Excel°CC andand subroutine chosenchosen pH pH that and and calculates alkali alkali metal metal the concentrations compositionconcentrations (Supplementaryof (theSupplementary assay Material). Mate- medium at 25rial °C) .and The chosen choice pH between and alkali MgPP metali and concentrations Mg2PPi as the (Supplementary true substrate isMate- largely arbitrary 2+ rial). becauseThe thechoice ratio between of Mg2 PPMgPPi andi and MgPP Mgi2PPconcentrationsi as the true substrate is constant is largely at a fixed arbitrary Mg con- be- 2+ The choicecausecentration, between the ratio andMgPP of switching Mgi and2PP Mgi and from2PP MgPPi oneas the complexi concentrations true substrate to the other is is constant largely would arbitraryat only a fixed change be- Mg the concentra- apparent cause the ratiotionvalue of ,Mg and of2PP theswitchingi and Michaelis MgPP fromi constant.concentrations one complex In most tois theconstant reported other atwould studies, a fixed only Mg MgPP change2+ concentra-i has the been apparent assumed value to tion, and switchingofbe the the fromMichaelis true substrateone complex constant. for PPasesto In the most other of familiesreported would I only andstudies, IIchange and MgPP Mg the2i PPapparenthasi to been be suchvalueassumed for membrane to be the of the Michaelistrue constant. substrate In for most PPases reported of families studies, I and MgPP II andi has Mg been2PPi to assumed be such tofor be membrane the PPases. true substrateHowever, for PPases one of fshouldamilies keepI and in II mindand Mg that2PP steadyi to be- statesuch forkinetic membrane studies PPases.can define only stoi- However, onechiometry should keep of thein mind statistical that lysteady significant-state kinetic enzyme studies species can, but define not onlythe waysstoi- of their for- chiometry of mationthe statistical becausely schemessignificant assuming enzyme different species, truebut substratesnot the ways will oflead their to thefor- same rate law mation because schemes assuming different true substrates will lead to the same rate law

Molecules 2021, 26, 2356 9 of 13

Molecules 2021, 26, x FOR PEER REVIEW 9 of 13 PPases. However, one should keep in mind that steady-state kinetic studies can define only stoichiometry of the statistically significant enzyme species, but not the ways of their formation because schemes assuming different true substrates will lead to the same rate andlaw are and, therefore are, therefore,, indistinguishable. indistinguishable. These These considerations considerations are especially are especially important important to re- to memberremember when when worki workingng with with the the kinetic kinetic schemes schemes considering considering both both substrate substrate and and Mg2+ bindingbinding to to the the enzyme. enzyme. − 2− PPi iisis represented represented by by a amixture mixture of of H H2PO2PO4- 4andand HPO HPO42- forms4 forms in the in pH the range pH range 4–10,4–10 and , 2+ + + onlyand the only latter the species latter species forms 1:1 forms complexes 1:1 complexes with Mg with2+, K+ Mg, and,K Na+, (Scheme and Na 3)(Scheme. The Mg3P).i complexThe MgP isi generallycomplex isassumed generally to be assumed the true to substrate be the true in the substrate PPase-catalyzed in the PPase-catalyzed PPi synthesis. 2+ ThePPi totalsynthesis. concentrations The total of concentrations Mg2+ and Pi needed of Mg to andmaintain Pi needed the required to maintain concentrations the required of 2+ theconcentrations MgPi complex of theand MgP freei Mgcomplex2+ ions and are freecalculated Mg ions using are the calculated apparent using dissociation the apparent con- stantdissociation for MgP constanti. The latter for MgPis obtainedi. The latter similarly is obtained at each similarly pH value at and each alkali pH value metal and concen- alkali trationmetal concentrationfrom the dissociation from the constants dissociation of the constants individual of the Pi individualcomplexes Pwithi complexes H+, Mg2+ with, K+, + 2+ + + andH , Na Mg+ [42,K–45].and This Na algo[42rithm–45]. Thiswas algorithmalso embedded was also in an embedded Excel subroutine in an Excel (Supplemen- subroutine tary(Supplementary Material), which Material), additionally which additionally calculates the calculates amount the of amountthe alkali of needed the alkali to neededcompen- to satecompensate for the acidification for the acidification of the assay of the medium assay medium because because of the selective of the selective complexation complexation of the 2− 2+ HPOof the42- HPOspecies4 byspecies Mg2+. by Mg .

i + + 2+2+ + + + + SchemeScheme 3. 3. ComplexComplex formation formation between between P P,i ,HH , Mg, Mg, K,K, and, and Na Na ionsions under under physiological physiological condi- condi- tions.tions. The The number number above above or beside arrows refersrefers toto thethe minus minus logarithm logarithm of of the the respective respective dissociation dissociation constant [42–45]. constant [42–45].

Supplementary Materials: The following is available online. Microsoft Excel file: Calculations of mSupplementaryedium composition. Materials: The following is available: Microsoft Excel file: Calculations of medium composition. Author Contributions: writing—original draft preparation, A.A.B.; software and visualization, V.A.A.;Author writing Contributions:—review Writing—originaland editing, A.M.M. draft Allpreparation, authors have A.A.B.; read and software agreed and to the visualization, published versionV.A.A.; of writing—review the manuscript. and editing, A.M.M. All authors have read and agreed to the published version of the manuscript. Funding: This work was supported by the Academy of Finland (grant numbers 307775 and 335377) andFunding: by LomonosovThis work Moscow was supported State University. by the Academy of Finland (grant numbers 307775 and 335377) and by Lomonosov Moscow State University. Data Availability Statement: The Excel subroutine that calculates the composition of the assay me- diumData at Availability chosen pH Statement:and alkali metalThe Excelconcentrations subroutine is available that calculates as Supplementary the composition Material. of the assay medium at chosen pH and alkali metal concentrations is available as Supplementary Material. Conflicts of Interest: The authors declare no conflicts of interest. Conflicts of Interest: The authors declare no conflict of interest. Appendix A Appendix A Estimation of Initial Velocities from Product Formation Curves Estimation of Initial Velocities from Product Formation Curves If substrate (PPi) concentration remains saturating during the recording time, resulting inIf a substrate linear time (PP-course,i) concentration the initial remains velocity saturating is obtained during straightforwardly. the recording time, However, resulting if substratein a linear consumption time-course, exceeds the initial 20%, velocity drawing is obtained the tangent straightforwardly. to the product However, accumulation if sub- curvestrate by consumption eye may result exceeds in a 20%, large drawing error in thethe tangent initial velocity, to the product more accumulationcommonly underesti- curve by matingeye may [46] result (pp. in 80 a– large82). There error are in thetwo initial waysvelocity, to increase more the commonly accuracy of underestimating such analysis. One [46] can(pp. derive 80–82). the There explicit are equation two ways or to system increase of the equations accuracy that of suchdescribe analysis. the integral One can reacti deriveon kineticsthe explicit and equationfit it to the or product system formation of equations curve. that A describe simpler the alternative integral is reaction to use kineticsa semi- empiricaland fit it toprocedure the product to manually formation draw curve. the A zero simpler-time alternativetangent to the is to curve. use a The semi-empirical procedure procedure to manually draw the zero-time tangent to the curve. The procedure described described below determines the second point, though, which the tangent must pass, in below determines the second point, though, which the tangent must pass, in addition addition to the zero-time point. The required initial information includes the instrument signal (absorbance increase in recorder paper divisions) upon complete substrate conversion (Pinf). This parameter is calculated from the expected Pi concentration upon complete

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Molecules 2021, 26, x FOR PEER REVIEW 10 of 13 to the zero-time point. The required initial information includes the instrument signal (absorbance increase in recorder paper divisions) upon complete substrate conversion (Pinf). This parameter is calculated from the expected Pi concentration upon complete substrate substrate conversion (twice the initial PPi concentration) and instrument sensitivity. One conversion (twice the initial PPi concentration) and instrument sensitivity. One will also will also need an approximate Km value in terms of total PPi. need an approximate Km value in terms of total PP . In a reaction with substrate exhaustion, the producti accumulation curve will deviate In a reaction with substrate exhaustion, the product accumulation curve will deviate from the the tangent tangent at at the the zero zero-time-time point, point, corresponding corresponding to initial to initial velocity velocity (Figure (Figure A1). A1The). differenceThe difference between between the two the curves two curves (∆P) increases (∆P) increases with time, with and time, its and knowledge its knowledge at a single at a valuesingle of value P suffices of P sufﬁces to draw to the draw zero the-time zero-time tangent. tangent.The smaller The the smaller correction the correction (∆P), the more (∆P), accuratethe more is accurate the initial is velocity the initial estimate. velocity Obviously, estimate. the Obviously, ∆P value the will∆ decreaseP value willwith decrease increasing Pinf and decreasing P and Km values. The equation for ∆P is obtained by combining with increasing Pinf and decreasing P and Km values. The equation for ∆P is obtained by Equation A1 and Equation A2, where V is the maximal velocity, t is time, Km is the Mich- combining Equation A1 and Equation A2, where V is the maximal velocity, t is time, Km is aelis constant, and Pinf is the initial substrate concentration. Equation A1 describes product the Michaelis constant, and Pinf is the initial substrate concentration. Equation A1 describes (P1) accumulation in time in a zero-order reaction proceeding with the rate equal to the product (P1) accumulation in time in a zero-order reaction proceeding with the rate equal enzymeto the enzyme-catalyzed-catalyzed reaction's reaction’s initial initialvelocity velocity.. Equation Equation A2 describes A2 describes the true the integral true integral kinet- 1 icskinetics of the of enzyme the enzyme-catalyzed-catalyzed reaction reaction [46] [46 (p.] (p.78) 78).. At At any any time time point point t, t, PP1 == PP ++ ∆∆PP,, and, and, accordingly, Equation Equation A3 A3 is isvalid. valid. After After its rearrangement, its rearrangement, one obtains one obtains Equation Equation A4, which A4, whichlinks ∆ linksP to P ∆infP ,toP ,P andinf, PK, mandvalues. Km values.

P1 = Vt/(1 + Km/Pinf) (A1) P1 = Vt/(1 + Km/Pinf) (A1)

AiP/Km + Km ln[Pinf/(Pinf-P)] = Vt (A2) AiP/Km + Km ln[Pinf/(Pinf − P)] = Vt (A2)

P/KmP+/KKmm +ln[ KmP ln[inf/(PinfP/inf(Pinf−-P))]] = ( (PP ++ ∆∆PP)()(11 + + KKmm/P/infP)inf. ). (A3)(A3)

∆P = {P∆P+ =K {mP ln[+ KPminf ln[/(PPinfinf/(P−infP-P)]}/(1)]}/(1 ++ KKmm/P/Pinfinf)–)P− P (A4)(A4)

Figure A A1.1. TimeTime-course-course of of product product accumulation accumulation in the in theenzyme enzyme-catalyzed-catalyzed reaction reaction (solid (solid line). line). The dashedThe dashed straight straight line is line the iszero the-time zero-time tangent tangent to the solid to the curve, solid with curve, the with slope the equal slope to the equal initial to the velocity.initial velocity.

The dependencies dependencies of of ∆∆PP onon PinfPinf calculatedcalculated at several at several fixe fixedd P andP and Km valuesKm values are pre- are sentedpresented in Figure in Figure A2. A2 These. These graphs graphs are areused used to determine to determine ∆P at∆P givenat given Pinf andPinf andP valuesP values and drawand draw the tangent the tangent for any for reaction any reaction with with substrate substrate depletion. depletion. The Thetop left top panel left panel applies applies to a firstto a- first-orderorder reaction. reaction. As Asexpected, expected, the the ∆P∆ valueP value decreases, decreases, and and the the accuracy accuracy of of the the initial velocity estimate increases accordingly with increasing Pinf andand decreasing decreasing PP.. Optimally, Optimally, P should be chosen between 20 and 50% of PPinfinf,, also also keeping keeping in in mind mind that that the the signal signal-to--to- noise ratio becomes unfavorable at low P values. Although this treatment involves visual interpolation and is approximate, it decreases the error in the estimated initial velocity to less than 10%, which which is sufficient sufficient for most u uses.ses. The The simplicity simplicity of the procedure procedure compared to that of Cornish-Bowden [47] and other known ones [46] (pp. 80–85) has made it a useful aid in the kinetic studies of PPase. Although we have been mainly using this correction

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to that of Cornish-Bowden [47] and other known ones [46] (pp. 80–85) has made it a useful aid in the kinetic studies of PPase. Although we have been mainly using this correction procedureprocedure in in the the continuous continuous assa assays,ys, it it is is also also applicable applicable to to and and is is especially especially important important for for thethe fixed ﬁxed-time-time assay assay carried carried out out at at non non-saturating-saturating substrate substrate concentration. concentration.

FigureFigure A A2.2. TheThe dependence dependence of ∆P in Figure A1A1 ononP Pinfinf atat sevenseven ﬁxedfixed values values of ofP P(shown (shown on on one one panel panel and and kept kept same same on on the theother other panels) panels and) and six six values values of Kofm K(shownm (shown on on the the panels) panels for) for an an enzyme-catalyzed enzyme-catalyzed reaction. reaction. For For simplicity, simplicity, the the values values of of∆ P∆,PP, infPinf, P, Pand, andKm Karem are shown shown in in terms terms of theof the same same arbitrary arbitrary unit, unit, for instance,for instance, recorder recorder paper paper division. division. These These graphs graphs were werecreated created for an for enzyme an enzyme that obeys that obeys simple simple Michaelis–Menten Michaelis–Menten kinetics kinetics with the with product the product to substrate to substrate ratio of one.ratio To of useone. these To use these graphs for PPase, which produces two Pi molecules from one PPi molecule, one must divide by two the measured graphs for PPase, which produces two Pi molecules from one PPi molecule, one must divide by two the measured values of values of P and Pinf if they are expressed in terms of Pi. Note that axis scaling is different on the two bottom panels. P and Pinf if they are expressed in terms of Pi. Note that axis scaling is different on the two bottom panels. References References 1. Heinonen, J.K. Biological Role of Inorganic Pyrophosphate; Kluwer Academic Publishers: London, UK, 2001. 2.1. Baykov,Heinonen, A.A.; J.K. Malinen,Biological A.M.; Role ofLuoto, Inorganic H.H Pyrophosphate.; Lahti, R. Pyrophosphate; Kluwer Academic-fueled Publishers:Na+ and H+ London,transport UK, in prokaryotes 2001. Microbiol. Mol. + + 2. Biol.Baykov, Rev. A.A.;2013, Malinen,77, 267–276 A.M.;. Luoto, H.H.; Lahti, R. Pyrophosphate-fueled Na and H transport in prokaryotes Microbiol. Mol. 3. Tsai,Biol. J. Rev.-Y.; 2013Kellosalo,, 77, 267–276. J.; Sun, Y. [CrossRef-J.; Goldman,][PubMed A. Proton/sodium] pumping pyrophosphatases: The last of the primary ion pumps. Curr. Opin. Struct. Biol. 2014, 27, 38–47.

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