Carbon Acidity in Enzyme Active Sites

Abstract

The pK_a values for substrates acting as carbon acids (i.e., C-H deprotonation reactions) in several enzyme active sites are presented. The information needed to calculate them includes the pK_a of the active site acid/base catalyst and the equilibrium constant for the deprotonation step. Carbon acidity is obtained from the relation pK_eq = p ${\text{K}}_{\text{a}}^{\text{r}}$ -p ${\text{K}}_{\text{a}}^{\text{p}}$ = ΔpK_a for a proton transfer reaction. Five enzymatic free energy profiles (FEPs) were calculated to obtain the equilibrium constants for proton transfer from carbon in the active site, and six additional proton transfer equilibrium constants were extracted from data available in the literature, allowing substrate C-H pK_as to be calculated for 11 enzymes. Active site-bound substrate C-H pK_a values range from 5.6 for ketosteroid isomerase to 16 for proline racemase. Compared to values in water, enzymes lower substrate C-H pK_as by up to 23 units, corresponding to 31 kcal/mol of carbanion stabilization energy. Calculation of Marcus intrinsic barriers (Δ ${\text{G}}_0^{\text{‡}}$ ) for pairs of non-enzymatic/enzymatic reactions shows significant reductions in Δ ${\text{G}}_0^{\text{‡}}$ for cofactor-independent enzymes, while pyridoxal phosphate dependent enzymes appear to increase Δ ${\text{G}}_0^{\text{‡}}$ to a small extent as a consequence of carbanion resonance stabilization. The large increases in carbon acidity found here are central to the large rate enhancements observed in enzymes that catalyze carbon deprotonation.

Keywords: PKA; carbanion stability; carbon acid; enzyme; general acid/base catalysis; marcus theory; pyridoxal phosphate.

Scheme 1

C-H pK calculation for Alanine Racemase.

Figure 1

Results of global optimization with KSI. SSR, sum of squared residuals of the fit to the target function. Each point results from an independent optimization run. The figure was generated from ~100,000 independent runs, each starting from randomized sets of rate constants. The inset presents the intrinsic KIE resulting from global optimization.

Scheme 2

Definition of the Marcus intrinsic barrier.

Figure 2

Results of global optimization with mandelate racemase. SSR, sum of squared residuals of the fit to the target function. Each point results from an independent optimization run. The figure was generated from ~40,000 independent runs, each starting from randomized sets of rate constants. The inset presents the intrinsic kinetic isotope effect resulting from global optimization. The fit to the target function is shows significant sensitivity to the values of k₄ and k₅ when they are < 10⁶ s⁻¹. Therefore, these are the lower limits on the values of these rate constants.

Figure 3

Results of global optimization with fumarase. SSR, sum of squared residuals of the fit to the target function. The figure was generated from ~40,000 independent runs, each starting from randomized sets of rate constants. The fit to the target function is shows significant sensitivity to the values of k₄ and k₅ when they are < 10⁷ s⁻¹ and < 10⁸ s⁻¹. Therefore, these are the lower limits on the values of these rate constants.

Figure 4

Results of global optimization for the L-asp/oxalacetate half-reaction of aspartate aminotransferase. SSR, sum of squared residuals of the fit to the target function. The figure was generated from ~40,000 independent runs, each starting from randomized sets of rate constants. The insets show that the correlation between the association and dissociation rate constants for L-Asp binding. The individual rate constants are not well-determined, but their ratio is over a broad range of values, indicating rapid equilibrium binding. The observed ratio of the rate constants is 4.8mM, which is the K_M value for L-Asp. The intrinsic KIE calculated in the global optimization is also presented as an inset.

Figure 5

Results of global optimization for the L-Ala/pyruvate half-reaction of dialkylglycine decarboxylase. SSR, sum of squared residuals of the fit to the target function. The figure was generated from ~40,000 independent runs, each starting from randomized sets of rate constants. The inset shows the ratios of the association and dissociation rate constants for both L-Ala and pyruvate binding. The linear correlation over a very large range of values indicates rapid equilibrium binding of both.