Kinetic analysis of the transient phase and steady state of open multicyclic enzyme cascades

This paper presents a kinetic analysis of the whole reaction course, i.e. of both the transient phase and the steady state, of open multicyclic enzyme cascade systems. Equations for fractional modifications are obtained which are valid for the whole reaction course. The steady state expressions for the fractional modifications were derived from the latter equations since they are not restricted to the condition of rapid equilibrium. Finally, the validity of our results is discussed and tested by numerical integration. Apart from the intrinsic value of knowing the kinetic behaviour of any of the species involved in any open multicyclic enzyme cascade, the kinetic analysis presented here can be the basis of future contributions concerning open multicyclic enzyme cascades which require the knowledge of their time course equations (e.g. evaluation of the time needed to reach the steady state, suggestion of kinetic data analysis, etc.), analogous to those already carried out for open bicyclic cascades.     

On the time course of the reversible Michaelis-Menten reaction

The methods of Padé approximants and Euler transformation are used to construct approximate solutions for the time course of the reversible Michaelis-Menten reaction. The solutions are found to describe the concentrations of the various species quite accurately throughout and beyond the transient phase. To illustrate the results, the ratio of the reverse bi-molecular rate constant to the forward bi-molecular rate constant, k2/k1, is varied from 0.1 to 5, and the initial enzyme-to-substrate concentration ratio is changed from 0.01 to 5. Only when k-2/k1 is less than one, the concentration of the intermediate complex, y(t), undergoes a maximum (steady state); for all other values of this ratio, y(t) increases monotonically with time t, to the equilibrium value, i.e. no maximum is attained. The present methods are particularly useful when the total enzyme concentration is comparable to, or greater than the initial substrate concentration, a situation commonly found under in vivo conditions.     

Kinetic analysis of the RNAi enzyme complex

The siRNA-directed ribonucleoprotein complex, RISC, catalyzes target RNA cleavage in the RNA interference pathway. Here, we show that siRNA-programmed RISC is a classical Michaelis-Menten enzyme in the presence of ATP. In the absence of ATP, the rate of multiple rounds of catalysis is limited by release of the cleaved products from the enzyme. Kinetic analysis suggests that different regions of the siRNA play distinct roles in the cycle of target recognition, cleavage, and product release. Bases near the siRNA 5' end disproportionately contribute to target RNA-binding energy, whereas base pairs formed by the central and 3' regions of the siRNA provide a helical geometry required for catalysis. Finally, the position of the scissile phosphate on the target RNA seems to be determined during RISC assembly, before the siRNA encounters its RNA target.     

Kinetic analysis of enzyme systems with suicide substrate in the presence of a reversible, uncompetitive inhibitor.

We present a general kinetic analysis of enzyme catalyzed reactions evolving according to a Michaelis-Menten mechanism, in which an uncompetitive, reversible inhibitor acts. Simultaneously, enzyme inactivation is induced by an unstable suicide substrate, i.e. it is a Michaelis-Menten mechanism with double inhibition: one originating from the substrate and another originating from the reversible inhibitor. Rapid equilibrium of the reversible reaction steps involved is assumed and the time course equations for the reaction product have been derived under the assumption of limiting enzyme. The goodness of the analytical solutions has been tested by comparison with simulated curves obtained by numerical integration. A kinetic data analysis to determine the corresponding kinetic parameters from the time progress curve of the product is suggested.     

Kinetic studies of the reaction of heme-thiolate enzyme chloroperoxidase with peroxynitrite

The kinetics of the reaction of chloroperoxidase with peroxynitrite was studied under neutral and acidic pH by stopped-flow spectrophotometry. Chloroperoxidase catalyzed peroxynitrite decay with the rate constant, k_c, increasing with decreasing pH. The values of k_c obtained at pH 5.1, 6.1 and 7.1 were equal to: (1.96 ± 0.03) × 10⁶, (1.63 ± 0.04) × 10⁶ and (0.71 ± 0.01) × 10⁶ M⁻¹ s⁻¹, respectively. Chloroperoxidase was converted to compound II by peroxynitrite with pH-dependent rate constants: (12.3 ± 0.4) × 10⁶ and (3.8 ± 0.3) × 10⁶ M⁻¹ s⁻¹ at pH 5.1 and 7.1, respectively. After most of peroxynitrite had disappeared, the conversion of compound II into the ferric form of chloroperoxidase was observed. The recovery of the native enzyme was completed within 1 s and 5 s at pH 5.1 and 7.1, respectively. The possible reaction mechanisms of the catalytic decomposition of peroxynitrite by chloroperoxidase are discussed.     

Kinetic analysis of enzyme systems with suicide substrate in the presence of a reversible competitive inhibitor, tested by simulated progress curves

The use of suicide substrates remains a very important and useful method in enzymology for studying enzyme mechanisms and designing potential drugs. Suicide substrates act as modified substrates for the target enzymes and bind to the active site. Therefore the presence of a competitive reversible inhibitor decreases the rate of substrate-induced inactivation and protects the enzyme from this inactivation. This lowering on the inactivation rate has evident physiological advantages, since it allows the easy acquisition of experimental data and facilitates kinetic data analysis by providing another variable (inhibitor concentration). However despite the importance of the simultaneous action of a suicide substrate and a competitive reversible inhibition, to date no corresponding kinetic analysis has been carried out. Therefore we present a general kinetic analysis of a Michaelis-Menten reaction mechanism with double inhibition caused by both, a suicide substrate and a competitive reversible inhibitor. We assume rapid equilibrium of the reversible reaction steps involved, while the time course equations for the reaction product have been derived with the assumption of a limiting enzyme. The goodness of the analytical solutions has been tested by comparison with the simulated curves obtained by numerical integration. A kinetic data analysis to determine the corresponding kinetic parameters from the time progress curve of the product is suggested. In conclusion, we present a complete kinetic analysis of an enzyme reaction mechanism as described above in an attempt to fill a gap in the theoretical treatment of this type of system.     

Kinetic analysis of zymogen autoactivation in the presence of a reversible inhibitor.

Limited proteolysis is a highly specific irreversible process, which can serve to initiate physiological function by converting a precursor protein into a biologically active form. When the activating enzyme and the activated enzyme coincide, the process is an autocatalytic zymogen activation (i.e. reactions in which the zymogens serves as a substrate for the corresponding active enzyme). The activity of proteases is frequently regulated by the binding of specific protease inhibitors. Thus, to understand the biological regulation of proteolysis, one must understand the role of protease inhibitors. In the present study, a detailed kinetic analysis of autocatalytic reaction modulated by a reversible inhibitor is represented. On the basis of the kinetic equation, a novel procedure is developed to evaluate the kinetic parameters of the reaction. As an example of the application of this method, effects of acetamidine, p-amidinobenzamidine and benzamidine on the autoactivation of trypsinogen by trypsin were studied.     

Kinetic analysis of the fluorescence reaction of histamine with orthophthalaldehyde

Histamine reacts with orthophthalaldehyde (OPA) in an alkaline medium to form an unstable fluorescent adduct (F_base). Acidification of the solution gives a stable adduct (F_acid). In order to elucidate the mechanism of this fluorescence reaction, a kinetic study of this reaction was carried out. Although F_base was believed to be the precursor of F_acid, it was shown not to be the precursor of F_acid owing to the effects of the reaction time in an alkaline medium and OPA concentration on the yields of F_base and F_acid. The kinetic analysis of the formation and degradation of F_base revealed the pathway of the fluorescence reaction. On the basis of the results obtained in this study, the mechanism of the fluorescence reaction is proposed.     

Kinetic isotope effect analysis of the ribosomal peptidyl transferase reaction

The ribosome is the macromolecular machine responsible for protein synthesis in all cells. Here, we establish a kinetic framework for the 50S modified fragment reaction that makes it possible to measure the kinetic effects that result from isotopic substitution in either the A or P site of the ribosome. This simplified peptidyl transferase assay follows a rapid equilibrium random mechanism in which the reverse reaction is nonexistent and the forward commitment is negligible. A normal effect (1.009) is observed for (15)N substitution of the incoming nucleophile at both low and high pH. This suggests that the first irreversible step is the formation of the tetrahedral intermediate. The observation of a normal isotope effect that does not change as a function of pH suggests that the ribosome promotes peptide bond formation by a mechanism that differs in its details from an uncatalyzed aminolysis reaction in solution. This implies that the ribosome contributes chemically to catalysis of peptide bond formation.     

Thermodynamically consistent Bayesian analysis of closed biochemical reaction systems

Background  

Estimating the rate constants of a biochemical reaction system with known stoichiometry from noisy time series measurements of molecular concentrations is an important step for building predictive models of cellular function. Inference techniques currently available in the literature may produce rate constant values that defy necessary constraints imposed by the fundamental laws of thermodynamics. As a result, these techniques may lead to biochemical reaction systems whose concentration dynamics could not possibly occur in nature. Therefore, development of a thermodynamically consistent approach for estimating the rate constants of a biochemical reaction system is highly desirable.     

Kinetic analysis of enzyme reactions with slow-binding inhibition.

In this paper we present a general kinetic study of slow-binding inhibition processes, i.e. enzyme reactions that do not respond instantly to the presence of a competitive inhibitor. The analysis that we present is based on the equation that describes the formation of products with time in each case on the experimental progress curve. It is carried out under the condition of limiting enzyme concentration and allows the discrimination between the different cases of slow-binding inhibition. The mechanism in which the formation of complex enzyme-inhibitor is a single or two slow steps or follow a rapid equilibrium, has been considered. The corresponding explicit equations of each case have been obtained and checked by numerical integration. A kinetic data analysis to evaluate the corresponding kinetic parameters is suggested. We illustrate the method, numerically by computer simulation, of the reaction and present some numerical examples that demonstrate the applicability of our procedure.     

Kinetic analysis of enzyme inactivation by an autodecaying reagent

A simple method is described for the determination of both the pseudo-first-order rate constant and the second-order rate constant for enzyme inactivation by a chemical reagent which itself undergoes exponential decay. The validity of this method has been demonstrated in two test cases in which the labile diethyl pyrocarbonate was used to inactivate salicylate hydroxylase and bacterial luciferase.