Biochemical Engineering Fundamentals, Part 1 - Bailey J., Ollis D. 1989

Kinetics of enzyme-catalyzed reactions

In the previous chapter, we learned that The Cell contains a multitude of chemical compounds. How are they synthesized and how do they interact with one another at sufficiently high rates under relatively low temperatures and pressures? How does the cell choose which specific substances to react at any given moment, and which molecules to degrade? The answer to both questions is the same: all cellular reactions are carried out and regulated by Enzymatic Catalysis; and Enzymes, as we already know, are Globular Proteins.

The turning point in The Development of enzymology was 1897, when Buchner first isolated active enzymes from living Cells. This work was highly significant from two Perspectives. First, it showed that catalysts operating in a living Organism can function completely independently of any other cellular process; as we will see in the next chapter, isolated enzymes are now widely used. Second, Buchner's discovery stimulated research on the Isolation and Purification of individual enzymes. An enzyme was first isolated in pure form by Sumner in 1926. Its study showed it to be a protein; it is now known that all enzymes are proteins.

Following Sumner's pioneering work, the number of known enzymes has steadily increased and now far exceeds 1500. Judging by The amount of Genetic information stored even in simple organisms like E. coli, it can be confidently predicted that many new enzymes will be identified and characterized in the future. Indeed, the single DNA molecule making up the E. coli chromosome carries enough information to encode the structures of 3000 to 4500 different proteins.

Since we will mention A number of specific enzymes in this chapter and later, it is appropriate to say a few words about their nomenclature. Unfortunately, there are no general nomenclature rules applicable to all enzymes. In the vast majority of cases, the name of an enzyme reflects its function rather than its Structure; typically, the suffix -ase is added to the name of the substrate (for example, urease is the enzyme that catalyzes the decomposition of urea). Sometimes the same suffix is added to the name of the reaction catalyzed by the enzyme (Alcohol dehydrogenase, for example, catalyzes the oxidative dehydrogenation of alcohol). Exceptions to this rule are historical names of enzymes (usually long-known ones); these include Pepsin and Trypsin from the Human digestive tract, rennin used in cheesemaking, and the 'old yellow' enzyme, which causes browning on sliced apples.

Enzymes catalyze six Major Types of reactions, which form The basis of the Classification and numerical designation system recommended by the Enzyme Commission (EC) (Table 3.1). This 'official' system allows the diverse Functions performed by enzymes to be tabulated and classified, although the older, more traditional Enzyme Nomenclature is still widely used alongside it.

To avoid any misunderstanding, let us recall what a catalyst is in general. A catalyst is defined as a substance that increases The rate of a chemical reaction without undergoing irreversible chemical change. While increasing the reaction rate, the catalyst does not affect the reaction equilibrium (Fig. 3.1). Equilibrium concentrations can be calculated solely from the thermodynamic Properties of the substrates (recall that in biochemistry, a substrate is the substance entering an enzyme-catalyzed reaction) and the reaction products. Reaction kinetics, however, depend on Molecular Dynamics and cannot currently be predicted with sufficient accuracy without experimental data.

To study a reaction and design an appropriate technological process, it is necessary to have a mathematical expression that defines the reaction rate (i.e., the number of moles of substance reacting per unit time per unit volume) as a function of the composition, Temperature, pressure, and other parameters of the reaction mixture. If you have previously studied catalytic reactions, you should be familiar with the General Principles of deriving rate equations. Typically, reasonable assumptions are first made regarding the elementary reactions occurring at THE MOLECULAR LEVEL. Then, using certain approximations concerning the dynamics of one or more reactive intermediates, and applying simple mathematical transformations, an expression for the overall reaction rate is derived. In this chapter, we will use this exact approach to evaluate the rates of enzyme-catalyzed reactions.

Class="center">Table 3.1. Classification of Enzymes in accordance with the recommendations of the International Enzyme Commission (showing class name, Enzyme Commission code numbers, and type of catalyzed reactions)^a

^a Reproduced from: Lehninger A. L., Biochemistry, 2d ed., table 8-1, Worth Publishers, Inc., New York, 1975; There is a Introduction/27.html">Translation of the first edition: Lehninger A., Biochemistry. — M.: Mir, 1976.

FIG. 3.1. A catalyst lowers the activation energy of a reaction, thereby enabling the enzyme to react with substrate molecules that possess low internal energy. [Reproduced with permission from: Lehninger A. L., Bioenergetics, 2d ed., p. 35, W. A. Benjamin, Inc., Menlo Park, CA, 1971.]

The analogy between synthetic catalysts and enzymes is not limited to the principles of reaction kinetics modeling. The mathematical expressions determining the rates of Reactions Catalyzed by these Two Types of catalysts are very similar, and sometimes even identical. This is because, as is well known, in both cases, an intermediate complex is formed between the reactant (substrate) and the catalyst; the General mechanism of catalytic processes naturally yields identical rate equations. We will briefly return to this point later.

At the same time, It is important to keep in mind the significant differences between synthetic catalysts and enzymes, some of which have already been mentioned. The vast majority of synthetic catalysts are non-specific, meaning they can catalyze similar reactions involving A wide variety of reactants. Some enzymes also lack high Specificity, but many catalyze only a single transformation of an extremely limited number of substrates. Generally, the degree of an enzyme's specificity corresponds to its biological function. High specificity is undesirable, for example, for an enzyme whose primary role is to hydrolyze proteins into small Peptides and Amino Acids. Conversely, an enzyme that catalyzes the isomerization of a single specific compound must be highly specific. As mentioned above in Sec. 2.2.4, Enzyme Specificity is believed to arise from its complex three-dimensional structure, which enables The formation of the Active Site responsible for the enzyme's catalytic properties.

Another distinguishing feature of many enzymes is the presence of Cofactors required for enzymatic activity. A cofactor is a non-protein compound that binds to an inactive protein (apoenzyme) to form a catalytically active complex. Biochemists often refer to the latter as a holoenzyme, though we will more frequently call it simply an enzyme. There are two distinct types of cofactors. The simplest cofactors are Metal Ions (Table 3.2). Complex Organic compounds, known as Coenzymes, can also serve as cofactors. In the previous chapter, we mentioned the coenzymes NAD, FAD, and coenzyme A (CoA); occasionally, ATP can also act as a cofactor. Often, cofactors are weakly bound to enzymes, establishing an equilibrium between the enzyme, apoenzyme, and cofactor. Generally, tightly bound non-protein structural elements are also coenzymes, such as the heme group in cytochrome c. However, as previously noted, such irreversibly bound groups are more commonly referred to as prosthetic groups.

The data presented in Table 3.2 are also of interest because they contain information we will repeatedly refer to when studying enzyme isolation and application. Note that the sources of isolation are indicated next to the names of some enzymes; for example, glucose isomerase from the bacterium Bacillus coagulans exhibits maximum activity in the presence of a cobalt cofactor. To precisely identify the enzyme in question, it is often necessary to specify its origin. This is because other organisms also synthesize enzymes that catalyze the isomerization of glucose to fructose, and are thus also called glucose isomerases. However, enzymes with the same name isolated from different organisms often have different Amino acid sequences and, consequently, differ in their properties and catalytic activity. For example, glucose isomerase from B. coagulans requires a Co²⁺ ion, whereas glucose isomerase from a mutant strain of the same organism is active at pH>8 even in the absence of cobalt. It should always be kept in mind that the name of an enzyme alone reveals nothing about The Nature of a specific protein with particular properties and corresponding technological requirements. To avoid ambiguity, the full name of the producing organism must be specified.

Table 3.2. Some enzymes containing metal ions as cofactors or exhibiting activity only in the presence of metal ions

Both synthetic and biological catalysts gradually lose activity in the course of performing their catalytic function; however, enzymes are generally much more short-lived. The complex and intricate three-dimensional METABOLISM/9.html">Structure of enzymes, which accounts for their exceptionally high specificity and activity, is easily disrupted, leading to the loss of catalytic properties. Various pathways of Enzyme inactivation and The kinetics of these processes will be discussed in Sec. 3.7.

Table 3.3. Comparative activity of enzymes and synthetic solid catalysts (N is the number of substrate molecules converted by one Active Site of the catalyst per second)^a

^a Reproduced from: Maatman R. W., Enzyme and Solid Catalyst Efficiencies and Solid Catalyst Site Densities, Catal. Rev., 8, 1 (1973).

It is often asserted that enzymes are more active in the sense that they enhance reaction rates to a greater extent than non-biological catalysts. The level of catalyst activity is typically expressed as the turnover number, which represents the number of substrate molecules reacting per active site of the catalyst per unit time. For comparison, Table 3.3 lists the parameters of several reactions catalyzed by enzymes and synthetic catalysts. It appears that within the temperature range where enzymes are most active, they indeed accelerate reaction rates to a greater degree than most synthetic catalysts. At higher temperatures, however, The activity of artificial catalysts usually surpasses that of enzymes. Unfortunately, enzymatic activity cannot increase indefinitely with temperature; on the contrary, enzymes typically lose their activity at relatively low temperatures, often just a few degrees above the normal temperature of a living cell.

A distinctive feature of enzymatic catalysis is The ability to be regulated by low-molecular-weight compounds. Some enzymes are 'turned off' in the presence of specific substances, which are often the End products of the reaction pathway involving the regulated enzyme. This characteristic of enzymes plays a crucial role in the normal Life Cycle of the cell. We will study some kinetic aspects of such enzymatic reactions in Sec. 3.5, and in Chap. 6, we will explore how altering the normal regulatory pathways of intracellular reactions can dramatically enhance the efficiency of industrial bioprocesses.

Before modeling the Kinetics of Enzymatic catalysis, we will examine the available experimental data on the Nature of the molecular transformations that actually occur during enzyme-catalyzed reactions. Based on this, we can formulate well-founded hypotheses regarding The sequence of elementary reactions and then apply these hypotheses to derive mathematical expressions for the reaction rates.