Reversible Enzymatic Reactions

CK catalyzes the reversible phosphorylation of creatine in the presence of ATP and magnesium. When creatine phosphate is the substrate, the resulting creatine can be measured as the ninhydrin fluorescent compound, as in the continuous flow Auto Analyzer method. Kinetic methods based on coupled enzymatic reactions are also popular. Tanzer and Gilvarg (40) developed a kinetic method using the two exogenous enzymes pyruvate kinase and lactate dehydrogenase to measure the CK rate by following the oxidation of NADH. In this procedure the main reaction is run in a less favorable direction. 

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) ... 

In this chapter we have seen that enzymatic catalysis is initiated by the reversible interactions of a substrate molecule with the active site of the enzyme to form a non-covalent binary complex. The chemical transformation of the substrate to the product molecule occurs within the context of the enzyme active site subsequent to initial complex formation. We saw that the enormous rate enhancements for enzyme-catalyzed reactions are the result of specific mechanisms that enzymes use to achieve large reductions in the energy of activation associated with attainment of the reaction transition state structure. Stabilization of the reaction transition state in the context of the enzymatic reaction is the key contributor to both enzymatic rate enhancement and substrate specificity. We described several chemical strategies by which enzymes achieve this transition state stabilization. We also saw in this chapter that enzyme reactions are most commonly studied by following the kinetics of these reactions under steady state conditions. We defined three kinetic constants—kai KM, and kcJKM—that can be used to define the efficiency of enzymatic catalysis, and each reports on different portions of the enzymatic reaction pathway. Perturbations... 

As we have seen before, the enzymatic reaction begins with the reversible binding of substrate (S) to the free enzyme ( ) to form the ES complex, as quantified by the dissociation constant Ks. The ES complex thus formed goes on to generate the reaction product(s) through a series of chemical steps that are collectively defined by the first-order rate constant kCM. The first mode of inhibitor interaction that can be con-... 

Various chiral lumazines produced from the parent pterins by an enzymatic reaction were separated using achiral-chiral multidimensional LC-LC by Klein et al. (1994). A Ci 8 column and a flavoprotein column were used in the reverse-phase mode to achieve the separation of the threo forms of the lumazines. The flavoprotein column was unable to resolve the erythro forms. 

Though the assumption of an irreversible dissociation of the product considerably simplifies the mathematical analysis, all enzymatic reactions are inherently reversible. To account for the presence of a significant amount of product within the intracellular medium, we must allow the reverse reaction [96,140,157]. In this case, using an augmented scheme,... 

For reversible enzymatic reactions, the Haldane relationship relates the equilibrium constant KeqsNith the kinetic parameters of a reaction. The equilibrium constant Keq for the reversible Michaelis Menten scheme shown above is given as... 

The importance of the Haldane relationship Eq. (42) relates to the fact that the kinetic parameters of a reversible enzymatic reaction are not independent but are constraint by the equilibrium constant of the overall reaction [157]. 

The simplest possible enzymatic reaction scheme was proposed in 1913 by Michealis and Menten. They assumed the molecule undergoing reaction (the substrate, S) is adsorbed reversibly on a specific site of the enzyme E to form a complex ES whose decomposition into product P is rate controlling. The scheme resembles that for unimolecular decomposition (see Chapter 14). 

Drugs are also used to inhibit the enzymatic reactions of foreign pathogens that enter the human body. An example is the use of reverse transcriptase inhibitor and protease inhibitor for combating the human immunodeficiency virus (HIV), as shown in Exhibit 2.12. Some new inhibitors are used to block HIV from attaching to the human cell, CD4, thus stopping replication and infection of other cells, as presented in Exhibit 2.13. 

In MET, a low-molecular-weight, redox-active species, referred to as a mediator, is introduced to shuttle electrons between the enzyme active site and the electrode.In this case, the enzyme catalyzes the oxidation or reduction of the redox mediator. The reverse transformation (regeneration) of the mediator occurs on the electrode surface. The major characteristics of mediator-assisted electron transfer are that (i) the mediator acts as a cosubstrate for the enzymatic reaction and (ii) the electrochemical transformation of the mediator on the electrode has to be reversible. In these systems, the catalytic process involves enzymatic transformations of both the first substrate (fuel or oxidant) and the second substrate (mediator). The mediator is regenerated at the electrode surface, preferably at low overvoltage. The enzymatic reaction and the electrode reaction can be considered as separate yet coupled. 

Although RMs are thermodynamically stable, they are highly dynamic. The RMs constantly colhde with each other and occasionally a colhsion results in the fusion of two RMs temporarily. During this fusion surfactant molecules and the contents residing inside RMs may be exchanged. In AOT reverse micellar system, this dynamic behavior exhibits second-order kinetics with rate constants in the order of 10 to 10 M s [37]. This dynamic nature not only influences the properties of the bulk system but also affects the enzymatic reaction rates [38]. 

One of the most common reasons for using low-water media for enzymatic reactions is that one wants to use a hydrolase for catalyzing reactions other than hydrolysis. In low-water media these enzymes can be efficiently used to catalyze reversed hydrolytic reactions and various types of tranferase reactions. 

Recently, Senoh, Tokuyama, and Witkop (37) have studied a metal-activated enzymatic reaction in the presence and the absence of enzyme, and have discovered that the order of effectiveness of the metals is exactly the reverse in the enzymatic and nonenzymatic processes. The reaction was O-methylation of 3,4-dihydroxybenzaldehyde. In the absence of divalent metal ions, the nonenzymatic reaction yields very predominantly the paramethylated product in neutral solution, since the p-hydroxyl group is the more electronegative. Metal complex formation... 

Here kf and kr refer to the rates in the forward and reverse directions. If the pKa s of HA and HB are equal k( and kr will be the same, but if they are very far from equal the reaction will be slowed in one direction. If proton transfer is a step in an enzymatic reaction it may be slowed enough to become rate limiting. 

The mechanism of the cleavage of the pyruvate in Eq. 15-37 is not obvious. Thiamin diphosphate is not involved, and free C02 is not formed. The first identified intermediate is an acetyl-enzyme containing a thioester linkage to a cysteine side chain. This is cleaved by reaction with CoA-SH to give the final product. A clue came when it was found by Knappe and coworkers that the active enzyme, which is rapidly inactivated by oxygen, contains a long-lived free radical.326 Under anaerobic conditions cells convert the inactive form E to the active form Ea by an enzymatic reaction with S-adenosylmethionine and reduced flavodoxin Fd(red) as shown in Eq. 15-38.327-329 A deactivase reverses the process.330... 

The principle of microscopic reversibility or detailed balance is used in thermodynamics to place limitations on the nature of transitions between different quantum or other states. It applies also to chemical and enzymatic reactions each chemical intermediate or conformation is considered as a state. The principle requires that the transitions between any two states take place with equal frequency in either direction at equilibrium.52 That is, the process A — B is exactly balanced by B — A, so equilibrium cannot be maintained by a cyclic process, with the reaction being A — B in one direction and B — > C — A in the opposite. A useful way of restating the principle for reaction kinetics is that the reaction pathway for the reverse of a reaction at equilibrium is the exact opposite of the pathway for the forward direction. In other words, the transition states for the forward and reverse reactions are identical. This also holds for (nonchain) reactions in the steady state, under a given set of reaction conditions.53... 

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