KM, kcat, and kcat KM

max 是指 最大反应速度。当 底物浓度 足够大时，体系中 酶的活性中心达到饱和状态，其反应速度达到最大。 由此可见，最大反应速度 max 随 酶浓度的变化而变化。 kcat 指反应常数 ( catalytic constant )， kcat 可以由 这个公式计算得到：

kcat = max/[E]

[E] 指 酶浓度，由此可以说， kcat 表示了每单位时间内（秒）每摩尔的酶（或者说每摩尔的活性中心）能够把多少摩尔的底物转化成产物。

Km 俗称 米氏常数，以浓度做单位，米氏常数定义为 反应速度 达到 最大反应速度一半时 的底物浓度。 Km 可以反映出酶与底物的亲和力，Km越低，亲和力越大。

kcat/Km 称为 催化效率，常常以此来比较 不同的酶而同一底物， 或者 不同底物而同一种酶。

KM, kcat, and kcat /KM

KM - The Michaelis constant, KM, is often associated with the affinity of the enzyme for substrate, but this is not always correct. A more accurate statement is that, for reactions obeying Michaelis-Menten kinetics, KM is a measure of the substrate concentration required for effective catalysis to occur. That is, an enzyme with a high KM requires a higher substrate concentration to achieve a given reaction velocity than an enzyme with a low KM. lists values of KM, kcat, and kcat/KM

for selected enzymes.

kcat - The Michaelis-Menten equation, V = Vmax[S]/(KM + [S]), can be rewritten as V = kcat[E]t[S] / ( KM + [S])

where Vmax = kcat[E]t. kcat incorporates the rate constants for all the reactions between ES and E + P in a multistep enzymatic process. For a two-step reaction, kcat = k2. For more complex reactions, kcat depends on which steps in the process are rate-limiting. kcat gives a direct measure of the catalytic production of product under optimum

conditions (saturated enzyme). The units of kcat are seconds-1. The reciprocal of kcat can be thought of as the time required by an enzyme molecule to "turn over" one substrate molecule. Alternatively, kcat measures the number of substrate molecules

turned over per enzyme molecule per second. Thus, kcat is sometimes called the turnover number. Some typical turnover numbers are shown in , as well.

kcat/KM - This ratio is often thought of as a measure of enzyme efficiency. Either a large value of kcat (rapid turnover) or a small value of KM (high affinity for substrate) makes kcat/KM large.

When [S] << KM (dilute solution), equation 11.27 becomes V (kcat/KM)[E][S]

Here, kcat/KM behaves as a second-order rate constant for the reaction between substrate and free enzyme. This ratio is important, for it shows what the enzyme and substrate can accomplish when abundant enzyme sites are available, and it allows direct comparison of the effectiveness of an enzyme toward different substrates. When an

enzyme has a choice of two substrates, A or B, present at equal, dilute concentrations,

shows that when an enzyme has different substrates on which it can work, the range of efficiencies may vary considerably. Note that for chymotrypsin the kcat/KM ratio

varies 1-million fold.

As a second-order rate constant, kcat/KM has a maximum possible value, which is determined by the frequency with which enzyme and substrate molecules can collide. A reaction which attains such a velocity is said to be "diffusion-limited" because every

encounter leads to reaction. If every collision results in formation of an enzyme-substrate complex, diffusion theory predicts that kcat/KM will attain a value of about 108 to 109 (mol/L)-1s-1. The enzymes carbonic anhydrase, fumarase, and triose phosphate isomerase actually approach this limit.

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