Question

Antigen and antibody interaction is shown by the following scheme
\[ \text{Ab} + \text{Ag} \; \xrightleftharpoons[k_{-1}]{k_{1}} \; \text{Ab-Ag} \] Where Ab is antibody, Ag is antigen and Ab–Ag is antigen–antibody complex. The values of $k_{1}$ and $k_{-1}$ are $5 \times 10^{5}\ \mu\mathrm{M}^{-1}\mathrm{s}^{-1}$ and $2 \times 10^{-2}\ \mathrm{s}^{-1}$ respectively. The dissociation constant for the complex is .............. nM.

Hint:

For binding reactions, a lower $K_d$ means higher affinity of antibody for antigen.

Answer 1

Correct Answer: 4

Step 1: Recall formula for dissociation constant $K_d$.
\[ K_d = \frac{k_{-1}}{k_1} \] Step 2: Substitute values.
\[ K_d = \frac{2 \times 10^{-2}}{5 \times 10^{5}} = 4 \times 10^{-8}\ \mathrm{M} \] Step 3: Convert to nM.
\[ 4 \times 10^{-8}\,\mathrm{M} = 40\,\mathrm{nM} \] Step 4: Conclusion.
The dissociation constant is $40$ nM.