Quantum Mechanical Analysis of Nonenzymatic Nucleotidyl Transfer Reactions: Kinetic and Thermodynamic Effects of β–γ Bridging Groups of dNTP Substrates

Rate (<i>k</i>) and equilibrium (<i>K</i>) constants for the reaction of tetrahydrofuranol with a series of Mg²⁺ complexes of methyl triphosphate analogues, CH₃O-P­(O₂)-O-P­(O₂)-X-PO₃^4–, X = O, CH₂, CHCH₃, C­(CH₃)₂, CFCH₃, CHF, CHCl, CHBr, CFCl, CF₂, CCl₂, and CBr₂, forming phosphate diester and pyrophosphate or bisphosphonate in aqueous solution were evaluated by B3LYP/TZVP//HF/6-31G* quantum chemical calculations and Langevin dipoles and polarized continuum solvation models. The calculated log <i>k</i> and log <i>K</i> values were found to depend linearly on the experimental p<i>K</i>_a4 of the conjugate acid of the corresponding pyrophosphate or bisphosphonate leaving group. The calculated slopes of these Brønsted linear free energy relationships were β_lg = −0.89 and β_eq = −0.93, respectively. The studied compounds also followed the linear relationship Δlog <i>k</i> = 0.8Δlog <i>K</i>, which became less steep, Δlog <i>k</i> = 0.6Δlog <i>K</i>, after the range of studied compounds was extended to include analogues that were doubly protonated on γ-phosphate, CH₃O-P­(O₂)-O-P­(O₂)-X-PO₃H₂^2–. The scissile P_α–O_lg bond length in studied methyl triphosphate analogues slightly increases with decreasing p<i>K</i>_a of the leaving group; concomitantly, the CH₃OP_α(O₂) moiety becomes more positive. These structural effects indicate that substituents with low p<i>K</i>_a can facilitate both P_α–O_lg bond breaking and the P_α–O_nuc bond forming process, thus explaining the large negative β_lg calculated for the transition state geometry that has significantly longer P_α–O_nuc distance than the P_α–O_lg distance