Ill-conditioning associated with the "end-point" method for the determination of kinetic parameters describing irreversible enzyme inactivation by an unstable inhibitor

Study of the complete time-course of irreversible enzyme inhibition by an unstable inhibitor yields more information than can be obtained by recording data only at the end point of reaction. Time-course analysis of co-operative irreversible enzyme inhibition by an unstable inhibitor has been shown to be considerably less susceptible to ill-conditioning than the "end-point" method for the determination of kinetic parameters describing inactivation. As a result, mechanisms that cannot be distinguished by the "end-point" method are readily differentiated by time-course analysis without the need to isolate intermediate species.     

Kinetics of irreversible enzyme inhibition by an unstable inhibitor (Short Communication)

A mathematical treatment for the general case of enzyme inactivation by an inhibitor that breaks down in solution in a first-order reaction is presented. Cathepsin D was inactivated by fluorescein isothiocyanate with a K(i) of 4.47mum. Kinetic constants were also determined for the inactivation of cathepsin D by 1,1-bis(diazoacetyl)-2-phenylethane, and the inactivation of pepsin C by diazoacetyl-dl-norleucine methyl ester.     

Integrated steady state rate equations and the determination of individual rate constants.

Integrated steady state rate equations have been used to determine the kinetic constants (Vs, Ks, Vp, and Kp) and rate constants (k1, k2, k3, and k4) of the reversible enzyme mechanism: (see article). The fumarase reaction has been used as a model to illustrate the procedures for determining these constants. In contrast to initial velocity studies, the values of the constants have been obtained by examining the enzyme reaction in only one direction rather than in both forward and reverse directions. To accomplish this, a new procedure is described for fitting data to integrated rate equations which eliminates problems encountered when data are analyzed graphically. The advantages of examining on enzyme reaction in one direction with these new procedures allow this method to be extended to the examination of enzymes with simple mechanisms where initial velocities are difficult to measure because either the substrate or product is not readily available, or because the reaction is not readily reversible.     

Kinetics of vanadate dissociation: estimation of the rate by inhibitor inactivation

Vanadate (+5) is a potent inhibitor of a variety of ATPases including dynein ATPase. We describe a method useful for estimating the functional dissociation rate of vanadate from the active site which does not rely on classical physical separation techniques. The method involves spectrophotometrically monitoring the enzymatic activity as the inhibitor dissociates from the enzyme and is inactivated by norepinephrine. Norepinephrine effectively reverses vanadate inhibition by reducing vanadate (+5) to oxovanadium (+4). This reduction by norepinephrine is sufficiently fast for these purposes--addition of vanadate after norepinephrine shows no inhibition of ATPase activity. The mathematical estimation procedure is generally useful for estimation of dissociation rates of other reversible inhibitors which can be quickly inactivated after dissociation from the enzyme. The rate of dissociation of vanadate from dynein with ATP and 2-N3ATP as substrates using this method was estimated to be in the ranges 0.0023-0.0042 and 0.0057-0.0075 s-1, respectively. These rates permit estimation of the rates of vanadate association with dynein by using the reported dissociation constant for vanadate. The results are consistent with the very fast and potent inhibition of dynein ATPase activity observed.     

Analysis of a procedure for the determination of kinetic rate constants

This paper is concerned with a mathematical analysis of the modified Guggenheim procedure. Theorems concerning the solutions of the differential equations which describe the general reaction

$$E + SB\xrightarrow{{k_2 }}C + X, C\xrightarrow{{k_3 }}E + D$$     

A simple method for the determination of individual rate constants for substrate hydrolysis by serine proteases

A simple method is presented for the determination of individual rate constants for substrate hydrolysis by serine proteases and other enzymes with similar catalytic mechanism. The method does not require solvent perturbation like viscosity changes, or solvent isotope effects, that often compromise nonspecifically the activity of substrate and enzyme. The rates of substrate diffusion into the active site (k1), substrate dissociation (k-1), acylation (k2), and deacylation (k3) in the accepted mechanism of substrate hydrolysis by serine proteases are derived from the temperature dependence of the Michaelis-Menten parameters kcat/Km and kcat. The method also yields the activation energies for these molecular events. Application to wild-type and mutant thrombins reveals how the various steps of the catalytic mechanism are affected by Na+-binding and site-directed mutations of the important residues Y225 in the Na+ binding environment and L99 in the S2 specificity site. Extension of this method to other proteases should enable the derivation of detailed information on the kinetic and energetic determinants of protease function.     

Protein/enzyme inactivation during different chromatographic methods of separation.

Protein denaturations encountered during the different types of chromatographic separations are presented. The analysis of different protein denaturations presented along with the causes of such denaturations provides a judicious framework to compare protein denaturations encountered by such separation techniques. Especially of interest are those studies which compare the mass recovery of proteins and the retention of activity by different chromatographic techniques. Reversed-phase chromatography is presented even though it is utilized nowadays only for specialized cases such as separation of small peptides. It appears that relatively mild interactions that are encountered generally in hydrocarbon-interaction chromatography are favorable to the preservation of the native (active) protein state. The few available mechanistic studies presented provide judicious physical insights into protein conformational behavior on chromatographic columns.     

Allowance for antibody bivalence in the determination of association rate constants by kinetic exclusion assay

This investigation completes the amendment of theoretical expressions for the characterization of antigen–antibody interactions by kinetic exclusion assay—an endeavor that has been marred by inadequate allowance for the consequences of antibody bivalence in its uptake by the affinity matrix (immobilized antigen) that is used to ascertain the fraction of free antibody sites in a solution with defined total concentrations of antigen and antibody. A simple illustration of reacted site probability considerations in action confirms that the square root of the fluorescence response ratio, R_Ag/R_o, needs to be taken in order to determine the fraction of unoccupied antibody sites, which is the parameter employed to describe the kinetics of antigen uptake in the mixture of antigen and antibody with defined initial composition. The approximately 2-fold underestimation of the association rate constant (k_a) that emanates from the usual practice of omitting the square root factor gives rise to a corresponding overestimate of the equilibrium dissociation constant (K_d)—a situation that is also encountered in the thermodynamic characterization of antigen–antibody interactions by kinetic exclusion assay.     

Kinetic evidence for the existence of an unstable intermediate in the trinitrophenylation-induced rhodanese inactivation reaction.

1. Rhodanese inactivation by 2,4,6-trinitrobenzenesulphonate, in the presence of n-butylamine in the reaction medium, has been studied by a kinetic analysis of the data, based on the assumption that enzyme inactivation is brought about by direct reaction of this with the modifying agent. 2. Initial reaction rates for rhodanese activity loss were determined by a mathematical analysis of the first three recorded values of rhodanese residual activity. 3. It was found that fractional rhodanese activity values, at infinite reaction time with 2,4,6-trinitrobenzenesulphonate (end-point values), were significantly lower than the values calculated on the assumption of rhodanese inactivation being entirely due to direct trinitrophenylation of enzyme protein. 4. Also, initial enzyme inactivation values were higher in the presence, rather than in the absence, of n-butylamine. 5. These results indicate that 2,4,6-trinitrobenzenesulphonate-induced rhodanese inactivation, in the presence of n-butylamine in the reaction medium, is due to the generation of a highly reactive, unstable intermediate, probably a free radical species.     

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.