Biochemistry: The Chemical Reactions of Living Cells, Volume 2 - D. Metzler 1980

Enzymes: The Protein Catalysts of Cells
Fundamentals of Enzyme Kinetics
Formation and Transformation of the ES Complex

Since Enzymes cannot act at a distance²), the first step in an enzymatic reaction must be The formation of the ES complex:

This process is reversible: the ES complex, in turn, is converted (usually via a unimolecular reaction type) into a product or products. If reaction (6-14) is overall irreversible, then three rate constants are required to describe such a system. Describing the kinetic Properties of the system is generally a rather complex task; however, in the vast majority of experiments, the Enzyme Concentration is exceptionally low (on the order of 10^-8 M), while the substrate is present in large excess¹⁾. Under these conditions, in most situations of biochemical interest, the steady-state assumption is valid. It is assumed that the Formation of the ES complex from the free enzyme and substrate is exactly balanced by The conversion of ES to P; this means that over the relatively short time interval required for the experimental determination of velocity, the concentration of ES remains practically constant. In reality, the steady-state assumption is a strong simplification. As Jencks pointed out [12], the steady-state regime is realized only when the absolute rate of change of the intermediate concentration is negligibly small compared to the rates of change of reactant and product concentrations.

²⁾ Until quite recently, chemists believed that an enzyme and substrate could interact at a distance of 10 nm or more. Consider what types of experiments could be conducted to disprove such a hypothesis.

The dependence of the initial velocity of a single-substrate enzyme-catalyzed reaction on the Substrate Concentration is described by the Michaelis–Menten Equation

where K_M = (k₂+k₃)/k₁²). This equation can be derived by equating The rate of formation of the ES complex (i.e., the term k₁ [Е]|[S]) to the rate of its dissociation (the term (k₂+k₃) [ES]). In this case

Using this equation and the material balance equation for the enzyme, which implies that [Е] = [Е]_t—[ES], we obtain the following expression for the fraction of the enzyme present as the enzyme-substrate complex:

The maximum velocity V_max = k₃[Е]_t is achieved only when all the enzyme is converted into the ES form. Under other conditions, v = k₃ [ES] and the following relation holds

Substituting the expression for [ES]/[E]_t into equation (6-17), we arrive at the Michaelis–Menten equation (6-15).

Equation (6-15) relates the velocity observed at a given substrate concentration to the maximum velocity that would occur if the substrate concentration were infinitely high. The values of V_max and K_M are frequently used as kinetic parameters of an enzyme, and their determination is an essential part of characterizing any enzyme.

In many cases, the rate of the reverse Conversion of the ES complex into free enzyme and substrate greatly exceeds the rate of conversion of ES into products (k₂≫k₃). Then the constant K_M is approximately equal to k₂/k₁, i.e., the dissociation constant of the ES complex into free enzyme and substrate. Thus, the constant K_M is sometimes inversely proportional to the strength of substrate binding by the enzyme. In such cases, the reciprocal of K_M serves as a measure of substrate affinity for the substrate-binding site of the enzyme. The value 1/K_M can also be used to characterize a series of different substrates converted by the same enzyme: substrates that bind more tightly exhibit lower K_M values. It should be kept in mind, however, that the condition k₃≪k₂ may hold for some (poorer) substrates and not at all for others.

¹⁾ In Cells, however, the ratio between enzyme and substrate concentrations may be reversed [11].

²⁾ The parameter K_M is called the Michaelis constant. — Transl. note.

FIG. 6-2. Plot of reaction velocity v versus substrate concentration [S] for a simple enzymatic process.

Fig. 6-2 depicts the theoretical dependence of reaction velocity on substrate concentration described by equation (6-15). The ordinate marks THE POSITION OF the maximum velocity (V_max); however, it is clear that, except in cases where K_M is extremely small, the experimentally observed velocity (v) can never reach V_max, but only asymptotically approaches it. From Fig. 6-2, K_M can be determined as the value of [S] at which v = V_max/2. It should be noted that due to the difficulty of determining V_max, the graph presented in Fig. 6-2 is rarely used. However, it is very illustrative and is coming back into use with the advent of computerized Methods for estimating V_max and K_M parameters. Note also that the curve shown in Fig. 6-2 is identical in shape to the saturation curves for reversible binding (Fig. 4-1).