Identification of the catalytic mechanism and estimation of kinetic parameters for fumarase

Abstract

The enzyme fumarase catalyzes the reversible hydration of fumarate to malate. The reaction catalyzed by fumarase is critical for cellular energetics as a part of the tricarboxylic acid cycle, which produces reducing equivalents to drive oxidative ATP synthesis. A catalytic mechanism for the fumarase reaction that can account for the kinetic behavior of the enzyme observed in both isotope exchange studies and initial velocity studies has not yet been identified. In the present study, we develop an 11-state kinetic model of the enzyme based on the current consensus on its catalytic mechanism and design a series of experiments to estimate the model parameters and identify the major flux routes through the mechanism. The 11-state mechanism accounts for competitive binding of inhibitors and activation by different anions, including phosphate and fumarate. The model is identified from experimental time courses of the hydration of fumarate to malate obtained over a wide range of buffer and substrate concentrations. Further, the 11-state model is found to effectively reduce to a five-state model by lumping certain successive steps together to yield a mathematically less complex representation that is able to match the data. Analysis suggests the primary reaction route of the catalytic mechanism, with fumarate binding to the free unprotonated enzyme and a proton addition prior to malate release in the fumarate hydration reaction. In the reverse direction (malate dehydration), malate binds the protonated form of the enzyme, and a proton is generated before fumarate is released from the active site.

FIGURE 1.

Possible reaction mechanisms for fumarase. A, five-state reversible mechanism proposed by Hansen et al. (2), including the requisite addition and release steps for malate (M), fumarate (F), hydroxyl (OH⁻), and proton (H⁺) and two alternative pathways for binding-release of fumarate and one for malate. Subscripts 1, 2, and 3 denote free, malate-bound, and fumarate-bound unprotonated enzyme, respectively; states 4 and 5 correspond to free and fumarate-bound protonated enzyme, respectively. B, six-state reversible mechanism, including an additional protonated enzyme-malate complex E₆ (3). Both fumarate and malate can either bind to the protonated or to the unprotonated enzyme. C, 11-state reversible mechanism adapted from Rose et al. (6), including isomechanism-isomerization steps to account for the substrate specificity of the enzyme form and the recycling process. Subscripts f and m denote fumarate and malate specificity, respectively.

FIGURE 2.

A, 11-state reversible catalytic mechanism adapted from Rose et al. (6), accounting for the isomechanism for enzyme recycling with first-order rate constants. Subscripts f and m denote fumarate and malate specificity, respectively. Dashed line boxes indicate states that are lumped through quasi-equilibrium assumptions. Dead end competitive binding of fumarate and phosphate are not represented. B, six-state model obtained from applying quasi-equilibrium assumptions to the 11-state model in A.

FIGURE 3.

Fumarate concentration versus time for the fumarase-catalyzed hydration of fumarate to malate, at 25 °C, pH ∼6.78, in five different phosphate buffer concentrations (1, 3.2, 10, 32, and 100 mm P_i from top to bottom). For each of the five phosphate concentrations, four different initial fumarate concentrations were tested (∼0.1–100 mm from left to right). The gray shaded bars indicate means ± S.E. of the experimental data; the solid black lines are optimum model fits; and the dashed lines correspond to model fits obtained from using average parameter values (n = 3–6).

FIGURE 4.

Fumarate concentration versus time for the fumarase-catalyzed hydration of fumarate to malate, at 25 °C, 100 mm phosphate, and two different pH values (pH 6 and 8). For each of the pH values, four different initial fumarate concentrations were tested (∼0.1–100 mm from top to bottom). The gray shaded bars indicate means ± S.E. of the experimental data; the solid black lines are model fits; and dashed lines correspond to model fits obtained from using average parameter values (n = 3–6).

FIGURE 5.

Primary routes for both forward (F → M) and reverse (M → F) reactions, along with associated relative net fluxes for each individual pathway. Approximate physiological conditions are used (pH 7, 1 mm fumarate (f) or malate (m) and 1 mm P_i).

FIGURE 6.

Reduced five-state mechanism adapted from the model of Fig. 2B. The pathway implicating the free unbound enzyme state E_1m is neglected. The identified inhibition pattern is also illustrated.

FIGURE 7.

Predictions of the quasi-steady-state net flux of the forward reaction as a function of pH, at 25 °C, 133 mm P_i, for several values of fumarate concentration (1–13.33 mm, as indicated).