Derive the complete rate equation using the King altman method. Example is shown above the reaction mechanism. All the N terms must be derived.

Biochemistry
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Chapter1: Biochemistry: An Evolving Science
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Derive the complete rate equation using the King altman method. Example is shown above the reaction mechanism. All the N terms must be derived. 

### Transcription of the Image: Kinetic Reaction Mechanisms

#### Mathematical Equations and Derivations:

1. **Equation for NFA:**
   \[
   NFA = k_1k_Ak_4k_6(I) + k_1k_3k_4k_6(I)(A)(I)
   \]
   \[
   + k_5k_6k_3k_4k_{10}(A)(E) + k_4k_6k_6k_{10}(P)(I)
   \]

2. **Expression for \( v_0 \):**
   \[
   v_0 = E_T \left[ \frac{k_1N_Er - k_8(P)N_E}{\sum N_i} \right]
   \]

3. **Relationship showing the chemical equilibrium:**
   \[
   E + A \rightleftharpoons EA \overset{k_3}{\rightleftharpoons} EAB \underset{k_8}{\overset{k_6}{\rightleftharpoons}} EP \rightleftharpoons E + P
   \]

#### Conceptual Notes:

- **Derivation Objective:**
  Derive the complete rate equation \( v_0 = \).

- **Inhibition Context:**
  Competitive inhibition with respect to \( A \).

#### Diagrams:

- **Chemical Reaction Diagram:**
  - Shows various rate constants and interactions between substrates and enzymes (represented by \( E \), \( A \), \( I \), \( P \)).
  - Reactions are indicated with double-headed arrows (e.g., \(\rightleftharpoons\) for equilibrium) and specific reaction rate constants (e.g., \( k_1, k_3, k_4, k_6, k_{10} \)).

This transcription provides an overview of kinetic reactions involving enzymes and inhibitors, ideal for educational purposes.
Transcribed Image Text:### Transcription of the Image: Kinetic Reaction Mechanisms #### Mathematical Equations and Derivations: 1. **Equation for NFA:** \[ NFA = k_1k_Ak_4k_6(I) + k_1k_3k_4k_6(I)(A)(I) \] \[ + k_5k_6k_3k_4k_{10}(A)(E) + k_4k_6k_6k_{10}(P)(I) \] 2. **Expression for \( v_0 \):** \[ v_0 = E_T \left[ \frac{k_1N_Er - k_8(P)N_E}{\sum N_i} \right] \] 3. **Relationship showing the chemical equilibrium:** \[ E + A \rightleftharpoons EA \overset{k_3}{\rightleftharpoons} EAB \underset{k_8}{\overset{k_6}{\rightleftharpoons}} EP \rightleftharpoons E + P \] #### Conceptual Notes: - **Derivation Objective:** Derive the complete rate equation \( v_0 = \). - **Inhibition Context:** Competitive inhibition with respect to \( A \). #### Diagrams: - **Chemical Reaction Diagram:** - Shows various rate constants and interactions between substrates and enzymes (represented by \( E \), \( A \), \( I \), \( P \)). - Reactions are indicated with double-headed arrows (e.g., \(\rightleftharpoons\) for equilibrium) and specific reaction rate constants (e.g., \( k_1, k_3, k_4, k_6, k_{10} \)). This transcription provides an overview of kinetic reactions involving enzymes and inhibitors, ideal for educational purposes.
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