BMS 123 · Common Core (Tronc commun)Section 6.1 · Dose–response, interactions and variability
Section 23 of 27
Graded dose–response curves
Explain what a dose–response curve is, why the graded curve is sigmoid, and how to read Emax, EC50 and potency from it.
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Why this matters
Almost every decision about a drug begins with the same question: how much drug produces how much effect? The graded dose–response curve answers it. If you can read the plateau you know the ceiling of the drug, and if you can read the horizontal position you know how much you must give. Without this skill you can only memorise doses; with it you can compare an unfamiliar drug to a familiar one and reason about what will happen when the dose changes.
What you need to know first
You should be comfortable with the words receptor, agonist and affinity from Unit 5, and with reading a simple graph. No mathematics beyond “a logarithm turns multiplication into addition” is needed.
Words to know (5)
Dose–response curve (DRC)
A graph showing how the size of a drug’s effect changes when the dose or concentration changes. Plotting heart rate against the concentration of adrenaline gives a dose–response curve.
Graded (continuous) response
A response measured as a number that can take any value between zero and a maximum, in one subject. The fall in blood pressure produced by increasing doses of a drug in one volunteer.
Emax
The maximum response a drug can produce, read from the plateau of the graded curve. A full agonist reaches Emax; a partial agonist stays below it at every dose.
EC50
The concentration that produces 50% of Emax, read from the steep middle of the curve. A drug with an EC50 of 10 units needs 10 units to give half of its maximal effect.
Potency
The amount of drug needed to produce a given effect, shown by the horizontal position of the curve. Morphine is more potent than aspirin: a smaller quantity relieves the same pain.
One idea at a timeIdea 1 / 5
In one sentence A dose–response curve is the correlation between drug concentration and drug response, drawn with response on the vertical axis and the logarithm of the dose on the horizontal axis.
A dose–response curve links how much to how much effect
To read the correlation, place response on the vertical (Y) axis and the logarithm of dose on the horizontal (X) axis. The logarithmic dose axis makes the relationship readable across the wide range over which drugs act: a concentration with no effect and one that acts may differ a hundredfold, yet both remain visible on one graph. Reading the curve then turns a table of doses and effects into a shape that can be interpreted for potency, efficacy and changes in response.
For example
If a drug is tested at 1, 10, 100 and 1000 units, the four points are equally spaced on a log axis but crowd together at the left on an ordinary axis. The log axis is what makes the whole curve visible.
Think of it like
A dose–response curve is like a volume dial on a radio: turning it a little changes nothing at first, then the sound rises quickly, and finally the loudest point is reached and turning further does nothing. The limit of the analogy is that a dial has a human hand, while a receptor has only the concentration of drug reaching it.
Pause and check yourself
Why is the log of the dose used on the horizontal axis of a dose–response curve?
Show the answer
Because active doses span a very wide range, and a logarithmic axis compresses that range so the whole curve, from no effect to maximum effect, fits on one readable graph.
Read detailed explanations
Why the curve can be maximal before every receptor is occupied
The theoretical statement “response is maximal when all receptors are occupied” is deliberately cautious, and experimental pharmacology explains why. Many tissues possess more receptors than they need to produce a full response, a phenomenon called receptor reserve or spare receptors. Adrenaline acting on the heart is the standard illustration: a maximal increase in contractile force can be obtained when only a small fraction of the β₁ receptors are occupied, because the intracellular signal is amplified — one occupied receptor activates many G proteins, each enzyme produces many messenger molecules, and each messenger alters many targets. The consequence is that the concentration–occupancy curve and the concentration–effect curve are not superimposable: the effect curve sits to the left, and its EC50 is lower than the dissociation constant of the drug–receptor complex. This matters clinically in two ways. First, a drug can lose a substantial fraction of its receptors, through disease or through irreversible blockade, and still produce a near-normal maximal response. Second, when the reserve is exhausted, a small further loss of receptors produces a sudden fall in the maximum effect, which is why a gentle decline in organ function can be followed by a rapid clinical deterioration. A related concept is partial agonism: a partial agonist may occupy every receptor and still produce a sub-maximal response, which proves that occupancy and response are separate steps.
Linear, semilogarithmic and logarithmic plots
The same experiment can be drawn three ways, and each view hides something. Plotted with a linear dose axis, a sigmoid curve is squeezed against the left edge: the interesting middle happens within the first few millimetres and the rest of the graph is a flat plateau. Plotted with a logarithmic dose axis, the sigmoid becomes a symmetrical S whose middle is a straight line; that straight portion is why the notes say the log of the dose is assumed to be proportional to the response, and it allows a potency comparison between two drugs to be read as a horizontal distance. A third presentation plots the response as a fraction of Emax on a probit or logit scale, which converts the sigmoid into a straight line so that the slope and the midpoint can be compared numerically; a steep slope means that a small change in concentration produces a large change in effect, which is typical of a cooperative receptor system. The practical skill is to know which transform you are looking at before you read a number off the graph. A concentration read from a log axis is not a linear distance; a curve that looks flat may simply be plotted on the wrong axis; and an EC50 read from a linear plot will be wrong because the axes are not linear. When you compare drugs, always confirm that the curves were obtained in the same tissue, the same species and with the same units for the response.
Explore the diagram
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Anatomy of a graded dose–response curve
One drug, many doses: the response climbs slowly at first, rises steeply through the middle, and levels off at the maximum effect, where Emax and EC50 are read off.
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01 / 5Graded curve
If the drawing is wider than this panel, scroll it sideways. Labels stay readable; the numbered explanations below show the same ideas.
Graded curve
One subject receives many different doses of one drug. The response is measured on a continuous scale — millimetres of mercury, litres per minute, grams of force — so every dose gives a number rather than a yes or no. The result is the familiar S-shaped (sigmoid) curve.
Schematic, not to scale. The horizontal axis is logarithmic, so equal distances are equal multiples of dose, and the steep middle of the curve is where a small dose change matters most.
Key points to remember
✓A dose–response curve plots the response against the logarithm of the dose, because active doses span a very wide range.
✓Graded curves measure a continuous response in one subject; quantal curves count the percentage of responders in a population.
✓The graded curve is sigmoid because low doses occupy too few receptors, the middle is steep, and the top is limited by saturation.
✓Emax, read from the plateau, is the most important comparison between drugs; EC50 and potency, read from the horizontal position, tell you how much drug is needed.
Go deeper
Worked example
Reading three curves from one experiment. Three analgesic drugs, A, B and C, are tested on the same pain model. The graph shows A reaching a maximum response at low doses, B reaching the same maximum but only at higher doses, and C flattening at about half of that maximum whatever the dose. You must describe the three drugs using the words potency, efficacy and Emax.
Start with the plateau, because efficacy is the first question. A and B reach the same height, so they have equal Emax, while C stops at about half of it, so C has lower efficacy however large the dose becomes.
Now compare the horizontal position of A and B. Their common plateau is reached at a lower concentration for A, so A is more potent than B; the EC50 of A lies to the left of the EC50 of B.
Compare C with the others on both axes. C is less potent than A and B, since its curve lies to the right, and it is also less efficacious, since its plateau is lower. Only efficacy says what C can never achieve.
State the clinical consequence. If the patient needs the full effect, only A or B can give it, and B will need a larger dose. C could relieve mild pain but cannot substitute for A or B when the pain is severe.
Efficacy is read from the plateau and answers “how much can this drug do?”; potency is read from the horizontal position and answers “how much drug do I need?”. A report that mentions only potency has not told you whether the drug is worth using.
Common misconception
Beginners often believe that a more potent drug is a stronger drug, so potent must mean better. Potency only means that less drug is needed for the same effect. A drug can be very potent and have a low ceiling of effect, or be less potent and achieve far more. The two properties are read from different parts of the graph.
Check your reasoning
A colleague says: “Drug A is twice as potent as drug B, so it is the better choice for severe pain.” Explain what information is missing from that argument.
Reveal an answer
Potency says nothing about the maximum effect. Before accepting the argument you need the two Emax values: if B reaches a higher maximum, B is the more effective drug for severe pain and A’s potency is irrelevant to that decision. You would also want the therapeutic index, because the more potent drug may be closer to its toxic dose.
Where this comes from
BMS 123 General Pharmacology II lecture notes, Part 2 — Principles of Pharmacodynamics · Unit 3.4, Dose-response curves: definition, graded curves and importance of the graded DRC (Emax, EC50, potency)
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About this course and its sources
Bilingual lessons organised from the supplied BMS 123 General Pharmacology II lecture notes (Principles of Pharmacokinetics and Principles of Pharmacodynamics). Diagrams are original educational schematics; pharmacology, nursing and French-language review are pending.