The Michaelis-Menten equation describes the rate of enzymatic reactions by relating reaction rate to substrate concentration. Here’s a step-by-step derivation of the equation:
1. Enzyme-Substrate Complex Formation
Consider a simple enzymatic reaction where an enzyme ( E ) binds to a substrate ( S ) to form an enzyme-substrate complex ( ES ), which then breaks down to release a product ( P ) and regenerate the enzyme ( E ):
![](https://theconceptbeacon.com/wp-content/uploads/2024/06/Screenshot-2024-06-18-205824.png)
2. Assumptions
![](https://theconceptbeacon.com/wp-content/uploads/2024/06/Screenshot-2024-06-18-213845.png)
3. Formation and Breakdown of ( ES )
![](https://theconceptbeacon.com/wp-content/uploads/2024/06/Screenshot-2024-06-18-213710.png)
4. Applying the QSSA
![](https://theconceptbeacon.com/wp-content/uploads/2024/06/Screenshot-2024-06-18-211603.png)
5. Expressing [E] in Terms of [E]0
![](https://theconceptbeacon.com/wp-content/uploads/2024/06/Screenshot-2024-06-18-213625.png)
6. Substituting [E] into the QSSA Equation
![](https://theconceptbeacon.com/wp-content/uploads/2024/06/Screenshot-2024-06-18-213527.png)
7. Solving for [ES]
![](https://theconceptbeacon.com/wp-content/uploads/2024/06/Screenshot-2024-06-18-212230.png)
8. Introducing the Michaelis Constant (KM)
![](https://theconceptbeacon.com/wp-content/uploads/2024/06/Screenshot-2024-06-18-212426.png)
9. Rate of Product Formation
![](https://theconceptbeacon.com/wp-content/uploads/2024/06/Screenshot-2024-06-18-212617.png)
10. Maximum Rate (Vmax)
![](https://theconceptbeacon.com/wp-content/uploads/2024/06/Screenshot-2024-06-18-213040.png)
11. Final Michaelis-Menten Equation
![](https://theconceptbeacon.com/wp-content/uploads/2024/06/Screenshot-2024-06-18-213153.png)
Summary
![](https://theconceptbeacon.com/wp-content/uploads/2024/06/Screenshot-2024-06-18-213258.png)