For single-substrate enzymes

While many enzymes have a single substrate, many others have two—and sometimes more than two—substrates and products. The fundamental principles discussed above, while illustrated for single-substrate enzymes, apply also to multisubstrate enzymes. The mathematical expressions used to evaluate multisubstrate reactions are, however, complex. While detailed kinetic analysis of multisubstrate reactions exceeds the scope of this chapter, two-substrate, two-product reactions (termed Bi-Bi reactions) are considered below. 

Additionally, the concentration of the substrate upon which the enzyme acts is a major factor in the reaction rate. The reaction rates for single-substrate enzymes can often be modeled using so-called Michaelis-Menten kinetics, which describes the reaction rate in terms of the concentration of the substrate. A canonical plot of this relationship is shown in the graph below. 

This constant, K , is variously called the half-velocity constant, the Michaelis-Menten constant, and is indicative of the strength of the bond between enzyme and substrate. The lower the value of K, the greater is the affinity between enzyme and substrate. Values of for single substrate-enzyme reactions are generally between 10 and 10 M. The significance of this range of values is that it only requires 10" to 10 M of substrate to allow an enzyme to operate at half of its maximum rate. 

Determining balanced conditions for a single substrate enzyme reaction is usually straightforward one simply performs a substrate titration of reaction velocity, as described in Chapter 2, and sets the substrate concentration at the thus determined Ku value. For bisubstrate and more complex reaction mechanism, however, the determination of balanced conditions can be more complicated. 

The derivation of the steady-state enzyme rate equation for the single substrate enzyme-catalyzed reaction is provided in the entry entitled Enzyme Rate Equations (L The Basics). 

The results in Fig. 3 may be considered according to Frieden s treatment67 of the action of modifiers on single-substrate enzymes. This approach calls for no assumptions as to whether the modifier is an inhibitor or an activator, or whether it acts at the active center in the enzyme or not. It can be depicted as follows. 

Fiqtire 3.5 (a) Competitive inhibition inhibitor and substrate compete for the same binding site. For example, indole, phenol, and benzene bind in the binding pocket of chymotrypsin and inhibit the hydrolysis of derivatives of tryptophan, tyrosine, and / phenylalanine, (b) Noncompetitive inhibition inhibitor and substrate bind simultaneously to the enzyme. An example is the inhibition of fructose 1,6-diphosphatase by AMP. This type of inhibition is very common with multisubstrate enzymes. A rare example of / uncompetitive inhibition of a single-substrate enzyme is the inhibition of alkaline phosphatase by L-phenylalanine. This enzyme is composed of two identical subunitjs, so presumably the phenylalanine binds at one site and the substrate at the other. [From N. K. Ghosh and W. H. Fishman, J. Biol. Chem. 241, 2516 (1966) see also M. Caswell and M. Caplow, Biochemistry 19, 2907 (1980). 

Figure 4.3 Lineweaver-Burk, or double-reciprocal, plot for single-substrate irreversible Michaelis-Menten enzyme. A plot of 1/7 versus 1/[S] yields estimates of Vmax and Km, as illustrated in the figure.

Previous sections of this chapter have focused on developing general principles for enzyme-catalyzed reactions based on analysis of single-substrate enzyme systems. Yet the majority of biochemical reactions involve multiple substrates and products. With multiple binding steps, competitive and uncompetitive binding interactions, and allosteric and covalent activations and inhibitions possible, the complete set of possible kinetic mechanisms is vast. For extensive treatments on a great number of mechanisms, we point readers to Segel s book [183], Here we review a handful of two-substrate reaction mechanisms, with detailed analysis of the compulsory-order ternary mechanism and a cursory overview of several other mechanisms. 

I energetically unfavorable unless it is supplied with the energy of. substrate binding. Figure 4.2.4 is a schematic illustration of the energy diagram for a single-substrate, enzyme ( z)-mediated reaction. 

The mechanisms of enzyme inhibition fall into three main types, and they yield particular forms of modified Michaelis-Menten equations. These can be derived for single-substrate/single-product enzymic reactions using the steady-state analysis of Sec. 5.10, as follows. 

Single-substrate enzymes (see) display first order kinetics. The rate equation for such a unimolecular or pseudounimolecular reaction is v = -d[S]/dt = k[S]. The reaction is characterized by a half-life tv, = In2/ k = 0.693/k, where k is the first-order rate constant. The relaxation time, or the time required for [S] to fall to (1/e) times its initial value is x t= 1/k = tv,/ln 2. 

Scheme 1.5, Fig. 1.3). This type of inhibition is relatively rare with single-substrate enzymes. It is not completely overcome by high substrate concentrations and lowers both and V by a factor of (1 + [I]/K ). No change occurs for k /K. ... 

Unlike many of the catalysts that chemists use in the laboratory, enzymes are usually specific in their action. Often, in tact, an enzyme will catalyze only a single reaction of a single compound, called the enzyme s substrate. For example, the enzyme amylase, found in the human digestive tract, catalyzes only the hydrolysis of starch to yield glucose cellulose and other polysaccharides are untouched by amylase. 

Different enzymes have different specificities. Some, such as amylase, are specific for a single substrate, but others operate on a range of substrates. Papain, for instance, a globular protein of 212 amino acids isolated from papaya fruit, catalyzes the hydrolysis of many kinds of peptide bonds. In fact, it s this ability to hydrolyze peptide bonds that makes papain useful as a meat tenderizer and a cleaner for contact lenses. 

Most enzymes catalyse reactions and follow Michaelis-Menten kinetics. The rate can be described on the basis of the concentration of the substrate and the enzymes. For a single enzyme and single substrate, the rate equation is ... 

The biological activity of a compound can often be affected dramatically by the presence of even a single fluorine substituent that is placed in a particular position within the molecule. There are diverse reasons for this, which have been discussed briefly in the preface and introduction of this book. A few illustrative examples of bioactive compounds containing a single fluorine substituent are given in Fig. 3.1. These include what is probably the first example of enhanced bioactivity due to fluorine substitution, that of the corticosteroid 3-1 below wherein Fried discovered, in 1954, that the enhanced acidity of the fluorohydrin enhanced the activity of the compound.1 Also pictured are the antibacterial (3-fluoro amino acid, FA (3-2), which acts as a suicide substrate enzyme inactivator, and the well-known anti-anthrax drug, CIPRO (3-3). 

Rate Expressions for Enzyme Catalyzed Single-Substrate Reactions. The vast majority of the reactions catalyzed by enzymes are believed to involve a series of bimolecular or unimolecular steps. The simplest type of enzymatic reaction involves only a single reactant or substrate. The substrate forms an unstable complex with the enzyme, which subsequently undergoes decomposition to release the product species or to regenerate the substrate. 

Enzymes are usually named in terms of the reaction that is catalyzed, commonly adding the suffix -ase to the name of the stoichiometrically converted reactant or substrate. For instance, an enzyme that catalyses the hydrolysis of urea is urease. Enzyme names can only be applied to single enzymes, especially those with termination -ase. For systems that involve the action of two or more enzymes the use of the term should be avoided and the word system should be included. 

In the presence of sucrose alone as the single substrate, initial reaction rates follow Michaelis-Menten kinetics up to 200 mM sucrose concentration, but the enzyme is inhibited by higher concentrations of substrate.30 The inhibitor constant for sucrose is 730 mM. This inhibition can be overcome by the addition of acceptors.31,32 The enzyme activity is significantly enhanced, and stabilized, by the presence of dextran, and by calcium ions. 

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