Structural Biochemistry - Study Guide - E. A. Bessolitsyna 2015

Catalysts are substances that accelerate Chemical Reactions; they undergo physical changes during the reaction, but return to their original state upon its completion. Enzymes are biological catalysts. The majority of enzymes are Proteins. There are also ribozymes, which are enzymes made of RNA molecules. Ribozymes include the RNA of the large ribosomal subunit, which carries out METABOLISM/35.html">Protein Biosynthesis, RNase P, which cleaves tRNA precursors, and self-splicing introns in the Cell/35.html">Mitochondria of certain Ciliates.

Unlike non-protein catalysts (H⁺, OH^-, Metal Ions), each enzyme is capable of catalyzing only a very small number of reactions, often just one. Thus, enzymes are reaction-specific catalysts. Practically all biochemical reactions are catalyzed by enzymes.

Initially, enzymes were named by adding the suffix -ase to the name of the substrate upon which the enzyme acts. Thus, enzymes hydrolyzing starch (amylon) were named amylases; enzymes hydrolyzing fats (lipos), lipases; and enzymes hydrolyzing proteins, proteinases. Later, enzymes catalyzing similar types of reactions began to be named after the corresponding reaction type—dehydrogenases, oxidases, Decarboxylases, acylases, etc. Many of these names are still in use today. The nomenclature introduced by the International Union of Biochemistry (IUB) may seem complex and cumbersome at first glance, but it is unambiguous. Its core principle is that enzymes are named and classified According to the type of chemical reaction catalyzed and its mechanism; this greatly facilitates the systematization of data relating to various aspects of metabolism. The Main Features of the system introduced by the IUB are as follows.

1. Reactions and the enzymes that catalyze them are divided into six classes, each containing several subclasses (ranging from four to 13).

2. The name of an enzyme consists of two parts: the first part is the name of the substrate (or substrates); the second indicates the type of reaction catalyzed and ends in -ase.

3. Additional information, if necessary for clarification, is enclosed in parentheses. For example, The enzyme catalyzing the reaction L-malate + NAD+ = Pyruvate + CO2 + NADH + H+, has the number 1.1.1.37 and is called L-malate: NAD+ oxidoreductase (decarboxylating).

4. Each enzyme has an Enzyme Commission (EC) code number: the first digit characterizes the Class of the reaction, the second is the subclass, and the third is the sub-subclass. The fourth digit indicates the serial number of the enzyme within its sub-subclass. Thus, EC 2.7.1.1 means that the enzyme belongs to class 2 (transferase), subclass 7 (phosphotransferase), and sub-subclass 1 (where the phosphate acceptor is an alcohol). The last digit designates the enzyme hexokinase, or ATP: D-hexose-6-phosphotransferase, i.e., the enzyme that catalyzes The transfer of a phosphate group from ATP to the hydroxyl group of the carbon atom at position six of glucose. Below are all six classes of enzymes along with some specific Examples. The recommended name is indicated in parentheses.

Enzymes are divided into six classes according to the type of reaction they catalyze:

1. Oxidoreductases. Enzymes that catalyze oxidation-reduction Reactions Involving Two substrates, S and Ś:

S_red + Ś_ox = S_ox + Ś_red

They catalyze reactions involving groups such as CH — OH, CH — CH, C = O, CH — NH2, and — CH — NH —. Some subclasses:

1.1. Enzymes acting on the CH — OH group of Donors (electron donors). For example:

1.1.1.1. Alcohol: NAD+ oxidoreductase [Alcohol dehydrogenase]

Alcohol + NAD+ = Aldehyde or ketone + NADH + H+.

1.4. Enzymes acting on the CH — NH2 group of donors. For example:

1.4.1.3. L-Glutamate: NAD(P)+ oxidoreductase (deaminating) [Glutamate dehydrogenase from animal Liver]. The notation NAD(P)+ indicates that either NAD+ or NADP+ can serve as the electron acceptor.

L-Glutamate + H2O + NAD(P)+ = = α-Ketoglutarate + NH+4 + NAD(P)H + H+.

2. Transferases. Enzymes that catalyze the transfer of a group G (other than hydrogen) from a substrate S to a substrate Ś:

S — G + Ś = Ś — G + S.

They catalyze the transfer of single-carbon groups, aldehyde or ketone residues, as well as acyl, alkyl, glycosyl groups, and groups containing phosphorus and sulfur. Some subclasses:

2.3. Acyltransferases. For example:

2.3.1.6. Acetyl-CoA: Choline O-acetyltransferase [choline acetyltransferase]

Acetyl-CoA + Choline = CoA + O-Acetylcholine.

2.7. Enzymes catalyzing the transfer of phosphorus-containing groups. For example:

2.7.1.1. ATP: D-hexose 6-phosphotransferase [hexokinase]

ATP + D-Hexose = ADP + D-Hexose-6-phosphate.

3. Hydrolases. Enzymes catalyzing the Hydrolysis of ester, peptide, and glycoside bonds, acid anhydrides, C–C, C-halide, and P–N bonds.

S-Ś + H₂O = S + Ś

For example:

3.1. Enzymes acting on ester bonds. For example: 3.1.1.8. Acylcholine acylhydrolase [pseudocholinesterase]

Acylcholine + H₂O = Choline + Acid.

3.2. Enzymes acting on glycosyl compounds. For example:

3.2.1.23. β-D-Galactoside galactohydrolase [β-galactosidase]

β-D-Galactoside + H₂O = Alcohol + D-Galactose.

3.4. Enzymes acting on peptide bonds.

The Classification (divided into 11 subclasses) takes into account the differences between peptidases and proteases, distinguishes between enzymes that hydrolyze dipeptides or larger Peptides, those that cleave off one or more Amino Acids, and those attacking the bond at the C- or N-terminus. According to their catalytic mechanism, proteinases are subdivided into Serine, thiol, and metal-dependent enzymes. For example:

3.4.21. Serine proteinases. For example: Chymotrypsin, Trypsin, plasmin, Blood Coagulation factors IXa and XIa.

3.4.23. Carboxyl (acid) proteinases. For example, pepsins A, B, and C.

4. Lyases. Enzymes that cleave groups from substrates by non-hydrolytic mechanisms, resulting in The formation of double bonds.

Figure 79. Mechanism of lyase action

Enzymes acting on C–C, C–O, C–N, C–S, and C–halide bonds. Some subgroups include:

4.1.2. Aldehyde lyases. For example:

4.1.2.7. Ketose-1-phosphate aldolase [aldolase]

Ketose-1-phosphate = Dihydroxyacetone phosphate + Aldehyde.

4.2. Carbon–oxygen lyases. For example:

4.2.1.2. L-malate hydro-lyase [fumarase]

L-malate = Fumarate + H₂O.

5. Isomerases. This class includes all enzymes catalyzing the interconversion of optical, geometrical, or positional isomers.

S _D↔ S _L

Some subclasses:

5.2. Cis-trans isomerases. For example:

5.2.1.3 11-cis-trans isomerase [retinal isomerase]

5.3. Enzymes catalyzing the interconversion of aldoses and ketoses. For example:

5.3.1.1. D-Glyceraldehyde-3-phosphate ketol-isomerase [Triosephosphate isomerase]

D-Glyceraldehyde-3-phosphate = Dihydroxyacetone phosphate.

6. Ligases. (from Lat. ligare — to bind). Enzymes catalyzing the joining of two molecules, coupled with The breakdown of a pyrophosphate bond of ATP or a similar compound. This class includes enzymes that catalyze reactions resulting in the formation of C — O, C — S, C — N, and C — C bonds.

S + Ś = S-Ś

Some subclasses:

6.3. Enzymes catalyzing the formation of C — N bonds. For example:

6.3.1.2. L-Glutamate: ammonia ligase (ADP) [Glutamine Synthetase]

ATP + L-Glutamate + NH₄⁺ = ADP + Orthophosphate + L-Glutamine.

6.4. Enzymes catalyzing the formation of C — C bonds. For example:

6.4.1.2. Acetyl-CoA: CO₂ ligase (ADP) [acetyl-CoA carboxylase]

ATP + Acetyl-CoA + CO₂ = ADP + P_i + Malonyl-CoA.

Holoenzyme — a fully functional enzyme molecule

Apoenzyme — the protein moiety of an enzyme

Coenzyme — a specific, thermostable, low-molecular-weight organic compound that participates in an enzymatic reaction as an additional substrate, accepting chemical groups from one substrate and transferring them to another. Essentially, it acts as a second substrate permanently bound to the catalytic center.

If the enzyme is a simple protein, then holoenzyme = apoenzyme.

If the enzyme is a conjugated protein, holoenzyme = apoenzyme + coenzyme.

During the reaction, the coenzyme undergoes chemical changes that are precisely opposite to the changes occurring in the substrate. For example, in redox dehydrogenase reactions, the substrate molecule is oxidized while the coenzyme molecule is reduced. Similarly, in Transamination reactions, Pyridoxal phosphate acts both as a second substrate in two coupled reactions and as an amino group carrier between various α-amino and α-keto acids.

The second reason why a coenzyme can be considered an equal participant in the reaction is that its involvement can be of fundamental physiological significance. For instance, Muscle contraction under anaerobic conditions is accompanied by The conversion of pyruvate to lactate. However, neither lactate nor pyruvate is the primary focus here; the actual purpose of the reaction is the conversion of NADH to NAD+. In the absence of NAD+, Glycolysis cannot proceed, and anaerobic ATP synthesis (and consequently, Muscle Function) ceases. The reduction of pyruvate to lactate under anaerobic conditions ensures The oxidation of NADH to NAD+, which is essential for ATP synthesis. Other reactions can also fulfill the function of regenerating NAD+.

The Significance of this process becomes apparent when shifting from animals to Other forms of life. In Bacteria and Yeasts growing under anaerobic conditions, the substances derived from pyruvate act as oxidizing agents for NADH while being reduced themselves.

A coenzyme may be bound to the apoenzyme by covalent or non-covalent bonds. Reactions requiring the presence of coenzymes include oxidation-reduction reactions, group transfer and isomerization reactions, as well as Condensation reactions (classes 1, 2, 5, and 6 according to the IUB system). Cleavage reactions, such as hydrolytic Reactions Catalyzed by digestive enzymes, proceed in the absence of a coenzyme.

The following classification of coenzymes can be proposed (Table 3):

Table 3. Classification of coenzymes

All chemical reactions occur in accordance with Collision Theory.

Kinetic theory, or collision theory, is based on two key principles.

1. For a collision to be productive (i.e., leading to a reaction), the reacting molecules must possess sufficient energy to overcome the energy barrier.

It follows that when reacting molecules have sufficient energy, all factors increasing the frequency of their collisions will increase the reaction rate. Conversely, factors decreasing the frequency of molecular collisions or their kinetic energy lower the reaction rate.

If not all molecules in a population possess sufficient energy for the reaction to proceed, an increase in Temperature—accompanied by an increase in the kinetic energy of the molecules—will lead to an accelerated reaction rate. In case A, none of the molecules; in case B, a portion; and in case C, all molecules possess sufficient kinetic energy to overcome the energy barrier.

This collision energy is termed transition energy. In other words, molecules possessing excess energy collide and enter into a reaction.

Like any catalyst, enzymes lower the transition energy. In both cases, the Free energy of activation for the Transition State characterizes the energy barrier of the overall reaction (Figure 80). However, the energy barrier of the reaction proceeding through the [Y-R-•Х] transition state is lower than that of the reaction proceeding through the [Y-R-X] transition state. In the example above, [Y-R-X] represents the transition state of the uncatalyzed reaction, whereas [Y-R-X] b is the transition state of the catalyzed reaction. All catalysts, including enzymes, reduce the free energy of activation ΔG₀. Furthermore, note that the catalyst does not affect the magnitude of ΔG₀: The change in free energy of the overall reaction is independent of the presence of catalysts. The Equilibrium Constant of a chemical reaction is a function of the Standard Free Energy change of that reaction:

ΔG₀ = -RT ln Keq

It follows that enzymes and other catalysts do not affect the reaction equilibrium constant.

2. For a reaction to take place, molecules must collide with one another, i.e., approach each other to distances sufficient for bond formation. This can be achieved either by increasing the concentration of reactants or by bringing them together at a single point in space, thereby increasing their local concentration—a process that frequently occurs during the functioning of catalysts.

This representation emphasizes three important features of enzymatic group-transfer reactions.

1. Each half-reaction is accompanied by both the cleavage and the formation of a covalent bond.

2. The enzyme acts as an equal reactant, just like D — G and A.

3. While the enzyme Functions as a catalyst in the overall reaction (i.e., it is required only in trace amounts and is regenerated to its original state upon completion of the reaction), in each half-reaction the enzyme acts as a stoichiometric reactant (i.e., it reacts with other reactants in a 1:1 molar ratio). Many other biochemical reactions can be viewed as special cases of transfer reactions in which either A, D, or both reactants are absent. For example, an isomerization reaction (such as the interconversion of glucose-6-phosphate and glucose-1-phosphate) can be represented as a transfer reaction lacking D and A.

Figure 80. Mechanism of enzyme Action. A — free energy profile during a chemical reaction, B — local concentration changes during enzyme catalysis

From the foregoing, it is clear that for a reaction to proceed, all participating reactants must approach one another to distances sufficient for bond formation (or cleavage), i.e., they must collide. In homogeneous solution chemistry, the concentration of reacting molecules in the absence of catalysts is considered uniform throughout the solution. However, in the presence of a catalyst, this condition no longer holds. For efficient function, a catalyst must possess binding sites for reactant molecules on its surface. Such binding is a reversible process, but the equilibrium lies heavily in the direction of complex formation. Qualitatively, this can be represented as follows:

Reactant + Catalyst = Reactant-catalyst complex.

The Stability of the complex formed by reactant R and catalyst C can be quantified using the dissociation constant of the R — C complex (Kd). An important consequence follows from this: the binding of a reactant to a catalyst leads to a marked increase in the local concentration of the reactant compared to its concentration in the bulk solution.

If the catalyst of a biomolecular reaction (involving two reactants) binds both reactants, the local concentration of each increases, with the degree of this increase depending on the affinity of the catalyst for the given reactant (Kd). One of the key factors enabling an enzyme to function as a catalyst is its ability to efficiently bind one or (more frequently) both reactants participating in a bimolecular reaction, leading to an increased local concentration of the reactants and, consequently, a local acceleration of the reaction rate. The fact that enzymes are exceptionally efficient and highly selective compared to most non-protein catalysts requires further explanation. To understand these distinctive Properties of Enzymes, we must introduce THE CONCEPT OF the active, or catalytic, site.

The size of proteins far exceeds that of low-molecular-weight substrates, which led to the concept that only a limited region of the enzyme molecule participates in catalysis. We refer to this region as the catalytic center. The catalytic center consists of several amino acid residues that form a distinct part of the protein where the enzymatic reaction takes place. Initially, it was unclear why enzyme molecules are so large if only a fraction of their Structure is involved in substrate binding and direct catalysis. However, as 3D structural analysis of enzymes has shown, a much larger portion of the protein molecule interacts with the substrate than previously assumed. When one also considers the involvement of allosteric centers of similar size, the bulkiness of enzymes is hardly surprising.

Most substrates form at least three bonds with the enzyme. Thanks to this "three-point attachment", a symmetrical molecule can exhibit Asymmetry. To illustrate this, let us imagine the substrate-binding region of an enzyme as a flat surface (although, as we will soon see, the substrate-binding "site" of an enzyme is rarely flat, and perhaps never is). If a substrate molecule can approach this site from only one side, and only complementary structures of the substrate and enzyme can interact (both of which conditions are met in real enzymes), then the substrate molecule can bind to the enzyme in only one way, even if groups 1 and 3 are identical. Mentally running through all possible spatial orientations of the substrate molecule, one can verify that the molecule can bind to three points on a flat surface (on the same side) in only a single orientation. It follows that groups 1 and 3, although identical, become non-equivalent upon binding to the enzyme due to differences in their microenvironment. Chemical changes will occur exclusively at group 1 and not at group 3 (or vice versa). Generalizing this reasoning, we can now explain why the enzymatic reduction of optically inactive pyruvate yields specifically L-lactate rather than D,L-lactate. It is precisely this mode of attachment that ensures Enzyme Specificity.

Figure 81. Mechanism of binding at a minimum of 3 points

The ability of an enzyme to catalyze one and only one specific reaction is arguably its most important property. Consequently, the rates of specific Metabolic pathways can be regulated by altering the catalytic activity of specific enzymes. Admittedly, Many enzymes catalyze reactions of a single type (e.g., phosphoryl transfer, oxidation-reduction reactions), with small numbers of structurally similar compounds serving as substrates. Reactions with alternative substrates occur when these substrates are present in high concentrations. Whether all reactions theoretically possible with a given enzyme actually take place in living organisms depends on the relative intracellular concentration of alternative substrates and the relative affinity of the enzyme for those substrates.

With the exception of epimerases (racemases), which catalyze the interconversion of optical isomers, enzymes generally exhibit absolute optical specificity, at least with respect to one part of the substrate molecule. For instance, Enzymes of the glycolytic and direct oxidative pathways catalyze the transformation of D-phosphosugars exclusively, never L-phosphosugars. With rare exceptions (such as mammalian renal D-Amino Acid Oxidase), most mammalian enzymes catalyze the transformation of L-isomers of amino acids only.

Optical specificity may apply to a molecular fragment or to the molecule as a whole. A case in point is the specificity of glycosidases. These enzymes catalyze the hydrolysis of glycosidic bonds between a sugar and an alcohol group: they are highly specific for both the sugar moiety and the configuration of the glycosidic bond (α or β), yet relatively non-specific for the alcohol moiety of the molecule.

Lytic enzymes act on specific chemical groups: glycosidases on glycosidic bonds, Pepsin and trypsin on peptide bonds. The action of these enzymes extends across a wide range of substrates, allowing the Organism to make do with a modest repertoire of digestive enzymes—otherwise, a vastly greater number would be required.

Certain lytic enzymes display even higher group specificity. For example, chymotrypsin preferentially hydrolyzes peptide bonds in which the carboxyl group belongs to aromatic amino acids such as phenylalanine, Tyrosine, or Tryptophan. Carboxypeptidases and aminopeptidases cleave amino acids one at a time from the carboxy- and amino-termini, respectively.

Some oxidoreductases can utilize both NAD+ and NADPH as electron acceptors, but the majority employ only one of them. In summary, mammalian oxidoreductases involved in biosynthetic processes (such as fatty acid or steroid synthesis) typically use NADPH as the reductant, whereas those participating in Catabolism rely on NADH.

The original model of the catalytic center, proposed by Emil Fischer, depicted the interaction between substrate and enzyme by analogy with a "lock and key" system. This model, sometimes referred to as the "rigid template" model, remains valuable for understanding certain enzyme properties, such as their capacity for strictly defined binding of two or more substrates, or for explaining substrate saturation kinetics (Figure 82 A).

Figure 82. Models of enzyme-substrate interaction. A—lock-and-key model, B—induced-fit model

A limitation of Fischer's model is its inherent assumption of a rigid catalytic center. A more generalized concept is the induced-fit model (Figure 82 B) proposed by Koshland, which is supported by compelling experimental evidence. Its defining feature is The flexibility of the catalytic center. While Fischer's model assumes the catalytic center is pre-molded to fit the shape of the substrate molecule, the induced-fit model posits that the substrate induces Conformational Changes in the enzyme; only As a result of these changes do The amino acid residues and other groups of the enzyme attain the precise spatial orientation required for substrate binding and catalysis. Concurrently, other amino acid residues may become buried deep within the interior of the enzyme molecule. As the substrate approaches the enzyme, it induces conformational changes that position the relevant groups properly for binding and catalysis. Simultaneously, the spatial arrangement of other residues shifts—bringing Lys and Met into close proximity. Substrate analogs can also trigger conformational changes, though not all of them result in the "correct" fit. When the true substrate binds (A), all groups fall into their proper places. Conversely, when a substrate analog—whether too bulky or too small—binds, it induces an improper alignment of these groups.

Under laboratory conditions, the Rate of Enzymatic reactions is influenced by the following factors:

Enzyme Concentration

Substrate Concentration

temperature

pH

presence of inhibitors.

Within a certain limited temperature range, The rate of an enzymatic reaction increases with rising temperature. The coefficient indicating the factor by which the reaction rate increases with a 10° temperature rise is called the temperature coefficient and is denoted by Q₁₀. For many biological reactions, a 10° temperature rise doubles the rate (Q₁₀ = 2), and conversely, a 100 drop in temperature halves it. Many physiological processes (for example, the contraction rate of an isolated Heart muscle) are also characterized by a Q₁₀ coefficient close to two. However, at a certain optimal temperature, the reaction rate reaches its maximum. The increase in reaction rate as the optimum temperature is approached is explained by the growth in kinetic energy of the reacting molecules. With a further increase in temperature, the kinetic energy of the enzyme molecule becomes sufficient to break the bonds maintaining the Introduction/11.html">Secondary structure of the enzyme in its native, catalytically active state (thermal Denaturation of the enzyme occurs). The secondary and tertiary structures of the enzyme are disrupted, which is accompanied by a loss of catalytic activity. Enzyme denaturation leads to a decrease in the reaction rate due to a reduction in the concentration of the enzyme (catalyst).

For most enzymes, the optimum temperature is equal to or higher than the temperature normally experienced by Cells. For enzymes of microorganisms adapted to living in natural hot springs, the optimum temperature can be close to the boiling point of Water.

Moderate pH changes affect the ionic state of the enzyme, and frequently of the substrate as well. As measurements of enzymatic activity at various pH levels show, the activity optimum typically lies between pH 5.0 and 9.0. At the same time, certain enzymes, such as pepsin, remain active at pH values far beyond this range.

The dependence of activity on pH is determined by the following factors.

1. Denaturation of the enzyme at very high or very low pH values. When the pH changes, enzymes may undergo conformational changes. Maintaining an active tertiary or quaternary structure may require the presence of a specific charge on a group located away from the substrate-binding site; precisely this situation is observed in the case of Hemoglobin. If the charge of this group changes, it can lead to a partial unfolding of the protein chain, or conversely, to the compaction of the molecule, or its dissociation into protomers—in all cases resulting in a loss of activity.

2. Changes in the charge magnitude of the substrate or enzyme molecules. Enzyme activity can change as a result of alterations in either its structure or the charge of functional residues participating in catalysis or substrate binding. Let us consider, for example, the interaction between a negatively charged enzyme (Enz^-) and a positively charged substrate (SH⁺). At low pH values, protonation of Enz^- occurs, while at high pH values, deprotonation of the substrate takes place. Since only SH⁺ and Enz^- can interact with one another, under extreme pH conditions the effective concentration of Enz^- or SH⁺ will be low, leading to a decrease in the reaction rate.

In many cases, knowing simply that a given enzyme is present in the system is not enough; information about its quantity is also required. Under certain conditions, the rate of an enzymatic reaction is directly proportional to The amount of enzyme. This is not always the case, which can be illustrated using the example of a forward reaction proceeding under equilibrium conditions. Even if we know that the forward reaction is indeed taking place, its rate will appear to be zero because the reverse reaction is proceeding at the exact same rate. However, when an enzymatic reaction is just beginning, product is practically absent and the reverse reaction does not take place. Furthermore, at the initial stage of the reaction, the substrate concentration corresponds to its initial amount. Therefore, the rate at the beginning of the reaction—i.e., its initial velocity (v), will be directly proportional to the enzyme concentration [Enz].

The enzyme acts as a reactant that combines with the substrate to form an enzyme-substrate complex Enz — S, which dissociates into the free enzyme and product P. In its simplest form, this can be written as

Thus, enzyme concentration has no effect on the equilibrium constant. Keq is independent of how equilibrium is reached—whether with or without the participation of an enzyme (recall the value of ΔG°). The enzyme alters the pathway by which the reaction proceeds, but not the final (equilibrium) concentrations of reactants and products upon which Keq and ΔG° depend.

Thus, enzyme concentration affects the rate of an enzymatic reaction only at the Initial Stages of the process; consequently, this mechanism of influencing the reaction rate is inefficient and therefore not utilized. On the other hand, small amounts of Enzymes can be used to drive a reaction to completion.

When studying the Dependence of enzymatic reaction rate on substrate concentration, enzyme reactions involving a single substrate and a single product have been examined. Such a situation is indeed observed for certain enzymatic reactions, but the majority of them proceed with the participation of two or more substrates and products. This, however, does not diminish the value of the following Discussion in the slightest. What holds true for a single substrate remains valid for two.

With an increase in substrate concentration [S] and all other conditions remaining constant, the initial velocity v (the rate measured during the period when a very small fraction of the substrate has been consumed) will increase up to a maximum value Kmах, after which it remains constant.

As the substrate concentration increases, the rate will grow until the enzyme becomes saturated with the substrate. The initial velocity measured under such conditions will no longer increase with a further rise in substrate concentration. Note that the substrate is usually taken in a significant molar excess relative to the enzyme. For example, if an enzyme with a Molecular Weight of 100,000 interacts with a substrate having a molecular weight of 100, and both are present at a concentration of 1 mg/mL, there will be 1,000 moles of substrate for every mole of enzyme. More realistic values are as follows:

[Enz] = 0.1 µg/mL = 10^—9 M, [S] = 0.1 mg/mL = 10^—3 M,

i.e., the molar excess of substrate relative to the enzyme is 10⁶.

Even if [S] is reduced by a factor of 100, its concentration will still exceed that of the enzyme by 10,000 times. At points A and B, only a fraction of the enzyme molecules are complexed with the substrate, even though substrate molecules vastly outnumber enzyme molecules. This occurs because the equilibrium constant of the reaction Enz + S +± Enz — S (Formation of the Enz — S complex), although large, is finite. Thus, at points A and B, an increase or decrease in [S] will lead to an increase or decrease in the fraction of Enz molecules bound to S (i.e., the fraction of Enz — S molecules), and v will depend on [S]. At point C, practically all enzyme molecules are bound to the substrate, and a further increase in [S], although it will increase the frequency of collisions between Enz and S, cannot lead to an increase in the reaction rate—since there are no longer any enzyme molecules available to react with the substrate.

Case B is of special theoretical interest because exactly half of the enzyme molecules are saturated with substrate under these conditions. Accordingly, the rate is equal to half the maximum velocity (V_mdJ2) achievable at the given enzyme concentration.

The Michaelis-Menten equation describes the dependence of the enzymatic reaction rate on substrate concentration. Enzyme E combines with substrate S to form an ES complex; the rate constant for this process is k₁. The Fate of the ES complex can unfold in two ways: it can either dissociate into E and S with a rate constant k₂, or undergo further transformation to yield product P with a rate constant k₃ (Figure 83–1). It is postulated that the reaction product P does not revert to the starting substrate S; this condition is met during the initial stage of the reaction, before the product concentration reaches a significant level.

How is the rate of catalysis related to the concentrations of substrate and enzyme and the rate constants of individual reaction steps? To begin with, the rate of an enzymatic reaction is equal to the product of the concentration of the ES complex and the constant k₃ (Figure 83–2).

Let us express [ES] in terms of known quantities. Rates of formation and breakdown of ES (Figure 83—3,4).

Let us determine the rate of catalysis under steady-state conditions. Steady-state conditions are characterized by the fact that the concentration of intermediate products remains constant, whereas the concentrations of initial and final products change. This occurs when the rate of Synthesis of the ES complex equals the rate of its breakdown. If the left-hand sides of the equalities are equal to each other, then the right-hand sides are equal as well (Figure 83—5).

Let us transform this equation (Figure 83—6).

The equation can be simplified by introducing a new constant, K_m, called the Michaelis constant (Figure 83—7).

Let us substitute K_m into the equation (Figure 83—8).

Let us examine the numerator in the last expression. The concentration of uncomplexed substrate [S] is practically equal to the total substrate concentration, provided that the enzyme concentration is significantly lower than the substrate concentration. The concentration of uncomplexed enzyme (E) is equal to the total enzyme concentration E_t minus the concentration of the ES complex (Figure 83—9).

Let us substitute this expression into the equation (Figure 83—10).

Solving the equation for [ES] yields (Figure 83—11) or (Figure 83—12).

Let us substitute this expression into the reaction rate equation (Figure 83—13).

After transformation, we obtain the final version of the Michaelis—Menten equation (Figure 83—15).

Figure 83. Derivation of the Michaelis-Menten equation

Graphical Determination of the Michaelis constant K_m

The substrate concentration at which the velocity is half of the maximum is designated as K_m and is called the Michaelis constant. It can be determined from the plot of v versus [S]. Note that K_m has the dimensions of molar concentration.

Figure 84. Graph of the enzymatic reaction rate versus substrate concentration (described by the Michaelis-Menten equation)

When [S] approaches K_m, v becomes highly sensitive to changes in [S]; in this region, the enzyme operates at half-maximal velocity. Many enzymes are characterized by K_m values that roughly correspond to the physiological concentrations of their substrates.

The Michaelis—Menten equation describes The behavior of many enzymes as substrate concentrations change (Figure 84). Using this equation, the dependence of the initial enzymatic reaction rate on [S] and K_m can be illustrated by the following specific examples.

1. [S] is much less than K_m (point A).

In this case, the term [S] in the denominator can be neglected, and the denominator will be practically equal to K_m. The ratio of the two constants, V_max and K_m, can be replaced by a new constant k. Thus, we have:

In other words, when the substrate concentration is significantly lower than that at which the reaction rate is half of the maximum (i.e., much less than K_m), the initial velocity v is proportional to the substrate concentration [S].

2. [S] is much greater than K_m (point C). In this case, the term K_m in the denominator can be neglected, i.e., This means that at a substrate concentration [S] far exceeding K_m, the initial velocity v equals the maximum velocity V_max.

3. [S] = K_m (point B). This means that at a substrate concentration equal to K_m, the initial reaction rate v is half of the maximum. This also suggests a way to estimate K_m: one must experimentally determine the substrate concentration at which the initial velocity is half-maximal.

As can be seen from the figure, the graph described by the Michaelis-Menten equation is a curve. For the curve to be accurate, a maximum number of points is required for its construction; consequently, a multitude of reaction rate measurements at various substrate concentrations is necessary. Whereas plotting a straight line requires only 3–5 points and thus 3–5 measurements, this is precisely why the Michaelis-Menten equation was transformed (Figures 85, 86). The graph is plotted in reciprocal coordinates 1/V and 1/[S]. For the transformation, 1 must be divided by the equation:

Figure 85. Lineweaver-Burk transformation

As can be seen from the transformation, this equation can be reduced to the linear equation y = ax + b, where y = 1/V; x = 1/[S]. Named after its authors, this transformation is known as the Lineweaver-Burk plot.

When using the Lineweaver-Burk plot in practice to estimate K_m, one sometimes encounters the problem that almost all data points cluster in the region of low substrate concentrations. This occurs when measurements are taken at equal intervals of [S]. To avoid this, measurements should be carried out at [S] values that correspond to equal intervals on the reciprocal scale.

Figure 86. Lineweaver–Burk plot

Estimates of Km have significant practical value. At substrate concentrations 100 times higher than Km, the enzyme operates at nearly maximum velocity; therefore, the maximum velocity (Vmax) reflects the amount of active enzyme present. This crucial aspect is utilized to assess enzyme content in a preparation. The Km value provides a useful guide for determining how much substrate should be added to measure Vmax. Double-reciprocal plots find widespread application in evaluating the action of inhibitors.

On the other hand, Km is related to the dissociation constant of the enzyme–substrate complex, that is, to the affinity of the enzyme for its substrate (Figure 87).

Figure 87. Relationship between Km and Kd

The affinity of an enzyme for its substrate is equal to the reciprocal of the dissociation constant K of the Enz — S complex:

In other words, the lower the tendency of the enzyme–substrate complex to dissociate, the higher the affinity of the enzyme for the substrate. The Kd value can serve as an approximate measure of Km for a given enzyme with respect to its substrate. However, this is only valid if the assumption used in deriving the Michaelis–Menten Equation holds true. This assumption states that the first step of the enzymatic reaction is rapid and that equilibrium is consistently maintained at this stage. In other words, the rate of dissociation of Enz — S into Enz + S is much higher than the rate of dissociation into enzyme and product. It follows from the Michaelis–Menten equation that the concentration [S] at which v = 1/2Vmax is equal to

Under these conditions, 1/KM = 1/Kd, which corresponds to the enzyme's affinity for the substrate. If k2 + k-1 does not equal k-1, then 1/Km will yield an underestimated value of affinity.

Certain enzymes and other Ligand-binding proteins, such as hemoglobin, do not obey classical Michaelis–Menten saturation kinetics. In this case, the plot of v versus [S] is sigmoidal in nature. This typically indicates cooperative substrate binding by multiple sites—binding at one site affects binding at another, as occurs with hemoglobin. Under such circumstances, the graphical method described above for estimating the substrate concentration at which the reaction rate is half-maximal becomes inapplicable (a straight line in the corresponding coordinates is no longer obtained). Instead, one must turn to the graphical representation of the Hill equation, originally proposed to describe the Cooperative binding of O₂ to hemoglobin.

Figure 88. The Hill equation and its corresponding plot

The Hill equation, rearranged so that its plot in appropriate coordinates yields a straight line, takes the form where k′ is a constant. It follows from the equation that under conditions where [S] is small compared to k′, the reaction rate increases as the n-th power of [S]. A Hill plot constructed from kinetic data for an enzyme characterized by cooperative substrate binding is shown (Figure 88). The plot of log (V/Vmax — V) versus log [S] is a straight line with a slope equal to n, where n is an empirical parameter that depends on the number of substrate-binding sites and The Nature of the interactions between them. When n = 1, the binding sites are independent of one another. When n > 1, cooperative interaction exists between the sites; the larger n, the higher the degree of cooperativity and the more pronounced the sigmoidal shape of the saturation curves. When n < 1, negative cooperativity is observed. When the reaction rate is equal to half the maximum (V = Vmax/2, V/ (Vmax -V) = 1, and log [V/ (Vmax —V)] = 0. Thus, to determine the value of S50 (the substrate concentration at which the velocity is half-maximal), one drops a perpendicular from the point on the line where log [V/ (Vmax — V)] = 0 to the x-axis.

Inhibitors are chemical substances that decrease the rate of an enzymatic reaction.

Enzyme Inhibitors are broadly divided into two major classes—Competitive and non-competitive—based on whether their inhibitory effect is diminished (competitive inhibition) or unaffected (non-competitive inhibition) by increasing substrate concentration. In practice, many inhibitors do not exhibit the properties typical of purely competitive or purely non-competitive inhibition. Another classification approach is based on the nature of their binding site. Some inhibitors bind to the enzyme at the same site as the substrate (the catalytic site), while others bind at a considerable distance from the Active Site (the allosteric site). Inhibition is also subdivided into

Competitive Inhibition by Substrate Analogues

Classical competitive inhibition is based on the binding of an inhibitor to the substrate-binding (catalytic) site. The Chemical Structure of a substrate analogue acting as an inhibitor (I) is typically similar to that of the substrate (S). Therefore, the inhibitor can reversibly bind to the enzyme, forming an Enz — I complex instead of an Enz — S complex (i.e., an enzyme-inhibitor complex). When both the substrate and this type of inhibitor are present simultaneously in the reaction mixture, they compete for the same binding site on the enzyme's surface. One of the most thoroughly studied examples of competitive inhibition is the inhibition of succinate dehydrogenase by malonate (I), which competes for the same site with the substrate succinate (S). In competitive inhibition, the apparent K_m is affected; as the substrate concentration increases, the probability of inhibitor binding decreases and the reaction rate increases. Thus, in competitive inhibition, the reaction rate can approach its normal maximum, but only at very high substrate concentrations.

Reversible Non-Competitive Inhibition

As the name implies, in this case there is no competition between the substrate (S) and the inhibitor (I). The inhibitor typically bears no structural resemblance to S and is presumed to bind to a different region of the enzyme. Reversible non-Competitive Inhibitors lower the maximum velocity achievable with a given amount of enzyme (decrease V_max), but generally do not affect K_m. Since I and S bind to different sites, the formation of both the Enz — I complex and the Enz — IS complex is possible. The Enz — IS complex also breaks down to yield the product, albeit at a lower rate than the Enz — S complex; therefore, the reaction will slow down but not stop. Consequently, the following competing reactions may take place:

Irreversible Non-Competitive Inhibition

Enzymatic activity can be reduced in the presence of numerous "poisons," such as iodoacetamide, heavy metal ions (Ag⁺, Hg²⁺), oxidizing agents, etc. In the presence of one or more substrates or products, the rate of Enzyme inactivation may decrease. In this case, inhibition is caused by partial denaturation of the enzyme.

The Cell also regulates the rates of enzymatic reactions to control its metabolism. However, a cell cannot alter the temperature or pH of its environment, and changes in substrate concentrations serve as a signal to adjust reaction rates. This situation is closely linked to the concept of Homeostasis. Homeostasis is the state of constancy in the internal environment and physiological functions (such as temperature and pH) of both the cell and the organism as a whole.

Therefore, within a living cell, the rates of enzymatic reactions can be regulated by altering the following parameters:

1) the absolute amount of enzyme present;

2) the pool of reactants (other than the enzyme);

3) the catalytic efficiency of the enzyme.

Most life forms utilize all Three types of regulation.

Regulation of enzyme quantity through the control of its Synthesis and degradation rates

The absolute amount of an enzyme within a cell is determined by the rates of its synthesis (K_синт) and degradation (K_расп). Consequently, the enzyme level increases either as a result of an accelerated synthesis rate (increased K_синт), a reduced degradation rate (decreased K_расп), or both simultaneously. Regulation occurs at the level of Gene Expression. By increasing the rate of gene expression—primarily Transcription and, to a lesser extent, Translation—the amount of protein can be augmented. Conversely, blocking gene transcription reduces the amount of the gene-encoded protein until it disappears entirely.

Conversion of proenzymes into active enzymes

Enzymatic activity can be regulated by converting an inactive proenzyme into a catalytically active form. To transition into this state, the proenzyme must undergo Limited proteolysis accompanied by conformational changes; this process either unmasks or forms the catalytic center. Synthesis in the form of catalytically inactive proenzymes is a hallmark of digestive enzymes, as well as enzymes involved in blood clotting and Fibrinolysis.

Enzyme compartmentalization

The Role of compartmentalization (spatial Separation) of metabolic processes in Eukaryotic cells, including mammalian cells, cannot be overstated. The localization of specific metabolic processes in the Cytosol or within cellular Organelles facilitates the independent regulation of these pathways. Advanced compartmentalization of metabolic processes is particularly characteristic of higher life forms, allowing for the most fine-tuned REGULATION OF METABOLISM. At the same time, this gives rise to a new challenge: The transport of metabolites across separating barriers. This problem is solved using "shuttle mechanisms" that convert the metabolite into a form capable of crossing the barrier. Once on the other side of the barrier, the reverse reaction converts the metabolite back to its original form. Due to the presence of these barriers, There is a need for the functioning of, for example, cytosolic and mitochondrial forms of certain enzymes. Because these enzyme forms are physically separated, their independent regulation is greatly facilitated.

Allosteric Regulation

In allosteric regulation, low-molecular-weight compounds, or Allosteric regulators, bind to the enzyme, resulting in A change in protein conformation. It should be recalled that when this molecule embeds itself, bonds within the Protein Structure are altered—a process characteristic of any protein-ligand binding. This leads to a rearrangement of bonds and, consequently, a change in protein conformation. These molecules can lead to two opposite outcomes. Depending on the molecule, the bonds formed may differ, and consequently so do the structural rearrangements within the protein molecule. Therefore, allosteric modulators can alter protein conformation either toward increasing affinity for the substrate—thus enhancing protein activity, in which case the molecule acts as a positive modulator—or conversely, by embedding itself and altering the conformation such that the protein becomes less active, resulting in noncompetitive reversible inhibition.

Around 1963, Monod drew attention to the lack of structural similarity between a feedback inhibitor acting on an enzyme and the enzyme's substrate. The lack of isostericity with the substrate justifies referring to the corresponding effectors as allosteric. Based on this, Monod suggested that enzymes regulated by such allosteric effectors (specifically feedback inhibitors) bind the effector at an allosteric site that is physically distinct from the catalytic center. Thus, allosteric enzymes are those whose catalytic center activity is modulated by allosteric effectors binding at an allosteric site. Data confirming the presence of physically separate allosteric sites in regulatory enzymes are summarized as follows.

1. Regulatory enzymes, after modification by chemical or physical Methods, often become insensitive to allosteric effectors while retaining their catalytic activity.

2. Allosteric effectors often protect the catalytic center from denaturation under conditions where the substrate exerts no such protective effect.

3. Mutant bacterial and mammalian cells have been discovered in which regulatory enzymes exhibit significantly different regulatory properties compared to wild-type enzymes, yet retain identical catalytic properties.

4. It has been shown that the binding of substrates and allosteric effectors to a regulatory enzyme occurs independently.

5. In some enzymes (e.g., ATPase), the allosteric and catalytic centers are localized on different protomers.

Covalent Modification of enzymes

The reversible alteration of enzyme catalytic activity can be achieved through the covalent attachment of a phosphate group (predominant in mammals) or a nucleotide (predominant in bacteria). Enzymes subject to covalent modification accompanied by changes in activity are referred to as reversibly modified enzymes.

Reversibly modified enzymes can exist in two states, one characterized by high catalytic efficiency and the other by low catalytic efficiency. Depending on the specific case, the more active catalyst may be either the phospho- or the dephospho-enzyme.

Typically, a specific serine residue is phosphorylated, forming an O-phosphoserine residue; less commonly, a tyrosine residue is phosphorylated to form an O-phosphotyrosine residue. Although a reversibly modified enzyme may contain many serine or tyrosine residues, phosphorylation occurs with a high degree of selectivity, affecting only a small number (1–3) of residues. These sites presumably do not form part of the catalytic center; thus, we have yet another example of allosteric effects.

This modification requires a donor molecule supplying the modifying group and an enzyme that carries out the modification. In eukaryotes, the phosphate group donor for modification is ATP, and the modification is catalyzed by protein Kinases. Protein kinases constitute a very large class of proteins that specifically phosphorylate various enzymes. In prokaryotes, the donor of ADP-ribose is NAD. Differences in the modifying groups led to a divergence in the modifying and demodifying enzymes. Consequently, eukaryotes lack enzymes capable of removing ADP-ribose from a modified enzyme. This feature forms the basis for the Action of Certain toxins. For example, diphtheria toxin ADP-ribosylates the ribosome, completely blocking its function; human cells lack enzymes to remove this modifying group, leading inevitably to cell death due to halted protein biosynthesis. Cholera toxin irreversibly ADP-ribosylates adenylate cyclase in The Plasma Membrane of small intestinal epithelial cells, severely disrupting all absorption processes.

Isoenzymes are enzymes that differ in activity within a single organism across different Tissues, during ontogenesis, or among different individuals of the same species.

Isoenzymes differ both in their population distribution and in their tissue localization. Much like isoproteins, isoenzymes can exhibit varying distributions across body tissues and during ontogenesis. The term "isoenzyme" (or "isozyme") encompasses all aforementioned physically distinct proteins possessing a given catalytic activity; however, in practice—particularly in clinical medicine—it is used in a narrower sense to denote physically distinct and separable forms of a given enzyme present in different cell types of a given eukaryotic organism, such as humans. Isoenzymes are invariably found in the serum and tissues of all vertebrates, insects, and unicellular organisms, though their number and concentration vary widely. Isoenzymatic forms of dehydrogenases, oxidases, transaminases, Phosphatases, transphosphorylases, and Proteolytic Enzymes are well documented. Different tissues may contain distinct isoenzymes, and these isoenzymes may exhibit different substrate affinities.

Lactate dehydrogenase isoenzymes differ at the level of quaternary structure. The oligomeric lactate dehydrogenase molecule (molecular weight 130,000) consists of four protomers of two types, H and M (each with a molecular weight of approximately 34,000). Only the tetrameric molecule possesses catalytic activity. Assuming the order of subunit assembly does not matter, the protomers can be arranged in five ways:

HHHH

HHHM

HHMM

HMMM

MMMM

Markert selected conditions for the dissociation and reassociation of the Quaternary Structure and successfully elucidated the relationships among lactate dehydrogenase isoenzymes. Cleavage and reassembly of lactate dehydrogenases I₁ and I₅ do not lead to the formation of new isoenzymes. Consequently, these two isoenzymes contain only a single type of protomer. When a mixture of lactate dehydrogenases I₁ and I₅ was subjected to the same Procedure, forms I₂, I₃, and I₄ also appeared. The ratio of the isozymes corresponds to the subunit composition given below:

I₁— HHHH

I₂— HHHM

I₃-HHMM

I₄— HMMM

I₅ -MMMM

The synthesis of H- and M-subunits is determined by different genetic loci, and they are expressed differently across various tissues (for instance, in cardiac and skeletal Muscles).

Another example is provided by isoforms of cytochrome P450, which exists in two forms: normal and highly active, the latter being responsible for the organism's predisposition to various oncological diseases. Most commonly, The Emergence of protein isoforms is caused by point Mutations that have not been subjected to the pressure of natural Selection.