Enzyme kinetics: Michaelis–Menten equation

Energetics and the Enzyme-Substrate Complex

For molecules to enter into a chemical reaction, they require additional energy—activation energy (Ea). Enzymes act as biological catalysts: they lower the height of this energy barrier. As a result, a larger proportion of substrate molecules acquire the ability to react, and the conversion rate increases sharply. It is important to note that an enzyme does not change the overall thermodynamics of the process (the energy difference between initial substances and final products); it affects solely the kinetics.

At the heart of catalysis lies the formation of the enzyme-substrate complex (ES). The process proceeds according to the following scheme: the enzyme binds to the substrate, a chemical transformation occurs within the intermediate complex, after which the finished product dissociates. The enzyme itself is then released unchanged and is ready to enter a new catalytic cycle.

The Michaelis-Menten Equation and Main Constants

The dependence of the initial reaction velocity (v) on the substrate concentration ([S]) is described by the Michaelis-Menten equation:

v = (Vmax · [S]) / (Km + [S])

Two crucial kinetic characteristics figure into this equation:

• Maximum velocity (Vmax). This is the limiting value that the velocity approaches with an infinitely large increase in substrate concentration. It reflects the maximum possible performance of the enzyme under conditions where all its active sites are saturated.
• Michaelis constant (Km). Numerically, it is equal to the substrate concentration at which the reaction velocity is exactly half of the maximum possible (1/2 Vmax).

Km serves as the main indicator of enzyme-substrate affinity. This relationship is inversely proportional: the lower the value of Km, the higher the affinity. The physical meaning of the constant is closely related to the substrate constant (Ks), which characterizes the equilibrium of the first stage of catalysis. The smaller Ks is, the greater the proportion of the enzyme that exists as the ES complex, which accelerates the overall reaction.

Graphical Analysis of Kinetics

If you plot the dependence of reaction velocity on substrate concentration, you get a portion of an equilateral hyperbola—a typical saturation curve.

• At low values of [S], velocity increases almost linearly.
• At high values of [S], the graph reaches a plateau, gradually approaching the limit—Vmax.

For a more convenient analysis of kinetics, the Lineweaver-Burk plot (double-reciprocal method) is used. This is a plot of 1/v versus 1/[S]. In these coordinates, the hyperbola turns into a straight line. It intersects the ordinate axis at the point 1/Vmax and the abscissa axis in the negative zone at the point -1/Km.

Complex Reactions and the Effect of Inhibitors

In nature, two-substrate reactions are common and proceed via two main mechanisms:

1. Sequential mechanism: all substrates must bind to the enzyme before product release begins.
2. Ping-pong mechanism: the first substrate binds, is cleaved, and the first product leaves, but a part of the substrate molecule remains on the enzyme. Only after this does the second substrate bind. This mechanism is characteristic, for example, of transaminases.

The kinetic parameters of an enzyme can change under the influence of regulators. Thus, in competitive inhibition, the maximum velocity (Vmax) remains unchanged, since an excess of substrate is able to completely displace the inhibitor from the active site. However, the Michaelis constant (Km) increases, which indicates an apparent decrease in enzyme-substrate affinity.

Class and exam questions

What else to study on this topic

• Calculation of substrate concentration given Vmax and Km (using small intestine peptidase as an example)
• Physical meaning of the substrate constant (Ks) and rate constants of individual stages of catalysis
• Classical models of substrate binding: Fischer's "lock-and-key" and Koshland's "induced fit"
• Detailed analysis of two-substrate reaction mechanisms (sequential and ping-pong)
• Recalculation of experimental Vmax per unit amount of enzyme (specific activity)

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Prepared by WhiteCoat Pro faculty in accordance with the medical school curriculum. For educational purposes only.