Enzyme kinetics refers to the catalytic behavior of enzymes, specifically focusing on reaction rates.

Catalysis is the process of accelerating a reaction by lowering the activation energy (E_a). Enzymes increase the rate of the reaction without affecting the equilibrium (K_eq) or the thermodynamically favorable direction of the reaction. Different reactions are enhanced by different catalysts. However, all catalysts share several features:

• All catalysts increase the rate of reaction by lowering the energy of activation.
• All catalysts form transient complexes with reactants but are never consumed or permanently changed by the reaction. Therefore, they are required in small amounts.
• Catalysts never change the equilibrium of a reaction. Therefore, they have no effect on the thermodynamic spontaneity of a reaction.

Michaelis-Menten

The rate of reaction can be measured by the appearance of a product or the disappearance of the substrate. Most enzymes exhibit an increased rate of reaction with increasing substrate concentration. As the substrate concentration increases, the increase in the rate of the reaction is reduced (resulting in a hyperbolic curve). The enzyme eventually approaches saturation, a point beyond which increasing the substrate concentration will not change the rate of the reaction. At saturation, increasing the substrate concentration does not change the rate of the reaction because all of the molecules of the enzyme are engaged in catalysis. Saturation is a fundamental characteristic of an enzyme-catalyzed reaction, which distinguishes it from an uncatalyzed reaction.

The relationship between the initial rate of a reaction (v) and the substrate concentration ([S]) is described by a mathematical equation proposed by the two enzymologists Leonor Michaelis and Maud Menten. The Michaelis-Menten equation is written:

The initial rate of a reaction (v) is a function of Vmax multiplied by the substrate concentration ([S]), divided by the substrate concentration plus the Michaelis constant (Km). Vmax is the maximal velocity, or rate of a reaction, at saturating substrate concentrations. The Michaelis constant (Km) is defined as the substrate concentration when the velocity of the reaction reaches one-half Vmax. In most cases, Km is a measure of the affinity of the enzyme for the substrates. The Michaelis-Menten equation can be used to generate a plot for any enzyme that Vmax and Km are defined. Both Vmax and Km are constants for any given enzyme, and they are independent of substrate concentration. Vmax is a function of enzyme concentration. At saturation, the enzyme concentration is rate-limiting; therefore, if the reaction is run at a higher enzyme concentration, then Vmax will increase.

 

A Lineweaver-Burk plot (also called the double-reciprocal plot) is a useful tool for analyzing kinetic data using Michalis-Menten relationships. Enzymatic reaction data is plotted with 1/[concentration of substrate] on the x-axis, and 1/velocity of the reaction on the y-axis. With the data graphed in this way, the y-intercept of the best-fit line is equal to 1/Vmax, the x-intercept is 1/Km and the slope is Km/Vmax.

Lineweaver-Burk plots use measurements of enzyme activity to determine kinetic properties of enzymes. A measurement of specific activity is used to describe the purity of an enzymatic mixture. The specific activity is equal to the activity of an enzyme per milligram of total protein in the mixture.

Cooperativity is a unique type of allosteric regulation observed in proteins composed of multiple identical subunits. Here, the binding of substrates by one subunit induces a conformational change and increases the affinity of other unoccupied subunits for the substrates. One of the best-studied examples of cooperativity is hemoglobin, which binds oxygen in red blood cells. Hemoglobin is composed of four globin chains, each capable of binding oxygen. At low oxygen levels, only one of the four will bind oxygen, and when it does, it will induce a conformational change in the other globin chains to facilitate oxygen binding.

Binding can often be assisted by cooperativity and it is accepted there are three general mechanisms of substrate binding:

1. Ping-pong mechanism also called a double-displacement reaction, is characterized by the change of the enzyme into an intermediate form when the first substrate to product reaction occurs.
2. In an ordered mechanism, one particular substrate has to first bind to the enzyme, followed by the other substrate.
3. In random sequential reactions, the substrates and products are bound and then released in no preferred order, or “random” order.

The cooperativity of an enzyme can be measured by the Hill coefficient. The Hill coefficient is a dimensionless parameter that has long been used as a measure of the extent of cooperativity. Originally derived from the oxygen‐binding curve of human hemoglobin. A Hill coefficient of 1 indicates independent binding, a value of greater than 1 shows positive cooperativity binding of one ligand facilitates binding of subsequent ligands at other sites on the multimeric receptor complex.

Effects of local conditions on enzyme activity 

Environmental conditions can affect an enzyme’s active site and, therefore, the rate at which a chemical reaction can proceed. Increasing the environmental temperature generally increases reaction rates because the molecules are moving more quickly and are more likely to come into contact with each other.

However, increasing or decreasing the temperature outside of an optimal range can affect chemical bonds within the enzyme and change its shape. If the enzyme changes shape, the active site may no longer bind to the appropriate substrate, and the rate of reaction will decrease. Dramatic changes to the temperature and pH will eventually cause enzymes to denature.

 

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Key Points

• Enzyme kinetics refers to the catalytic behavior of enzymes, specifically focusing on reaction rates.

• Enzymes can bind to substrates in 3 ways, ordered, random or ping pong mechanisms.

• Catalysis is the process of accelerating a reaction by lowering the energy of activation (E_a).

• The relationship between the initial rate of a reaction (v) and the substrate concentration ([S]) is described by a mathematical equation known as the Michaelis-Menten equation:

• At saturation, the enzyme concentration is rate-limiting; therefore, if the reaction is run at a higher enzyme concentration, then Vmax will increase.

• A Lineweaver-Burk plot uses experimental data to determine the Km and Vmax of an enzymatic reaction

• Cooperativity is a unique type of allosteric regulation observed in proteins composed of multiple identical subunits. Here, the binding of substrates by one subunit induces a conformational change and increases the affinity of other unoccupied subunits for the substrates.

• The Hil coefficient Is a measure of cooperativity in a binding process. A Hill coefficient of 1 indicates independent binding, a value of greater than 1 shows positive cooperativity binding

• Increasing the temperature generally increases the rate of a reaction, but dramatic changes in temperature and pH can denature an enzyme, thereby abolishing its action as a catalyst.

Key Terms

Saturation: A point beyond which increasing the substrate concentration will not change the rate of the reaction.

Michaelis-Menten equation: The rate equation for a one-substrate enzyme-catalyzed reaction.

Vmax: The maximal velocity, or rate of a reaction, at saturating substrate concentrations.

Lineweaver-Burk plot: A method for experimentally determining the kinetic parameters of an enzymatic reaction. The slope is equal to Km/Vmax.

Specific activity: a measurement of purity of enzymatic activity, measured as the amount of enzyme per total protein (in milligrams)

Cooperativity: A phenomenon in which the shape of one subunit of an enzyme consisting of several subunits is altered by the substrate (the substance upon which an enzyme acts to form a product) or some other molecule so as to change the shape of a neighbouring subunit

Activation energy: the energy required to get a reaction to start

Michaelis constant (Km:) is defined as the substrate concentration when the velocity of the reaction reaches one-half Vmax. Km is a measure of the affinity of the enzyme for the substrate

Denature: change shape due to heat and pH.