Q: You prepare a solution with $$[P] = 10 mM $$and $$[L] = 10 mM. At $$equilibrium, $$[PL] = 5 mM. $$What is the $$K_d$$ for this reaction?

$$K_d = \frac{[P][L]}{[PL]} = \frac{(10\ \text{mM})(10\ \text{mM})}{5\ \text{mM}} = 20\ \text{mM}$$

Q: If a protein-ligand system has $$K_a = 2 \times 10^6$\ \text{M}^{-1}$$, what is the $$K_d$$?

$$K_d = 5 \times 10$$^{-7}$$\ \text{M}$$

Q: Which equation correctly relates the fraction of occupied binding sites ($$\theta) to $$ligand concentration ($$[L]) $$and $$K_d$$?

$$\theta = \frac{[L]}{[L] + K_d}$$

Question 1

Which of the following best describes the relationship between the protein-ligand association constant ($$K_a) $$and dissociation constant ($$K_d$$)?

Accepted Answer

$$K_a is $$the reciprocal of $$K_d$$; $$K_a = \frac{1}{K_d}.$$

Question 2

A protein has a $$K_d of 10 nM $$for its ligand. What does this indicate about the protein's affinity for the ligand?

Accepted Answer

The protein has a high affinity for the ligand.

Question 3

Given the equilibrium $$P + L \rightleftharpoons PL$$, which equation correctly represents the dissociation constant $$K_d$$?

Accepted Answer

$$K_d = \frac{[P][L]}{[PL]}$$

Question 4

If Protein A has a $$K_d of 54 nM $$for ligand X and Protein B has a $$K_d of 58 nM $$for ligand X, which protein has a stronger affinity for ligand X?

Accepted Answer

Protein A

Question 5

Which of the following statements about $$K_d is $$correct?

Accepted Answer

$$K_d$$ decreases as protein-ligand affinity increases.

Question 6

You prepare a solution with $$[P] = 10 mM $$and $$[L] = 10 mM. At $$equilibrium, $$[PL] = 5 mM. $$What is the $$K_d$$ for this reaction?

Accepted Answer

$$K_d = \frac{[P][L]}{[PL]} = \frac{(10\ 	ext{mM})(10\ 	ext{mM})}{5\ 	ext{mM}} = 20\ 	ext{mM}$$

Question 7

If a protein-ligand system has $$K_a = 2 	imes 10^6$\ 	ext{M}^{-1}$$, what is the $$K_d$$?

Accepted Answer

$$K_d = 5 	imes 10$$^{-7}$$\ 	ext{M}$$

Question 8

Which of the following is true regarding the units of $$K_a$$ and $$K_d$$?

Accepted Answer

$$K_a$$ has units of $$M^{-1}$$, $$K_d$$ has units of M

Question 9

A researcher finds that a protein binds its ligand with $$K_d = 1 \muM. If $$the ligand concentration is $$1 \muM$$, what fraction of the protein binding sites are occupied?

Accepted Answer

50%

Question 10

If $$K_d$$ for a protein-ligand interaction is very small, what does this imply about the equilibrium between free and bound states?

Accepted Answer

The equilibrium favors the bound complex ($$PL).$$

Question 11

Which scenario would result in a higher $$K_a$$ value for a protein-ligand interaction?

Accepted Answer

Strong binding between protein and ligand.

Question 12

A protein has two binding sites for a ligand. If $$K_d$$ for site 1 is 10 nM and $$K_d$$ for site 2 is 100 nM, which site has higher affinity?

Accepted Answer

Site 1

Question 13

If $$K_d is $$defined as the concentration of ligand at which half of the protein binding sites are occupied, what is the value of $$[L]$$ when $$	heta = 0.5$$?

Accepted Answer

$$[L] = K_d$$

Question 14

Which equation correctly relates the fraction of occupied binding sites ($$	heta) to $$ligand concentration ($$[L]) $$and $$K_d$$?

Accepted Answer

$$	heta = \frac{[L]}{[L] + K_d}$$

Question 15

A mutation in a protein increases its $$K_d$$ for a ligand from 10 nM to 100 nM. What is the most likely effect?

Accepted Answer

The protein's affinity for the ligand decreases.

Question 16

If $$K_a$$ for a protein-ligand interaction is $$1 	imes 10^7$\ 	ext{M}^{-1}$$, what is the $$K_d$$?

Accepted Answer

$$K_d = 1 	imes 10$$^{-7}$$\ 	ext{M}$$

Question 17

Which of the following would NOT affect the value of $$K_d$$ for a protein-ligand interaction?

Accepted Answer

Ligand concentration

Question 18

A drug is designed to bind a target protein with high affinity. Which $$K_d$$ value would be most desirable?

Accepted Answer

$$K_d = 1 nM$$

Question 19

If $$K_d$$ for a protein-ligand interaction is 50 nM, what is the $$K_a$$?

Accepted Answer

$$K_a = 2 	imes 10^7$\ 	ext{M}^{-1}$$

Protein-Ligand Equilibrium Constants: Association and Dissociation in Biochemistry

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