First order reaction, enzyme

In the normal process ( ), step (J) occurs very rapidly and step (/) is the rate-determining step, whereas in the inhibition process (B), step (3) occurs very slowly, generally over a matter of days, so that it is rate determining. Thus it has been demonstrated with AChE that insecticides, eg, tetraethyl pyrophosphate and mevinphos, engage in first-order reactions with the enzyme the inhibited enzyme is a relatively stable phosphorylated compound containing one mole of phosphoms per mole of enzyme and as a result of the reaction, an equimolar quantity of alcohoHc or acidic product HX is hberated. 

Pyruvic acid is an intermediate in the fermentation of grains. During fermentation the enzyme pyruvate carboxylase causes the pyruvate ion to release carbon dioxide. In one experiment a 200.-mL aqueous solution of the pyruvate in a sealed, rigid 500.-mL flask at 293 K had an initial concentration of 3.23 mmol-L -l. Because the concentration of the enzyme was kept constant, the reaction was pseudo-first order in pyruvate ion. The elimination of CU2 by the reaction was monitored by measuring the partial pressure of the C02 gas. The pressure of the gas was found to rise from zero to 100. Pa in 522 s. What is the rate constant of the pseudo-first order reaction ... 

Summarizing the results of many investigations, monosaccharides and such derivatives as D-mannitol and D-glucitol are rather weak acceptors. Disaccharides, including such acceptor products as isomaltose, are much better acceptors, except for certain molecules, for instance leucrose, which is not an acceptor.29,46,47 The decrease of enzyme activity with time has been described in terms of a first-order reaction. The inactivation parameters have been calculated for the immobilized enzyme. The inactivation constants kd were 0.0135 (1/d) when maltose was the acceptor (stabilizing), and 0.029 (1/d) when fructose was the acceptor.38... 

First-order rate constants are used to describe reactions of the type A — B. In the simple mechanism for enzyme catalysis, the reactions leading away from ES in both directions are of this type. The velocity of ES disappearance by any single pathway (such as the ones labeled k2 and k3) depends on the fraction of ES molecules that have sufficient energy to get across the specific activation barrier (hump) and decompose along a specific route. ES gets this energy from collision with solvent and from thermal motions in ES itself. The velocity of a first-order reaction depends linearly on the amount of ES left at any time. Since velocity has units of molar per minute (M/min) and ES has units of molar (M), the little k (first-order rate constant) must have units of reciprocal minutes (1/min, or min ). Since only one molecule of ES is involved in the reaction, this case is called first-order kinetics. The velocity depends on the substrate concentration raised to the first power (v = /c[A]). 

An exponential function that describes the increase in product during a first-order reaction looks a lot like a hyperbola that is used to describe Michaelis-Menten enzyme kinetics. It s not. Don t get them confused. If you can t keep them separated in your mind, then just forget all that you ve read, jump ship now, and just figure out the Michaelis-Menten description of the velocity of enzyme-catalyzed reaction—it s more important to the beginning biochemistry student anyway. 

An enzyme is immobilized by adsorption on porous pellets of a carrier. The differential equation for the concentration of a reactant in a porous spherical pellet is derived in problem P7.03.01 and integrated for a first order reaction, rc = kC, in problem P7.03.06. An expression is derived for the effectiveness of the adsorbed enzyme for first order reaction as... 

A first-order reaction may become zero order when the enzyme system is saturated. 

The kinetics of enzyme-catalyzed reactions (i. e the dependence of the reaction rate on the reaction conditions) is mainly determined by the properties of the catalyst, it is therefore more complex than the kinetics of an uncatalyzed reaction (see p.22). Here we discuss these issues using the example of a simple first-order reaction (see p.22)... 

In the absence of an enzyme, the reaction rate v is proportional to the concentration of substance A (top). The constant k is the rate constant of the uncatalyzed reaction. Like all catalysts, the enzyme E (total concentration [E]t) creates a new reaction pathway, initially, A is bound to E (partial reaction 1, left), if this reaction is in chemical equilibrium, then with the help of the law of mass action—and taking into account the fact that [E]t = [E] + [EA]—one can express the concentration [EA] of the enzyme-substrate complex as a function of [A] (left). The Michaelis constant lknow that kcat > k—in other words, enzyme-bound substrate reacts to B much faster than A alone (partial reaction 2, right), kcat. the enzyme s turnover number, corresponds to the number of substrate molecules converted by one enzyme molecule per second. Like the conversion A B, the formation of B from EA is a first-order reaction—i. e., V = k [EA] applies. When this equation is combined with the expression already derived for EA, the result is the Michaelis-Menten equation. 

There are many examples of first-order reactions dissociation from a complex, decompositions, isomerizations, etc. The decomposition of gaseous nitrogen pentoxide (2N2O5 4NO2 + O2) was determined to be first order ( d[N205]/dt = k[N205j) as is the release of product from an enzyme-product complex (EP E -t P). In a single-substrate, enzyme-catalyzed reaction in which the substrate concentration is much less than the Michaelis constant (i.e., [S] K ) the reaction is said to be first-order since the Michaelis-Menten equation reduces to... 

An equation allowing an investigator to determine the chemical reaction order of a non-enzyme-catalyzed reaction and the rate expression for a non-first-order process by noting that half-lives for non-first-order reactions are dependent on the initial reactant concentration. 

The heat sterilization of microorganisms and heat inactivation of enzymes are examples of first-order reactions. In the case of an enzyme being irreversibly heat-inactivated as follows ... 

When the rate of diffusion is very slow relative to the rate of reaction, all substrate will be consumed in the thin layer near the exterior surface of the spherical particle. Derive the equation for the effectiveness of an immobilized enzyme for this diffusion limited case by employing the same assumptions as for the distributed model. The rate of substrate consumption can be expressed as a first-order reaction. 

An enzyme is immobilized by copolymerization technique. The diameter of the spherical particle is 2 mm and the number density of the particles in a substrate solution is 10,000/L. Initial concentration of substrate is 0.1 mole/L. A substrate catalyzed by the enzyme can be adequately represented by the first-order reaction with k0 = 0.002 mol/Ls. It has been found that both external and internal mass-transfer resistance are significant for this immobilized enzyme. The mass-transfer coefficient at the stagnant film around the particle is about 0.02 cm/s and the diffusivity of the substrate in the particle is 5 x 10-6 cm2/s. 

Mechanism (1), first suggested almost three decades ago [150], continues to be the most invoked explanation of the role of the enzyme in promoting homolysis. Cleavage of the C—Co bond of sterically hindered alkylcobalamins (e.g., neopentylcobalamin) was markedly increased by diol dehydrase [72], Such cobal-amins do not function as coenzymes but convert to enzyme-bound hydroxocobal-amin in stoichiometric first-order reactions. The strong competitive inhibition by AdoB 12 indicates that labilization occurs at the active site of the enzyme and is suggested to be caused by a steric distortion of the corrin ring. 

Equation [17] is the conversion of A to B, assuming an irreversible first-order reaction catalyzed by the enzyme e. The rules governing the initial encounter, PB(Aei) and J(Ae4), are set at the beginning of each run. The next step in the reaction is modeled as shown in Eqs. [18]. 

In order to evaluate dextransucrase operational stability during isomaltose formation, enzyme half-lives were investigated over extended time of operation with the given parameters of the reaction over 6 h. The decrease of enzyme activity E as a function of time may be described by a first order reaction ... 

The electron transfer from cytochrome c to O2 catalyzed by cytochrome c oxidase was studied with initial steady state kinetics, following the absorbance decrease at 550 nm due to the oxidation of ferrocyto-chrome c in the presence of catalytic amounts of cytochrome c oxidase (Minnart, 1961 Errede ci a/., 1976 Ferguson-Miller ei a/., 1976). Oxidation of cytochrome c oxidase is a first-order reaction with respect to ferrocytochrome c concentration. Thus initial velocity can be determined quite accurately from the first-order rate constant multiplied by the initial concentration of ferrocytochrome c. The initial velocity depends on the substrate (ferrocytochrome c) concentration following the Michaelis-Menten equation (Minnart, 1961). Furthermore, a second catalytic site was found by careful examination of the enzyme reaction at low substrate concentration (Ferguson-Miller et al., 1976). The Km value was about two orders of magnitude smaller than that of the enzyme reaction previously found. The multiphasic enzyme kinetic behavior could be interpreted by a single catalytic site model (Speck et al., 1984). However, this model also requires two cytochrome c sites, catalytic and noncatalytic. 

It has also been shown by Kunitz that trypsinogen is activated by first-order reactions induced by other enzymes such as enterokinase and mold proteases. As in autoactivation, activation by purified enterokinase runs parallel with the appearance of an NH2-terminal isoleucine (57). But the hexaf ptide has not been isolated in this experiment and enterokinase acts in a pH range where autoactivation occurs at a quick rate. More work is clearly needed before the identity of both proces.ses is firmly established. 

Stability.—(i) Influence of temperature. Cohn and Monod have shown that the thermal inactivation of /3-galactosidase is a first-order reaction. At 55°, the activity is completely lost in less than 1 minute, whereas, at 47.3°, there is less than 5% inactivation in 10 minutes. Similar results were reported by Zarnitz with crystalline /3-galactosidase of E. coli, ML 309 at lower temperatures, the enzyme is exceptionally stable. 

Methods in which some property related to substrate concentration (such as absorbance, fluorescence, chemiluminescence, etc.) is measured at two fixed times during the course of the reaction are known as two-point kinetic methods. They are theoreticahy the most accurate for the enzymatic determination of substrates. However, these methods are technically more demanding than equifibrium methods and all the factors that affect reaction rate, such as pH, temperature, and amount of enzyme, must be kept constant from one assay to the next, as must the timing of the two measurements. These conditions can readily be achieved in automatic analyzers. A reference solution of the analyte (substrate) must be used for calibration. To ensure first-order reaction conditions, the substrate concentration must be low compared to the K, (i.e., in the order of less than 0.2 X K, . Enzymes with high K , values are therefore preferred for kinetic analysis to give a wider usable range of substrate concentration. 

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