Q.40
The dissociation constant Kd for ligand binding to the receptor is 10-7 M.
The concentration of ligand required for occupying 10% of receptors is
Options:
(A) 10-6 M
(B) 10-7 M
(C) 10-8 M
(D) 10-9 M
Ligand Concentration Required for 10% Receptor Occupancy Using Kd
Receptor–ligand binding follows equilibrium principles that relate ligand concentration
to receptor occupancy through the dissociation constant (Kd). This problem
calculates the ligand concentration needed to occupy 10% of receptors.
Key Concept
Fractional receptor occupancy (θ) is given by:
θ = [L] / ([L] + Kd)
Where:
- θ = fraction of occupied receptors
- [L] = ligand concentration
- Kd = dissociation constant
Step-by-Step Solution
Given:
- Kd = 10−7 M
- θ = 10% = 0.1
Substitute into the equation:
0.1 = [L] / ([L] + 10−7)
Solve:
0.1([L] + 10−7) = [L]
0.1[L] + 10−8 = [L]
[L] − 0.1[L] = 10−8
0.9[L] = 10−8
[L] ≈ 1.1 × 10−8 M
Approximation for exams:
[L] ≈ 10−8 M
Correct Answer
Option (C): 10−8 M
Quick Exam Rules
- [L] = Kd → 50% occupancy
- [L] = 0.1 × Kd → ~10% occupancy
- [L] = 10 × Kd → ~90% occupancy
Conclusion
A ligand concentration of 10−8 M is required to occupy
10% of receptors when Kd is 10−7 M. Hence, the correct answer
is Option (C).
