Enhancement of the rate of pyrophosphate hydrolysis by nonenzymatic catalysts and by inorganic pyrophosphatase

Abstract

To estimate the proficiency of inorganic pyrophosphatase as a catalyst, (31)P NMR was used to determine rate constants and thermodynamics of activation for the spontaneous hydrolysis of inorganic pyrophosphate (PP(i)) in the presence and absence of Mg(2+) at elevated temperatures. These values were compared with rate constants and activation parameters determined for the reaction catalyzed by Escherichia coli inorganic pyrophosphatase using isothermal titration calorimetry. At 25 °C and pH 8.5, the hydrolysis of MgPP(i)(2-) proceeds with a rate constant of 2.8 × 10(-10) s(-1), whereas E. coli pyrophosphatase was found to have a turnover number of 570 s(-1) under the same conditions. The resulting rate enhancement (2 × 10(12)-fold) is achieved entirely by reducing the enthalpy of activation (ΔΔH(‡) = -16.6 kcal/mol). The presence of Mg(2+) ions or the transfer of the substrate from bulk water to dimethyl sulfoxide was found to increase the rate of pyrophosphate hydrolysis by as much as ∼ 10(6)-fold. Transfer to dimethyl sulfoxide accelerated PP(i) hydrolysis by reducing the enthalpy of activation. Mg(2+) increased the rate of PP(i) hydrolysis by both increasing the entropy of activation and reducing the enthalpy of activation.

FIGURE 1.

A, rate constants for the hydrolysis of PP_i⁴⁻, PP_i³⁻, PP_i²⁻, and MgPP_i²⁻ were determined in this work. The K_d or pK_a values are shown for each species. The conformation of MgPP_i²⁻ that is shown is the most stable in solution, although not necessarily the reactive species. B, reaction diagram for the proposed enzyme reaction. In the PPase active site, the nucleophilic water molecule is thought to be coordinated by two Mg²⁺ ions, which lower the pK_a of the water molecule, facilitating proton transfer to a base within the active site. The hydrolysis reaction is hypothesized to proceed through an associative mechanism, in which the attack by the nucleophile occurs prior to the phosphate-phosphate bond breaking. In this work, the thermodynamic effect of the two Mg²⁺ ions on water deprotonation was examined.

FIGURE 2.

Arrhenius plots of the rate constants for the hydrolyses of PP_i²⁻ at pH 5.0 (○) and PP_i⁴⁻ in 1 m KOH (▴) and 2 m KOH (△). For comparison, the expected location of an Arrhenius plot of the rate constants for the hydrolysis of PP_i³⁻, determined from the estimated activation parameters, is shown as a dashed line.

FIGURE 3.

Relationship between pH and ΔG^‡ at 25 °C (left panel) or ΔH^‡ (right panel) of PP_i hydrolysis. ΔG^‡ and ΔH^‡ values were estimated from Arrhenius plots obtained at each pH value. The solid lines represent the best fits to Equation 1.

FIGURE 4.

Arrhenius plot of the rate constants for the hydrolysis of MgPP_i²⁻. Data points were obtained under three different sets of experimental conditions: 1 × 10⁻² m Mg²⁺, 2 × 10⁻³ m PP_i, and 1 × 10⁻² m ethyl phosphonate (pH 7.5), measured with ³¹P NMR (green circles); 1 × 10⁻² m Mg²⁺, 2 × 10⁻³ m PP_i, and 2 × 10⁻³ m ethyl phosphonate (pH 8.0), measured with the acid-molybdate assay (blue triangles); and 2 × 10⁻⁴ m Mg²⁺, 2 × 10⁻⁵ m PP_i, and 2 × 10⁻³ m sodium borate (pH 8.7), measured with the acid-molybdate assay (white squares).

FIGURE 5.

Measurement of k_cat using isothermal titration calorimetry. A, the reaction was initiated by injecting 5 × 10⁻³ ml of PP_i into 1.45 ml of reaction mixture (positive spike at 100 s). The upper trace (blue) shows the instrument output in the absence of PPase. When PPase is present in the reaction mixture (lower trace, black), heat is generated in proportion to substrate turnover. The velocity (dP/dt) at any time t was determined using Equation 4. An example of the measurement of dQ/dt is indicated on the plot, and the shaded region represents the total heat released by the reaction. B, velocity measurements were used to generate a continuous Michaelis-Menten plot (solid black line). Data were fit to the Michaelis-Menten equation (red dashed line) using SigmaPlot, from which k_cat and K_m values were extracted.

FIGURE 6.

Arrhenius plot of the rate constants (k_cat) for PP_i hydrolysis by E. coli PPase.

FIGURE 7.

Arrhenius plot of the rate constants for PP_i hydrolysis in DMSO (●) compared with the rate constants for PP_i⁴⁻ hydrolysis in water (○). The rate constants for PP_i hydrolysis in DMSO are for 1 m H₂O and are corrected to reflect the equilibrium between PP_i and PO₄ that was observed under these reaction conditions (see “Results”).

FIGURE 8.

van 't Hoff plot of the equilibrium constants for the formation of MgOH⁺ from MgH₂O²⁺.