Precise, facile initial rate measurements

Abstract

Progress curve analysis has been used sparingly in studies of enzyme-catalyzed reactions due largely to the complexity of the integrated rate expressions used in data analysis. Using an experimental design that simplifies the analysis, the advantages and limitations of progress curve experiments are explored in a study of four different enzyme-catalyzed reactions. The approach involves relatively simple protocols, requires 20-25% of the materials, and provides 10- to 20-fold signal enhancements compared to analogous initial rate studies. Product inhibition, which complicates integrated rate analysis, was circumvented using cloned, purified enzymes that remove the products and draw the reaction forward. The resulting progress curves can be transformed into the equivalent of thousands of initial rate and [S] measurements and, due to the absence of product inhibition, are plotted in the familiar, linear double-reciprocal format. Allowing product to accumulate during a reaction produces a continuously changing substrate/product ratio that can be used as the basis for obtaining product inhibition constants and to distinguish among the three classical inhibition mechanisms. Algebraic models describing the double-reciprocal patterns obtained from such inhibition studies are presented. The virtual continuum of substrate concentrations that occurs during a progress curve experiment provides a nearly errorless set of relative concentrations that results in remarkably precise data; kinetic constant standard deviations are on the order of 0.5%.

Figure 1

Initial rate and double-reciprocal progress curve studies of the phosphomevalonate kinase reaction. (A) Double-reciprocal plot of the data obtained using both methods. The thick, solid line represents a progress curve in which phosphomevalonate is consumed and [ATP] is held fixed at 5.0 mM using a regenerating system. The open circles represent the results of a study in which initial rates were obtained at each of four phosphomevalonate concentrations (100, 20, 11, and 7.7 μM); [ATP] = 5.0 mM (36K_m). Straight lines through the data represent the behavior predicted by the best-fit parameters (see Table 1) obtained from a weighted fit of the progress curve data to a sequential model (see Materials and Methods). Experiments were performed in triplicate. The assay composition and conditions were as follows: phosphomevalonate kinase (0.05 μM), phosphomevalonate decarboxylase (0.60 U/ml), lactate dehydrogenase (10 U/ml), pyruvate kinase (25 U/ml), phosphomevalonate (0.08 mM), ATP (5.0 mM), PEP (1.0 mM), NADH (0.30 mM), MgCl₂ (6.0 mM), KCl (50 mM), Hepes (50 mM, pH = 8.0/K⁺), T = 25 ± 2°C. The reactions were monitored at 339 nm and initiated by addition of phosphomevalonate kinase. Data processing is described in Materials and Methods. (B) Close-up of the initial rate results.

Figure 2

Initial rate and double-reciprocal progress curve study of the pyruvate-kinase-catalyzed reaction. Thick, solid lines represent progress curves in which PEP was consumed and ADP was held fixed, at the four concentrations indicated, using a regenerating system. Open circles represent the results of initial rate measurements taken at four different concentrations of PEP (200, 50, 29, and 20 μM); [ADP] = 500 μM (3.7K_m). The lines through the data represent the behavior predicted by the best-fit constants (see Table 1) obtained from a weighted fit of the progress curve data to a model for a sequential mechanism (see Materials and Methods). The composition and conditions of the assay were as follows: pyruvate kinase (0.030 U/ml), hexokinase (4.8 U/ml), lactate dehydrogenase (2.0 U/ml), ADP (at the indicated concentrations), PEP (0.20 mM), NADH (0.30 mM), glucose (1.0 mM), KCl (100 mM), MgCl₂ (2.0 mM), Hepes (50 mM, pH = 8.0/K⁺), T = 25 ± 2°C. The reactions were initiated by the addition of ATP and monitored at 339 nm. Experiments were performed in triplicate.

Figure 3

Double-reciprocal progress curve study of the hexokinase-catalyzed reaction. (A) The thick, solid lines represent progress curves in which glucose is consumed and ADP is held fixed, at the concentrations indicated, using a regenerating system. The lines through the data represent the behavior predicted by the best-fit parameters (see Table 1) obtained from a weighted, least-squares fit to a model for a sequential mechanism (see Materials and Methods). The experiments were performed in triplicate and averaged. The composition and conditions of the assay were as follow: hexokinase (0.030 U/ml), pyruvate kinase (4.0 U/ml), glucose-6-phosphate dehydrogenase (6.0 U/ml), glucose (1.5 mM), ATP (at the concentrations indicated), NADP⁺ (1.8 mM), PEP (2.0 mM), MgCl₂ (1.5 mM), Hepes (50 mM, pH = 8.0/K⁺), T = 25 ± 2°C. The detection wavelength, 390 nm, was shifted away from the absorbance maximum to avoid high background. (B) The point of intersection.

Figure 4

Competitive product inhibition study: the ATP sulfurylase-catalyzed hydrolysis of GTP. (A) The thick, solid lines represent progress curves in which GTP is consumed and GDP, a competitive inhibitor, is allowed to accumulate. Lines through the data represent the behavior predicted by the best-fit parameters obtained from a weighted fit to a competitive inhibition model (see Materials and Methods). Phosphate was removed, and the optical signal used to monitor the reaction was generated using purine nucleoside phosphorylase with MESG as a substrate. The experiments were preformed in triplicate and averaged. The composition and conditions of the assay were as follows: ATP sulfurylase (0.50 μM), purine nucleoside phosphorylase (1.0 U/ml), GTP (at the concentrations indicated), MESG (0.90 mM), MgCl₂ (3.0 mM), AMP (2.0 mM), T = 25 ± 2°C. The reactions were initiated by addition of ATP sulfurylase and monitored at 360 nm. (B) The 1/υ axis close-up.