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What is enzyme kinetics?

The enzyme kinetics is a field of study that physical chemistry and biochemistry together to study chemical reactions catalyzed by enzymes. Enzymes are biological catalysts that increase the speed of a chemical reaction by lowering their activation energy.

Enzymes catalyze chemical reactions of great importance for the maintenance of life. They have both an optimal pH and temperature to exert their catalytic action on the substrate, so they are essential factors in the study of their activities.

The enzyme interacts with the substrate through a specialized region of its protein chain, which is called the active center, whose three-dimensional structure is coupled to the structure of the substrate. The interaction between the active center and the substrate is usually weak and non-covalent.

The number of active centers of the enzymes is limited, causing their saturation with the substrate molecules, which in turn prevents the reaction rate from increasing beyond a certain value, known as the maximum rate.

Enzyme kinetics not only combines biochemistry and physicochemistry, but also bioinorganics, supramolecular chemistry, computational chemistry, and statistics.

Among the models that describe it is that of Michaelis-Menten, which explains how the speed of an enzymatic reaction varies with a simple substrate as a function of the substrate concentration. Today it remains one of the most widely used models to describe enzyme kinetics.

Basics in enzyme kinetics

Enzymatic catalysis

Enzymes are proteins, with catalytic activities, capable of acting on a molecule called a substrate, catalyzing its transformation into another substance known as a product. The enzymes are not consumed during their catalytic action, their mass remains constant.

Catalytic activity

The catalytic activity of the enzyme is carried out in a specialized three-dimensional structure known as the active center. This is formed by the fold of the enzymatic protein chain that determines the interaction of a group of amino acids that form the active center.

Active center

The active center is not a rigid structure, but capable of geometrically conforming to the substrate to interact with it. The interaction is generally weak (Van der Waals forces), although there are enzymes that form a covalent bond with the substrate.

Decreased activation energy

The enzymes catalyze the reactions reducing the activation energy, and therefore, also reducing the consumption of free energy (G) necessary to carry out the catalyzed process. Enzymes do not alter the equilibrium point of uncatalyzed chemical reactions.

Note how the enzyme carbonic anhydrase decreases the activation energy for the conversion of CO 2 to H 2 CO 3 . Although the distance between the red and blue lines does not seem like a great deal, this enzyme increases the speed in the order of millions of times (10 6 ), compared to the reaction carried out without your participation.

Stereospecificity

Adenosine triphosphate and xylose substrates have the specific shape that matches the geometry of the active site of the hexokinase enzyme. Source: Thomas Shafee, CC BY 4.0 <https://creativecommons.org/licenses/by/4.0>, via Wikimedia Commons

Enzymes, in general, are highly specific for the reactions they catalyze, since the substrate molecules must interact with the active center that presents a set of requirements for their coupling with it.

Thus, for example, the active center of hexokinase, which is dynamic due to the molecular vibrations of the protein chains, offers the groups in the exact spatial orientations so that the adenosine triphosphate and xylose molecules fit together as if they were pieces filling holes. geometric.

The slightest physical or chemical disturbance, and the bluish region of hexokinase will no longer be able to accommodate substrates.

Maximum speed

Enzymes have a limited number of active centers, so as the substrate concentration increases, they will become saturated. This determines that the rate of the enzymatically catalyzed reaction cannot increase beyond a certain value, known as the maximum rate.

Sensitivity to temperature and pH

The enzymatic catalytic activity is dependent on temperature and pH, having optimal values ​​of these parameters for its operation. Likewise, because enzymes are protein molecules, they are susceptible to chemical or thermal denaturation.

Cofactors

Some enzymes increase their catalytic activity due to the influence of certain factors, which can be metals or organic compounds known as coenzymes.

Also, enzymes can be competitively and non-competitively inhibited. In the case of hexokinase above, Mg 2+ (yellow sphere) acts as a cofactor.

Enzyme reaction rate

The rate of an enzyme reaction depends on the concentration of the substrate and the enzyme concentration. When the substrate concentration is low, there is an almost linear relationship between the enzyme rate and the substrate concentration.

Therefore, the enzyme rate increases in direct proportion to the concentration of the substrate; but by increasing the substrate concentration to a value that saturates the active sites of the enzyme, the maximum speed is reached.

Once this occurs, the enzyme speed becomes constant, that is, it is independent of the substrate concentration and the enzyme speed is said to be zero order. Furthermore, the catalytic enzyme rate is proportional to the concentration of the enzyme-substrate complex [ES].

As the mathematical expression shows:

V = k 2 [ES]

The maximum rate is directly proportional to the total concentration of the enzyme, as it appears in the following formula:

max = K cat E t

cat is the turnover or turnover number and represents the number of substrate molecules that each enzyme site converts to product per unit of time. Meanwhile, E t represents the number of catalytic enzymatic sites. If E t has a high value, a larger [S] is required to saturate the active sites or centers.

Michaelis-Menten equation

Model

The Mihaelis-Menten model is based on the action of enzymes that act on a simple substrate and is not applicable to allosteric enzymes; that is, those that have a regulatory region of the catalytic activity of the active site.

Enzymes at a low substrate concentration have a catalytic activity that is linear with the substrate concentration; but at high substrate concentrations, the catalytic activity is independent of the substrate concentration.

In 1913, Leonor Michelis and Maud Menten proposed a model to explain the indicated enzymatic behavior, being of importance in the model the existence of an intermediate enzyme-substrate complex [ES].

General equation

The relationship of this complex with the other components of the enzymatic process, as well as with the constants (K) that relate them, are indicated in the following diagram:

Enzyme (E) combines with substrate (S) to form the enzyme-substrate complex with a rate constant K 1 . The ES complex can dissociate into E and S with a reaction rate constant K -1 .

Likewise, the ES complex can originate a product (P) and the separation of the enzyme, which can be recycled to fulfill another cycle of enzymatic activity. An equilibrium situation can be reached for the state [ES] in which its rate of formation is equal to its rate of decomposition.

1 [ES] [S] = (K -1 + K 2 ) [ES] (1)

Regrouping terms and clearing [ES], we have:

[ES] = ([E] [S]) / (K -1 + K 2 / K 1 ) (2)

M = (K -1 + K 2 ) / K 1

M is a constant introduced by Michaelis.

Terms of the Michaelis-Menten equation

Now substituting K M in (2) we continue:

[ES] = [E] [S] / K M (3)

The uncombined enzyme concentration is:

[E] = [E T ] – [ES] (4)

Where [E] is the free enzyme and [E T ] the total enzyme concentration.

Combining equations 3 and 4, making the appropriate substitutions, and also taking into account V max , we arrive at the Michaelis-Menten equation, expressed as follows:

V = (V max [S]) / ([S] + K M )

The maximum rate of the enzymatic reaction occurs when the substrate concentration is much higher than K M and the catalytic sites of the enzymes are saturated with substrate. This occurs when the ratio [S] / [S] + K M approaches 1.

When [S] is equal to K M , the portion of the equation [S] / [S] + K M is equal to 1/2, indicating that K M is the substrate concentration that produces an enzymatic reaction rate that is half the maximum speed.

Furthermore, K M is a measure of the affinity of an enzyme for the substrate: the higher the K M value , the lower the affinity of the enzyme for the substrate and vice versa. Therefore, at a high K M the rate of the enzymatic reaction will be low.

Lineweaver-Burk plot

Lineweaver-Burk line. Source: Pro Bug catcher via Wikipedia.

The transformation of the Michaelis-Menten equation to produce its inverse form has the following form:

1 / V = ​​(K M / V max ) (1 / [S]) + 1 / V max

The importance of this line is that it has an intersection with the X axis at – 1 / K M , and with the Y axis at Y = 1 / V max (upper image). The line has a slope of K M / Vmax. This makes it possible to obtain information about V max and K M by plotting the inverse of the velocities as a function of the inverse of the substrate concentrations.

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