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Multiple Choice
Calculate the dissociation rate constant (kd) at equilibrium if [P] = 20 mM, [L] = 10 mM, [PL] = 5 mM, and the association rate constant (ka) = 100 mM-1s-1.
A
400.
B
4,000 s-1.
C
4,000 mM-1s-1.
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.
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.
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.
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.
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).