The maximum rate of the enzymatic reaction. Enzymatic reactions kinetics

Almost all biochemical reactions are enzymatic. Enzymes(biocatalysts) are substances of a protein nature activated by metal cations. About 2000 different enzymes are known, and about 150 of them have been isolated, some of which are used as drugs. Trypsin and chymotrypsin are used to treat bronchitis and pneumonia; pepsin - for the treatment of gastritis; plasmin - for the treatment of heart attack; pancreatin - for the treatment of the pancreas. Enzymes differ from conventional catalysts in (a) higher catalytic activity; (b) high specificity, i.e. selective action.

The mechanism of a single-substrate enzymatic reaction can be represented by the scheme:

where E is an enzyme,

S - substrate,

ES - enzyme-substrate complex,

R is the product of the reaction.

The characteristic of the first stage of the enzymatic reaction is Michaelis constant (K M). K M is the reciprocal of the equilibrium constant:

the Michaelis constant (KM) characterizes the stability of the enzyme-substrate complex (ES). The smaller the Michaelis constant (KM), the more stable the complex.

The rate of an enzymatic reaction is equal to the rate of its rate-limiting step:

where k 2 is the rate constant, called number of revolutions or molecular activity of the enzyme.

molecular activity of an enzyme(k 2) is equal to the number of substrate molecules undergoing transformations under the influence of one enzyme molecule in 1 minute at 25 0 C. This constant takes values ​​in the range: 1 10 4< k 2 < 6·10 6 мин‾ 1 .

For urease, which accelerates the hydrolysis of urea, k 2 = 1.85∙10 6 min‾ 1; for adenosine triphosphatase, which accelerates the hydrolysis of ATP, k 2 = 6.24∙10 6 min‾ 1; for catalase, which accelerates the decomposition of H 2 O 2, k 2 = 5∙10 6 min‾ 1.

However, the kinetic equation of the enzymatic reaction in the form in which it is given above is practically impossible to use due to the impossibility of experimentally determining the concentration of the enzyme-substrate complex (). Expressing in terms of other quantities, easily determined experimentally, we obtain the kinetic equation of enzymatic reactions, called Michaelis-Menten equation (1913):

,

where the product k 2 [E]tot is the value of the constant, which is denoted by (maximum speed).

Respectively:

Consider special cases of the Michaelis-Menten equation.

1) At a low substrate concentration, K M >> [S], therefore

which corresponds to the kinetic equation of the first order reaction.

2) At a high concentration of the substrate K m<< [S], поэтому

which corresponds to the kinetic equation of the zero order reaction.

Thus, at a low substrate concentration, the enzymatic reaction rate increases with an increase in the substrate content in the system, and at a high substrate concentration, the kinetic curve reaches a plateau (the reaction rate does not depend on the substrate concentration) (Fig. 30).

Figure 30. - Kinetic curve of the enzymatic reaction

If [S] = K M, then

which allows you to graphically determine the Michaelis constant K m (Fig. 31).

Figure 31. - Graphical definition of the Michaelis constant

Enzyme activity is influenced by: (a) temperature, (b) acidity of the medium, (c) the presence of inhibitors. The effect of temperature on the rate of an enzymatic reaction is discussed in chapter 9.3.

The influence of the acidity of the medium on the rate of the enzymatic reaction is shown in Figure 32. The maximum activity of the enzyme corresponds to the optimal value of the pH value (pH opt).

Figure 32. - Influence of the acidity of solutions on the activity of enzymes

For most enzymes, the optimal pH values ​​coincide with physiological values ​​(7.3 - 7.4). However, there are enzymes that require a strongly acidic (pepsin - 1.5-2.5) or fairly alkaline environment (arginase - 9.5 - 9.9) for their normal functioning.

Enzyme inhibitors- These are substances that occupy part of the active centers of the enzyme molecules, as a result of which the rate of the enzymatic reaction decreases. Heavy metal cations, organic acids and other compounds act as inhibitors.

Lecture 11

The structure of the atom

There are two definitions of the term "atom". Atom is the smallest particle of a chemical element that retains its chemical properties.

Atom is an electrically neutral microsystem consisting of a positively charged nucleus and a negatively charged electron shell.

The doctrine of the atom has come a long way of development. The main stages in the development of atomistics include:

1) natural-philosophical stage - the period of formation of the concept of the atomic structure of matter, not confirmed by experiment (5th century BC - 16th century AD);

2) the stage of formation of the hypothesis about the atom as the smallest particle of a chemical element (XVIII-XIX centuries);

3) the stage of creating physical models that reflect the complexity of the structure of the atom and make it possible to describe its properties (beginning of the 20th century)

4) the modern stage of atomistics is called quantum mechanical. Quantum mechanics is a branch of physics that studies the motion of elementary particles.

PLAN

11.1. The structure of the nucleus. Isotopes.

11.2. Quantum-mechanical model of the electron shell of the atom.

11.3. Physical and chemical characteristics of atoms.

The structure of the nucleus. isotopes

atom nucleus- This is a positively charged particle, consisting of protons, neutrons and some other elementary particles.

It is generally accepted that the main elementary particles of the nucleus are protons and neutrons. Proton (p) - it is an elementary particle whose relative atomic mass is 1 amu and whose relative charge is + 1. Neutron (n) - it is an elementary particle that does not have an electric charge, the mass of which is equal to the mass of a proton.

The nucleus contains 99.95% of the mass of an atom. Special nuclear forces of extension act between elementary particles, significantly exceeding the forces of electrostatic repulsion.

The fundamental characteristic of an atom is charge his nuclei, equal to the number of protons and coinciding with the serial number of the element in the periodic system of chemical elements. A collection (type) of atoms with the same nuclear charge is called chemical element. Elements with numbers from 1 to 92 are found in nature.

isotopes- These are atoms of the same chemical element containing the same number of protons and a different number of neutrons in the nucleus.

where the mass number (A) is the mass of the nucleus, z is the charge of the nucleus.

Each chemical element is a mixture of isotopes. As a rule, the name of isotopes coincides with the name of a chemical element. However, special names have been introduced for hydrogen isotopes. The chemical element hydrogen is represented by three isotopes:

Number p Number n

Protium H 1 0

Deuterium D 1 1

Tritium T 1 2

Isotopes of a chemical element can be either stable or radioactive. Radioactive isotopes contain nuclei that spontaneously collapse with the release of particles and energy. The stability of a nucleus is determined by its neutron-proton ratio.

Getting into the body, radionuclides disrupt the course of the most important biochemical processes, reduce immunity, doom the body to diseases. The body protects itself from the effects of radiation by selectively absorbing elements from the environment. Stable isotopes take precedence over radioactive isotopes. In other words, stable isotopes block the accumulation of radioactive isotopes in living organisms (Table 8).

S. Shannon's book "Nutrition in the Atomic Age" provides the following data. If a blocking dose of a stable isotope of iodine, equal to ~100 mg, is taken no later than 2 hours after I-131 enters the body, then the absorption of radioiodine in the thyroid gland will decrease by 90%.

Radioisotopes are used in medicine

for the diagnosis of certain diseases,

for the treatment of all forms of cancer,

for pathophysiological studies.

Table 8 - Blocking effect of stable isotopes

Kinetics of enzymatic reactions. Kinetics studies the rates, mechanisms of reactions and the influence of such factors as the concentration of enzymes and substrates, temperature, pH of the medium, the presence of inhibitors or activators.

At a constant substrate concentration, the reaction rate is directly proportional to the enzyme concentration. The graph of the dependence of the rate of the enzymatic reaction on the concentration of the substrate has the form of an isosceles hyperbola.

Dependence of the enzymatic reaction rate on the concentration of the enzyme (a) and substrate (b)

The dependence of the enzymatic reaction rate on the substrate concentration is described Michaelis-Menten equation:

where V is the stationary rate of the biochemical reaction; Vmax - maximum speed; Km - Michaelis constant; [S] - substrate concentration.

If the substrate concentration is low, i.e. [S]<< Кm, то [S] в знаменателе можно пренебречь.

Then

Thus, at low substrate concentrations, the reaction rate is directly proportional to the substrate concentration and is described by a first-order equation. This corresponds to the initial straight section of the curve V = f[S] (figure b).

At high substrate concentrations [S] >> Km, when Km can be neglected, the Michaelis-Menten equation takes the form, i.e. V=Vmax.

Thus, at high substrate concentrations, the reaction rate becomes maximum and is described by a zero order equation. This corresponds to a section of the curve V =f [S], parallel to the x-axis.

At substrate concentrations numerically comparable to the Michaelis constant, the reaction rate increases gradually. This is quite consistent with the ideas about the mechanism of the enzymatic reaction:


where S is the substrate; E - enzyme; ES - enzyme-substrate complex; P - product; k1 is the rate constant for the formation of the enzyme-substrate complex; k2 is the rate constant of the decomposition of the enzyme-substrate complex with the formation of initial reagents; k3 is the rate constant of the decomposition of the enzyme-substrate complex with the formation of the product.

Substrate Conversion Rate with the formation of the product (P) is proportional to the concentration of the enzyme-substrate complex. At low substrate concentrations, the solution contains a certain number of free enzyme molecules (E) that are not bound into a complex (ES). Therefore, with an increase in the concentration of the substrate, the concentration of the complexes increases, and, consequently, the rate of product formation also increases. At high substrate concentrations, all enzyme molecules are bound into an ES complex (enzyme saturation phenomenon), therefore, a further increase in the substrate concentration practically does not increase the concentration of complexes, and the rate of product formation remains constant.

Thus, the physical meaning of the maximum rate of the enzymatic reaction becomes clear. Vmax is the rate at which an enzyme reacts, existing entirely as an enzyme-substrate complex..

The Michaelis constant numerically corresponds to such a substrate concentration at which the stationary velocity is equal to half the maximum. This constant characterizes the dissociation constant of the enzyme-substrate complex:

The physical meaning of the Michaelis constant in that it characterizes the affinity of the enzyme for the substrate. Km has small values ​​when k1 > (k2 + k3), i.e. the process of formation of the ES complex prevails over the processes of dissociation of ES. Therefore, the lower the Km value, the greater the affinity of the enzyme for the substrate. Conversely, if Km is large, then (k2 + k3) > k1 and ES dissociation processes predominate. In this case, the affinity of the enzyme for the substrate is low.

Enzyme inhibitors and activators . Enzyme inhibitors called substances that reduce the activity of enzymes. Any denaturing agents (for example, heavy metal salts, acids) are non-specific enzyme inhibitors.

Reversible inhibitors are compounds that interact non-covalently with an enzyme. irreversible inhibitors- these are compounds that specifically bind the functional groups of the active center and form covalent bonds with the enzyme.

Reversible inhibition is divided into competitive and non-competitive. Competitive inhibition suggests structural similarity between inhibitor and substrate. The inhibitor occupies a place in the active site of the enzyme, and a significant number of enzyme molecules is blocked. Competitive inhibition can be removed by increasing the concentration of the substrate. In this case, the substrate displaces the competitive inhibitor from the active site.

Reversible inhibition can be non-competitive regarding the substrate. In this case, the inhibitor does not compete for the site of attachment to the enzyme. The substrate and the inhibitor bind to different sites, so there is the possibility of the formation of the IE complex, as well as the ternary IES complex, which can decompose with the release of the product, but at a slower rate than the ES complex.

By the nature of your action inhibitors are divided into:

  • specific,
  • non-specific.

Specific inhibitors have their effect on the enzyme, joining with a covalent bond in the active center of the enzyme and turning it off from the sphere of action.

Non-specific inhibition involves the effect on the enzyme of denaturing agents (salts of heavy metals, urea, etc.). In this case, as a result of the destruction of the quaternary and tertiary structure of the protein, the biological activity of the enzyme is lost.

Enzyme Activators are substances that increase the rate of an enzymatic reaction. Most often, metal ions (Fe2+, Fe3+, Cu2+, Co2+, Mn2+, Mg2+, etc.) act as activators. Distinguish between metals that are part of metalloenzymes, which are cofactors and acting as enzyme activators. Cofactors can bind strongly to the protein part of the enzyme, but as for activators, they are easily separated from the apoenzyme. Such metals are obligatory participants in the catalytic act, which determine the activity of the enzyme. Activators enhance the catalytic effect, but their absence does not prevent the enzymatic reaction from proceeding. As a rule, the metal cofactor interacts with the negatively charged groups of the substrate. A metal with variable valence takes part in the exchange of electrons between the substrate and the enzyme. In addition, they are involved in the formation of a stable transitional conformation of the enzyme, which contributes to a more rapid formation of the ES complex.

Regulation of enzyme activity . One of the main mechanisms for regulating metabolism is the regulation of enzyme activity. One example is allosteric regulation, regulation by activators and inhibitors. It is often the case that the end product of the metabolic pathway is an inhibitor of the regulatory enzyme. This type of inhibition is called retroinhibition, or negative feedback inhibition.

Many enzymes are produced as inactive proenzyme precursors and then activated at the right time by partial proteolysis. Partial proteolysis- cleavage of a part of the molecule, which leads to a change in the tertiary structure of the protein and the formation of the active center of the enzyme.

Some oligomeric enzymes can change their activity due to associations - dissociations of subunits included in their composition.

Many enzymes can be found in two forms: as a simple protein and as a phosphoprotein. The transition from one form to another is accompanied by a change in catalytic activity.

The rate of an enzymatic reaction depends on enzyme amounts, which in the cell is determined by the ratio of the rates of its synthesis and decay. This way of regulating the rate of an enzymatic reaction is a slower process than the regulation of enzyme activity.

Enzymatic kinetics studies the rate of reactions catalyzed by enzymes depending on various conditions (concentration, temperature, pH, etc.) of their interaction with the substrate.

However, enzymes are proteins that are sensitive to the influence of various external influences. Therefore, when studying the rate of enzymatic reactions, mainly the concentrations of reactants are taken into account, and the influence of temperature, pH of the medium, activators, inhibitors, and other factors is tried to be minimized and standard conditions are created. First, this is the optimal pH value of the medium for this enzyme. Secondly, it is recommended to keep the temperature at 25°C, where possible. Thirdly, complete saturation of the enzyme with the substrate is achieved. This point is especially important, since at a low substrate concentration, not all enzyme molecules participate in the reaction (Fig. 6.5, a), which means that the result will be far from the maximum possible. The highest power of the catalyzed reaction, other things being equal, is achieved if each enzyme molecule is involved in the transformation, i.e. at a high concentration of the enzyme-substrate complex (Fig. 6.5, in). If the concentration of the substrate does not ensure complete saturation of the enzyme (Fig. 6.5, b), then the rate of the proceeding reaction does not reach the maximum value.

Rice. 65.

a - at low substrate concentration; 6 - with insufficient concentration of the substrate; in - when the enzyme is completely saturated with the substrate

The rate of an enzymatic reaction, measured under the above conditions, and the complete saturation of the enzyme with the substrate is called maximum rate of enzymatic reaction (V).

The rate of the enzymatic reaction, determined when the enzyme is not completely saturated with the substrate, is denoted v.

Enzymatic catalysis can be simplistically described by the scheme

where F is an enzyme; S - substrate; FS - enzyme-substrate complex.

Each stage of this process is characterized by a certain speed. The unit for measuring the rate of an enzymatic reaction is the number of moles of the substrate converted into a unit of time(like the rate of a normal reaction).

The interaction of the enzyme with the substrate leads to the formation of an enzyme-substrate complex, but this process is reversible. The rates of the forward and reverse reactions depend on the concentrations of the reactants and are described by the corresponding equations:

Equation (6.3) is valid in equilibrium, since the rates of the forward and reverse reactions are equal.

Substituting the rates of direct (6.1) and reverse (6.2) reactions into equation (6.3), we obtain the equality:

The state of equilibrium is characterized by the corresponding equilibrium constant K p, equal to the ratio of the constants of direct and reverse reactions (6.5). The reciprocal of the equilibrium constant is called substrate constant K s , or the dissociation constant of the enzyme-substrate complex:


From equation (6.6) it is clear that the substrate constant decreases at a high concentration of the enzyme-substrate complex, i.e. with great stability. Therefore, the substrate constant characterizes the affinity of the enzyme and the substrate and the ratio of the rate constants for the formation and dissociation of the enzyme-substrate complex.

The phenomenon of saturation of an enzyme with a substrate was studied by Leonor Michaelis and Maud Mepten. Based on the mathematical processing of the results, they derived equation (6.7), which received their names, from which it is clear that at a high concentration of the substrate and a low value of the substrate constant, the rate of the enzymatic reaction tends to the maximum. However, this equation is limited because it does not take into account all parameters:

The enzyme-substrate complex during the reaction can undergo transformations in different directions:

  • dissociate into the original substances;
  • be converted into a product from which the enzyme is separated unchanged.

Therefore, to describe the overall effect of the enzymatic process, the concept Michaelis constants K t, which expresses the relationship of the rate constants of all three reactions of enzymatic catalysis (6.8). If both terms are divided by the rate constant of the reaction of formation of the enzyme-substrate complex, then the expression (6.9) will be obtained:


An important corollary follows from equation (6.9): the Michaelis constant is always greater than the substrate constant by k 2 /kv

Numerically K t is equal to such a concentration of the substrate at which the reaction rate is half the maximum possible rate and corresponds to such saturation of the enzyme with the substrate, as in Fig. 6.5, b. Since in practice it is not always possible to achieve complete saturation of the enzyme with the substrate, it is K t used to compare the kinetic characteristics of enzymes.

The rate of the enzymatic reaction in the case of incomplete saturation of the enzyme with the substrate (6.10) depends on the concentration of the enzyme-substrate complex. The coefficient of proportionality is the reaction constant for the release of the enzyme and the product, since this changes the concentration of the enzyme-substrate complex:

After transformations, taking into account the dependences presented above, the rate of the enzymatic reaction in the case of incomplete saturation of the enzyme with the substrate is described by equation (6.11), i.e. depends on the concentrations of the enzyme, substrate and their affinity Ks:

The graphical dependence of the rate of the enzymatic reaction on the concentration of the substrate is not linear. As is obvious from Fig. 6.6, with an increase in the concentration of the substrate, an increase in the activity of the enzyme is observed. However, when the maximum saturation of the enzyme with the substrate is reached, the rate of the enzymatic reaction becomes maximum. Therefore, the factor limiting the reaction rate is the formation of an enzyme-substrate complex.

Practice has shown that the concentrations of substrates, as a rule, are expressed in values ​​much less than unity (10 6 -10 3 mol). It is quite difficult to operate with such quantities in the calculations. Therefore, G. Lineweaver and D. Burke proposed to express the graphic dependence of the enzymatic reaction rate not in direct coordinates, but in reverse ones. They proceeded from the assumption that for equal values, their reciprocals are also equal:

Rice. 6.6.

After the transformation of expression (6.13), an expression is obtained, called Lineweaver-Burk equation (6.14):

The graphical dependence of the Lineweaver-Burk equation is linear (Fig. 6.7). The kinetic characteristics of the enzyme are determined as follows:

  • the segment cut off on the y-axis is equal to 1/V;
  • the segment cut off on the x-axis is -1 /K t.

Rice. 6.7.

It is believed that the Lineweaver - Burke method allows you to more accurately determine the maximum reaction rate than in direct coordinates. Valuable information regarding enzyme inhibition can also be extracted from this graph.

There are other ways to transform the Michaelis-Menten equation. Graphic dependencies are used in studying the influence of various external influences on the enzymatic process.

This section of enzymology studies the influence of various factors on the rate of an enzymatic reaction. Taking into account the general equation of enzymatic catalysis of the reversible reaction of the transformation of one substrate into one product (1),

the main factors influencing the rate of an enzymatic reaction should be named: substrate concentration [S], enzyme concentration [E], and reaction product concentration [P].

The interaction of some enzymes with their substrate can be described by a hyperbolic curve of the dependence of the enzymatic reaction rate V on the concentration of the substrate [S] (Fig. 19):

Fig. 19. Dependence of the rate of the enzymatic reaction on the concentration of the substrate.

Three segments can be distinguished on this curve, which can be explained by the positions of the mechanism of interaction of the enzyme with the substrate: OA is the segment of the directly proportional dependence of V on [S], the active sites of the enzyme are gradually filled with substrate molecules with the formation of an unstable complex ES; section AB - curvilinear dependence of V on [S], complete saturation of the active centers of the enzyme with substrate molecules has not yet been achieved. The ES complex before reaching the transition state is unstable, the probability of back dissociation to E and S is still high; section BC - dependence is described by a zero-order equation, the section is parallel to the [S] axis, complete saturation of active enzymes with substrate molecules is achieved, V=V max .

The characteristic shape of the curve is described mathematically by the Briggs-Haldane equation:

V=V max ● [S]/ Km + [S] (2),

where Km is the Michaelis-Menten constant, numerically equal to the substrate concentration at which the rate of the enzymatic reaction is equal to half V max .

The lower the K m of the enzyme, the higher the affinity of the enzyme for the substrate, the faster the transition state for the substrate is reached, and it turns into a reaction product. The search for Km values ​​for each of the enzyme's substrates with group specificity is important in determining the biological role of this enzyme in the cell.

For most enzymes, it is impossible to construct a hyperbolic curve (Fig. 19). In this case, the double reciprocal method (Lineweaver-Burk) is used, i.e. a graphical dependence of 1/[V] on 1/[S] is plotted (Fig. 20). The method of constructing such curves in an experiment is very convenient when studying the effect of various types of inhibitors on the activity of enzymes (see the text below).

Fig.20. Plot of 1/[V] versus 1/[S] (Lineweaver-Burk method),

where y-cut-off area - , and x – cut-off area - , the tangent of the angle α - .

Dependence of the enzymatic reaction rate V on the enzyme concentration [E].

This graphical dependence (Fig. 21) is considered at the optimal temperature and pH of the environment, at substrate concentrations that are significantly higher than the saturation concentration of the active sites of the enzyme.

Rice. 21. Influence of enzyme concentration on the rate of enzymatic reaction.

Dependence of the enzymatic reaction rate on the concentration of the cofactor or coenzyme. For complex enzymes, it should be borne in mind that the deficiency of coenzyme forms of vitamins in hypovitaminosis, a violation of the intake of metal ions into the body necessarily lead to a decrease in the concentration of the corresponding enzymes necessary for the course of metabolic processes. Therefore, it should be concluded that the activity of the enzyme is directly dependent on the concentration of the cofactor or coenzyme.

Influence of the concentration of products on the rate of the enzymatic reaction. For reversible reactions occurring in the human body, it must be taken into account that the products of the direct reaction can be used by the enzyme as substrates for the reverse reaction. Therefore, the direction of the flow and the moment of reaching V max are dependent on the ratio of the concentrations of the initial substrates and reaction products. For example, the activity of alanine aminotransferase, which catalyzes the transformation:

Alanine + Alpha-ketoglutarate ↔ Pyruvate + Glutamate

depends in the cell on the ratio of concentrations:

[alanine + alpha-ketoglutarate] / [pyruvate + glutamate].

MECHANISM OF ENZYME ACTION. THEORIES OF ENZYMATIVE CATALYSIS

Enzymes, like non-protein catalysts, increase the rate of a chemical reaction due to their ability to lower the activation energy of that reaction. The activation energy of an enzymatic reaction is calculated as the difference between the energy value in the system of the ongoing reaction that has reached the transition state and the energy determined at the beginning of the reaction (see the graphical dependence in Fig. 22).

Rice. 22. Graphical dependence of the energy state of a chemical reaction without an enzyme (1) and in the presence of an enzyme (2) on the time of the reaction.

The works of V. Henry and, in particular, L. Michaelis, M. Menten on the study of the mechanism of monosubstrate reversible enzymatic reactions made it possible to postulate that the enzyme E first reversibly and relatively quickly combines with its substrate S to form an enzyme-substrate complex (ES):

E+S<=>ES (1)

The formation of ES occurs due to hydrogen bonds, electrostatic, hydrophobic interactions, in some cases covalent, coordination bonds between the side radicals of the amino acid residues of the active center and the functional groups of the substrate. In complex enzymes, the non-protein part of the structure can also perform the function of contact with the substrate.

The enzyme-substrate complex then breaks down in a second slower reversible reaction to form the reaction product P and the free enzyme E:

ES<=>EP<=>E + P (2)

At present, thanks to the work of the above-mentioned scientists, as well as Kaylin D., Chance B., Koshland D. (the theory of "induced conformity"), there are theoretical provisions on four main points in the mechanism of enzyme action on the substrate, which determine the ability of enzymes to accelerate chemical reactions. reactions:

1. Orientation and proximity . The enzyme is able to bind the substrate molecule in such a way that the bond attacked by the enzyme is not only located in the immediate vicinity of the catalytic group, but also correctly oriented with respect to it. The probability that the ES complex will reach the transition state due to orientation and approach is greatly increased.

2. Stress and strain : induced fit. Attachment of the substrate can cause conformational changes in the enzyme molecule, which lead to tension in the structure of the active site, as well as somewhat deform the bound substrate, thereby facilitating the achievement of the transition state by the ES complex. There is a so-called induced correspondence between E and S molecules.

COURSE WORK

Kinetics of enzymatic reactions

Introduction

The basis of the life of any organism is chemical processes. Almost all reactions in a living organism proceed with the participation of natural biocatalysts - enzymes.

Berzelius in 1835 for the first time suggested that the reactions of a living organism are carried out due to a new force, which he called "catalytic". He substantiated this idea mainly by an experimental observation: diastase from potatoes hydrolyses starch faster than sulfuric acid. As early as 1878, Kuhne called a substance that has catalytic power in a living organism an enzyme.

The kinetics of enzyme action is a branch of enzymology that studies the dependence of the rate of a reaction catalyzed by enzymes on the chemical nature and conditions of interaction of the substrate with the enzyme, as well as on environmental factors. In other words, the kinetics of enzymes makes it possible to understand the nature of the molecular mechanisms of action of factors affecting the rate of enzymatic catalysis. This section was formed at the intersection of such sciences as biochemistry, physics and mathematics. The earliest attempt to mathematically describe enzymatic reactions was made by Duclos in 1898.

In fact, this section on the study of enzymes is very important in our time, namely for practical medicine. It gives pharmacologists a tool to change the cell metabolism, a huge number of pharmaceuticals and various poisons - these are enzyme inhibitors.

The purpose of this work is to consider the question of the dependence of the reaction rate on various factors, how the reaction rate can be controlled and how it can be determined.

1. Michaelis-Menten kinetics

Preliminary experiments on the study of the kinetics of enzymatic reactions showed that the reaction rate, contrary to theoretical expectations, does not depend on the concentration of the enzyme (E) and substrate (S) in the same way as in the case of a conventional second-order reaction.

Brown and, independently of him, Henri were the first to put forward a hypothesis about the formation of an enzyme-substrate complex during the reaction. Then this assumption was confirmed by three experimental facts:

a) papain formed an insoluble compound with fibrin (Wurtz, 1880);

b) the invertase substrate sucrose could protect the enzyme from thermal denaturation (O'Sullivan and Thompson, 1890);

c) enzymes have been shown to be stereochemically specific catalysts (Fischer, 1898-1899).


They introduced the concept of maximum speed and showed that saturation curve(i.e., the dependence of the reaction rate on the concentration of the substrate) is an isosceles hyperbola. They proved that the maximum observed speed is one of the asymptotes to the curve, and the segment cut off on the x-axis (in the region of its negative values) by the second asymptote, i.e. constant in the rate equation, equal in absolute value to the substrate concentration required to achieve half of the maximum rate.

Michaelis and Menten suggested that the reaction rate is determined by the breakdown of the ES complex, i.e. constant k 2 . This is only possible under the condition that k 2 is the smallest of the rate constants. In this case, the equilibrium between the enzyme-substrate complex, the free enzyme and the substrate is established quickly compared to the rate of the reaction (rapid equilibrium).

The initial reaction rate can be expressed by the following formula:

v = k2

Since the dissociation constant of the enzyme-substrate complex is

K S \u003d [E] [S] / \u003d k -1 / k 1

then the concentration of the free enzyme can be expressed as

[E]=K S / [S]

The total concentration of the enzyme in the reaction mixture is determined by the formula

[E] t = [E] + [ES] = K S [ES] / [S] + [ES]

The reaction reaches its maximum rate when the substrate concentration is high enough so that all enzyme molecules are in the form of an ES complex (an infinitely large excess of substrate). The ratio of the initial speed to the theoretically possible maximum speed is equal to the ratio of [ES] to [E] t:

v / V max = / [E] t = / (K S / [S] + ) = 1 / (K S + [S] +1)


This is the classic equation Michaelis and Menten, which, since its publication in 1913, has been the fundamental principle of all enzyme kinetic studies for decades, and, with some limitations, has remained so to this day.

It was later shown that the original Michaelis-Menten equation had several constraints. It is fair, i.e. correctly describes the kinetics of the reaction catalyzed by this enzyme only if all of the following restrictive conditions are met:

) a kinetically stable enzyme-substrate complex is formed;

) constant K S is the dissociation constant of the enzyme-substrate complex: this is true only if ;

) the substrate concentration does not change during the reaction, i.e. the concentration of the free substrate is equal to its initial concentration;

) the reaction product is rapidly cleaved off from the enzyme, i.e. no kinetically significant amount of the ES complex is formed;

) the second stage of the reaction is irreversible; more precisely, we take into account only the initial speed, when the back reaction (due to the actual lack of product) can still be neglected;

) only one substrate molecule binds to each active site of the enzyme;

) for all reactants, their concentrations can be used instead of activities.

The Michaelis-Menten equation serves as the starting point for any quantitative description of the action of enzymes. It should be emphasized that the kinetic behavior of most enzymes is much more complicated than it follows from the idealized scheme underlying the Michaelis-Menten equation. In deriving this equation, it is assumed that there is only one enzyme-substrate complex. Meanwhile, in reality, in most enzymatic reactions, at least two or three such complexes are formed, arising in a certain sequence.

Here, EZ denotes the complex corresponding to the true transition state, and EP denotes the complex between the enzyme and the reaction product. It can also be pointed out that in most enzymatic reactions more than one substrate is involved and two or more products are formed, respectively. In a reaction with two substrates, S 1 and S 2 , three enzyme-substrate complexes can be formed, namely ES 1 , ES 2 and ES 1 S 2 . If the reaction produces two products, P 1 and P 2 , then there may be at least three additional complexes EP 1 , EP 2 and EP 1 P 2 . In such reactions, there are many intermediate steps, each of which is characterized by its own rate constant. The kinetic analysis of enzymatic reactions involving two or more reactants is often extremely complex and requires the use of electronic computers. However, when analyzing the kinetics of all enzymatic reactions, the starting point is always the Michaelis-Menten equation discussed above.

1.1 The nature of the constantKin the equation

equation enzymatic reaction kinetics

The second postulate states that the constant K S in the equation is the dissociation constant of the enzyme-substrate complex.

Briggs and Haldane proved in 1925 that the original Michaelis-Menten equation is valid only for , i.e. when the equilibrium of the elementary stage E+S ES is established very quickly compared to the rate of the next stage. Therefore, such kinetic mechanisms (obeying the Michaelis-Menten initial condition and having one slow elementary stage, with respect to which equilibria in all other elementary stages are established quickly) are called satisfying the assumption of "fast equilibrium". If, however, k 2 is comparable in order of magnitude to k -1 , the change in the concentration of the enzyme-substrate complex over time can be expressed by the following differential equation:

d / dt \u003d k 1 [E] [S] - k -1 - k 2

Since we are considering the initial reaction rate, i.e. the moment when the reverse reaction does not yet occur, and the pre-stationary stage has already passed, then due to the excess of the substrate, the amount of the formed enzyme-substrate complex is equal to the amount of the decomposed ( the stationarity principle, or the kinetics of Briggs and Haldane, or the Bodenstein principle in chemical kinetics) and it is true that

d/dt=0

Substituting this into the differential equation, we obtain an expression for the concentration of free enzyme:

[E] \u003d (k -1 + k 2) / k 1 [S]

[E] T = [E] + = [(k -1 + k 2) / k -1 [S] + 1] =

= (k -1 + k 2 + k -1 [S]) / k 1 [S]

Steady state equation:

K 1 [S] [E] T / (k -1 + k 2 + k 1 [S])

Because v = k 2 , then we get that

v = k 1 k 2 [S] [E] T / (k -1 + k 2 + k 1 [S]) = k 2 [S] [E] T / [(k -1 + k 2) / k 1 + [S]]

In this case

V max = k 2 [E] T

and equals the maximum speed obtained from the Michaelis-Menten equation. However, the constant in the denominator of the Michaelis-Menten equation is not K S , those. not the dissociation constant of the enzyme-substrate complex, but the so-called Michaelis constant:

K m \u003d (k -1 + k 2) / k 1

K m is equal to K S only if .

In case, the constant in the denominator of the velocity equation is expressed by the formula

K k \u003d k 2 / k 1

and is called, according to Van Slyke, kinetic constant.

The steady state equation can also be obtained from the differential equation without the assumption that d / dt = 0. If we substitute the value [E] = [E] T - into the differential equation, after transformations we get

= (k 1 [S] [E] T - d / dt) / (k 1 [S] + k -1 + k 2)

In order to obtain the steady state equation from this equation, it does not have to be d / dt = 0. It suffices that the inequality d / dt<< k 1 [S] [E] T . Этим объясняется, почему можно достичь хорошего приближения в течение длительного времени при использовании принципа стационарности.

The differentiated steady state equation looks like this:

d / dt \u003d T / (k 1 [S] + k -1 + k 2) 2] (d [S] / dt)

This expression obviously does not equal 0.

1.2 Transformation of the Michaelis-Menten equation

The original Michaelis-Menten equation is a hyperbolic equation, where one of the constants (V max) is the asymptote to the curve. Another constant (K m), the negative value of which is determined by the second asymptote, is equal to the substrate concentration required to achieve V max / 2. This is easy to verify, since if

v=Vmax / 2, then

Vmax / 2 = Vmax [S] / (Km + [S])

V max / V max = 1 = 2 [S] / (K m + [S]) m + [S] = 2 [S], i.e. [S] = K m for v = V max /2.

The Michaelis-Menten equation can be algebraically transformed into other forms that are more convenient for graphical representation of experimental data. One of the most common transformations is simply to equate the reciprocals of the left and right sides of the equation


As a result of the transformation, we obtain the expression


which bears the name Lineweaver-Burk equations. According to this equation, a graph plotted in the coordinates 1/[S] and 1/v is a straight line, the slope of which is equal to K m /V max , and the segment cut off on the y-axis is equal to 1/V max . Such a double reciprocal graph has the advantage that it makes it possible to determine V max more precisely; on a curve plotted in [S] and v coordinates, V max is an asymptotic quantity and is determined much less accurately. The segment cut off on the x-axis on the Lineweaver-Burk plot is equal to -1/K m . Valuable information regarding enzyme inhibition can also be extracted from this graph.

Another transformation of the Michaelis-Menten equation is that both sides of the Lineweaver-Burk equation are multiplied by V max *v and after some additional transformations we get


The corresponding plot in v and v/[S] coordinates represents with e 4, fig. one]. Such a graph ( Edie-Hofsty chart) not only makes it possible to very easily determine the values ​​of V max and K m , but also allows you to identify possible deviations from linearity that are not detected on the Lineweaver-Burk plot.

The equation can also be linearized in another form

[S] / v = K m / V max + [S] / V max

In this case, the dependence [S] / v on [S] should be built. The slope of the resulting straight line is 1 / V max ; the segments cut off on the ordinate and abscissa axes are equal to (K m / V max) and (- K m), respectively. This chart is named after the author Haynes chart.

Statistical analysis has shown that the Edie-Hofstee and Haynes methods give more accurate results than the Lineweaver-Burk method. The reason for this is that in the graphs of Edie - Hofstee and Haynes, both dependent and independent variables are included in the values ​​plotted on both coordinate axes.

1.3 Effect of substrate concentration on reaction kinetics

In many cases, the condition of constant substrate concentration is not satisfied. On the one hand, an excess of the substrate is not used in the in vitro reaction with some enzymes due to the often occurring inhibition of the enzymatic activity of the substrate. In this case, only its optimal concentration can be used, and this does not always provide the excess of the substrate necessary to fulfill the kinetic equations of the mechanisms discussed above. Moreover, in the cell in vivo, the excess of the substrate required to fulfill this condition is usually not achieved.

In enzymatic reactions where the substrate is not in excess and, therefore, its concentration changes during the reaction, the dissociation constant of the enzyme-substrate complex is

K S = ([S] 0 - - [P]) [E] T - )/

([S] 0 - substrate concentration at t = 0). In this case, the initial reaction rate (in the steady state) is given by

v= V max / (K m + )

where is the concentration of the substrate at a point in time.

However, it is possible to write an approximate solution for two cases where [S] o = :

) if this inequality is satisfied due to large values ​​of t, i.e. when more than 5% of the initial concentration of the substrate was consumed during the reaction;

) if the concentration of the enzyme cannot be neglected compared to the concentration of the substrate and thus the concentration of the enzyme-substrate complex must be taken into account.

If t is large, and the concentration is negligible compared to [S] 0 , then the equation for the dissociation constant of the enzyme-substrate complex becomes the following:

K S = ([S] 0 - [P]) ([E] T - ) /

For the value of concentration , which changes during the reaction, the value ([S] 0 + )/2 serves as a satisfactory approximation. Since = [S] 0 - [P], the average speed; can be expressed as


Substituting this expression and the approximate value into

v= V max / (K m + ),

we get:

When comparing the values ​​calculated on the basis of this approximation with the values ​​obtained from the exact, integrated Michaelis-Menten equation, it turns out that the error in determining K m is 1 and 4% when spending 30 and 50% of the substrate, respectively. Therefore, the error in this approximation is negligible compared to the measurement error.

When the consumption of the substrate does not exceed 5% of the initial concentration, but the concentration of the enzyme is so high that it cannot be ignored compared to [S] 0, the dissociation constant of the enzyme-substrate complex is equal to:

K s = ([S] 0 - ) ([E] T - ) /

His solution regarding gives

Of the two possible solutions, only the negative one can be chosen, since only it satisfies the initial conditions: = 0 at [S] 0 = 0 or [E] T = 0. By analogy with the equation for the ratio v/V max, we have obtained the initial velocity equation. The quadratic equation obtained from the equation of the dissociation constant of the enzyme-substrate complex, found a little higher, using the formulas v \u003d k 2 and V max \u003d k 2 [E] T, can be reduced to the following form:

[S] 0 V max / v = K s V max / (V max - v) + [E] T

Two limiting cases should be taken into account. In the first case [S]<

v = (Vmax / Km) [S] = k[S]

Thus, we have obtained the apparent first order reaction and k=V max /K m - the apparent first order kinetic constant. Its actual dimension is time -1 , but it is a combination of the first and second order rate constants of several elementary stages, i.e. k 1 k 2 [E] T /(k -1 + k 2) . Under conditions of apparent first order k is a measure of the progress of the reaction.

Another limiting case: [S] >> K m . Here the constant K m is negligible compared to [S], and thus we get v = V max .

1.4 Formation of a kinetically stable enzyme-product complex

If a kinetically stable enzyme-product complex is formed during the reaction, the reaction mechanism is as follows:

Applying the steady state assumption, we can write the differential equations:

d / dt = k 1 [E] [S] + k -2 - (k -1 + k 2) = 0 / dt = k 2 - (k -2 + k 3) = 0

From these equations it follows that

= [(k -2 + k 3) / k 2]

[E] = [(k -1 k -2 + k -1 k -3 + k 2 k 3) / k 1 k 2 [S]]

Since v = k 3

and [E] T = [E] + + =

= [(k -1 k -2 + k -1 k -3 + k 2 k 3) / k 1 k 2 [S] + (k -2 + k 3) / k 2 + 1] =

= ( (k -2 + k 3) + k 1 k 2 [S]] / k 1 k 2 [S])

we get

K 1 k 2 [S] [E] T / (k -2 + k 3 + k 2)]= k 1 k 2 k 3 [S] [E] T / (k -2 + k 3 + k 2) ]=

= [E] T [S] / [(k -1 k -2 + k -1 k -3 + k 2 k 3) / k 1 (k -2 + k 3 + k 2) + [S]]

I.e

V max \u003d [E] Tm \u003d (k -1 k -2 + k -1 k -3 + k 2 k 3) / k 1 (k -2 + k 3 + k 2)

In this case, it is already very difficult to calculate the specific values ​​of the individual rate constants, since only their ratio can be directly measured. The situation becomes even more complicated when the mechanism of the enzymatic reaction becomes more complex, when more than two complexes are involved in the reaction, because the number of rate constants in the equation, of course, is much larger, and their ratios are also more complicated.

However, the situation is simplified if, after the reversible reaction of the formation of the first complex, the subsequent elementary steps are irreversible. Important representatives of enzymes that obey this mechanism are proteolytic enzymes and esterases. Their reaction mechanism can be written as follows:

where ES` is an acyl-enzyme intermediate that decomposes on exposure to water. We can write

V max \u003d k 2 k 3 [E] 0 / (k 2 + k 3) \u003d k cat [E] 0m \u003d k 3 (k -1 + k 2) / (k 2 + k 3) k 1 cat / K m \u003d k 2 k 1 / (k -1 + k 2) \u003d k 2 / K m '

The Michaelis constant of the acylation step is K m "K s. The greater the ratio k cat / K m , the higher the specificity of the substrate.

The determination of the constants is greatly simplified if the experiment is carried out in the presence of a nucleophilic agent (N) capable of competing with water. Then

k 3 \u003d k 3 ’ and P i (i \u003d 1, 2, 3) are products.

v i = k cat, i [S] / (K m + [S]) cat, 1 = k 2 (k 3 + k 4 [N]) / (k 2 + k 3 + k 4 [N]) cat, 2 = k 2 k 3 / (k 2 + k 3 + k 4 [N]) cat, 3 = k 2 k 4 [N] / (k 2 + k 3 + k 4 [N]) m = K s ( k 3 + k 4 [N]) / (k 2 + k 3 + k 4 [N])

/v N = K s (k 3 + k 4 [N]) / k 2 k 3 [S] + (k 2 + k 3 + k 4 [N]) / k 2 k 3

Since it is known that K s / k 2 = K m / k cat, and if the nucleophile is absent, then

1/v = K s / k 2 [S] + (k 2 + k 3) / k 2 k 3

and to determine the constants, you can use the point of intersection of lines in the coordinates 1/v N (and 1/v) - 1/[S]. Two straight lines in double inverse coordinates intersect in the second quadrant. In the absence of a nucleophile, the point of intersection of the line with the vertical axis is defined as 1/V max and 1/k cat , and with the horizontal axis as -1/K m . The coordinates of the point of intersection of two lines: -1/K s and 1/k 3 . The distance between 1/V max and 1/k 3 is 1/k 2 .

1.5 Analysis of the complete reaction kinetic curve

The Michaelis-Menten equation in its original form refers only to irreversible reactions, i.e. to reactions where only the initial rate is considered, and the reverse reaction does not appear due to an insufficient amount of the product and does not affect the reaction rate. In the case of an irreversible reaction, the complete kinetic curve can be easily analyzed (for an arbitrary time interval t ), integrating the original Michaelis-Menten equation. In this case, therefore, the assumption remains that only one intermediate enzyme-substrate complex is formed in the course of the reaction. Since for the time interval t there are no restrictions, the concentration of the substrate at the time of analysis cannot be equal to the initially introduced concentration. Thus, it is also necessary to take into account the change in [S] during the course of the reaction. Let S 0 be the initial concentration of the substrate, (S 0 - y ) - concentration at time t . Then, based on the original Michaelis-Menten equation (if y is the amount of substrate converted), we can write

dy / dt \u003d V max (S 0 - y) / (K m + S 0 - y)

Taking the reciprocals and dividing the variables, we integrate over y between 0 and y (V max is indicated as V):

(2.303 / t) lg = V / K m - (1 / K m) (y / t)

Thus, having plotted the dependence of the left side of the equation on y / t (Foster-Niemann coordinates) , get a straight line with a slope (-1/K m) , cutoff segment on the y-axis (V/K m) , and on the abscissa axis - the segment V. The integral equation can also be linearized in a different way:

t / 2.3031 lg = y / 2.303 V lg + K m / V

or t/y = 2.3031 K m lg / V y +1/V

If we are studying a reversible reaction, it is necessary to pay attention to what time interval we are dealing with. At the moment of mixing of the enzyme with the substrate, the so-called pre-stationary phase begins, lasting several micro- or milliseconds, during which the enzyme-substrate complexes corresponding to the stationary state are formed. In the study of reversible reactions over sufficiently long time intervals, this phase does not play a significant role, since in this phase the reaction does not proceed at full speed in any of the directions.

For a reaction proceeding from left to right, the enzyme-substrate complexes involved in the reaction reach the rate-limiting concentration only at the end of the prestationary phase. Quasi-stationary state, in which the concentrations of the rate-determining enzyme-substrate complexes approach the maximum values ​​of the concentrations in the steady state, lasts a few tenths of a second or a second. During this phase, the rate of product formation (or substrate consumption) is almost linear in time. Theoretically, the formation of the product has not yet occurred here, but in practice its concentration is so low that the rate of the reverse reaction does not affect the rate of the direct one. This linear phase is called the initial reaction rate, and so far we have only taken it into account.

The reaction from right to left in the next phase is also accelerated due to the gradual increase in product concentration. (transition state; the linearity observed so far in time disappears). This phase continues until the reaction rate from left to right becomes equal to the reaction rate from right to left. This is the state dynamic balance, because the reaction continues in both directions at the same rate.

2. Factors on which the rate of the enzymatic reaction depends

.1 Dependence of the enzymatic reaction rate on temperature

With an increase in the temperature of the medium, the rate of the enzymatic reaction increases, reaching a maximum at some optimal temperature, and then drops to zero. For chemical reactions, there is a rule that with an increase in temperature by 10 ° C, the reaction rate increases by two to three times. For enzymatic reactions, this temperature coefficient is lower: for every 10°C, the reaction rate increases by a factor of 2 or even less. The subsequent decrease in the reaction rate to zero indicates the denaturation of the enzyme block. The optimal temperature values ​​for most enzymes are in the range of 20 - 40 0 ​​C. The thermolability of enzymes is associated with their protein structure. Some enzymes are already denatured at a temperature of about 40 0 ​​C, but most of them are inactivated at temperatures above 40 - 50 0 C. Some enzymes are inactivated by cold, i.e. at temperatures close to 0°C, denaturation occurs.

An increase in body temperature (fever) accelerates biochemical reactions catalyzed by enzymes. It is easy to calculate that an increase in body temperature for every degree increases the reaction rate by about 20%. At high temperatures of about 39-40°C, the wasteful use of endogenous substrates in the cells of a diseased organism is required to replenish their intake with food. In addition, at a temperature of about 40°C, a part of very thermolabile enzymes can be denatured, which disrupts the natural course of biochemical processes.

Low temperature causes a reversible inactivation of enzymes due to a slight change in its spatial structure, but sufficient to disrupt the corresponding configuration of the active center and substrate molecules.

2.2 Dependence of the reaction rate on the pH of the medium

For most enzymes, there is a certain pH value at which their activity is maximum; above and below this pH value, the activity of these enzymes decreases. However, not in all cases the curves describing the dependence of enzyme activity on pH are bell-shaped; sometimes this dependence can also be expressed directly. The dependence of the enzymatic reaction rate on pH mainly indicates the state of the functional groups of the active center of the enzyme. Changing the pH of the medium affects the ionization of acidic and basic groups of amino acid residues of the active center, which are involved either in the binding of the substrate (in the contact area) or in its transformation (in the catalytic area). Therefore, the specific effect of pH can be caused either by a change in the affinity of the substrate for the enzyme, or by a change in the catalytic activity of the enzyme, or both.

Most substrates have acidic or basic groups, so pH affects the degree of ionization of the substrate. The enzyme preferably binds to either the ionized or non-ionized form of the substrate. Obviously, at optimal pH, both functional groups of the active center are in the most reactive state, and the substrate is in a form that is preferable for binding by these groups of the enzyme.

When constructing curves describing the dependence of enzyme activity on pH, measurements at all pH values ​​are usually carried out under conditions of saturation of the enzyme with the substrate, since the K m value for many enzymes changes with pH.

The curve characterizing the dependence of enzyme activity on pH can have a particularly simple shape in those cases where the enzyme acts on electrostatically neutral substrates or substrates in which charged groups do not play a significant role in the catalytic act. An example of such enzymes is papain, as well as invertase, which catalyzes the hydrolysis of neutral sucrose molecules and maintains a constant activity in the pH range of 3.0-7.5.

The pH value corresponding to the maximum activity of the enzyme does not necessarily coincide with the pH value characteristic of the normal intracellular environment of this enzyme; the latter can be both above and below the pH optimum. This suggests that the effect of pH on enzyme activity may be one of the factors responsible for the regulation of enzymatic activity within the cell. Since the cell contains hundreds of enzymes, and each of them reacts differently to changes in pH, the pH value inside the cell is perhaps one of the important elements in the complex system of regulation of cellular metabolism.

2.3 Determining the amount of the enzyme by its activity

) the total stoichiometry of the catalyzed reaction;

) the possible need for cofactors - in metal ions or coenzymes;

) the dependence of the enzyme activity on the concentrations of the substrate and cofactor, i.e. K m values ​​for both substrate and cofactor;

) the pH value corresponding to the maximum activity of the enzyme;

) the temperature range at which the enzyme is stable and retains high activity.

In addition, it is necessary to have at your disposal some fairly simple analytical technique that allows you to determine the rate of disappearance of the substrate or the rate of appearance of the reaction products.

Whenever possible, enzyme analysis is carried out under standard conditions that maintain optimal pH and maintain a substrate concentration above saturation concentration; in this case, the initial rate corresponds to the zero order of the reaction with respect to the substrate and is proportional only to the concentration of the enzyme. For enzymes requiring cofactors, metal ions or coenzymes, the concentration of these cofactors must also exceed the saturation concentration so that the enzyme concentration is the rate-limiting factor. In general, the measurement of the rate of formation of the reaction product can be performed with greater accuracy than the measurement of the rate of disappearance of the substrate, since the substrate generally must be present in relatively high concentrations to maintain zero order kinetics. The rate of formation of the reaction product (or products) can be measured by chemical or spectrum-photometric methods. The second method is more convenient, since it allows you to continuously record the course of the reaction on the recorder's mite.

By international agreement, a unit of enzymatic activity is the amount of enzyme capable of causing the conversion of one micromole of substrate per minute at 25°C under optimal conditions. Specific activity enzyme is the number of units of enzymatic activity per 1 mg of protein. This value is used as a criterion for the purity of the enzyme preparation; it increases as the enzyme is purified and reaches its maximum value for an ideally pure preparation. Under number of revolutions understand the number of substrate molecules undergoing transformation per unit time per one molecule of the enzyme (or per one active site) under conditions where the reaction rate is limited by the concentration of the enzyme.

2.4 Enzyme activation

The regulation of enzymes can be carried out by interaction with them of various biological components or foreign compounds (for example, drugs and poisons), which are commonly called modifiers or regulators enzymes. Under the influence of modifiers on the enzyme, the reaction can be accelerated (activators) or slowed down ( inhibitors).

The activation of enzymes is determined by the acceleration of biochemical reactions that occurs after the action of the modifier. One group of activators consists of substances that affect the region of the active site of the enzyme. These include enzyme cofactors and substrates. Cofactors (metal ions and coenzymes) are not only obligatory structural elements of complex enzymes, but also essentially their activators.

Metal ions are quite specific activators. Often, some enzymes require ions of not one, but several metals. For example, for Na + , K + -ATPase, which transports monovalent cations through the cell membrane, magnesium, sodium and potassium ions are necessary as activators.

Activation with the help of metal ions is carried out by different mechanisms. In some enzymes, they are part of the catalytic site. In some cases, metal ions facilitate the binding of the substrate to the active center of the enzyme, forming a kind of bridge. Often, the metal combines not with the enzyme, but with the substrate, forming a metal-substrate complex, which is preferable for the action of the enzyme.

The specificity of the participation of coenzymes in the binding and catalysis of the substrate explains the activation of enzymatic reactions by them. The activating effect of cofactors is especially noticeable when acting on an enzyme that is not saturated with cofactors.

The substrate is also an activator within known concentration limits. After reaching saturating concentrations of the substrate, the activity of the enzyme does not increase. The substrate increases the stability of the enzyme and facilitates the formation of the desired conformation of the active site of the enzyme.

Metal ions, coenzymes and their precursors and active analogues,

substrates can be used in practice as preparations that activate enzymes.

Activation of some enzymes can be carried out by modification that does not affect the active center of their molecules. Several modifications are possible:

1) activation of an inactive predecessor - proenzyme, or zymogen. For example, the conversion of pepsinogen to pepsin ;

2) activation by attaching any specific modifying group to the enzyme molecule;

3) activation by dissociation of an inactive complex protein - active enzyme.

2.5 Enzyme inhibition

There are reagents that can interact more or less specifically with one or another side chain of proteins, which leads to inhibition of enzyme activity. This phenomenon makes it possible to study the nature of the amino acid side residues involved in this enzymatic reaction. However, in practice, one should take into account numerous subtleties that make an unambiguous interpretation of the results obtained with specific inhibitors rather difficult and often doubtful. First of all, for the reaction with an inhibitor to be suitable for studying the nature of the side chains involved in the reaction, it must satisfy the following criteria:

) be specific, i.e. the inhibitor should block only the desired groups;

) inhibit the activity of the enzyme, and this inhibition should become complete with an increase in the number of modified groups;

) the reagent should not cause non-specific denaturation of the protein.

There are 2 groups of inhibitors: reversible and irreversible action. The division is based on the criterion for the restoration of enzyme activity after dialysis or a strong dilution of an enzyme solution with an inhibitor.

According to the mechanism of action, competitive, non-competitive, non-competitive, substrate and allosteric inhibition are distinguished.

Competitive inhibition

Competitive inhibition was discovered in the study of inhibition caused by analogs of the substrate. This is the inhibition of the enzymatic reaction caused by the binding to the active center of the enzyme of an inhibitor similar in structure to the substrate and preventing the formation of an enzyme-substrate complex. In competitive inhibition, the inhibitor and substrate, being similar in structure, compete for the active site of the enzyme. The compound of molecules, which is larger, binds to the active center.

Such ideas about the mechanism of inhibition were confirmed by experiments on the kinetics of competitive inhibition reactions. Thus, it was shown that, in the case of competitive inhibition, the substrate analog does not affect the rate of decomposition of the already formed enzyme–substrate complex; when using an “infinitely large” excess of the substrate, the same maximum rate is obtained both in the presence and in the absence of an inhibitor. On the contrary, the inhibitor affects the value of the dissociation constant and the Michaelis constant. From this we can conclude that the inhibitor reacts with protein groups involved in one way or another in binding the substrate, therefore, due to its interaction with these groups, the binding strength of the substrate decreases (i.e., the number of enzyme molecules capable of binding the substrate decreases) .

Later it was shown that kinetically competitive inhibition can be caused not only by substrate analogues, but also by other reagents, the chemical structure of which is completely different from that of the substrate. In these cases, it was also assumed that this reagent interacts with the group responsible for binding the substrate.

There are theoretically two possibilities for competitive inhibition:

1) binding and catalytic sites of the enzyme overlap; the inhibitor binds to them, but affects only the binding center groups;

2) the binding center and the catalytic center in the enzyme molecule are spatially isolated; the inhibitor interacts with the binding site.

where I is an inhibitor, and K I is the dissociation constant of the enzyme-inhibitor complex.

Relative rate (ratio of enzymatic reaction rate measured in the presence of an inhibitor (v i) , to the maximum speed) is equal to

v i / V = ​​/ [E] T

since for the total concentration of the enzyme it is true

[E]T = [E] + +

then 1 / v i = (K s / V[S]) (1 + [I] / K I) + 1 / V

Obviously, if [I] = K I , then the slope of the straight line becomes twice as large as for the dependence of 1/v 0 on [S] (v 0 is the rate of the enzymatic reaction in the absence of an inhibitor).

The type of inhibition is usually determined graphically. Competitive inhibition is most easily recognized by plotting Lineweaver-Burk plots (i.e. plots in 1/v i and 1/[S]) at different inhibitor concentrations. With true competitive inhibition, a set of straight lines is obtained that differ in the tangent of the slope angle and intersect the y-axis (axis 1/v i) at one point. At any concentration of the inhibitor, it is possible to use such a high concentration of the substrate that the activity of the enzyme will be maximum.

An example of competitive inhibition is the effect of various substances on the activity of succinate dehydrogenase. This enzyme is part of the enzymatic cyclic system - the Krebs cycle. Its natural substrate is succinate, and its competitive inhibitor is oxaloacetate, an intermediate product of the same Krebs cycle:

A similar competitive inhibitor of succinate dehydrogenase is malonic acid, which is often used in biochemical research.

The action of many pharmacological preparations, pesticides used to destroy agricultural pests, and chemical warfare agents is based on the principle of competitive inhibition.

For example, a group of anticholinesterase drugs, which include derivatives of quaternary ammonium bases and organophosphorus compounds, are competitive inhibitors of the cholinesterase enzyme with respect to its substrate acetylcholine. Cholinesterase catalyzes the hydrolysis of acetylcholine, a mediator of cholinergic systems (neuromuscular synapses, parasympathetic system, etc.). Anticholinesterase substances compete with acetylcholine for the active site of the enzyme, bind to it, and turn off the catalytic activity of the enzyme. Drugs such as prozerin, physostigmine, sevin inhibit the enzyme reversibly, while organophosphorus drugs such as armin, nibufin, chlorophos, soman act irreversibly, phosphorylating the catalytic group of the enzyme. As a result of their action, acetylcholine accumulates in those synapses where it is a mediator of nervous excitation, i.e. the organism is poisoned by the accumulated acetylcholine. The action of reversible inhibitors gradually disappears, since the more acetylcholine accumulates, the faster it displaces the inhibitor from the active center of cholinesterase. The toxicity of irreversible inhibitors is incomparably higher; therefore, they are used to combat agricultural pests, household insects and rodents (for example, chlorophos) and as chemical warfare agents (for example, sarin, soman, etc.).

Noncompetitive inhibition

In non-competitive inhibition, a specific inhibitor does not affect the dissociation constant of the enzyme-substrate complex. On the other hand, the maximum achievable reaction rate is lower in the presence of an inhibitor than in its absence, even at an infinitely large excess of the substrate. The presence of inhibition proves that the inhibitor binds to the protein. The invariance of the dissociation constant both in the presence and absence of the inhibitor, in turn, indicates that, unlike the substrate, the inhibitor binds to another group. From a theoretical point of view, the mechanism of such inhibition can be interpreted in various ways.

a) The binding site and the catalytic site of the enzyme are different. In this case, the inhibitor associated with the catalytic center reduces the activity of the enzyme and the maximum achievable
speed without affecting the formation of the enzyme-substrate complex.

b) The binding site and the catalytic site overlap on
surface of the enzyme, and the inhibitor binds to other groups of the protein. Due to the binding of the inhibitor to the surface of the enzyme, the information of the protein changes and becomes unfavorable for the implementation of catalysis.

c) The inhibitor does not bind to either the catalytic site or the binding site, and thus does not affect the conformation of the protein. However, it can locally change the charge distribution on a region of the protein surface. Inhibition of activity can also occur in this case, if, for example, the ionization of groups essential for the manifestation of activity is made impossible, or if, on the contrary, ionization of groups active only in non-ionized form occurs. This phenomenon is observed mainly when using strongly acidic or strongly alkaline reagents.

The inhibitor and the substrate do not affect each other's binding to the enzyme, but the enzyme complexes containing the inhibitor are completely inactive. In this case, the following elementary stages can be assumed:

v i / V = ​​/ [E] T

[E] T = [E] + + +

/ v i = (K s / V [S]) (1 + [I] / K I) + (1 / V) (1 + [I] / K I)

If [I] = K I, the slopes of the straight lines and the ordinates of the point of intersection with the vertical axis are doubled compared to 1/v 0 .

Non-competitive inhibitors are, for example, cyanides, which are strongly associated with ferric iron, which is part of the catalytic site of the hemic enzyme - cytochrome oxidase. Blockade of this enzyme turns off the respiratory chain, and the cell dies. Non-competitive enzyme inhibitors include heavy metal ions and their organic compounds. Therefore, heavy metal ions of mercury, lead, cadmium, arsenic and others are very toxic. They block, for example, SH-groups included in the catalytic site of the enzyme.

Non-competitive inhibitors are cyanides, which are strongly associated with ferric iron, which is part of the catalytic site of the hemic enzyme - cytochrome oxidase. Blockade of this enzyme turns off the respiratory chain, and the cell dies. It is impossible to remove the action of a non-competitive inhibitor with an excess of the substrate (as the action of a competitive one), but only with substances that bind the inhibitor - reactivators.

Non-competitive inhibitors are used as pharmacological agents, toxic substances for pest control in agriculture and for military purposes. In medicine, preparations containing mercury, arsenic, bismuth are used, which non-competitively inhibit enzymes in the cells of the body or pathogenic bacteria, which determines one or another of their effects. In case of intoxication, the binding of poison or its displacement from the enzyme-inhibitor complex is possible with the help of reactivators. These include all SH-containing complexones (cysteine, dimercaptopropanol), citric acid, ethylenediaminetetraacetic acid, etc.

Uncompetitive inhibition

This type of inhibition is also called anticompetitive inhibition in the literature. or associated inhibition , however, the term "uncompetitive inhibition" is the most widely used. The characteristic of this type of inhibition is that the inhibitor is not able to attach to the enzyme, but it does attach to the enzyme-substrate complex.

In the case of uncompetitive inhibition, the complex containing the inhibitor is inactive:

v i / V = ​​/ [E]

[E]T = [E] + +

/ v i = Ks / V[S] + (1 / V) (1 + [I] / K I)

substrate inhibition

Substrate inhibition is the inhibition of an enzymatic reaction caused by an excess of substrate. Such inhibition occurs due to the formation of an enzyme-substrate complex that is not capable of undergoing catalytic transformations. The ES 2 complex is unproductive and makes the enzyme molecule inactive. Substrate inhibition is caused by an excess of the substrate, therefore, it is removed when its concentration decreases.

Allosteric inhibition

Allosteric regulation is characteristic only for a special group of enzymes with a quaternary structure, which have regulatory centers for binding allosteric effectors. Negative effectors that inhibit the conversion of the substrate in the active site of the enzyme act as allosteric inhibitors. Positive allosteric effectors, on the contrary, accelerate the enzymatic reaction, and therefore they are referred to as allosteric activators. Allosteric effectors of enzymes are most often various metabolites, as well as hormones, metal ions, and coenzymes. In rare cases, substrate molecules play the role of an allosteric effector of enzymes.

The mechanism of action of allosteric inhibitors on the enzyme is to change the conformation of the active site. The decrease in the rate of the enzymatic reaction is either a consequence of an increase in K m or a decrease in the maximum rate V max at the same saturating substrate concentrations, i.e. the enzyme is partially idle.

Allosteric enzymes differ from other enzymes in their specific S-shaped curve of reaction rate versus substrate concentration. This curve is similar to the oxygen saturation curve of hemoglobin; it indicates that the active centers of the subunits do not function autonomously, but cooperatively, i.e. the affinity of each next active center for the substrate is determined by the degree of saturation of the previous centers. The coordinated work of the centers is determined by allosteric effectors.

Allosteric regulation manifests itself in the form of inhibition by the end product of the first enzyme in the chain. The structure of the final product after a series of transformations of the starting substance (substrate) is not similar to the substrate, so the final product can act on the initial enzyme of the chain only as an allosteric inhibitor (effector). Outwardly, such regulation is similar to the regulation by the feedback mechanism and allows you to control the output of the final product, in the event of accumulation of which the work of the first enzyme in the chain stops. For example, aspartate carbamoyltransferase (ACTase) catalyzes the first of six reactions in the synthesis of cytidine triphosphate (CTP). CTP is an allosteric AKTase inhibitor. Therefore, when CTP accumulates, AKTase inhibition occurs and further CTP synthesis stops. Allosteric regulation of enzymes with the help of hormones has been discovered. For example, estrogens are an allosteric inhibitor of the enzyme glutamate dehydrogenase, which catalyzes the deamination of glutamic acid.

Thus, even the simplest kinetic equation for an enzymatic reaction contains several kinetic parameters, each of which depends on the temperature and environment in which the reaction takes place.

Inhibitors make it possible not only to understand the essence of enzymatic catalysis, but also are a kind of tool for studying the role of individual chemical reactions, which can be specifically switched off with the help of an inhibitor of a given enzyme.

3. Some devices useful for determining initial reaction rates

Many problems of enzymatic kinetics lead to the determination of the initial reaction rates (v 0). The main advantage of this method is that the values ​​of v0 determined at the initial moment of time will give the most accurate representation of the activity of the enzymes under study, since the accumulating reaction products do not yet have time to exert an inhibitory effect on the enzyme and, in addition, the reacting system is in a state of stationary equilibrium. .

In laboratory practice, however, when using conventional spectrophotometric, titrimetric, or other techniques for recording the progress of such reactions, at best, up to 15–20 seconds from the initial time for introducing the enzyme to the substrate, mixing the reacting system, setting up the cell, etc. is lost. And this is unacceptable, since in this case the tangent is brought to the point where tg ά 2< tg ά 1 . Не компенсируется потеря начального времени и при математической обработке таких кривых при записи выхода v 0 на максимальный уровень (V). Кроме того, протекание реакций без constant mixing is further complicated by fluctuations in the concentrations of reagents by volume.

The simple devices proposed below for a spectrophotometer, a pH meter, and the like make it possible to significantly reduce the sources of the indicated errors in determining v 0 .

3.1 Device to the spectrophotometer

The device for the spectrophotometer consists of a dispenser 1, a rotating Teflon thread 2 (a stirrer) and a fixing cap 3.

The dispenser is a micropipette, one end of which is formed with a needle 4, the other - with a widening 5 (to prevent the enzyme from entering the rubber tip 6).

The Teflon cover 3 covering the spectral cuvette 7 has two holes: one (8) in the center of the cover, the second (9) above the middle of the gap between the opaque wall of the cuvette 7 and the light beam 10. Teflon tube 11 (inner diameter 1 -1.5 mm) is fixed at one end in hole 9, the other - on a fixed ledge 12 in front of the motor rotor 13. Teflon thread 2 is inserted inside the tube (thread thickness 0.5-0.6 mm). One end of the thread is fixed on the rotating rotor of the motor 13, the second - passed into the cuvette 7 - is shaped in the form of a spiral (to enhance mixing). The position of the thread is determined by the fixing cap 3, regardless of the distance of the motor, which is convenient when working requiring frequent changes of cuvettes.

Principle of operation. The quartz cuvette of the spectrophotometer 7 is filled with substrate 14 (about 1.5-2.0 ml), inserted into the thermostatic cuvette holder of the spectrophotometer, closed with a lid 3 with a rotating Teflon thread 2, which is immersed in the substrate 14, and all further operations are performed already in the beam of light of the spectrophotometer and recorded on the recorder.

At the beginning of work, the substrate is mixed, and the pen of the recorder writes a flat horizontal (or “zero”) line. The dispenser (with the enzyme) is inserted into hole 8 (the needle is immersed in the substrate solution 14), by quickly squeezing the tip 6, the enzyme (usually about 0.03-0.05 ml) is introduced into the substrate, and the dispenser is removed. The mixing of the components ends in 2.5-3 s, and the pen of the recorder fixes the beginning of the reaction by deviating the curve of optical density (ΔA) versus time.

Such a device also makes it possible to take samples from the reacting system for analysis; add inhibitors and activators to the system; change the reaction conditions (change the pH, ionic strength, etc.) without disturbing the registration of the reaction course, which is very convenient, for example, when studying the splitting n-NFF "acidic" phosphatases, where cleavage n-NFF is carried out at pH 5.0 (or pH 6-7), and the activity of enzymes is determined by the accumulation n-nitrophenolate ions at pH 9.5-10.0.

Such a device is also convenient for carrying out spectrophotometric titration of enzymes, etc.

3.2 Device for pH meter

The device for the pH meter consists of a modified tip of the flow electrode 1, a semi-microcell 2, a dispenser 3, and an electronic circuit for connecting the pH meter to the recorder. In addition, the device includes a standard pH meter electrode (4), a cell holder cover (5), a thermostatic flow chamber (6), a substrate solution (7), a passive magnet (8), and an active magnet (9).

The standard tip of the flow electrode of the pH meter (LPU-01) is replaced by a Teflon tube 1 (inner diameter 1.3-1.5 mm), filled with asbestos thread, pre-treated with a saturated KCl solution. The filling density of the thread is controlled so that the flow rate of the KCl solution through the tube is close to the flow rate of the original unmodified electrode. This replacement of the tip makes it possible to reduce the size of the original working cell from 20–25 to 2 ml, which makes it possible to manage with minimal volumes (1.5 ml) of solutions of expensive biochemical preparations.

The electronic circuit for connecting the pH meter (LPU-01) to the recorder consists of a power source (DC battery 12 V), a variable wire resistance R 1 (10 - 100 Ohm), which sets a voltage of 9 V at the D809 zener diode according to the voltmeter reading, a variable wire resistance R 2 (15-150 Ohm), which regulates the setting of the "zero" (reference point) of the pH meter readings on the scale of the recorder, and variable wire resistance R 3 (35-500 Ohm), which regulates the scale of expansion (amplification) of the readings of the pH scale - meters on the recorder. The circuit operates reliably until the source voltage drops below 9 V.

Principle of operation. 1.5 ml of the substrate is introduced into the cell (a glass cylinder 1.7x2.4 cm), and the cell is fixed on the fixing cap 5. Stirring 9 is turned on, and the recorder pen writes an even (basic) reference line. With the help of a dispenser, 0.03 ml of the enzyme solution is introduced into the substrate, and the pen of the recorder fixes the beginning of the reaction by deviating the curve of pH versus time (t).

Such a device does not replace a pH stat, but taking into account the possibility of expanding the pH meter scale, it allows you to reliably record minor changes in pH 0.004-0.005.

3.3 Nomogram rulers, convenient for determining the initial speed

Considerable complexity of determining the initial velocity in the method of tangents is the calculation of the ratios of changes in the concentrations of reagents (Δ[S]) per unit time (Δt), i.e. expression v 0 in M/min from the conditions that

v 0 = lim Δ[S] / Δt, at, t 0.

In practice, such a procedure usually consists of three or four separate operations: a tangent is drawn to the initial section of the reaction curve, then the number of units of the registered value (optical density, rotation angle, etc.) per a certain time interval is counted, and this leads to unit of time and, finally, recalculate the readings of the recorder for the change in the concentration of the reagent for 1 min (M/min). The proposed two types of nomogram ruler make it possible to simplify this procedure.

Rectangular ruler. v 0 is the ratio Δ[S]/Δt, i.e. tg ά, where ά is the angle of inclination of the tangent to the time axis t. The same tangent is also the hypotenuse of the corresponding right triangle with legs [S] and t. The larger v 0 , the steeper the slope of the tangent. Therefore, if we limit ourselves to a certain time interval, for example 1 min, then we will get a series of right-angled triangles with different values ​​of the leg [S] (actually, different values ​​of v 0). If, however, both legs are graduated: horizontal - in units of time reference (1 min), and vertical - in units of change in reagent concentrations, for example, in millimoles (mM), and apply the resulting segments to a suitable format from a transparent material (plexiglass about 2 mm thick) , then you can get a convenient ruler for determining the initial reaction rates. All numbers and lines are printed on the reverse side of the ruler to eliminate parallax errors when determining v 0 .

The procedure for determining v 0 is reduced in this case to two simple operations: a tangent is drawn to the initial section of the kinetic curve t 2 and combine the zero point of the horizontal leg t of the ruler with the beginning of the tangent, the continuation of the tangent will now cross the concentration scale [S] at the point that determines the value of v 0 in M/min (when the leg t is horizontal, no additional operations are required.

Arc line. The procedure for determining v 0 can be simplified to one operation if the concentration scale is plotted along an arc of a certain radius.

A straight ("basic") line 2 is applied to a plate of transparent material (all numbers and lines are also applied on the reverse side of the ruler) and from the zero point (t=0, min) of this line with a radius equal to the leg length t=1 min [ , draw an arc [S], from top to bottom along which the scale of changes in the concentrations of the reagent (for example, substrate in mM) is laid.

The described types of rulers, a device for a spectrophotometer and a pH meter have been used for a number of years to determine the initial reaction rates (v 0), in the study of the substrate specificity of enzymes, for spectrophotometric titration, etc.

Conclusion

In this paper, a section of enzymology was considered that studies the dependence of the rate of chemical reactions catalyzed by enzymes on a number of environmental factors. The founders of this science are considered to be Michaelis and Menten, who published their theory of the general mechanism enzymatic reactions, derived an equation that has become the fundamental principle of all kinetic studies of enzymes, it serves as a starting point for any quantitative description of the action of enzymes. The original Michaelis-Menten equation is a hyperbolic equation; Lineweaver and Burke contributed to the kinetics by transforming the Michaelis-Menten equation and obtaining a graph of a straight line from which the value of V max can be most accurately determined.

Over time, the change in the rate of the enzymatic reaction in the enzymatic reaction under experimental conditions decreases. A decrease in the rate can occur due to a number of factors: a decrease in the concentration of the substrate, an increase in the concentration of a product that can have an inhibitory effect, changes in the pH of the solution, and changes in the temperature of the medium can occur. Thus, for every 10°C rise in temperature, the reaction rate doubles or even less. Low temperature reversibly inactivates enzymes. The dependence of the rate of the enzymatic reaction on pH indicates the state of the functional groups of the active center of the enzyme. Each enzyme reacts differently to changes in pH. Chemical reactions can be stopped by acting on them with various types of inhibition. The initial reaction rate can be quickly and accurately determined with the help of such devices as nomogram rulers, a spectrophotometer device and a pH meter. This allows the most accurate representation of the activity of the studied enzymes.

All this is actively used today in medical practice.

List of sources used

1. Belyasova N.A. Biochemistry and molecular biology. - Minsk: book house, 2004. - 416 p., ill.

Keleti T. Fundamentals of enzymatic kinetics: Per. from English. - M.: Mir, 1990. -350 p., ill.

3. Knorre D.G. Biological chemistry: Proc. for chemical, biol. and honey. specialist. universities. - 3rd ed., Rev. - M.: Higher. school 2002. - 479 p.: ill.

4. Krupyanenko V.I. Vector method for representing enzymatic reactions. - M.: Nauka, 1990. - 144 p.

5. Lehninger A. Biochemistry. Molecular bases of the structure and function of the cell: Per. from English. - M.: Mir, 1974.

6. Stroev E.A. Biological Chemistry: A Textbook for Pharmacy. in-tov and pharmac. fak. honey. in-comrade. - M.: Higher school, 1986. - 479 p., ill.

Severin E.S. Biochemistry. a. - 5th ed. - M.: GEOTAR - Media, 2009. - 786 p., ill.