Enzyme first-order kinetics

Kinetics First-order First-order after initial enzyme induction phase First-order First-order First-order... 

In order to predict the effect of a mixture of chemicals with the same target receptor, but with different nonlinear dose-effect relationships, either physiological or mathematical modeling can be applied. For interactions between chemicals and a target receptor or enzyme, the Michaelis-Menten kinetics (first order kinetics but with saturation) are often applicable. This kind of action can then be considered a special case of similar combined action (dose addition). 

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). 

Application of Kinetic Data to Thermal Processing. In most studies on ttiermal inactivation of indicator enzymes including peroxidase, lipoxygenase, and LAHase, reaction rate constants and thermodynamic parameters have been determined on the assumption that thermal inactivation of the enzymes follows first order reaction kinetics (22). However, a deviation from first order kinetics is generally observed fipm the residual activity curve. This deviation has been explained by several mechanisms, including the formation of enzyme aggregate with different heat stabilities, the presence of heat stable and labile enzymes, and the series type inactivation kinetics. 

Two steady-state kinetic constants are most useful in evaluating biocatalytic reactions. "k J is often known as the turnover number and higher values indicate more catalytically efficient enzymes. This first-order rate constant describes the speed at which an enzyme converts bound substrates to products and re-forms the free enzyme to prepare for the next round of catalysis. It includes both the "chemical" steps (bond making and bond breaking) as well as the product release step(s). Note that it is not uncommon for product release to be the slowest step. As a practical matter, one normally seeks enzymes with > 1 s under the process conditions to ensure reasonable space-time yields along with acceptable catalyst loading levels. 

On the other hand, for an enzyme that obeys Michaelis-Menten kinetics, the reaction is viewed as being first-order in S at low S and zero-order in S at high S. (See Chapter 14, where this distinction is discussed.)... 

Case 2 When [S] is small compared to K not all the enzyme molecules have S bound, and the kinetics are first order in S. 

The complex decays with first-order kinetics, releasing the enzyme to act again ... 

The inactivation is normally a first-order process, provided that the inhibitor is in large excess over the enzyme and is not depleted by spontaneous or enzyme-catalyzed side-reactions. The observed rate-constant for loss of activity in the presence of inhibitor at concentration [I] follows Michaelis-Menten kinetics and is given by kj(obs) = ki(max) [I]/(Ki + [1]), where Kj is the dissociation constant of an initially formed, non-covalent, enzyme-inhibitor complex which is converted into the covalent reaction product with the rate constant kj(max). For rapidly reacting inhibitors, it may not be possible to work at inhibitor concentrations near Kj. In this case, only the second-order rate-constant kj(max)/Kj can be obtained from the experiment. Evidence for a reaction of the inhibitor at the active site can be obtained from protection experiments with substrate [S] or a reversible, competitive inhibitor [I(rev)]. In the presence of these compounds, the inactivation rate Kj(obs) should be diminished by an increase of Kj by the factor (1 + [S]/K, ) or (1 + [I(rev)]/I (rev)). From the dependence of kj(obs) on the inhibitor concentration [I] in the presence of a protecting agent, it may sometimes be possible to determine Kj for inhibitors that react too rapidly in the accessible range of concentration. ... 

A model developed by Leksawasdi et al. [11,12] for the enzymatic production of PAC (P) from benzaldehyde (B) and pyruvate (A) in an aqueous phase system is based on equations given in Figure 2. The model also includes the production of by-products acetaldehyde (Q) and acetoin (R). The rate of deactivation of PDC (E) was shown to exhibit a first order dependency on benzaldehyde concentration and exposure time as well as an initial time lag [8]. Following detailed kinetic studies, the model including the equation for enzyme deactivation was shown to provide acceptable fitting of the kinetic data for the ranges 50-150 mM benzaldehyde, 60-180 mM pyruvate and 1.1-3.4 U mf PDC carboligase activity [10]. 

Although the molecular details of enzyme mechanisms are complex, the kinetic behavior of many enzymatic processes is first order in both the substrate and the enzyme. Example shows that the mechanism just outlined is consistent with this kinetic behavior. 

C15-0037. Write one-sentence explanations for the following kinetic terms (a) first order (b) second order (c) isolation method (d) elementaiy step (e) catalyst (f) intermediate and (g) enzyme. 

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) ... 

As an illustration of first-order kinetics, let us consider the simple dissociation of a binary enzyme-inhibitor complex ( 7) to the free enzyme (E) and the free inhibitor (/),... 

As a simple model for the enzyme penicillinase, Tutt and Schwartz (1970, 1971) investigated the effect of cycloheptaamylose on the hydrolysis of a series of penicillins. As illustrated in Scheme III, the alkaline hydrolysis of penicillins is first-order in both substrate and hydroxide ion and proceeds with cleavage of the /3-lactam ring to produce penicilloic acid. In the presence of an excess of cycloheptaamylose, the rate of disappearance of penicillin follows saturation kinetics as the cycloheptaamylose concentration is varied. By analogy to the hydrolysis of the phenyl acetates, this saturation behavior may be explained by inclusion of the penicillin side chain (the R group) within the cycloheptaamylose cavity prior to nucleophilic attack by a cycloheptaamylose alkoxide ion at the /3-lactam carbonyl. The presence of a covalent intermediate on the reaction pathway, although not isolated, was implicated by the observation that the rate of disappearance of penicillin is always greater than the rate of appearance of free penicilloic acid. 

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. 

In this case, most of the catalyst is in the form of M A and the reaction is zero order with respect to A. Thus, the kinetics move from first order at low cA toward zero order as cA increases. This feature of the rate saturating or reaching a plateau is common to many catalytic reactions, including surface catalysis (Section 8.4) and enzyme catalysis (Chapter 10). 

Silverman has pointed out that several criteria must be met to demonstrate that a compound is a true suicide substrate 1101 (1) Loss of enzyme activity must be time-dependent, and it must be first-order in [inactivator] at low concentrations and zero-order at higher concentrations (saturation kinetics), (2) substrate must protect the enzyme from inactivation (by blocking the active site), (3) the enzyme must be irreversibly inactivated and be shown to have a 11 stoichiometry of suicide substrate active site (dialysis of enzyme previously treated with radiolabeled suicide substrate must not release radiolabel into the buffer), (4) the enzyme must unmask the suicide substrate s potent electrophile via a catalytic step,1121 and (5) the enzyme must not be covalently labeled with the activated form of the suicide substrate following its escape from the active site (the presence of bulky scavenging thiol nucleophiles in the buffer must not decrease the observed rate of inactivation). 

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