Chapter 10 Enzyme Kinetics

酶动力学

2011.10.11

 酶促反应动力学：研究各种因素对酶促反应 速率的影响，并加以定量的阐述。  影响因素包括：酶浓度、底物浓度、pH、温 度、抑制剂、激活剂等。

① Elementary reaction and Stoichiometric equation 基元反应和化学计量方程式 ② Kinetic equation 动力学方程 ③ Rate limiting step 限速步骤 ④ Molecularity and order of reaction 分子数和反应级数

① First-order reaction v = k[S], k means rate constant ( 速率常数 ) [S] = [S 0 ]

e

-kt half-life: t 1/2 =0.6931/k ② Second-order reaction v = k[S A ][S B ], if [S A ] = [S B ], v = k[S] 2 t 1/2 =1/k[S] ③ Zero-order reaction v = k t 1/2 =[S]/2k

底物浓度对反应速率影响的作图呈矩形双曲线 V 0 : initial rate Vmax: maximum veloxity

 研究前提： ① 单底物、单产物反应； ② 酶促反应速率一般在规定的反应条件下，用 单位时间内底物的消耗量和产物的生成量来 表示； ③ 反应速率取其初速率，即底物的消耗量很小 （一般在5﹪以内）时的反应速率 ④ 底物浓度远远大于酶浓度。

Michaelis-Menten Model

Ks = k 1 /k -1 k -2 is ignored if P is negligible at initial stage

fast reversible step rate limiting step [E] = [Et] – [ES] [S] >> [Et], [S] unchanged steady-state assumption

Km = (k 2 + k -1 )/k 1 [S] 高，致使酶分子都被饱和，反应达到最大速度，则： [ES] = [Et] Vmax = k 2 [ES] = k 2 [Et]

Michaelis-Menten equation [S]

：底物浓度

V 0

：不同

[S]

时的初始反应速率

V max

：最大反应初速率 Ｋ

m

：米氏常数

Km 值等于酶促反应速率为最大反应速率一半时的底物 浓度，单位是 mol/L

Km

的意义：  Km 是酶的特征性常数之一，只与酶的结构、底物和 反应环境（如，温度、 pH 、离子强度）有关，与酶的 浓度无关  Km 可近似表示酶对底物的亲和力  同一酶对于不同底物有不同的 Km 值

Vmax

的意义  定义： Vmax 是酶完全被底物饱和时的反应初速 率，与酶浓度成正比。  意义： Vmax=k 2 [Et] 如果酶的总浓度已知，可从 Vmax 计算酶 的转换数 (turnover number ，单位为时间 -1) ， 即动力学常数 kcat (k 2 ) ，即酶被底物饱和时每 一酶分子或每一活性部位在单位时间内被转 变成产物的底物分子数。

当 [S] << Km ，大多数酶处于游离形式时，即 [Et] = [E] specificity constant 专一性常数 E+ S E + P kcat/Km: apparent second-order constant 表观二级速率常数，非真实的速率常数 反应了在远低于饱和量的底物浓度下酶的催 化效率指数，用来比较不同酶的催化效率

当 k 2 >> k -1 ， Km = k 2 /k 1 , kcat/Km = k 1 即酶的催化效率完全决定于酶和底物结合的比速率 k 1 catalytic perfection ( 催化活性的完美程度 )

Km >> [S]

[S] >> Km

V V max [S]  当底物浓度较低时： 反应速率与底物浓度成正比；反应为 一级反应。

V V max [S]  随着底物浓度的增高： 反应速率不再成正比例加速；反应为

混合级反应。

V V max [S]  当底物浓度高达一定程度： 反应速率不再增加，达最大速率；反 应为零级反应

Transformation of the Michaelis-Menten equation into double-reciprocal plot ( 双倒数作图）

Lineweaver-Burk equation

is rate-limiting (for most enzymes) Vmax = k 3 [Et] If the reaction has several steps and one is clearly rate limiting, k cat is equivalent to the rate constant for that limiting step; when several steps are partially rate limiting

,

k cat

=

f (k cat1 , k cat2 ,…. k catn )

Enzymatic Reactions with Two or More Substrates 1.Many of the principles developed for the single-substrate systems may be extended to multisubstrate systems.

2.The majority of enzymes involve two substrates.

3.Most reactions obey Michaelis-Menten kinetics when the concentration of one substrate is held constant and the other is varied.

Enzymatic reactions with two substrates usually involve transfer of an atom or a functional group from one substrate to the other : 

Sequential mechanism

（顺序反应机制）

Sequential mechanism Steady-state kinetic analysis of bisubstrate reactions double-reciprocal plot when [S1] fixed and [S2] varied, generating several intersecting lines,indicating that a ternary complex is formed in the reaction.

Ping-pong mechanism

（乒乓机制）

Enzyme activity is affected by pH and temperature

1. Each enzyme has an optimal pH or pH range （最适 pH) (where the enzyme has maximal activity).

① ② Change of ionization state of surface groups (which may affect the protein structure) sometimes is responsible for this phenomenon.

影响酶分子结构的表面基团需要正确的解离 ③ Requirements for the catalytic groups in the active site in appropriate ionization state is a common reason for this phenomenon.

活性部位的催化基团需要正确的解离 In rare cases, it is the change of ionization state of substrate that is responsible for this phenomenon.

底物也需要处于正确的解离状态

2. Each enzyme has an optimal temperature or temperature range （最适温度 ) (where the enzyme has maximal activity).

① Requirements for the appropriate conformation of ② the enzyme 酶分子需要处于正确的构象 At low temperature, thermal motion ( 热运动 ) of molecules is low, and thus reaction rate is low. (That’s why bilogical samples are usually kept in ③ fridge!) Within certain temperature range, the activity increases with the temperature until the maximal activity is reached (at optimum temperature).

At higher temperatures, enzymes will denature ( 变 性 ) to lose its appropriate conformation and thus its activity.

Enzymes are subject to reversible and irreversible inhibition

 酶的抑制剂 (inhibitor) 凡能使酶的催化活性下降而不引起酶蛋白 变性的物质称为酶的抑制剂。  酶的抑制区别于酶的变性：  抑制剂对酶有一定选择性，涉及酶的 局部结构  引起变性的因素对酶没有选择性，涉 及酶的整个三维结构

 抑制作用的类型 根据抑制剂和酶结合的紧密程度不同， 酶的抑制作用分为：  不可逆性抑制 (irreversible inhibition)  可逆性抑制 (reversible inhibition)  竞争性抑制 (competitive inhibition)  非竞争性抑制 (non-competitive inhibition)  反竞争性抑制 (uncompetitive inhibition)



Reversible inhibitors

: bind to enzyme non-covalently ①

Competitive inhibitor

competes with the substrate for the active site of an enzyme (binding of one prevents binding of the other, forming ES or EI complexes but no ESI complexes; of course, EI can not give off normal products! ). Competitive inhibitors are often compounds that resemble the substrates.

Transition state analogs （过渡态类似物） act as potent inhibitors for enzymes.

k i1 k i2 Km = k2+k3 k1 k i1 k1 k2 k3

1/V 抑制剂↑ 无抑制剂 1/[S]  抑制程度取决于抑制剂与酶的相对亲和力及底物浓 度；  动力学特点：

V max

不变，表观

K m

增大。

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 磺胺类药物的抑菌机制 ——与对氨基苯甲酸竞争二氢叶酸合成酶 二氢蝶呤啶 ＋ 对氨基苯甲酸 ＋ 谷氨酸 二氢叶酸 合成酶

H 2 N COOH

二氢叶酸

H 2 N SO 2 NHR

磺 胺 类 药 物

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②

Noncompetitive inhibitor

( 非竞争性抑制） binds at a site distinct from the substrate active site, and it binds to either E or ES.

抑制剂

↑ 1 / V

无抑制剂  抑制程度取决于抑制剂的浓度；  动力学特点：

V max

降低，表观

K m

不变。

1/[S]

Mixed inhibitor

( 混合型抑制） can form the complex EI with E, and affects the binding between E and S.  动力学特点：

V max

降低，表观

K m

增大。

③

Uncompetitive inhibitor

( 非竞争性抑制） binds at a site distinct from the substrate active site and only to the ES complex, but is unable to bind free E.

• 1/V

抑制剂

↑

无抑制剂

1/[S]

 抑制程度取决与抑制剂的浓度及底物的浓度；  动力学特点：

V max

和表观

K m

降低相同的倍数。

各种可逆性抑制作用的比较

作用特征 无抑制剂 与

I

结合的组分 动力学参数 表观

Km K m

最大速度

V max

林

-

贝氏作图 斜率 纵轴截距 横轴截距

K m /V 1/V max -1/K m max

竞争性抑制 非竞争性抑制 反竞争性抑制

E

增大 不变 增大 不变 增大

E

、

ES

不变 降低 增大 增大 不变

ES

减小 降低 不变 增大 减小 目录



Inreversible inhibitors

( 不可逆抑制剂） : bind very tightly (covalently or noncovalently) to the enzymes, and destroy the catalytic activity. chymotrypsin ( 异丙基氟磷酸 )

Suicide inhibitors

( 自杀性抑制剂） : bind to the active site of a specific enzyme, then undergo a few chemical steps of normal reactions, but instead of being transformed into the normal products, they are converted into a very reactive compound that combines irreversible with the enzymes. They are called

mechanism-based inactivators

.

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