BIOCHEMISTRY - L. Stryer - 1984

VOLUME 1

PART I. CONFORMATION AND DYNAMICS

CHAPTER 6. INTRODUCTION TO ENZYMOLOGY

6.10. V_max and К_м Can Be Determined Using Various Substrate Concentrations

If an enzyme operates According to the simple scheme presented in equation (1), it is straightforward to determine its Michaelis constant K_м and maximum velocity Vmax by measuring the reaction velocity at various substrate concentrations. It is convenient to transform the Michaelis-Menten Equation into a form that yields a straight line graphically. For this purpose, equation (15) is expressed in terms of reciprocals:

Class="center">(16)

By plotting 1/V versus 1/[S], we obtain a straight line whose intercept with the ordinate gives 1/Vmax, and whose slope is equal to Kм/Vmax (Fig. 6.13).

Fig. 6.13. Representation of enzyme reaction kinetics on a double-reciprocal plot: 1/V expressed as a function of 1/[S]. The slope of the curve is equal to K/_M/V_mах, the intercept with the y-axis corresponds to 1/V_mах, and the intercept with the X-axis = 1 /К_м

6.11. Significance of К_м and V_mах Values

K_м varies over a wide range of values for different Enzymes (Table 6.1). For most enzymes, the value of K_м lies within the range of 10^-1 to 10^-6 M. The K_м value of an enzyme depends on The Nature of the substrate as well as on environmental conditions such as Temperature and Ionic strength. The Michaelis constant K_м has two distinct meanings. First, K_м is the Substrate Concentration at which half of the enzyme's active sites are occupied. If K_м is known, one can calculate the fraction of occupied active sites ƒ_ES for any substrate concentration:

(17)

Table 6.1. K_м Values of Some Enzymes

Second, K_м is related to the rate constants of individual catalytic steps presented in equation (1). According to equation (7), Kм is equal to (к₂+к₃)/к₁. Let us consider the extreme case where к₂ is much greater than к₃, i.e., the dissociation of the ES complex into E and S occurs much faster than The formation of E plus the reaction product. Under these conditions (к₂ » к₃)

(18)

The dissociation constant of the ES complex is described by the equation

(19)

In other words, if к₃ is much smaller than к₂, then K_м is equal to the dissociation constant of the ES complex. Under this condition, K_м serves as a measure of the Stability of the ES complex: a high K_м indicates weak substrate binding, whereas a low K_м indicates strong enzyme-substrate interaction. It should be emphasized once again that the value of K_м can be used to assess the affinity of an enzyme for its substrate only under the condition that к₂ is significantly greater than к₃. In reality, this is true in many, though not all, cases.

The maximum velocity V_max reflects the turnover number of the enzyme if the concentration of active sites (E_T) is known, since

V_max = k_з [E_Т]. (20)

For example, at full substrate saturation, dissolved Carbonic anhydrase at a concentration of 10^-6 M catalyzes the formation of 0.6 M Н₂СО₃ per second. Hence, к₃ = 6 • 10^-5 s^-1. The kinetic constant к₃ is called the turnover number. The turnover number of an enzyme is the number of substrate molecules converted into product per unit time when the enzyme is fully saturated with substrate. The turnover number of 6 • 10⁵ s^-1, characteristic of carbonic anhydrase, is the largest known. Each successive catalytic event takes place after an interval equal to 1/k₃, which for carbonic anhydrase amounts to 1.7 µs. The turnover number of most enzymes utilizing physiological substrates lies within the range of 10⁴ per second (Table 6.2).

Table 6.2. Maximum Turnover Numbers of Some Enzymes