Calculate the dissociation rate constant (k_d) at equilibrium if [P] = 20 mM, [L] = 10 mM, [PL] = 5 mM, and the association rate constant (k_a) = 100 mM^-1s^-1.

• A. 400.
• B. 4,000 s^-1.
• C. 4,000 mM^-1s^-1.

Answer: (B)

Verified step by step guidance

1. Understand the relationship between the association rate constant (ka), dissociation rate constant (kd), and the equilibrium concentrations of the protein (P), ligand (L), and the protein-ligand complex (PL). The equilibrium constant (K) is given by the ratio of kd to ka.
2. The equilibrium constant (K) can be expressed in terms of the concentrations: \( K = \frac{[P][L]}{[PL]} \). This equation represents the ratio of the concentrations of the free protein and ligand to the concentration of the protein-ligand complex at equilibrium.
3. Rearrange the equation to solve for the dissociation rate constant (kd): \( kd = ka \times K \). This step involves substituting the expression for K into the equation for kd.
4. Substitute the given values into the equation: \( K = \frac{20 \text{ mM} \times 10 \text{ mM}}{5 \text{ mM}} \). Calculate the value of K using the provided concentrations.
5. Finally, calculate kd using the formula \( kd = 100 \text{ mM}^{-1}\text{s}^{-1} \times K \). This step involves multiplying the association rate constant (ka) by the calculated equilibrium constant (K) to find the dissociation rate constant (kd).