Use of progress curves to investigate product inhibition in enzyme-catalysed reactions. Application to the soluble mitochondrial adenosine triphosphatase

A Kinetic Process to Determine the Interaction Type Between Two Compounds, One of Which Is a Reaction Product, Using Alkaline Phosphatase Inhibition as a Case Study

This study describes the development of a new methodology based on a new integrated equation which allows the determination of the kinetic parameters for two mutually non-exclusive inhibitors when one of which is produced during the time-course reaction. Alkaline phosphatase simultaneously inhibited by phosphate and urea is used to illustrate this methodology, including the evaluation of interaction effects between them. Data analyses were carried out using two integrated velocity equations: exclusive linear mixed inhibition (EMI) and non-exclusive linear mixed inhibition (NEMI). Kinetic parameters are estimated using non-linear regression and results show that (i) the interaction between enzyme and the inhibitors urea and phosphate exhibit a mutually non-exclusive behavior; (ii) more specifically, these inhibitors are non-exclusive only in free enzyme (E) species; (iii) the inhibitors also show an interaction with enzyme classified as facilitation; (iv) phosphate is a competitive inhibitor and urea a mixed inhibitor; (v) the inhibition constant for phosphate is much lower than that determined for urea. In addition, a functional Excel Spreadsheet which can be adapted to any kinetic study is also included as a supplement.

Molecular system identification for enzyme directed evolution and design

The rational design of chemical catalysts requires methods for the measurement of free energy differences in the catalytic mechanism for any given catalyst Hamiltonian. The scope of experimental learning algorithms that can be applied to catalyst design would also be expanded by the availability of such methods. Methods for catalyst characterization typically either estimate apparent kinetic parameters that do not necessarily correspond to free energy differences in the catalytic mechanism or measure individual free energy differences that are not sufficient for establishing the relationship between the potential energy surface and catalytic activity. Moreover, in order to enhance the duty cycle of catalyst design, statistically efficient methods for the estimation of the complete set of free energy differences relevant to the catalytic activity based on high-throughput measurements are preferred. In this paper, we present a theoretical and algorithmic system identification framework for the optimal estimation of free energy differences in solution phase catalysts, with a focus on one- and two-substrate enzymes. This framework, which can be automated using programmable logic, prescribes a choice of feasible experimental measurements and manipulated input variables that identify the complete set of free energy differences relevant to the catalytic activity and minimize the uncertainty in these free energy estimates for each successive Hamiltonian design. The framework also employs decision-theoretic logic to determine when model reduction can be applied to improve the duty cycle of high-throughput catalyst design. Automation of the algorithm using fluidic control systems is proposed, and applications of the framework to the problem of enzyme design are discussed.

Enzyme inhibition studies by integrated Michaelis-Menten equation considering simultaneous presence of two inhibitors when one of them is a reaction product

To determine initial velocities of enzyme catalyzed reactions without theoretical errors it is necessary to consider the use of the integrated Michaelis-Menten equation. When the reaction product is an inhibitor, this approach is particularly important. Nevertheless, kinetic studies usually involved the evaluation of other inhibitors beyond the reaction product. The occurrence of these situations emphasizes the importance of extending the integrated Michaelis-Menten equation, assuming the simultaneous presence of more than one inhibitor because reaction product is always present. This methodology is illustrated with the reaction catalyzed by alkaline phosphatase inhibited by phosphate (reaction product, inhibitor 1) and urea (inhibitor 2). The approach is explained in a step by step manner using an Excel spreadsheet (available as a template in Appendix). Curve fitting by nonlinear regression was performed with the Solver add-in (Microsoft Office Excel). Discrimination of the kinetic models was carried out based on Akaike information criterion. This work presents a methodology that can be used to develop an automated process, to discriminate in real time the inhibition type and kinetic constants as data (product vs. time) are achieved by the spectrophotometer.

Quantitative full time course analysis of nonlinear enzyme cycling kinetics

Enzyme inhibition due to the reversible binding of reaction products is common and underlies the origins of negative feedback inhibition in many metabolic and signaling pathways. Product inhibition generates non-linearity in steady-state time courses of enzyme activity, which limits the utility of well-established enzymology approaches developed under the assumption of irreversible product release. For more than a century, numerous attempts to find a mathematical solution for analysis of kinetic time courses with product inhibition have been put forth. However, no practical general method capable of extracting common enzymatic parameters from such non-linear time courses has been successfully developed. Here we present a simple and practical method of analysis capable of efficiently extracting steady-state enzyme kinetic parameters and product binding constants from non-linear kinetic time courses with product inhibition and/or substrate depletion. The method is general and applicable to all enzyme systems, independent of reaction schemes and pathways.

Enzymatic kinetic of cellulose hydrolysis: inhibition by ethanol and cellobiose

The ethanol effect on the Trichoderma reesei cellulases was studied to quantify and clarify this inhibition type. To determine inhibition parameters of crude cellulase and purified exoglucanase Cel7A, integrated Michaelis-Menten equations were used assuming the presence of two inhibitors: cellobiose as the reaction product and ethanol as a possible bioproduct of cellulose fermentation. It was found that hydrolysis of cellulose by crude enzyme follows a model that considers noncompetitive inhibition by ethanol, whereas Cel7A is very slightly competitively inhibited. Crude cellulase is much more inhibited (K(iul) = K(icl) = 151.9 mM) than exoglucanase Cel7A (K(icl) = 1.6 x 1015 mM). Also, calculated inhibition constants showed that cellobiose inhibition is more potent than ethanol inhibition both for the crude enzyme as well as exoglucanase Cel7A.

Triggers of full-length tau aggregation: a role for partially folded intermediates

Alzheimer's disease is characterized in part by the accumulation of full-length tau proteins into intracellular filamentous inclusions. To clarify the events that trigger lesion formation, the aggregation of recombinant full-length four-repeat tau (htau40) was examined in vitro under near-physiological conditions using transmission electron microscopy and spectroscopy methods. In the absence of exogenous inducers, tau protein behaved as an assembly-incompetent monomer with little tertiary structure. The addition of anionic inducers led to fibrillization with nucleation-dependent kinetics. On the basis of circular dichroism spectroscopy and reactivity with thioflavin S and 8-anilino-1-naphthalenesulfonic acid fluorescent probes, the inducer stabilized a monomeric species with the folding characteristics of a premolten globule state. Planar aromatic dyes capable of binding the intermediate state with high affinity were also capable of triggering fibrillization in the absence of other inducers. Dye-mediated aggregation was characterized by concentration-dependent decreases in lag time, indicating increased nucleation rates, and submicromolar critical concentrations, indicating a final equilibrium that favored the filamentous state. The data suggest that the rate-limiting barrier for filament formation from full-length tau is conformational and that the aggregation reaction is triggered by environmental conditions that stabilize assembly-competent conformations.

Comparison of conformational changes and inactivation of soybean lipoxygenase-1 during urea denaturation

The unfolding and inactivation of soybean lipoxygenase-1 during urea denaturation has been compared. Equilibrium study indicates that inactivation of the enzyme occurs at low urea concentrations before significant conformational change of the molecule as a whole. In the presence of 6.0 M urea, the unfolding of soybean lipoxygenase-1, as monitored by fluorescence intensity, is a triphasic process, while the inactivation of the enzyme shows single-phase kinetics. The rate constant of inactivation is consistent with that of the fast conformational change of the enzyme. The results suggest that active sites of lipoxygenase-1 containing iron cofactor are situated in a limited region of the enzyme molecule that is more fragile to denaturants than the protein as a whole. The kinetic theory of substrate reactions catalyzed by unstable enzymes (Duggleby (1986) J. Theor. Biol. 123, 67-80) has been applied to study the effect of substrate on enzyme inactivation. On the basis of the kinetic equation of substrate reaction in the presence of urea, inactivation rate constants for the free enzyme and enzyme-substrate complex have been determined. The substrate, linoleic acid, has no effect on inactivation of the ferric form of lipoxygenase-1.

A novel method for determining kinetic parameters of dissociating enzyme systems

The theoretical analysis has been presented for the kinetics of dissociating-associating enzyme-catalyzed reactions. On the basis of the kinetic equation of substrate reaction, a general procedure is developed for determining the kinetic constants of dissociating-associating enzyme reactions. By analyzing the experimental data of initial velocity and steady-state velocity as functions of enzyme and substrate concentration, all unknown kinetic parameters can be determined from several simple, sequential calculations. This method is simple and rigorous, and the required experiments may also not be difficult for most dissociating enzyme systems. Therefore, the present method should be a useful addition to the available methods for studying subunit dissociation of enzymes. In comparison to other physical methods, the advantage of this method is not only its usefulness in the study of self-associating reactions at very low protein concentration but its convenience in the study of substrate effects on subunit-subunit interactions.

Kinetics of inactivation of bovine pancreatic ribonuclease A by bromopyruvic acid

The kinetic theory of substrate reaction during the modification of enzyme activity [Duggleby (1986) J. Theor. Biol. 123, 67-80; Wang and Tsou (1990) J. Theor. Biol. 142, 531-549] has been applied to a study of the inactivation kinetics of ribonuclease A by bromopyruvic acid. The results show that irreversible inhibition belongs to a non-competitive complexing type inhibition. On the basis of the kinetic equation of substrate reaction in the presence of the inhibitor, all microscopic kinetic constants for the free enzyme, the enzyme-substrate complex and the enzyme-product complex have been determined. The non-competitive inhibition type indicates that neither the substrate nor the product affects the binding of bromopyruvic acid to the enzyme and that the ionization state of His-119 may be the same in both the enzyme-substrate and the enzyme-product complexes.

Enzyme kinetic studies from progress curves

A method is described for fitting the velocities obtained from progress curves to a steady-state rate equation. It is based on the method of Markus & Plesser [(1981) in Kinetic Data Analysis: Design and Analysis of Enzyme and Kinetic Data (Edrenyi, ed.), pp. 317-339, Plenum Press, New York]. The obstacle of needing good initial estimates of kinetic parameters is removed by using the parameters provided graphically by a minor modification of the method of Yun & Suelter [(1977) Biochim, Biophys. Acta 480, 1-13]. This progress-curved-based method allows the same discrimination among rival models as do the initial-velocity-based methods, with a great saving of experimental time. The BASIC and FORTRAN 77 programs are deposited as Supplementary Publication SUP 50132 (17 pages) at the British Library (Lending Division), Boston Spa, Wetherby, West Yorkshire LS23 7BQ, U.K., from whom copies can be obtained on the terms indicated in Biochem. J. (1986) 233, 5-6.

Use of Swinbourne plots to study potential suicide substrates: effects of ATP and ADP on yeast mitochondrial F1-ATPase

A simple analytical procedure for comparing the rates of inactivation of an enzyme in the presence and absence of its substrate is proposed. The rapid inactivation of yeast F1-ATPase during the catalytic reaction was found to be due to certain anions rather than due to ATP or ADP. MgATP failed to protect the enzyme but substituting sulfate, acetate, bicarbonate, or N-tris(hydroxymethyl)methyl-2-aminoethane sulfonate anions and preincubation with ADP prevented the inactivation.

Integrated rate equations for enzyme-catalysed first-order and second-order reactions

Generalized rate equations covering all mechanisms giving hyperbolic initial-rate kinetics with stoichiometry A in equilibrium P, A in equilibrium P + Q, A + B in equilibrium P and A + B in equilibrium P + Q were integrated. The results are regular and reasonably economical.

An easy method for the determination of initial rates

When the Michaelis-Menten equation is obeyed, the rate near the beginning of an enzyme-catalyzed reaction (or of an experiment on transport) can be found accurately from the slope of a chord joining two points on the progress curve. This slope gives the rate at an intermediate concentration. Exact values of this intermediate concentration are easily calculated from equations in the text, and a number of values have also been tabulated. Methods of using two chords to find the initial rate are given. A mid-point formula for numerical differentiation is advocated when the Michaelis-Menten equation does not hold.

The pre-steady state and steady-state kinetics of the ATPase activity of mitochondrial F1

1. The lag time before maximum velocity of ATP hydrolysis is reached upon mixing ATP with F1 is much greater than can be explained by a simple Michaelis-Menten mechanism, and must be due to an activation reaction. The lag time is dependent on the concentration of MgATP (half-maximal at 30 microM) and is equal to 30 ms at infinite MgATP concentration. The initial rate of hydrolysis by nucleotide-depleted F1 is much greater than with normal F1. It is tentatively suggested that the activation reaction with normal preparations is due to replacement of firmly bound ADP by MaATP. 2. After the initial time lag, the reaction follows very closely first-order kinetics provided that the concentration of MgATP is much less than the Km and the reaction is completed within 2 s. This is not expected if the dissociation constant of the enzyme-MgADP complex, an intermediate in the enzymic reaction, is much lower than the Km as has been reported in the literature. The value of V/Km, calculated from the exponential decay, is very close to that calculated from independent measurements of V and Km. 3. The low values for Ki(ADP) reported in the literature were found to be due to a slow (in the order of seconds) formation of an inhibited MgADP-enzyme complex. Dissipation of this inhibited complex by ATP requires seconds. The dissociation constant of the MgADP-enzyme complex that is an intermediate in the enzyme reaction was found to be 150 microM. 4. ADP but not ATP becomes firmly bound to nucleotide-depleted F1 in the absence of Mg2+.

Mitochondrial adenosine triphosphatase from human placenta--purification and catalytic properties

1. The purification of ATPase (EC 3.6.1.3) from human placental mitochondria is described. The yield based on mitochondrial enzyme activity was about 70% and the purification was 380-fold. 2. The rate of Mg-ATP hydrolysis was 85 mumole per min per mg of protein under optimum conditions. 3. Nucleoside triphosphates were hydrolyzed by the purified enzyme at decreasing rates in the following order: GTP greater than ITP greater than ATP greater than epsilon-ATP greater than UTP greater than CTP in Tris-HCl buffer (pH 8.0), and in the order: ATP greater than GTP greater than or equal to ITP greater than epsilon-ATP greater than UTP greater than CTP in Tris-bicarbonate buffer at pH 8.0. 4. The values of kinetic parameters are reported. The ATPase reaction deviated from typical Michaelis-Menten kinetics in Tris-HCl buffer but not in Tris-bicarbonate. Eadie-Hofstee plots for Mg-ATP hydrolysis were biphasic in Tris-HCl (Km = 0.2 mM, 0.09 mM) and monophastic in Tris-becarbonate medium (Km = 0.16 mM). 5. In the presence of Mg-ITP or Mg-GTP as substrates no curvature of the reciprocal plots was observed. 6. The results presented reflect the fact that multiple conformations of the enzyme molecule do exist and are probably involved in its regulatory functions. 7. The existence of two kinetically distinct classes of catalytic sites and of an anion-binding site on the placental ATPase is proposed.

Some spectral and steady-state kinetic properties of Pseudomonas cytochrome oxidase

Some spectra of Pseudomonas cytochrome oxidase are reported, both for comparison with those of other workers and to illustrate the differences between the ascorbate- and dithionite-reduced forms of the enzyme. A spectrum of the reduced enzyme-CO complex, prepared in the absence of added reductants by incubation under CO, is also included. Ultracentrifugation studies yielded a value for the sedimentation coefficient (s20,w) of 7.5S, and an isoelectric point of pH6.9 was determined by isoelectric focusing. Steady-state kinetic constants of the electron donors, quinol, sodium ascorbate, reduced Pseudomonas azurin and Pseudomonas ferrocytochrome c551 were investigated giving Km values of 30mM, 4mM, 49muM and 5.6muM respectively. The two protein substrates were observed to be subject to product inhibition and the Ki for oxidized Pseudomonas azurin was evaluated at 4.9muM. Steady-state kinetics were also used to investigate the effects of the oxidation products of dithionite on the oxidase and nitrite reductase activities of Pseudomonas cytochrome oxidase. These experiments showed that whereas the oxidase activity was inhibited, the nitrite reductase activity was slightly enhanced.

Methods for fitting equations with two or more non-linear parameters

1. Descriptions are given of two ways for fitting non-linear equations by least-squares criteria to experimental data. One depends on solving a set of non-linear simultaneous equations, and the other on Taylor's theorem. 2. It is shown that better parameter estimates result when an equation with two or more non-linear parameters is fitted to all the sets of data simultaneously than when it is fitted to each set in turn.

Kinetic studies on insoluble cellulose-cellulase system

Enzymatic hydrolysis of insoluble amorphous cellulose by Trichoderma viride cellulase was investigated in a batch reactor at several substrate concentrations and three enzyme levels. The reactions were carried out at 50 degrees C and pH 4.8. Enzyme was rapidly adsorbed onto solids on contact, then gradually returned to the liquid phase as the reaction proceeded. A kinetic model that considered the fast adsorption which was followed by the slow reaction, and subsequent product inhibition was developed to interpret the experimental observations. The resulting equation successfully correlated the data for up to 70% conversion. The methods for determining the kinetic parameters are discussed.

The use of the direct linear plot for determining initial velocities

A new method is described for estimating initial velocities of enzyme-catalysed reactions. It is simple to apply either graphically or numerically, and is particularly appropriate for experiments in which the initial straight part of the progress curve is very short or non-existent. It requires no more knowledge than is readily available about the details of the system, such as the extent of reaction at equilibrium, the rate of enzyme inactivation, the nature of product inhibition etc., unlike some other methods of analysing progress curves, which are often invalidated by small errors in the defining assumptions.

Inhibition of the soluble adenosine triphosphatase from mitochondria by adenylyl imidodiphosphate

1. Adenylyl imidodiphosphate is an inhibitor with high affinity for the soluble ATPase (adenosine triphosphatase) from mitochondria. 2. The reaction of the inhibitor with the ATPase is slow and estimates for the association and dissociation reaction rate constants are given. 3. The number of binding sites for the inhibitor appears to be doubled in the presence of 2,4-dinitrophenol. 4. Adenylyl imidodiphosphate is less effective as an inhibitor of the ATPase activity of this enzyme than of the inosine triphosphatase activity. It is also less effective on the ATPase of frozen-thawed or intact mitochondria and did not inhibit ADP-stimulated respiration by intact mitochondria.