Enzyme kinetics pseudo first-order

E I is a kinetic chimera Kj and kt are the constants characterizing the inactivation process kt is the first-order rate constant for inactivation at infinite inhibitor concentration and K, is the counterpart of the Michaelis constant. The k,/K, ratio is an index of the inhibitory potency. The parameters K, and k, are determined by analyzing the data obtained by using the incubation method or the progress curve method. In the incubation method, the pseudo-first-order constants /cobs are determined from the slopes of the semilogarithmic plots of remaining enzyme activity... 

All enzymatic reactions are initiated by formation of a binary encounter complex between the enzyme and its substrate molecule (or one of its substrate molecules in the case of multiple substrate reactions see Section 2.6 below). Formation of this encounter complex is almost always driven by noncovalent interactions between the enzyme active site and the substrate. Hence the reaction represents a reversible equilibrium that can be described by a pseudo-first-order association rate constant (kon) and a first-order dissociation rate constant (kM) (see Appendix 1 for a refresher on biochemical reaction kinetics) ... 

Cytochrome P-450 from rat or human liver microsome preparations is inactivated when incubated anaerobically with carbon tetrachloride in the presence of NADPH and an oxygen-scavenging system (Manno et al. 1988 1992). Inactivation involved destruction of the heme tetrapyrrolic structure, and followed pseudo first-order kinetics with fast and slow half lives of 4.0 and 29.8 minutes. When compared with rat liver microsomes, the human preparations were 6-7 times faster at metabolizing carbon tetrachloride, and only about one- eighth as susceptible to suicide inactivation (about 1 enzyme molecule lost for every 196 carbon tetrachloride molecules metabolized). 

Such a reaction is described as first order and the proportionality constant k is known as the rate constant. Such first-order kinetics is observed for unimolecular processes in which a molecule of A is converted into product P in a given time interval with a probability that does not depend on interaction with another molecule. An example is radioactive decay. Enzyme-substrate complexes often react by unimolecular processes. In other cases, a reaction is pseudo-first order compound A actually reacts with a second molecule such as water, which is present in such excess that its concentration does not change during the experiment. Consequently, the velocity is apparently proportional only to [A]. 

In kinetic studies with neutral proteases, the substrates are relatively insoluble and Km values are generally high. For these enzymes, pseudo-first-order kinetic data can be obtained where (5) < Km, leading to a rate expression, v = kcit(E)(S)/Km. Values of kcJKm and Km are measured and data compared for various substrates. Table I presents data at pH = 8 for a neutral protease from B. subtilis (3). 

Mechanism-based inhibition should be irreversible. Dialysis, ultrafiltration, or washing the protein (e.g., by isolating microsomes by centrifugation and resuspending them in drug-free buffer) will not restore enzyme activity, and the inhibition is highly resistant to sample dilution. Mechanism-based inhibition should be saturable. The rate of inactivation is proportional to the concentration of the inactivator until all enzyme molecules are saturated, in accordance with Michaelis-Menten kinetics. Additionally, the decrease in enzymatic activity over time should follow pseudo-first-order kinetics. 

Based on this premise, y-acetylenic GABA (IV) waB synthesized (11) and found to be an irreversible inhibitor of GABA-T, in vitro and in vivo (12). Thus, when GABA-T, partially purified from pig brain, is incubated for varying time periods with y-acetylenic GABA, a time-dependent inactivation process is observed which follows pseudo first-order kinetics. Enzyme half lives range from 28 minutes to 9 minutes with concentrations of inhibitor between 0.029 mM and 0.29 mM. Time dependent inactivation is... 

By using a resonant mirror biosensor, the binding between YTX and PDEs from bovine brain was studied. The enzymes were immobilized over an aminosilae surface and the association curves after the addition of several YTX concentrations were checked. These curves follow a typical association profile that fit a pseudo-first-order kinetic equation. From these results the kinetic equilibrium dissociation constant (K ) for the PDE-YTX association was calculated. This value is 3.74 p,M YTX (Pazos et al. 2004). is dependent on YTX structure since it increases when 44 or 45 carbons (at C9 chain) group. A higher value, 7 p,M OH-YTX or 23 p,M carboxy-YTX, indicates a lower affinity of YTXs analogues by PDEs. 

Enzymatic assay methods are classified as fixed-time assays, fixed-change assays, or kinetic (initial rate) assays. Kinetic assays continuously monitor concentration as a function of time pseudo-first-order conditions generally apply up to 10% completion of the reaction to allow the initial reaction rate to be determined. If the initial substrate concentration is > 10Km, then the initial rate is directly proportional to enzyme concentration. At low initial substrate concentrations (< 0.1 Km), the initial rate will be directly proportional to initial substrate concentration (cf. Chapter 2). For enzyme quantitation, a plot of initial rate against [E] provides a linear... 

The reaction can be observed in either the kinetic or the equilibrium mode. The Bacillus fastidiosus enzyme has the highest Michaelis constant (1.0 x 10" mol/L) and the hog fiver has the lowest (1,7 x 10 mol/L), the choice of enzyme influencing the incubation period required to reach equilibrium and the conditions for a pseudo first-order Idnetic approach. The decrease of absorbance as urate is converted may be monitored by a spectrophotometer at 293 nm and this forms the basis of a proposed reference procedure. However, at this wavelength, most of the absorbance is due to plasma proteins. Therefore there is a high signal-noise ratio, which can compromise the precision of the method. A high quality spectrophotometer with narrow bandpass is required and this is rarely satisfied with automated analyzers. 

For determination of how these inhibitors interact with housefly acetyl cholinesterase the method of Aldridge and Davidson(3) was employed. The log % residual activity is plotted against (molar concentration)(incubation time). When straight line results, it is interpreted that the enzyme-inhibitor interaction is governed by pseudo first order kinetics and is a bimolecular reaction. For the... 

In certain cases, restriction of the experimental conditions to low substrate concentrations (cs< Km) is an acceptable condition for the investigation of biocatalyst properties. In this case, the enzyme kinetics can be simplified to the form of a pseudo-first order kinetics expressed by the relation... 

There are two important results from this analysis. First, the rate constants for binding and dissociation can be obtained from the slope and intercept, resp>ec-tively, of a plot of the observed rate versus concentration. In practice this is possible when the rate of dissociation is comparable to ki [S] under conditions that allow measurement of the reaction. At the lower end, resolution of i is limited by the concentration of substrate required to maintain pseudo-first-order kinetics with substrate in excess of enzyme and by the sensitivity of the method, which dictates the concentration of enzyme necessary to observe a signal. Under most circumstances, it may be difficult to resolve a dissociation rate less than 1 sec by extrapolation of the measured rate to zero concentration. Of course, the actual error must be determined by proper regression analysis in fitting the data, and these estimates serve only to illustrate the magnitude of the problem. In the upper extreme, dissociation rates in excess of 200 sec make it difficult to observe any reaction. At a substrate concentration required to observe half of the full amplitude, where [S] = it., the reaction would proceed toward equilibrium at a rate of 400 sec. Thus, depending upon the dead time of the apparatus, much of the reaction may be over before it can be observed at the concentrations required to saturate the enzyme with substrate. 

A summary of some recently discovered inactivators of E. coli PFL is presented in Table V. Consistent with these compounds acting as mechanism-based or active site-directed inhibitors is the observation of pseudo-first-order inactivation kinetics, substrate protection (by pyruvate or formate for inhibitors that are pyruvate or formate analogs, respectively), and isotope effects on the rates of inactivation by the deuterated analogs. The details of some of these studies, the proposed inactivation mechanisms, and the implications to the normal enzymic reaction are discussed below. 

In direct analogy to the Michaelis-Menten mechanism for reaction of enzyme with a substrate, the inactivator, I, binds to the enzyme to produce an E l complex with a dissociation constant K. A first-order chemical reaction then produces the chemically reactive intermediate with a rate constant k. The activated species may either dissociate from the active site with a rate constant to yield product, P, or covalently modify the enzyme ( 4). The inactivation reaction should therefore be a time-dependent, pseudo-first-order process which displays saturation kinetics. This is verified by measuring the apparent rate constant for the loss of activity at several fixed concentrations of inactivator (Fig. lA). The rate constant for inactivation at infinite [I], itj act (a function of k2, k, and k4), and the Ki can be extracted from a double reciprocal plot of 1/Jfcobs versus 1/ 1 (Fig. IB) (Kitz and Wilson, 1962 Jung and Metcalf, 1975). A positive vertical... 

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