What Does the Brønsted Slope Measure in the Phosphoryl Transfer Transition State?

Abstract

The structural and energetic features of phosphate and phosphonate hydrolysis in Protein Phosphatase-1 (PP1) and water are studied using quantum mechanical (QM) cluster models. The calculations are able to reproduce observed kinetic isotope effects and capture several key trends in the experimental Brønsted plots: the ${\beta }_{lg}$ values are rather different for phosphate and phosphonate ester hydrolysis in solution but are similar in PP1. Detailed analyses of structure, charge distribution and bond order of computed transition states support the general conclusion from experimental study that phosphoryl transfer transition states are different for the two classes of substrates in solution but similar in PP1. On the other hand, the microscopic models also highlight notable differences between the phosphate and phosphonate transition states, which are manifested in not only structure but also kinetic isotope effects. Overall, we find that while ${\beta }_{lg}/{\beta }_{EQ,lg}$ generally correlates with the partial charge on leaving group oxygen and the fractional bond order of the breaking P- ${\text{O}}_{lg}$ bond, the precise mapping between ${\beta }_{lg}/{\beta }_{EQ,lg}$ and P- ${\text{O}}_{lg}$ bond order in the transition state is difficult due largely to the cross talk between breaking and forming P-O bonds. Therefore, further supporting previous analyses of limitations of free energy relations, our results suggest that while free energy relation is a valuable tool for probing the nature of transition state, a quantitative mapping of ${\beta }_{lg}$ and ${\beta }_{lg}/{\beta }_{EQ,lg}$ values to structure or charge in the transition state should be conducted with great care.

Keywords: Brønsted slope; free energy relation; phosphoryl transfer; quantum mechanical cluster models; transition state.

Figure 1:

The overall structure of Protein Phosphatase-1 (PP1) and its active site: the nucleophile is a hydroxide bound to two Mn²⁺ ions, and the substrate shown is para-nitrophenyl phosphate.

Figure 2:

Examples for the key structures of phosphate (left column) and phosphonate (right column) hydrolysis in water with hydroxide as the nucleophile. RS, TS and PS represent reactant state, transition state and product state, respectively. Bond lengths for P-O_nuc and P-${\text{O}}_{lg}$ (in Å) optimized from B3LYP-D3/CPCM calculations are shown.

Figure 3:

Same as Fig. 2, but with neutral water as the nucleophile. A solvent-assisted mechanism is followed here as recent computational studies suggested that it is the favorable reaction pathway in solution;^, note that the nucleophilic water in the product state of phosphonate hydrolysis spontaneously deprotonates, leading to the formation of a hydronium ion nearby.

Figure 4:

Approximate Brønsted plots for the hydrolysis of (a) arylphosphate (PP) and (b) arylphosphonate (PMP) esters listed in Scheme 2 in water. The rate constants (k) are estimated using transition state theory by $\frac{k_{B}T}{h}exp\left[-\mathrm{\Delta }{G}^{{}^{‡}}/k_{B}T\right]$, and the pK_as are experimental values for the leaving groups; thermal contributions to ΔG^‡ are calculated using the harmonic-oscillator-rigid-rotor approximations.

Figure 5:

Same as Fig. 4, but for the arylphosphate (PP) and arylphosphonate (PMP) substrates hydrolysis in PP1.

Figure 6:

Comparison of (a-c) P-O distances and (d) fractional bond orders (fBOs) for optimized transition states structures in PP1 and water using QM cluster models: for the substrates, PP denotes phenyl phosphate, and PMP denotes phenyl phosphonate. For the case of phosphate hydrolysis in water with water as the nucleophile, the “product state” studied here corresponds to the intermediate state in the solvent assisted mechanism^, and thus has a weak P −O_nuc bond; the fBO results labeled as “PP-Nuc_water” are calculated using P-O_nuc Wiberg bond order in the product state when hydroxide is the nucleophile as the reference value. In (a-b), optimized P-${\text{O}}_{lg}$ and P-O_nuc distances in the transition state are plotted against the experimental pK_a values of the leaving group; in (c), the optimized P-${\text{O}}_{lg}$ and P-O_nuc distances in the transition state are plotted against each other, and in (d), the fBOs values for P-${\text{O}}_{lg}$ and P-O_nuc in the transition state are plotted against each other for the different substrates in water and in PP1.

Figure 7:

Examples of optimized transition state structures with cluster models for PP1 with (a) phosphate and (b) phosphonate ester substrates. The cases shown correspond to leaving groups with the lowest and highest pK_a values studied here. The results highlight that phosphate and phosphonate transition state structures respond differently to the nature of the leaving group.

Scheme 1:

Phosphate monoester hydrolysis through a concerted pathway: bond formation to the nucleophile and bond cleavage to the leaving group occur simultaneously but not necessarily synchronously.

Scheme 2:

Aryl Phosphate and aryl methylphosphonate substrates studied in this work.