Single-substrate enzyme reactions

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. 

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. 

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. 

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. 

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... 

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). 

Reversible inhibition occurs rapidly in a system which is near its equilibrium point and its extent is dependent on the concentration of enzyme, inhibitor and substrate. It remains constant over the period when the initial reaction velocity studies are performed. In contrast, irreversible inhibition may increase with time. In simple single-substrate enzyme-catalysed reactions there are three main types of inhibition patterns involving reactions following the Michaelis-Menten equation competitive, uncompetitive and non-competitive inhibition. Competitive inhibition occurs when the inhibitor directly competes with the substrate in forming the enzyme complex. Uncompetitive inhibition involves the interaction of the inhibitor with only the enzyme-substrate complex, while non-competitive inhibition occurs when the inhibitor binds to either the enzyme or the enzyme-substrate complex without affecting the binding of the substrate. The kinetic modifications of the Michaelis-Menten equation associated with the various types of inhibition are shown below. The derivation of these equations is shown in Appendix S.S. 

The bacterial enzyme chorismate mutase-prephenate dehydrogenase is peculiar because it is a single protein unit with two catalytic activities. It catalyzes the sequential reactions of mutation of chorismate to prephenate and then the reaction that leads to the formation of phenylalanine and tyrosine, through oxidation of prephenate. The first of these reactions is interesting because it is one of the few strictly single-substrate enzymatic reactions it entails... 

The effect of an inhibitor I on the rate of a single-substrate enzyme-catalyzed reaction was investigated and gave the following results ... 

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. 

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. 

Figure 5.6 Schematic free-energy profile for a single substrate, single product enzyme reaction and its analogous uncatalysed 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. 

The enzyme [E) binds a substrate (S) and produces a product [P]. Enzyme kinetics is the investigation of how enzymes bind substrates and turn them into products. An enzymatic reaction occurs in two stages. In the first stage, the substrate binds reversibly to the enzyme, forming the enzyme-substrate complex. This is called the "Michaelis complex. The mechanism of single-substrate enzyme catalytic reaction is shown in Fig. 4.2. 

Figure 4.2 Mechanism of single-substrate enzyme catalytic reaction.

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. 

Single-substrate enzymes enzymes which catalyse reactions involving only one substrate. They are usually isomerases or hydrolytic enzymes in the latter case, the water involved in the reaction is regarded as a constant, and there is frequently no special enzyme-water complex formed. 

Yi Liang, Wang Cunxin, Wu Dingquan, and Qu Songsheng, Thermokinetic studies of the irreversible inhibition of single-substrate, enzyme-catalyzed reactions, Thermochim. Acta., 1995, vol. 268, pp. 17-25. 

Liang Yi, Wang Cim-Xin, Wu Ding-Quan, and Qu Song-Sheng, Application of microcalorimetry to product inhibition of single-substrate enzymic-catalytic reaction, Acta Chim. Sin., 1996, vol. 54, no 1, pp. 38-44 (in Chinese). 

Equation 11-15 is known as the Michaelis-Menten equation. It represents the kinetics of many simple enzyme-catalyzed reactions, which involve a single substrate. The interpretation of as an equilibrium constant is not universally valid, since the assumption that the reversible reaction as a fast equilibrium process often does not apply. 

Thus far, we have considered only the simple case of enzymes that act upon a single substrate, S. This situation is not common. Usually, enzymes catalyze reactions in which two (or even more) substrates take part. 

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 response characteristics of enzyme electrodes depend on many variables, and an understanding of the theoretical basis of their function would help to improve their performance. Enzymatic reactions involving a single substrate can be formulated in a general way as... 

In what follows, enzyme reactions are treated as if they had only a single substrate and a single product. While most enzymes have more than one substrate, the principles discussed below apply with equal vaUdity to enzymes with multiple substrates. 

Let us consider an enzymatic reaction in which two substrates are utilized to from two products (in the nomenclature of enzyme reaction mechanisms this situation is referred to as a bi-bi mechanism). A reaction in which one substrate yields two products is referred to as a uni-bi mechanism, and one in which two substrates combine to form a single product is referred to as a bi-uni mechanism (see Copeland, 2000, for further details). For the purposes of illustration let us use the example of a group transfer reaction, in which a chemical species, X, is transferred from one substrate to the other in forming the products of the reaction ... 

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. 

The mode of action of enzymes can be found in detail in many biochemistry and enzymology textbooks31"33. The mechanisms of enzyme-catalyzed reactions are complex and all have several steps. The more generally written scheme involves a single substrate and a single intermediate ... 

---