Lesson 1
Binding: KD and Bmax
Three colored curves show normalized receptor occupancy, so changing KD shifts fractional binding on a fixed 0 to 1 scale.
Linear plot
Equation section
From binding equilibrium to the plot axes
Start with the reversible binding scheme, define KD, then derive the plotted occupancy axis [LR]/[R0] as a function of drug concentration [D].
L = D
Ligand = Drug
L + R
kon
⇌
koff
LR
KD = [L][R] [LR]
Derive the y-axis
- [R0] = [R] + [LR]
- From KD = [L][R]/[LR], then [R] = KD[LR]/[L]
- [R0] = KD[LR]/[L] + [LR]
- [R0] = [LR](KD/[L] + 1)
- [LR] [R0] = [L] [L] + KD
X-axis: [D] = [L]
Y-axis: [LR]/[R0]
Lesson 2
Efficacy: idealized KD = EC50
This idealized bridge shows how moving KD shifts EC50 when effect is displayed as the normalized fraction E/Emax. The interactive below separates the binding step from the activation step.
Log plot
Linear plot
Two-step model
Affinity and efficacy as separate steps
Binding determines total receptor occupancy. The structural conversion LR ↔ LR* is then governed by the forward activation rate kβ and backward rate kα.
2 steps: affinity then activation
Receptor status
Closed, inactive
L + R
0%
Binding step
->
KD = 10 nM
Receptor status
Closed, inactive
LR
0%
Structural conversion
↔
kβ = 1.00
kα = 0.50
Kact = 2.00
Receptor status
Open, active
LR*
0%
Binding then activation
Lesson 4
Antagonists
Compare competitive and noncompetitive antagonism while keeping the antagonist-alone line fixed at zero efficacy.
Antagonist model
Agonist-response log plot
Agonist-response linear plot
Inhibition log plot
Inhibition linear plot
Lesson 3
Antagonist classification
Use the branch map to move from broad mechanism to specific antagonist class, including orthosteric special cases such as inverse agonists and partial agonists.
Click any box in the diagram. The card underneath updates with the mechanism and the expected dose-response change.
Selected class
Competitive antagonist
Graph change
Example
Lesson 5
Partial agonists
First compare the drugs alone, then see how a fixed partial-agonist concentration can blunt the response to a full agonist by competing for the same receptor.
Agonists alone: log plot
Agonists alone: linear plot
Co-administration curves below show a full agonist response in the presence of a fixed partial-agonist concentration, for example heroin in the presence of buprenorphine.
Full agonist with partial agonist present: log plot
Full agonist with partial agonist present: linear plot
Lesson 6
Spare receptors
Occupancy and effect share the same 0 to 100 percent scale so receptor reserve shows up as a leftward shift in effect.
Log plot
Linear plot
Lesson 7
Quantal dose-response
Cumulative curves are logistic CDFs on a log-dose axis. The bell-shaped frequency curves are the derivatives scaled to percent in each dose interval.