Mathematical Modeling of Kinetics of Adenosine 5"-Triphosphate Hydrolysis Catalyzed by the Zn2+ Ion in the pH Range 7.4–8.3

Kinetic data on adenosine triphosphate (ATP) hydrolysis catalyzed by the Zn²⁺ ion in the pH range 7.4–8.3 are analyzed by the method of numerical simulation. The rates of forward and reverse reactions of isomeric conversion of the open conformation of ZnATP^2– (Op), which is inactive in hydrolysis to ADP, to the active cyclic conformation ZnATP^2– (Cy) in the specified range of pH are proportional to the concentration of H₃O⁺ and characterized by the same rate constants as in the range of pH above 8.5. The mechanism of the isomeric conversion Op Cy involves the formation of a pentacovalent state at -P, pseudorotation, and the abstraction of OH^– from -P of the pentacovalent intermediate with the participation of H₃O⁺ in a slow step. The sequence of steps for the formation and transformation of intermediates, which was established earlier for the ZnATP^2– associates in the pH range 7.1–7.4, is applicable to this range of pH as well. In the analyzed range of pH, the contributions from the pH-independent channel of hydrolysis of the ZnATP^2– associates and the pH-dependent channel of CyOH^– and Op(OH^–)₂ species, which determine the formation of ADP and AMP at pH > 8.5, are comparable. Changes in the concentrations of intermediate products (monomeric and associates) in the course of hydrolysis are described. General base catalysis by a nitrogen base in the steps of formation of active centers for hydrolysis, the general acid catalysis of a coordinated water molecule, the exchange of medium OH^– with OH of -phosphate, the catalysis of conversion of the inactive conformation ZnATP^2– to the active one by a proton, and a change of the rate-limiting stage of hydrolysis with a change in pH indicate the enzyme-like mechanism of the reaction.     

Mathematical modeling of kinetics of adenosine-5’-triphosphate hydrolysis catalyzed by the Zn2+ ion in the pH range 8.5–9.0

The kinetics of adenosine-5’-triphosphate (ATP) hydrolysis catalyzed by Zn²⁺ at pH 8.5–9.0 is analyzed by numerical simulation. The rates of product formation (adenosine diphosphate (ADP) and adenosine monophosphate (AMP)) are determined by a conformational transformation. In the sequence of steps of mutual transformations of cyclic (Cy) pH-dependent species, which are active in ATP hydrolysis to ADP, and open (Op) species, the rate-limiting step is the slow isomerization of ZnATP²-complexes. This slow step is determined by the abstraction of the OH^- group from a pentacovalent intermediate catalyzed by H₃O⁺. In the Op species,Zn ²⁺ is bound to the phosphate chain. In the Cy species, which can be hydrolized to ADP, Zn²⁺ coordinates a nitrogen atom in position 7 and γ-phosphate. The mutual transformations of conformers occur via pentacovalent intermediates with the participation of γ-phosphorus and include pseudotransformations. In the direct transformation CyOH^-⦚r OpOH^-, pseudotransformation is a rate-controlling step. The deprotonated open monomeric form OpOH^- is inactive in hydrolysis. Within the framework of the dimeric model and a more complex model that accounts for the role of trimeric associates ZnATP^2-, the general scheme of intermediate transformations is considered that accounts for the existence of a pH-independent pathway of hydrolysis. The rate and equilibrium constants are estimated. Concentration profiles for intermediate products during hydrolysis are described.     

Kinetics and mechanism of adenosine 5′-triphosphate hydrolysis catalyzed by the Cu2+ ion: The role of conformation and the catalytic effect of the OH− ion

The kinetics of 5′-ATP hydrolysis catalyzed by the Cu²⁺ ion has been investigated by HPLC in the pH range 5.6–7.8 at 25°C. Two series of experiments differing in the initial [Cu · ATP]₀ (1: 1) concentration have been carried out. The reaction was being conducted up to ≈40% ATP conversion. The (CuATP^2?)₂OH^??ub;DOH^??ub; complex, which consists of two monomeric Cy(CuATP^2?) molecules (in which the N7 atom and the γ-phosphate group are coordinated to Cu²⁺), is responsible for the formation of CuADP^? + P_i (P_i is an inorganic phosphate). The highest possible DOH^? concentration at a given pH is reached at the initial stage of hydrolysis. The pH value at which the highest initial rate of ADP formation is reached (pH_max (w _{0, ADP})) decreases as the D concentration increases. At pH > pH_max, the decrease in the ADP formation rate in the course of the processes is pH-independent and, once an ATP conversion of 20–26% is reached, hydrolysis proceeds in a steady-state regime such that ADP and AMP form from ATP by parallel reactions. The participation of the OH^? ion in the catalysis of the formation of hydrolysis intermediates is considered.     

Influence of additional metal ions on the ratio of the rates of intermediate product transformations in the hydrolysis of adenizine-5′-triphosphoric acid catalyzed by divalent Cu ions

It was shown earlier that the hydrolysis of the (CuATP²⁻)₂ dimeric complex to CuADP⁻ and inorganic phosphate P _i was an irreversible reaction. The main intermediate hydrolysis product, the formation of which should be taken into account at comparatively early hydrolysis stages, was the IntK pentacovalent intermediate. It was formed in parallel with hydrolysis to CuADP⁻ and P _i through the common intermediate product (CuATP²⁻)₂OH⁻ — DOH⁻. We studied the influence of the addition of various concentrations of Mg²⁺ ions to the reaction mixture at pH 7.1–7.2, a range for which the kinetics of hydrolysis is sensitive to the rate constants of deactivation of DOH⁻ active centers (conjugated with CuADP⁻ formation and occurring via the formation of IntK). The conversion of ATP above which stationary hydrolysis regime was observed decreased as the concentration of Mg²⁺ grew. The DOH⁻ $ \underset{{OH^ - }}{\overset{{OH^ - }}{\longleftrightarrow}}$ \underset{{OH^ - }}{\overset{{OH^ - }}{\longleftrightarrow}} IntK equilibrium according to the conversion of ATP was established more rapidly, and it was to a greater extent shifted toward IntK. It was assumed that hydrated Mg²⁺ linked as a second metal ion with ATP β and γ phosphate groups hydrated IntK much stronger than DOH⁻. The Cu · OH₂ · AMP complex played the role of a common acid catalyst and hydrated DOH⁻ better than Mg²⁺ · OH₂. The selective hydration of DOH⁻ by the CuOH₂ · AMP complex at early hydrolysis stages directed the process toward the formation of IntK, which caused the appearance of an induction period in the formation of CuADP⁻.     

Catalytic hydrolysis of ATP. pH-Dependence of the selectivity

Kinetic data on ATP^4– hydrolysis in a complex with Zn²⁺ confirm the enzyme-like mechanism of the reaction. Dependence of the selectivity on pH is observed, which is explained by parallel reactions of cyclic and open conformations.     

Influence of additional metal ions on the ratio of conversion rates of intermediate products of the hydrolysis of adenosine-5′-triphosphoric acid catalyzed by the Cu2+ ion: 1. Experimental study of the influence of Mg2+ ions in the ascending branch of the dependence of the initial hydrolysis rate on pH

The hydrolysis of the dimeric complex (CuATP^2?)₂ to CuADP^? and inorganic phosphate P _i is irreversible. The main intermediate hydrolysis product, whose formation should be taken into account at relatively early steps of hydrolysis, is the pentacovalent intermediate IntK formed in parallel with the hydrolysis to CuADP^? and P _i through the common intermediate product (CuATP^2?)₂OH^? (DOH^?) in step 1, which is the replacement of the nucleophile (OH^?) at the Cu²⁺ ion by OH^? at the positively charged phosphorus atom. The influence of the addition of Mg²⁺ ions is studied (depending on their concentration) on the rate constants of step 1 in the region of pH in the ascending branch of the dependence of the initial hydrolysis rate on pH at two values of pH: 6.48 and 6.70. This region of pH is sensitive to both the rate constant of DOH^? formation and the rate constants of step 1. The rate constant for the formation of DOH^? from D remains unchanged. An increase in the concentration of Mg²⁺ decreases the value of ATP conversion, above which the stationary hydrolysis regime is observed. The ratio [IntK]/[DOH^?] is higher when the stationary regime is attained. The applicability of the method proposed for the formation of the attacking nucleophile and the proposed sequence of steps to the enzymatic phosphoryl transfer processes is discussed.     

Effect of additional metal ions on the ratio between the rates of the transformation of the intermediate products of the hydrolysis of adenosine-5′-triphosphoric acid catalyzed the Cu2+ ion (Communication 2: Mathematical modeling of the kinetics of the hydrolysis in the presence of additional Mg2+ ions)

It was previously shown that the hydrolysis of the (CuATP^2? · OH₂)₂ dimeric complex to CuADP^? and an inorganic phosphate occurs in a sequence of two rapid and irreversible steps. Along with the hydrolysis through a common intermediate product, (CuATP^2?)₂OH^?-(DOH^?), the OH^? nucleophile at the Cu²⁺ ion is replaced by OH^? at the positively charged phosphorus atom to form an IntK pentacovalent intermediate (step 1). A mathematical modeling of the kinetics of the hydrolysis catalyzed by the Cu²⁺ base metal ion in the presence of additional Mg²⁺ ions at two pH values, 6.48 and 6.71 (at the ascending branch of the dependence of the initial rate of the hydrolysis on the pH value) is performed. Additional ions affect only the pathway of coupling of the conformational conversion of DOH^?. The rate constant for the forward reaction (IntK→ DOH^?), k ₁, increases from 2 · 10⁷ L mol^?1 min^?1 in the absence of Mg²⁺ to 2.9 · 10⁷ L mol^?1 min^?1 upon introduction of Mg²⁺ ions; rate constant of the reverse reaction IntK → DOH→, k ^?1, decreases from 1 · 10⁵ L mol^?1 min^?1 in the absence of Mg²⁺ to 3 · 10⁴ L mol^?1 min^?1 in the presence of Mg²⁺. The relative concentrations of the intermediate products are demonstrated to change during the irreversible hydrolysis. In the presence of Mg²⁺, IntK emerges at much earlier stages of the hydrolysis, the fraction of formed IntK in the balance of NuP₀ is substantially higher, and the growth of its relative concentration with time in the earlier stages of hydrolysis is much more dramatic.     

The role played by pentacovalent intermediates in the sequence of stages of the hydrolysis of 5′-ATP with metal ions

The earlier developed model of irreversible hydrolysis of 5′-ATP catalyzed by the main metal ion Cu²⁺ was used to consider the influence of additional metal ions on the deactivation of active centers conjugated with hydrolysis. It was assumed that conjugation in enzymes occurred through a sequence of stages including the formation of pentacovalent intermediates at early hydrolysis stages and their subsequent slow pseudorotation with the participation of the γ phosphorus atom of the pentacovalent intermediate. From this standpoint, the formal kinetic laws of the hydrolysis of Mg·ATP were analyzed for two enzymes, luciferase from fireflies and nitrogenase Azotobacter vinelandii. The roles played by Mg²⁺ OH⁻ ion formation with the participation of external OH⁻ ions and the selective hydration of intermediate hydrolysis products by a coordinated water molecule of the second metal ion, including the transition metal ion participating in hydrolysis, were considered.