Fig. 2

a Reactant, transition state (TS), and product structures showing ATP, Mg²⁺ (in green), and the sidechain of Glu-33 (E33), extracted from QM/MM calculations of the ATP-hydrolysis reaction. QM/MM free-energy profiles were calculated with the Arg-32/Glu-33 ion pair closed (black, r_R32-E33 < 5 Å) and open (blue, r_R32-E33 > 5 Å, see Fig. 3), as well as for the R32A mutant (red). b The reaction coordinate used for QM/MM calculations is R = r₄ − r₃ + r₂ − r₁, a linear combination of distances between Glu-33, the attacking water molecule, and the γ-phosphate of ATP. r₂ – r₁ is the difference between the bond-breaking (r₂) and bond forming (r₁) distances for the proton transfer from the water molecule to Glu-33. r₄ – r₃ is the difference between the bond-breaking (r₄) and bond forming (r₃) distances for the phosphate cleavage^{27, 28}. The reaction coordinate was optimized from reactants (R = −2.9 Å) to products (R = 2.6 Å). c Semi-concerted ATP-hydrolysis mechanism from QM/MM free-energy calculations (red dots) and during reaction path optimization (blue dots), showing the sampled reaction coordinates with the Arg-32/Glu-33 ion pair closed. The transition state (TS) of the reaction path optimization is marked with a black circle.