Cell Signaling · Unit 1: How a cell knows anything

Binding: Affinity, Occupancy and Dose–Response

A drug or hormone acts by occupying a receptor, and how much it occupies follows one equation. This lesson shows how to read affinity, potency and efficacy from binding and dose-response curves, and why a tissue can respond fully while most of its receptors are empty. You will finish able to calculate occupancy from Kd and to identify a blocker from the way it moves a curve.

Watch first A Full Response, Mostly Empty Receptors · 2:47

Naloxone can pull a person out of a morphine overdose within minutes, and it never reacts with a single molecule of morphine. The two drugs compete for the same place on the same cells. This lesson asks how much of that place a given dose fills, and how filling it becomes a response.

The idea: a drug acts at a site it has to occupy

In 1905 John Langley, in Cambridge, tested two drugs on skeletal muscle. Nicotine made the muscle contract and curare prevented it, and both still worked after the nerve to the muscle had been cut and had degenerated. So the drugs were acting on the muscle itself. Langley called the thing they acted on the receptive substance. A few years earlier Paul Ehrlich, working on how the body makes antitoxins, had coined a shorter word for a related idea about toxins and nutrients, not yet about drugs: receptor.

The picture that still works is Emil Fischer’s lock and key. An agonist is a molecule that binds a receptor and switches it on: the key fits and turns. An antagonist binds the same receptor and does nothing there: the key fits, will not turn, and keeps the other key out.

One equation: occupancy follows mass action

Picture a room with a fixed number of coat hooks. Coats go in, catch on hooks and drop off again. The hooks are receptors (R). The coats are ligand (L), meaning any molecule that binds the receptor. The fraction of hooks holding a coat is the fractional occupancy.

The real mechanism is a reversible reaction, L + R ⇌ LR. At equilibrium, binding and release happen at the same rate, and the balance point is the dissociation constant: Kd = [L] × [R] / [LR]. Solve for the fraction of receptors bound and you get this lesson’s one equation:

fractional occupancy = [L] / (Kd + [L])

Set [L] equal to Kd and the answer is one half. So Kd is the concentration of ligand that fills half of the receptors. It measures affinity: a small Kd means a tight grip, because very little ligand is needed to half-fill the sites.

This is the Michaelis–Menten equation from the enzyme kinetics lesson, with occupancy in place of v/Vmax and Kd in place of Km. Both are hyperbolas for the same reason: a fixed number of sites is being filled. One caution: Km combines several rate constants, while Kd is a pure binding constant. In 1926 Alfred Clark fitted this same hyperbola, which A. V. Hill had used for nicotine in 1909 and Irving Langmuir for gas sticking to a surface, to the response of frog heart muscle to acetylcholine.

At [L] = Kd/9, occupancy is 10%. At [L] = 9 × Kd, it is 90%. Getting from 10% to 90% takes an 81-fold increase in ligand, nearly two powers of ten. That is why these curves are drawn with concentration on a logarithmic axis. On a linear axis the low-dose end is crushed against the origin. On a log axis the hyperbola becomes a symmetric S-shaped curve with Kd at its midpoint. Try it in the explorer below.

Dose–response — potency, efficacy, antagonism⚙ original · interactive
Apparent EC₅₀ (relative units)
1.0
Ceiling response
100%

The dose that gives half-maximal response is the EC₅₀ — the lower it is, the more potent the drug. Efficacy is how high the curve can reach.

Potency (EC₅₀, the curve's horizontal position) and efficacy (Emax, its height) are independent. A competitive antagonist slides the curve right but can be overcome with more agonist; it never lowers the ceiling.

A climb from 10% to 90% in much less than 81-fold means the sites are not acting independently. That is cooperativity, which belongs to the lesson on protein binding and allostery.

Potency is not efficacy, and response is not occupancy

Occupancy counts the receptors that have ligand bound. Response is what the tissue does: a muscle shortens, a gland secretes. A dose–response curve plots the second, and it has two numbers of its own.

EC50 is the concentration that gives half of the drug’s maximum response. It measures potency: the lower the EC50, the less drug you need. Emax is the largest response the drug can produce, however much you add. It reflects efficacy: how well the drug switches the receptor on once it is bound.

These are separate properties. A full agonist can drive the tissue to its maximum. A partial agonist levels off below that maximum even when it occupies every receptor, like a key that turns the lock only part of the way. Buprenorphine is a partial agonist at the receptor that morphine activates and naloxone blocks.

Compare three drugs acting at one receptor in one tissue. The first has an EC50 of 1 nM and reaches 100%. The second has an EC50 of 100 nM and also reaches 100%: 100-fold less potent, with the same maximum. The third has an EC50 of 1 nM but tops out at 40%: as potent as the first, less efficacious.

Add a partial agonist to a tissue that is already responding fully to a full agonist, and the response falls. Each receptor the weak key takes is one the strong key has lost. In that setting the partial agonist behaves as an antagonist.

The response saturates before the receptors do

Clark assumed that response is proportional to occupancy, which would make EC50 equal to Kd. In 1956 Mark Nickerson published a short paper in Nature called “Receptor occupancy and tissue response.” He reported that a tissue can reach its full response before all of its receptors are occupied.

The reason is amplification in the pathway after the receptor. Picture a bottling line where the capper is the bottleneck: once it runs at full speed, extra filling machines add nothing. Likewise, once enough receptors are occupied to saturate the slowest step downstream, more occupied receptors change nothing you can measure. The receptors that are not needed are called spare receptors, and together they make up the receptor reserve. They are ordinary receptors. The tissue has more copies than the pathway can use at once.

Kd is a property of the receptor. EC50 is a property of the whole pathway. With a reserve, EC50 sits below Kd.

How far below? Say the pathway reaches its ceiling at 5% occupancy and responds in proportion below that. Half the maximum then needs 2.5% occupancy. Solving [L] / (Kd + [L]) = 0.025 gives [L] = Kd/39, so the EC50 is 39-fold below the Kd with no change in binding.

Treating an EC50 as a binding affinity is a common error in the research literature. You can also use the gap as a tool. If a treatment changes a drug’s EC50 and leaves its Kd alone, something after binding has changed, and you can look for it.

Design problem

A drug gives a full response when only about 5% of its receptors are occupied. State what that tells you, then design an experiment that would prove it.

One way to do it

What it tells you: for this drug in this tissue, about 95% of the receptors are spare. A step after the receptor saturates first, so the EC50 lies well below the Kd. The reserve belongs to the pair of drug and tissue. A weaker agonist on the same tissue might need every receptor.

The experiment: take receptors away and watch the curve. Use an irreversible antagonist, a blocker that bonds covalently to the receptor and cannot be washed off or outcompeted. Treat strips of tissue so that different fractions of the receptors are destroyed, wash, then run a full agonist dose–response curve on each strip. In matched samples, count with a radioactive ligand what fraction of the receptors each treatment removed.

The predictions, taking the 5% figure at face value:

  • Half of the receptors gone. The drug must now occupy 10% of the survivors. You still get a full response at a higher dose, so the curve moves right.
  • 90% gone. The drug must occupy half of the survivors. Still a full response, further right.
  • More than 95% gone. Even with every survivor occupied, the tissue is short of the number it needs. Now the maximum falls.

A rightward shift first and a lower maximum afterwards is the proof. With no reserve, the maximum would start to fall with the first receptors lost. Real tissues have no sharp threshold, so the maximum sags gradually near the limit, but the order of events is the same.

As a control, a second agonist acting through a different receptor should keep its full maximum, which shows that the blocker left the downstream pathway undamaged.

Blocking the receptor: the shape of the shift names the blocker

Go back to the coat hooks and throw in decoy coats that take up hooks and produce no response.

A competitive antagonist binds reversibly at the agonist’s own site. Add enough agonist and it wins the hooks back, so the maximum is unchanged. What changes is the dose you need. On a log axis the whole curve slides to the right, parallel to itself. This is what naloxone does to morphine.

The size of the slide is the dose ratio: how many times more agonist you need for the same response.

dose ratio = 1 + [B] / KB

[B] is the antagonist concentration and KB is the antagonist’s own dissociation constant. J. H. Gaddum wrote down the competition equation in 1937. In 1947 Heinz Schild turned it into a measurement he called pA2: the negative logarithm of the antagonist concentration that forces you to double the agonist dose. At a dose ratio of 2, [B] equals KB. Two ordinary dose–response curves therefore give the affinity of a blocker for a site that nobody has isolated.

A non-competitive antagonist takes receptors out of play in a way that more agonist cannot reverse. It may bind somewhere else on the receptor, or bind at the agonist’s site and never let go. Its signature is a lower maximum. In a tissue with a receptor reserve, as the design problem showed, the first receptors lost cost only a rightward shift.

Potency rankings also sort receptors into types. In 1948 Raymond Ahlquist ranked six adrenaline-like drugs by potency on many tissues. Blood delivers adrenaline to every organ at much the same concentration, yet it narrows arteries and relaxes airways. In arteries adrenaline and noradrenaline ranked high and isoproterenol low. In airways and heart the ranking ran nearly the other way. No third order appeared. One kind of pocket predicts one order everywhere, so he proposed two kinds and named them alpha and beta.

The proof: binding you can count

Every argument so far infers the receptor from a response. In 1973 Candace Pert and Solomon Snyder at Johns Hopkins measured binding itself, as did two other groups the same year. They mixed radioactive naloxone with ground-up brain tissue, pulled the mixture through a filter, washed the filter and counted the radioactivity that stayed behind.

Brain is greasy and will hold on to almost any small molecule. So how do you show that what stuck is a receptor?

The binding has to be saturable. A finite set of sites fills up along the occupancy curve, while sticking to grease keeps rising with concentration. It has to be specific: unlabelled opiates pushed the radioactive naloxone off in the order of their known potency as drugs. And it has to be stereospecific. Levorphanol, an active opiate, displaced the label. Dextrorphan, its mirror image, has almost no opiate action and was far weaker. Grease cannot tell a molecule from its mirror image. A shaped pocket can.

The saturation curve hands you the numbers in this lesson’s equation, now measured on the site itself: a Kd, and the total count of sites, called Bmax. Langley’s receptive substance had become something you could count.

How we measure it

Isolated-tissue bioassay (organ bath)

A strip of muscle or a piece of heart is kept alive in warm, oxygenated salt solution and connected to a recorder. You add a drug at rising concentrations and measure the contraction or relaxation at each one. The result is a dose-response curve, from which EC50 and Emax are read.

Radioligand binding assay

Membranes are incubated with a radioactive ligand, then filtered and washed, and the radioactivity left on the filter is counted. Repeating the incubation with a large excess of unlabelled ligand measures nonspecific sticking, which is subtracted. The specific binding that remains saturates, and its curve gives Kd and the number of sites (Bmax).

Schild analysis

You measure agonist dose-response curves at several concentrations of an antagonist and calculate the dose ratio for each. For a competitive antagonist, log(dose ratio − 1) plotted against log antagonist concentration is a straight line of slope 1. The point where the line crosses zero gives KB, the antagonist's dissociation constant.

Irreversible receptor inactivation

A tissue is treated with a blocker that bonds covalently to the receptor and is then washed, so that a fraction of the receptors is permanently removed. Comparing agonist curves before and after shows whether the curve moves right before its maximum falls. That order reveals a receptor reserve.

Finish line

Test yourself

8 questions

Practice and MCAT-style, with explained answers.

Next · Lesson 4

A Field Guide to Receptors

Acetylcholine starts a muscle twitch and slows a heart. Same molecule: what decides what it means?

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Nicotine — the agonist Langley used on muscle
Nicotine — the agonist Langley used on muscle ● LIVE · PubChem CID 89594
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A small molecule with two nitrogen-containing rings. Langley's argument for a receptive substance rested on what this compound does to muscle and on curare's power to block it.

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Morphine — an agonist at the mu-opioid receptor
Morphine — an agonist at the mu-opioid receptor ● LIVE · PubChem CID 5288826
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Note the rigid ring system and the methyl group on the nitrogen. Compare it with naloxone, which keeps most of this skeleton.

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Naloxone — a competitive antagonist at the same receptor
Naloxone — a competitive antagonist at the same receptor ● LIVE · PubChem CID 5284596
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The same morphinan skeleton as morphine, with an allyl group on the nitrogen in place of the methyl. It fits the same pocket and does not switch the receptor on.

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Mu-opioid receptor with an irreversible antagonist bound — the pocket itself
Mu-opioid receptor with an irreversible antagonist bound — the pocket itself ● LIVE · RCSB PDB 4DKL
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Find the morphinan ligand sitting in a pocket that opens to the outside of the cell. This antagonist is covalently attached to the receptor, the kind of blocker used to remove receptors when measuring a receptor reserve.

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John Newport Langley

John Newport Langley 1852–1925

Argued from drug antagonism that cells carry a specific "receptive substance" with which drugs combine, the idea that the occupancy equation later put into numbers.

Langley spent his working life in the physiology laboratory at Cambridge. In 1878, in the first volume of the Journal of Physiology, he reported that pilocarpine makes a cat's salivary gland secrete and that atropine stops it. He proposed that the two drugs compete to combine with some substance in the gland, according to their amounts and their affinity for it. He came back to the idea in 1905 with nicotine and curare on skeletal muscle. Nicotine made the muscle contract and curare blocked it, and both still acted after the nerve had been cut and had degenerated. The drugs therefore acted on the muscle cell itself, on what he called its receptive substance. He never isolated it, and nobody did in his lifetime. What the idea made possible was arithmetic. In 1909 his student A. V. Hill wrote an equation for a drug combining reversibly with a fixed number of sites, the form that Clark later built into occupancy theory.

✓ verbatim Langley, J. Physiol. 33:374 (1905); Maehle, 'Receptive substances: John Newport Langley and his path to a receptor theory of drug action', Medical History 48:153 (2004).
Alfred Joseph Clark

Alfred Joseph Clark 1885–1941

Fitted Langmuir's adsorption equation to drug responses in isolated tissue, which turned the receptor into a quantity described by mass action and a dissociation constant.

In 1926 Clark measured how strongly isolated frog heart muscle responded to graded doses of acetylcholine, and how atropine opposed it. Then he treated the curve as a binding curve, as A. V. Hill had done for nicotine in 1909. Irving Langmuir had written an equation for gas molecules sticking to a surface that has a fixed number of sites, and Clark described the acetylcholine curve as an adsorption process of that kind. The response followed a hyperbola, as it should if a finite set of sites were being filled under the law of mass action. He had confirmed none of the underlying picture, and in his 1933 book, The Mode of Action of Drugs on Cells, he said that he chose it because every alternative required less likely assumptions. Some of his contemporaries, Dale among them, doubted that the receptor did more than restate the data. Clark died in 1941, decades before any receptor was purified. His treatment let pharmacologists describe a drug by a dissociation constant and compare drugs by number, long before there was a molecule to point to.

✓ verbatim Clark, 'The reaction between acetyl choline and muscle cells', J. Physiol. 61:530 (1926); Clark, The Mode of Action of Drugs on Cells (Edward Arnold, London, 1933).
Heinz Otto Schild

Heinz Otto Schild 1906–1984

Defined pA2 and the analysis that bears his name, which give the affinity of a competitive antagonist from the rightward shift of an agonist dose-response curve.

Schild was born in Fiume and came to England in 1932 to work in Henry Dale's laboratory. As an Italian citizen he was interned on the Isle of Man during the war. In 1947, at University College London, he combined Gaddum's competition equation with a suggestion from Clark and Raventós and defined pA2, a single number for the strength of an antagonist that can be read from two dose-response curves. With Arunlakshana in 1959 he showed how to test whether a blocker is truly competitive. Antagonist affinities became the fingerprints by which pharmacologists told one receptor type from another, years before any receptor was isolated.

✓ verbatim Schild, 'pA, a new scale for the measurement of drug antagonism', Br. J. Pharmacol. Chemother. 2:189 (1947); Black, 'Heinz Otto Schild', Biographical Memoirs of Fellows of the Royal Society (1994).
Candace Pert

Candace Pert 1946–2013

As a graduate student with Solomon Snyder, measured saturable, stereospecific binding of radioactive naloxone to brain tissue, a direct demonstration of the opiate receptor.

Pert was a graduate student in Solomon Snyder's laboratory at Johns Hopkins when she was handed a new assay. Earlier attempts to find the opiate receptor had used radioactive opiates of low specific activity, which had to be used at concentrations so high that they saturated the receptor sites. The new assay used a custom batch of tritiated naloxone, an antagonist, at high specific radioactivity. Pert mixed it with ground-up brain, collected the tissue on filters with a manifold that could handle many samples and be washed vigorously, using techniques adapted from insulin-receptor binding work, and counted what stayed bound. She found specific binding. Active opiates displaced the label and their mirror-image forms did not. The paper appeared in Science in 1973. The 1978 Lasker Award for this field went to Snyder, John Hughes and Hans Kosterlitz, and Pert was not included. Her assay became a standard way to count receptors and to screen drugs by displacement. A binding site for a plant drug also strengthened the case that the brain makes opioids of its own, which Hughes and Kosterlitz isolated in 1975.

✓ verbatim Pert & Snyder, 'Opiate receptor: demonstration in nervous tissue', Science 179:1011 (1973); Snyder, Brainstorming: The Science and Politics of Opiate Research (Harvard University Press, 1989).
Test yourself
Question 1 of 8 Score 0 / 0

A ligand is present at a free concentration equal to its Kd for a receptor. At equilibrium, what fraction of the receptors is occupied?
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Every structure, slide, simulation, and clip on this page is listed below with the source it came from. None of the 3D structures is drawn by hand or by AI: each one loads by accession ID from RCSB PDB or PubChem. This panel is generated from the lesson's own data file, so what it lists is what the page loads.

Molecular structures live data

  • Mu-opioid receptor with an irreversible antagonist bound — the pocket itself — RCSB PDB 4DKL · coordinates CC0 · Mouse mu-opioid receptor with beta-funaltrexamine; Manglik et al., Nature 485:321 (2012)
  • Nicotine — the agonist Langley used on muscle — PubChem CID 89594 · PubChem CID 89594, (S)-nicotine
  • Morphine — an agonist at the mu-opioid receptor — PubChem CID 5288826 · PubChem CID 5288826
  • Naloxone — a competitive antagonist at the same receptor — PubChem CID 5284596 · PubChem CID 5284596

Simulations

  • Dose–response explorer · Original interactive — Biochemistrypedia (Deppmann Lab).

Scientist profiles & quotes

  • John Newport Langley — Langley, J. Physiol. 33:374 (1905); Maehle, 'Receptive substances: John Newport Langley and his path to a receptor theory of drug action', Medical History 48:153 (2004).
  • Alfred Joseph Clark — Clark, 'The reaction between acetyl choline and muscle cells', J. Physiol. 61:530 (1926); Clark, The Mode of Action of Drugs on Cells (Edward Arnold, London, 1933).
  • Heinz Otto Schild — Schild, 'pA, a new scale for the measurement of drug antagonism', Br. J. Pharmacol. Chemother. 2:189 (1947); Black, 'Heinz Otto Schild', Biographical Memoirs of Fellows of the Royal Society (1994).
  • Candace Pert — Pert & Snyder, 'Opiate receptor: demonstration in nervous tissue', Science 179:1011 (1973); Snyder, Brainstorming: The Science and Politics of Opiate Research (Harvard University Press, 1989).

Quotes are verbatim from the cited source. Profile text is original to this site and was checked against the sources cited.

Animated explainer

A Full Response, Mostly Empty Receptors · narration: an AI narrator voice (Gemini, Charon) reading narration written from this lesson's text · animation: AI-generated in code (Manim) by Claude, a schematic with no drawn molecular structures, plots computed from their equations · captions from the narration script.

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Like I'm five

Picture a wall of light switches and a bag of marbles you throw at it. Throw a few marbles and a few switches get hit. Throw lots and nearly all of them do, but the last few are the hardest to hit. Some marbles flip the switch they land on, and some just sit on it so no other marble can.
High school

A drug works by sticking to a matching protein on a cell, called a receptor. How much of the drug sticks depends on the dose and on how tightly the drug holds on. The dose that fills half of the receptors is called Kd, and a small Kd means a tight grip. Sticking is different from doing. One drug may stick and switch the receptor fully on, another may switch it on weakly, and a blocker sticks and switches nothing on. Scientists read this from a dose-response curve, a graph of how big the effect is at each dose. The dose that gives a half-sized effect shows how potent the drug is, and the height of the curve shows how strong its best effect can be.
College

Binding of a ligand to one class of independent sites follows the law of mass action: fractional occupancy = [L] / (Kd + [L]), a hyperbola with the same form as the Michaelis-Menten equation. Kd, the concentration that gives half occupancy, measures affinity. A dose-response curve reports two other things, potency (EC50) and efficacy (Emax). A full agonist reaches the tissue maximum, a partial agonist does not even at full occupancy, and an antagonist binds with no efficacy. Because the pathway after the receptor amplifies and saturates, many tissues respond fully with a minority of receptors occupied (a receptor reserve), which puts EC50 below Kd. A competitive antagonist moves the log dose-response curve to the right in parallel, by a dose ratio of 1 + [B] / KB, and leaves the maximum alone. A non-competitive or irreversible antagonist lowers the maximum, after first moving the curve right if a reserve exists. Radioligand binding measures Kd and the number of sites (Bmax) directly, and saturable, stereospecific binding is the evidence that the site is a receptor.
Graduate

For one class of non-interacting sites at equilibrium, occupancy follows the Hill-Langmuir equation with a Hill coefficient of 1, which is the 81-fold rule for 10% to 90%. Response is a further, saturating function of occupancy. In the operational model of Black and Leff (1983) with a hyperbolic transducer, E = Em × τ[A] / (KA + (1 + τ)[A]), where τ is receptor density divided by the concentration of occupied receptor that gives half of the system maximum Em. It follows that EC50 = KA / (1 + τ) and that the observed maximum is Em × τ / (1 + τ). A high-τ agonist looks full, with EC50 far below KA, and irreversible alkylation of receptors lowers τ, which moves EC50 toward KA before the maximum collapses. Furchgott's receptor-inactivation method (1966) uses that behaviour to estimate agonist KA. For competitive antagonists the Gaddum-Schild relation gives log(dose ratio − 1) = log [B] − log KB. A Schild plot with unit slope over a wide range of [B] is the test of simple competition, and slopes away from 1 point to non-equilibrium conditions, agonist uptake, allosteric interaction or more than one receptor.

An open question is how far these equilibrium constants predict effect in a living tissue. Concentrations in vivo can change faster than binding equilibrates, so the time a drug stays on its receptor may matter more than Kd. A single efficacy value also fails to describe a ligand that activates different downstream pathways to different degrees, and how to measure efficacy in a way that transfers between tissues is still argued over.
A rejected paper, ignored for a decade

Raymond Ahlquist was looking for a drug to relax the uterus and ease menstrual cramps when he ranked six adrenaline-like compounds on tissue after tissue in Augusta, Georgia. The leading pharmacology journal rejected the paper. It appeared in the American Journal of Physiology in 1948 through his friendship with the physiologist W. F. Hamilton, and it was largely ignored until about 1958. His alpha and beta receptors later gave drug designers the target that led to beta blockers.

— Ahlquist, 'A study of the adrenotropic receptors', Am. J. Physiol. 153:586 (1948); Quirke, 'Putting theory into practice: James Black, receptor theory and the development of the beta-blockers at ICI, 1958-1978', Medical History 50:69 (2006).
Two percent, and a stronger label

In 1971 Avram Goldstein at Stanford looked for the opiate receptor with radioactive levorphanol. He found binding that could tell the drug from its mirror image, but it was about 2% of the total. The rest was drug sticking nonspecifically to the tissue. Snyder later put the problem down to radiolabelled opiates of low specific activity, which had to be used at high concentrations. The fix was custom tritiated naloxone at high specific radioactivity, used at concentrations low enough for the specific sites to stand out.

— Goldstein, Lowney & Pal, Proc. Natl. Acad. Sci. USA 68:1742 (1971); Pert & Snyder, Science 179:1011 (1973); Snyder, J. Biol. Chem. 286:21023 (2011).
Receptor or receptive substance?

The word receptor is credited to Paul Ehrlich, who adopted it around 1900 in place of his earlier term for the side-chains of cells that bind toxins. At first he thought of receptors only for toxins, nutrients and ferments. Langley's work on drugs helped change his mind, and in 1907 he proposed chemoreceptors. Langley himself never adopted the word and went on writing receptive substance.

— Maehle, 'Receptive substances: John Newport Langley and his path to a receptor theory of drug action', Medical History 48:153 (2004); Maehle, 'A binding question: the evolution of the receptor concept', Endeavour 33:135 (2009).

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