34. A hypothetical polypeptide hormone binds to its receptor with an association rate constant (ka) of 3.0×104
M-1 sec-1 and a dissociation rate constant (kd) of 6.9×10-6
sec-1 . What is the equilibrium dissociation
constant?
1. 4.7×109 M-1
2. 2.3×10-10 M
3. 2.3×1010 M-1
4. 3.3×10-6 M
How to Calculate the Equilibrium Dissociation Constant for Hormone-Receptor Binding
In biochemistry, the binding between a polypeptide hormone and its receptor is often studied using the association rate constant (ka) and dissociation rate constant (kd). One important quantity derived from these constants is the equilibrium dissociation constant (Kd), which provides insight into the strength of the hormone-receptor interaction. In this article, we’ll explain how to calculate the equilibrium dissociation constant using given rate constants.
Given Information:
-
Association rate constant (ka): 3.0 × 10⁴ M⁻¹ sec⁻¹
-
Dissociation rate constant (kd): 6.9 × 10⁻⁶ sec⁻¹
What is the Equilibrium Dissociation Constant (Kd)?
The equilibrium dissociation constant (Kd) is a measure of the affinity between a ligand (hormone) and its receptor. It is the ratio of the dissociation rate constant (kd) to the association rate constant (ka):
Kd=kdkaK_d = \frac{k_d}{k_a}
This constant represents the concentration of the ligand required to occupy half of the available receptors at equilibrium. The lower the Kd value, the stronger the binding affinity between the hormone and the receptor.
Step-by-Step Calculation:
To calculate Kd, we simply divide the dissociation rate constant by the association rate constant:
Kd=6.9×10−63.0×104K_d = \frac{6.9 \times 10^{-6}}{3.0 \times 10^{4}} Kd=2.3×10−10 MK_d = 2.3 \times 10^{-10} \, \text{M}
Thus, the equilibrium dissociation constant for this hormone-receptor interaction is 2.3 × 10⁻¹⁰ M.
Correct Answer:
-
2. 2.3 × 10⁻¹⁰ M
Why Does This Matter?
The equilibrium dissociation constant (Kd) is a critical parameter in understanding the strength of binding interactions in biochemistry and pharmacology. A low Kd indicates a strong affinity between the hormone and its receptor, while a high Kd indicates weak binding. This is important for designing drugs, studying receptor-ligand interactions, and understanding physiological responses.
Summary
By using the association rate constant (ka) and dissociation rate constant (kd), we calculated the equilibrium dissociation constant (Kd) for a hypothetical polypeptide hormone interacting with its receptor. In this case, the Kd was determined to be 2.3 × 10⁻¹⁰ M, which indicates a strong binding affinity between the hormone and receptor.
