Michaelis Menten Equation | Enzyme Kinetics | Biochemistry

BIOCHEMISTRY MINDS

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เผยแพร่เมื่อ 26 ก.ย. 2024
Introduction to Enzymes
- **Definition**: Enzymes are biological catalysts that speed up chemical reactions in living organisms without being consumed in the process.
- **Nature**: Most enzymes are proteins, though some RNA molecules can also have catalytic activity (ribozymes).
- **Function**: Enzymes lower the activation energy required for a reaction, enabling it to proceed faster.
- **Specificity**: Each enzyme is specific to a particular substrate or type of reaction, dictated by the enzyme’s active site structure.
Mechanism of Enzyme Action
1. **Active Site**: The region on the enzyme where the substrate binds.
2. **Substrate Binding**:
- **Lock and Key Model**: The enzyme’s active site is exactly complementary to the shape of the substrate.
- **Induced Fit Model**: The enzyme changes shape slightly to accommodate the substrate more snugly.
3. **Formation of Enzyme-Substrate Complex**: When the substrate binds to the enzyme’s active site, they form an intermediate complex.
4. **Catalysis**:
- The enzyme catalyzes the conversion of the substrate to the product.
- This may involve breaking bonds, forming new bonds, or rearranging atoms.
5. **Product Release**: After the reaction, the products are released, and the enzyme is free to bind with new substrate molecules.
Factors Affecting the Rate of Reaction
1. **Substrate Concentration**:
- As substrate concentration increases, the reaction rate increases until a maximum rate (V_max) is reached, where the enzyme is saturated with substrate.
2. **Enzyme Concentration**:
- Increasing enzyme concentration increases the reaction rate, provided there is an excess of substrate.
3. **Temperature**:
- Reaction rate increases with temperature up to an optimum point, after which the enzyme denatures and activity decreases.
4. **pH**:
- Each enzyme has an optimal pH range. Deviations from this range can lead to decreased activity or denaturation.
5. **Inhibitors**:
- **Competitive Inhibitors**: Bind to the active site, competing with the substrate.
- **Non-competitive Inhibitors**: Bind to another part of the enzyme, changing its shape and reducing its activity.
6. **Cofactors and Coenzymes**:
- Non-protein molecules that assist in enzyme activity. Cofactors are often metal ions, while coenzymes are organic molecules.
What is Enzyme Kinetics?
- **Definition**: Enzyme kinetics is the study of the rates of enzyme-catalyzed reactions and how they change in response to changes in concentration of substrate, enzyme, and other factors.
- **Purpose**: Understanding enzyme kinetics helps in elucidating the mechanism of enzyme action and in designing drugs and treatments that can modulate enzyme activity.
Explanation of the Derivation of Enzyme Kinetics (Michaelis-Menten Equation)
1. **Basic Assumptions**:
- The formation of the enzyme-substrate complex (ES) is a fast and reversible reaction.
- The breakdown of the ES complex to form the product is the rate-limiting step.
2. **Michaelis-Menten Equation**:
\[
E + S \leftrightarrow ES
ightarrow E + P
\]
Where:
- \(E\) = Enzyme
- \(S\) = Substrate
- \(ES\) = Enzyme-Substrate complex
- \(P\) = Product
3. **Rate Equations**:
- Formation of ES: \( k_1 [E][S] \)
- Breakdown of ES: \( (k_{-1} + k_2)[ES] \)
4. **Steady-State Assumption**:
- The concentration of the ES complex remains constant over time.
\[
\frac{d[ES]}{dt} = k_1 [E][S] - (k_{-1} + k_2)[ES] = 0
\]
Solving for \([ES]\):
\[
[ES] = \frac{k_1[E][S]}{k_{-1} + k_2}
\]
5. **Total Enzyme Concentration**:
\[
[E_{total}] = [E] + [ES]
\]
Substitute \([E]\):
\[
[E] = [E_{total}] - [ES]
\]
6. **Michaelis Constant (\(K_m\))**:
\[
K_m = \frac{k_{-1} + k_2}{k_1}
\]
Thus, \([ES]\) can be rewritten as:
\[
[ES] = \frac{[E_{total}][S]}{K_m + [S]}
\]
7. **Reaction Rate (\(V\))**:
- The rate of product formation is:
\[
V = k_2[ES]
\]
Substitute \([ES]\):
\[
V = \frac{V_{\max}[S]}{K_m + [S]}
\]
Where \(V_{\max} = k_2[E_{total}]\)
8. **Michaelis-Menten Equation**:
\[
V = \frac{V_{\max}[S]}{K_m + [S]}
\]
Summary
- Enzymes are biological catalysts that speed up reactions by lowering activation energy.
- The enzyme-substrate interaction can be modeled by the induced fit model and forms an enzyme-substrate complex.
- Factors such as substrate concentration, enzyme concentration, temperature, pH, and inhibitors affect enzyme activity.
- Enzyme kinetics, particularly the Michaelis-Menten equation, helps us understand and quantify the rate of enzyme-catalyzed reactions.
n biochemistry, Michaelis-Menten kinetics, named after Leonor Michaelis and Maud Menten, is the simplest case of enzyme kinetics, applied to enzyme-catalysed reactions of one substrate and one product. It takes the form of a differential equation describing the reaction rate