Magnesium magnetic isotope effect: A key to the mechanochemistry of phosphorylating enzymes as molecular machines

The discovery of the powerful magnesium isotope effect on enzymatic ATP synthesis provides a new insight into the mechanochemistry of enzymes as molecular machines. The catalytic activities of ATPase, creatine kinase, and glycerophsphate kinase containing a Mg²⁺ ion with magnetic isotope nuclei (²⁵Mg) were found to be two to four times higher than those of the enzymes with spinless, nonmagnetic magnesium cation isotopes (²⁴Mg or ²⁶Mg). This demonstrates unambiguously that ATP synthesis is a spin-selective process involving Mg2+ as the electron-accepting reagent. ATP synthesis proceeds in an ion-radical pair consisting of an ADP oxyradical and Mg²⁺. In this process, the magnesium bivalent cation is the key agent that transforms the mechanics of a protein molecule into chemical processes. This ion is the crucial structural component of enzymes as mechanochemical molecular machines.     

The Influence of Low Magnetic Fields and Magnesium Isotopes on <Emphasis Type="Italic">E. coli</Emphasis> Bacteria

The combined effects of external low static magnetic fields at 0–22 mT and magnesium isotopes on the growth and development of E. coli bacteria has been studied. The magnetic field and ²⁵Mg magnetic isotope effects were obtained in two ranges: 0.8–3.0 and 8–13 mT. The experimental values of the growth rate, the number of CFUs and the ATP pool of bacteria enriched in magnetic magnesium isotope ²⁵Mg (nuclear spin, I = 5/2) in the range of 0.8–3.0 mT are significantly higher compared to bacteria enriched in nonmagnetic isotopes ²⁴Mg, ²⁶Mg, or natural magnesium. The increase in the growth rate, colony-forming ability, and intracellular ATP concentration in bacteria in all groups cultivated under exposure to an external static magnetic field in the range of 0.8 to 3.0 mT confirms the existence of magnetosensitive stages of enzymatic reactions that proceed via the ion-radical mechanism. The combined influence of the magnetic field in the range of 8 to 13 mT and the magnesium magnetic isotope ²⁵Mg on the colony forming ability of E. coli bacteria is associated with processes that are responsible for cell division. The above-mentioned effects of bacterial magnetosensitivity (to magnetic fields and magnetic isotopes) are in good agreement with theoretical predictions of the theory of spin-dependent enzymatic reactions.     

Nuclear spin catalysis in nanoreactors of living cells

It has been shown that bacteria Escherichia coli, which were previously enriched with magnetic isotope of magnesium, ²⁵Mg, essentially faster adapt to the new growth media by comparison with the cells, which were enriched with nonmagnetic isotopes ²⁴Mg or ²⁶Mg. In the experiments with another commonly accepted cell model, yeast Saccharomyces cerevisiae, it has been shown that magnetic ²⁵Mg, in comparison to nonmagnetic ²⁴Mg, essentially better stimulates recovery of the cells after short wave UV irradiation. Thus, for the first time, the magnetic isotope effects in vivo have been discovered. These findings reveal the novel, based on the stable magnetic isotopes, ways of control over efficiency and reliability of biological systems.     

Efficiency of ATP synthase as a molecular machine

The experimentally measured effect of the odd magnetic isotope ²⁵Mg on the rate of ATP synthesis by the mitochondrial F₀F₁ enzyme is used to compare the rates of the main reactions in the catalytic site, in the framework of a radical-ion process. The rate-limiting step of synthesis is the addition of the ADP oxyradical to the phosphate P=O bond. The relationship of the rate constants deduced from the magnetic isotope effect shows that the mechanochemical efficiency of ATP synthase operating with spinless ²⁴Mg or ²⁶Mg nuclei will not exceed 50%. The performance is nearly doubled with magnetic ²⁵Mg.     

Magnesium isotope fractionation during microbially enhanced forsterite dissolution

Bacillus subtilis endospore‐mediated forsterite dissolution experiments were performed to assess the effects of cell surface reactivity on Mg isotope fractionation during chemical weathering. Endospores present a unique opportunity to study the isolated impact of cell surface reactivity because they exhibit extremely low metabolic activity. In abiotic control assays, ²⁴Mg was preferentially released into solution during forsterite dissolution, producing an isotopically light liquid phase (δ²⁶Mg = ?0.39 ± 0.06 to ?0.26 ± 0.09‰) relative to the initial mineral composition (δ²⁶Mg = ?0.24 ± 0.03‰). The presence of endospores did not have an apparent effect on Mg isotope fractionation associated with the release of Mg from the solid into the aqueous phase. However, the endospore surfaces preferentially adsorbed ²⁴Mg from the dissolution products, which resulted in relatively heavy aqueous Mg isotope compositions. These aqueous Mg isotope compositions increased proportional to the fraction of dissolved Mg that was adsorbed, with the highest measured δ²⁶Mg (?0.08 ± 0.07‰) corresponding to the highest degree of adsorption (~76%). The Mg isotope composition of the adsorbed fraction was correspondingly light, at an average δ²⁶Mg of ?0.49‰. Secondary mineral precipitation and Mg adsorption onto secondary minerals had a minimal effect on Mg isotopes at these experimental conditions. Results demonstrate the isolated effects of cell surface reactivity on Mg isotope fractionation separate from other common biological processes, such as metabolism and organic acid production. With further study, Mg isotopes could be used to elucidate the role of the biosphere on Mg cycling in the environment.     

Spin biochemistry

The rates of adenosine triphosphate (ATP) production by isolated mitochondria and mitochondrial creatime kinase incubated in isotopically pure media containing, separately, ²⁴Mg²⁺, ²⁵Mg²⁺, and ²⁶Mg²⁺ ions were shown to be strongly dependent on the magnesium nuclear spin and magnetic moment. The rate of adenosine 5′-diphosphate phosphorylation in mitochondria with magnetic nuclei²⁵Mg is about twice higher than that with the spinless, nonmagnetic nuclei^24.26Mg. When mitochondrial oxidative phosphorylation was selectively blocked by treatment with 1-methylnicotine amide, ²⁵Mg²⁺ ions were shown to be nearly four times more active in mitochondrial ATP synthesis than ^24,26Mg²⁺ ions. The rate of ATP production associated with creatine kinase is twice higher for ²⁵Mg²⁺ than for ^24.26Mg and does not depend on the blockade of oxidative phosphorylation. There is no difference between ²⁴Mg²⁺ and ²⁶Mg²⁺ effects in both oxidative and substrate phophorylation. These observations demonstrate that the enzymatic phosphorylation is a nuclear spin selective process controlled by magnetic isotope effect. The reaction mechanism proposed includes a participation of intermediate ion-radical pairs with Mg⁺ cation as a radical partner. Therefore, the key mitochondrial phosphotransferases work as a magnesium nuclear spin mediated molecular machines.     

Magnetic isotope and magnetic field effects on the DNA synthesis

Magnetic isotope and magnetic field effects on the rate of DNA synthesis catalysed by polymerases β with isotopic ions ²⁴Mg²⁺, ²⁵Mg²⁺ and ²⁶Mg²⁺ in the catalytic sites were detected. No difference in enzymatic activity was found between polymerases β carrying ²⁴Mg²⁺ and ²⁶Mg²⁺ ions with spinless, non-magnetic nuclei ²⁴Mg and ²⁶Mg. However, ²⁵Mg²⁺ ions with magnetic nucleus ²⁵Mg were shown to suppress enzymatic activity by two to three times with respect to the enzymatic activity of polymerases β with ²⁴Mg²⁺ and ²⁶Mg²⁺ ions. Such an isotopic dependence directly indicates that in the DNA synthesis magnetic mass-independent isotope effect functions. Similar effect is exhibited by polymerases β with Zn²⁺ ions carrying magnetic ⁶⁷Zn and non-magnetic ⁶⁴Zn nuclei, respectively. A new, ion–radical mechanism of the DNA synthesis is suggested to explain these effects. Magnetic field dependence of the magnesium-catalysed DNA synthesis is in a perfect agreement with the proposed ion–radical mechanism. It is pointed out that the magnetic isotope and magnetic field effects may be used for medicinal purposes (trans-cranial magnetic treatment of cognitive deceases, cell proliferation, control of the cancer cells, etc).     

Magnetic-dependent ATP pool in <Emphasis Type="Italic">Escherichia coli</Emphasis>

The ATP pool in Escherichia coli is a magnetic-dependent characteristic of microorganism vital activity. It depends on the values of the external static magnetic field and the existence of magnetic moment of magnesium isotopes nuclei added to the growth nutrient medium. The combined effects of the magnetic field 70–95 mT and magnesium magnetic isotope ²⁵Mg on E. coli bacteria leads to increase intracellular concentration of ATP. Magnetic-field effects in the range of 0.8–16 mT, registered for all bacteria regardless of the magnesium-isotopic enrichment of nutrient medium, evidence about the sensitivity of intracellular processes to weak magnetic fields.     

Magnesium magnetic isotope effect: a key towards mechanochemistry of phosphorylating enzymes as molecular machines

A discovery of the huge magnesium isotope effect in enzymatic ATP synthesis provides a new insight into mechanochemistry of enzymes as the molecular machines. It has been found that the catalytic activity values of ATPase, creatine kinase and phosphoglycerate kinase are 2 to 4-fold higher once their active sites contain magnetic (25Mg) not spinless, non-magnetic (24Mg, 26Mg), magnesium cation isotopes. This clearly proves that the ATP synthesis is a spin-selective process involving Mg2+ as the electron accepting reagent. The formation of ATP takes place in an ion-radical pair resulted by two partners, ATP oxyradical and Mg+. The magnesium bivalent cation is a key player in this process, this ion transforms the protein molecule mechanics into a mere chemistry. This ion is a most critical detail of structure of the magnesium dependent phosphorylation enzymes as the mechanochemical molecular machines.     

The efficiency of ATP synthase as a molecular machine

On the basis of the experimentally measured isotope effect of magnesium (25)Mg on the rate of ATP synthesis by mithochondrial ATP synthase, the rate constants of the reactions in the catalytic site have been estimated. The limiting step of the synthesis is shown to be the addition of8phosphoryl anion-radical of ADP to the P=O bond of phosphate with the rate constant of 1,2 x 10(8) s(-1). From the ratio of the rate constants, the mechanochemical efficiency of ATP synthase was estimated to be about 10% for enzymes with (24, 26)Mg isotopes and to be doubled for enzymes with (25)Mg in the catalytic site.     

Magnetosensitivity of <Emphasis Type="Italic">E. coli</Emphasis> Bacteria in the Presence of Zinc Isotopes

The combined effect of the zinc magnetic isotope ⁶⁷Zn and weak magnetic field 25–35 mT causes a 2–4-fold increase in the colony-forming ability of bacteria E. coli in comparison with the nonmagnetic isotopes ^{64, 66}Zn. The effects of magnetic field in the range of 2.2–8 mT were detected for all bacteria regardless of the zinc-isotope enrichment of the media. This indicates the sensitivity of intracellular processes to weak magnetic fields. An increase in the ATP concentration in E. coli cells was only detected for the bacteria grown on the medium with the magnetic zinc isotope in the range of 2.2–4.2 mT. The obtained data confirm the existence of stages of intracellular enzymatic processes that are sensitive to magnetic fields and magnetic moments of atomic nuclei.     

Monitoring uptake and contents of Mg,Ca and K in Norway spruce as influenced by pH and Al,using microprobe analysis and stable isotope labelling

In a model system using intact spruce trees (Picea abies [L.] Karst.) we followed the path of magnesium, calcium and potassium during uptake into the root and during long-range transport into the shoot, by multiple stable isotope labelling. The roots of two- and three-year-old spruce trees originating from soil culture were removed from the soil and, in part or in toto, exposed to labelling solutions containing the stable isotopes ²⁵Mg or ²⁶Mg, ⁴¹K and ⁴²Ca or ⁴⁴Ca. Optical-emission-spectroscopy (ICP-OES) of plant fractions and labelling solutions was combined with the quantitative analysis of stable isotope ratios in sections of shock frozen, cryosubstituted material using the laser-microprobe-mass-analyser (LAMMA). This combination allowed us to distinguish, both in bulk samples and on the cellular level between (i) the fraction of elements originally present in the plant before the start of the labelling, (ii) the material taken up from the labelling solution into the plant and (iii) any material released by the plant into the labelling solution.In single-root labelling experiments, roots of three-year-old spruce trees, grown in nursery soil, were exposed to various pH conditions. The exchange of Mg and Ca with the labelling solution was nearly 100% in the cell walls of the mycorrhized finest roots. This exchange was only slightly affected by a step down to pH 3.5. The absolute Mg and Ca content in the cell walls was moderately reduced by incubation at pH 3.5 and strongly reduced in the presence of Al at this pH. After a pH 3.5 and 2 mM Al treatment we found Al in the xylem cell walls and the cortex cell lumina at elevated concentrations. To analyse the combined effect of high Al and high proton concentrations on the long-range transport, we used a split-root system. The root mass of an intact two-year-old spruce tree, grown in mineral soil, was divided into even parts and both halves incubated in solutions with two sets of different stable isotopes of Mg and Ca (side A: no Al, ²⁵Mg and ⁴²Ca; side B: +Al, ²⁶Mg and ⁴⁴Ca) and ⁴¹K on both sides. We observed a large uptake of Mg, Ca and K into the plant and a pronounced release. The net uptake of all three elements was lower from the Al-doted solution. In cross-sections of the apical shoot we found after seven-day labelling period about 60–70% of the Mg and Ca and 30% of the K content in the xylem cell walls originating from both labelling solutions. The clear majority of the Mg and Ca label originated from the Al-doted side.     

Mg isotopes and Mg/Ca values of coccoliths from cultured specimens of the species Emiliania huxleyi and Gephyrocapsa oceanica

Coccoliths from cultured specimens of two species of coccolithophores (Emiliania huxleyi and Gephyrocapsa oceanica) were sampled during two growth phases (late exponential and stationary), and their Mg isotope values (δ²⁶Mg) as well as Mg/Ca values were measured in order to investigate whether δ²⁶Mg can be used as a temperature proxy. Mg/Ca values were positively related with temperature (~ 0.002 mmol/mol/°C), without statistically significant differences between the two growth phases and the two species. Both species were depleted in heavier Mg isotopes relative to the culture medium, and δ²⁶Mg values were temperature dependent in both growth phases of E. huxleyi, although the δ²⁶Mg values differed in the two growth phases. In G. oceanica, a weak correlation between δ²⁶Mg values and temperature was seen in the late exponential growth phase only, and the δ²⁶Mg values differed between growth phases. The large differences between δ²⁶Mg values as measured in calcite formed during different growth phases indicate that Mg isotopes of coccoliths cannot be simply used as a temperature proxy. Our conclusions are preliminary and more data must be collected in order to fully evaluate the use of Mg isotopes of coccoliths as a temperature proxy.     

Magnetic isotope effect of magnesium <Superscript>25</Superscript>Mg on <Emphasis Type="Italic">E. coli</Emphasis> resistance to antibiotics

Effects of synergism and antagonism of antibacterial drugs and magnetic isotope of magnesium ²⁵Mg on antibiotic resistance of bacteria E. coli were discovered. Fourteen antibiotics from seven different groups were tested. The increase in antibiotic resistance in the presence of the ion ²⁵Mg²⁺ was discovered in E. coli cells incubated with quinolones/fluoroquinolones, indicating the inhibiting effect of the magnetic moments of nuclei ²⁵Mg on DNA synthesis. The change in antibiotic resistance was also detected in bacteria affected by magnesium ²⁵Mg and certain antibiotics from aminoglycoside and lincosamide groups.     

Effects of dicyclohexylcarbodiimide (DCCD) treatment on coupled activities of vanadate-sensitive ATPase from plasma membrane of maize roots

The presence of dicyclohexylcarbodiimide (DCCD) inhibited the activities of vanadate-sensitive H⁺ -ATPase in both native and reconstituted plasma membrane of maize (Zea mays L. cv. WF9 × Mo 17) roots. Concentration dependence of DCCD inhibition on adenosine triphosphate (ATP) hydrolysis of native plasma membrane vesicles suggested that the molar ratio of effective DCCD binding to ATPase was close to 1. The DCCD inhibition of ATP hydrolysis could be slightly reduced by the addition of ATP, Mg:ATP, adenosine monophosphate (AMP), Mg:AMP and adenosine diphosphate (ADP). More hydrophilic derivatives of DCCD such as l-ethyl-N^?-3-trimethyl ammonium carbodiimide (EDAC) or 1-ethyl-3-3-dimethyl-aminopropyl carbodiimide (EDC) gave no inhibition, indicating that the effective DCCD binding site was located in a hydrophobic region of the protein. The proton transport activity of reconstituted plasma membrane at a temperature below 20°C or above 25°C was much sensitive to DCCD treatment. Build-up of the proton gradient was analyzed according to a kinetic model, which showed that proton leakage across de-energized reconstituted plasma membranes was not affected by DCCD, but was sensitive to the method employed to quench ATP hydrolysis. Reconstituted plasma membrane vesicles treated with DCCD exhibited a differential inhibition of the coupled H⁺-transport and ATP hydrolysis. The presence of 50 μM DCCD nearly abolished transport but inhibited less than 50% of ATP hydrolysis. The above results suggest that the link between proton transport and vanadate-sensitive ATP hydrolysis is indirect in nature.     

Stable isotopes of Mg2+ as activators of the suppressed ATP-generating function of mitochondria

The ATP-generating activity of rat myocardial mitochondria and intramitochondrial creatine kinase was examined as a function of the isotopy of the incubation medium magnesium pool. The study was performed using in vitro systems prepared from the hearts of animals injected with 1-methylnicotine amide, which suppresses the NAD (NADP)-dependent reactions in vivo. It was shown that the presence of the 25Mg paramagnetic cations essential by compensates for the intramitochondrial ATP deficiency caused by the 1-methyl-nicotine amide-induced blockade of oxidative phosphorylation. This effect is hardey achievable in systems where the magnesium pool consists of isotopes with a zero nuclear spin (24Mg, 26Mg). The restoration of mitochondrial ATP synthesis involves the participation of creatine kinase since the activity of the latter does not depend on 1-methyl-nicotine amide. In this case, the high efficiency of this restaration seems to be a spin-selective phenomenon which requires predominantly 25Mg2+ cations. A possible meaning of the data for further studies on the mechanisms of enzymatic catalysis regulation is discussed.     

Modulation of the organization of erythrocyte membrane phospholipids by cytoplasmic ATP. The susceptibility of isoionic human erythrocyte ghosts to attack by detergents and phospholipase C

Human erythrocyte ghosts were prepared in media of physiological ionic composition, and these “isoionic” ghosts were then lysed and resealed in media of varying Ca²⁺, Mg²⁺ and ATP concentrations. The susceptibilities of these ghosts to limited attack by various detergents and by phospholipases C were then compared with the susceptibilities of intact cells to similar attack: attack was assessed by measurements of lysis and of phospholipid hydrolysis. Ghosts were more readily attacked than cells by anionic detergents (cholate, glycocholate, dodecyl sulphate) and by phospholipases C, but Triton X-100 and cetyltrimethylammonium attacked cells and ghosts to the same extent. Mg · ATP^2? partially protected ghosts from attack by the anionic detergents and by the phospholipases C of Bacillus cereus and of Clostridium perfringens. Protection by Mg · ATP^2? occurred only if Mg · ATP^2? had access to the cytoplasmic surface of the membrane. Adenylyl(β-γ-methylene)diphosphonate, a non-hydrolysable ATP analogue, protected as effectively as did Mg · ATP^2?. Internal Mg · ATP^2? caused a marked reduction in the hydrolysis by phospholipases of phosphatidylethanolamine and sphingomyelin, but had no appreciable effect upon the simultaneous hydrolysis of phosphatidylcholine. It therefore seems that interaction of ATP with sites on the cytoplasmic surface of the erythrocyte membrane can, without ATP hydrolysis, cause changes in the organization of the outer surface of the membrane that specifically render phosphatidylethanolamine and sphingomyelin less accessible to attack by extracellular phospholipases.     

An Industry-Scale Mass Marking Technique for Tracing Farmed Fish Escapees

Farmed fish escape and enter the environment with subsequent effects on wild populations. Reducing escapes requires the ability to trace individuals back to the point of escape, so that escape causes can be identified and technical standards improved. Here, we tested if stable isotope otolith fingerprint marks delivered during routine vaccination could be an accurate, feasible and cost effective marking method, suitable for industrial-scale application. We tested seven stable isotopes, ¹³⁴Ba, ¹³⁵Ba, ¹³⁶Ba, ¹³⁷Ba, ⁸⁶Sr, ⁸⁷Sr and ²⁶Mg, on farmed Atlantic salmon reared in freshwater, in experimental conditions designed to reflect commercial practice. Marking was 100% successful with individual Ba isotopes at concentrations as low as 0.001 µg. g^-1 fish and for Sr isotopes at 1 µg. g^-1 fish. Our results suggest that 63 unique fingerprint marks can be made at low cost using Ba (0.0002 – 0.02 $US per mark) and Sr (0.46 – 0.82 $US per mark) isotopes. Stable isotope fingerprinting during vaccination is feasible for commercial application if applied at a company level within the world’s largest salmon producing nations. Introducing a mass marking scheme would enable tracing of escapees back to point of origin, which could drive greater compliance, better farm design and improved management practices to reduce escapes.     

Dissociation between Ca2+-ATPase and alkaline phosphatase activities in plasma membranes of rat duodenum

The presence of Ca²⁺-ATPase activities with high-affinity sites for Ca²⁺ in brush border as well as basolateral plasma membranes of rat duodenal epithelium has been reported previously (Ghijsen, W.E.J.M. and van Os, C.H. (1979) Nature 279, 802–803). Since both plasma membranes contain alkaline phosphatase (EC 3.1.3.1), which also can be stimulated by Ca²⁺, the substrate specificity of Ca²⁺-induced ATP-hydrolysis has been studied to determine whether or not alkaline phosphatase and Ca²⁺-ATPase are two distinct enzymes. In basolateral fragments, the rate of Ca²⁺-dependent ATP-hydrolysis was greater than that of ADP, AMP and $\text{p-}\text{nitrophenylphosphate}$ at Ca²⁺ concentrations below 25 μM. At 0.2 mM Ca²⁺ the rates of ATP, ADP, AMP and $\text{p-}\text{nitrophenylphosphate}$ hydrolysis were not significantly different. In brush border fragments the rates of ATP, ADP and AMP hydrolysis were identical at low Ca²⁺, but at 0.2 mM Ca²⁺, Ca²⁺-induced hydrolysis of ADP and AMP was greater than either ATP or $\text{p-}\text{nitrophenylphosphate}$. Alkaline phosphatase in brush border and basolateral membranes was inhibited by 75% after addition of 2.5 mM theophylline. Ca²⁺-stimulated ATP hydrolysis at 1 μM Ca²⁺ was not sensitive to theophylline in basolateral fragments while the same activity in brush border fragments was totally inhibited. At 0.2 mM Ca²⁺, Ca²⁺-induced ATP hydrolysis in both basolateral and brush border membranes was sensitive to theophylline. Oligomycin and azide had no effect on Ca²⁺-stimulated ATP hydrolysis, either at low or at high Ca²⁺ concentrations. Chlorpromazine fully inhibited Ca²⁺-stimulated ATP hydrolysis in basolateral fragments at 5 μM Ca²⁺, while it had no effect in brush border fragments. From these results we conclude that, (i) Ca²⁺-ATPase and alkaline phosphatase are two distinct enzymes, (ii) high-affinity Ca²⁺-ATPase is exclusively located in basolateral plasma membranes, (iii) alkaline phosphatase activity, present on both sides of duodenal epithelium, is stimulated slightly by low Ca²⁺ concentrations, but this Ca²⁺-induced activity is inhibited by theophylline and shows no specificity with respect to ATP, ADP or AMP.     

The regulation of the rate of ATP hydrolysis by H-meromyosin

The effect of N-ethylmaleimide on the ATPase activity and ADP binding of tryptic H-meromyosin was studied at 6 and 23 °C temperatures. The affinity constant of H-meromyosin for ADP with Mg as activator was increased by small concentrations of N-ethylmaleimide (2.25 moles per mole of enzyme) at both temperatures, accompanied by activation of ATP hydrolysis at 25 °C and inhibition at 6 °C. With higher N-ethylmaleimide concentrations, the ATPase activity was inhibited at both temperatures, without comparable inhibition of ADP binding. Rapid kinetic analysis of the rate of development of difference spectrum after the addition of ATP or ADP to H-meromyosin indicates, that blocking of the S₁ and S₂ SH groups of H-meromyosin decreases both the formation (k₁) and the dissociation (k₂) rate constants of H-meromyosin substrate complex. At 6 °C, in the presence of Mg, the value of k₂ for ADP is similar to the turnover number of ATP hydrolysis, suggesting that dissociation of ADP from the active site may be the rate-limiting step of ATP hydrolysis. At 23 °C, the turnover number of Mg-moderated ATP hydrolysis is much smaller than k₂, indicating that the rate limitation shifted so another, so far unidentified, step.