Drug-Receptor Binding & Affinity: Sigmoidal Curves, Hill Plot, and Occupation Theory

Drug-receptor binding saturation

Binding of a drug to its receptor is saturable because there is a finite number of receptors in the tissue

Assumption 1 of law of mass

The amount of free drug added to a system is the same as the total amount of drug because it is only a negligible amount

Equation use (Kd=[D]([Rt]-[DR])/[DR]

used to know the binding affinity for a drug

Receptor concentration estimation

total number of receptors (Rt) minus [DR]

Plotting binding curve

Because [D] changes in small quantities, plot log[D] against r (fractional receptor occupancy) to get a sigmoidal curve

Sigmoidal curve linearity

The curve is approximately linear between 20-80% fractional occupancy

Complex drug-receptor interactions

Some receptors bind two drug molecules at once (e.g. nicotinic receptors)

Affinity states

Some receptors convert between high and low affinity forms

Modified binding equation

nD + R <=> DnR

Modified binding relationship

r = [D]^n / ([D]^n + Kd)

Hill plot meaning

Used to calculate the slope (n), representing cooperativity

Hill coefficient (n) > 1

Positive cooperativity

Hill coefficient (n) < 1

Negative cooperativity

Hill coefficient (n) = 1

Simple (non-cooperative) interaction

Occupation theory definition

Number of receptors occupied = effect of receptor [E]

Occupation theory assumption

Despite increasing [D], once all receptors are bound, there will be a maximum effect [E]

Occupation theory curve

Plotting [E]/Emax against drug concentration gives a sigmoidal curve

Occupation theory midpoint

1/2 of [E]/Emax gives Kd (EC50 = Kd)

Fractional response relationship

Graph of fractional response vs. drug concentration has same shape as fractional occupancy vs. drug concentration

pD2 definition

Negative log of agonist concentration that gives half-maximal response

pD2 purpose

Quantifies the affinity of an agonist for its receptor

pD2 positivity

pD2 is always positive; e.g. pD2 of 1.0×10⁻⁸ = 8

High pD2 meaning

Drugs with high pD2 values act at low concentrations

pD2 formula

pD2 = -log(Kd) or -log(EC50)