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How dose-response curves explain why medicine and poison are dose apart

September 30, 2026 · 10 min

Iris Holm & Hana Field

Dose-response curves explain why aspirin relieves pain at 500 mg but becomes toxic above roughly 150 mg per kilogram of body weight — same molecule, different dose. Paracelsus established this principle in the 1500s; today, the EC50 metric and therapeutic drug monitoring translate it into clinical practice, but individual variation means population averages often mislead.

The dose-response relationship is a foundational principle in pharmacology and toxicology, describing how a substance's biological effect changes as the amount administered increases. At sub-threshold doses, no measurable effect occurs. Within a defined therapeutic window, the substance produces a beneficial effect that scales with dose.

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About this episode

There's a principle old enough to predate modern chemistry that should answer almost every question you've ever had about a supplement label, a drug warning, or why your doctor cares so much about milligrams. Paracelsus articulated it in the 1500s: the dose makes the poison. Every substance — aspirin, water, turmeric, fish oil — follows a curve. Below a threshold, no effect. In a middle range, real benefit. Past a ceiling, harm. The shape is S-curved, and where you sit on it is a function of your age, kidney function, body weight, and what else you're taking. This episode works through that curve carefully — what the therapeutic window actually means, why the therapeutic index matters, how EC50 turned an old intuition into a number doctors can use, and why therapeutic drug monitoring exists as an acknowledgment that population averages aren't enough for individual patients. It also takes seriously the things the clean model can't handle: substances that behave differently at very low doses, the unsolved computational problem of fitting individual curves reliably, and the quiet collapse of single-substance logic the moment someone's morning involves three things at once. 'Natural' doesn't have a different curve. That's the argument, and it holds.

Frequently asked

What is a dose-response curve and why does it matter?

A dose-response curve is an S-shaped (sigmoidal) graph showing how a substance's effect scales with dose. Below a threshold, no effect registers. In the steep middle section — the therapeutic window — small dose changes produce large effects. Above the plateau, the same substance becomes toxic. The shape applies to every drug, supplement, and chemical.

What is the therapeutic index and why is a narrow one dangerous?

The therapeutic index is the ratio of a substance's toxic dose to its therapeutic dose. A ratio near two means doubling an effective dose already risks toxicity — a dangerously narrow margin. Aspirin sits in a narrow zone for some patients; blood salicylate concentrations above 300 micrograms per milliliter are the FDA's clearly toxic threshold.

Can drinking too much water actually be fatal?

Yes. Drinking excessive water causes hyponatremia — dangerously diluted blood sodium — and documented deaths have occurred in endurance athletes. This is the dose-response principle applied to water: even a substance essential for life becomes lethal at a high enough dose, illustrating that 'safe' is always a dose-dependent judgment, not an inherent property.

What does EC50 mean in pharmacology?

EC50 is the dose that produces 50 percent of a drug's maximum effect, and it quantifies potency on a dose-response curve. A lower EC50 means a drug is more potent — it reaches half-maximal effect at a smaller dose. EC50 shifts with age, liver function, and body weight, so the same dose can place different people at very different points on the curve.

Are natural supplements like fish oil and turmeric subject to dose-response limits?

Yes. Turmeric, fish oil, and vitamin A all have toxic thresholds governed by the same dose-response curves as prescription drugs. 'Natural' does not exempt a substance from pharmacological limits. Two supplements with similar marketed effects can have very different EC50 values, meaning one requires a far higher — and potentially harmful — dose to achieve the same result.

Grounded in 11 sources
Jeffrey Aronson: When I Use a Word . . . Dose-response curves - The BMJ ↗ · blogs.bmj.com
CurveCurator: a recalibrated F-statistic to assess, classify, and explore significance of dose–response curves | Nature Communications ↗ · nature.com
History of dose response ↗ · researchgate.net
Understanding Therapeutic drug monitoring (TDM) at a ... ↗ · researchgate.net
Dose-Response Relationship - an overview ↗ · sciencedirect.com
Introduction to toxicology - European Commission ↗ · ec.europa.eu
Frontiers | The double-edged sword of nutraceuticals: comprehensive review of protective agents and their hidden risks ↗ · frontiersin.org
Synergy, Additive Effects, and Antagonism of Drugs with Plant Bioactive Compounds ↗ · mdpi.com
Dose response curves ↗ · nigms.nih.gov
8 Supplements That Don’t Always Mix With Prescriptions ↗ · aarp.org
Dose–response relationship - Wikipedia ↗ · en.wikipedia.org
Read transcript

Hana Field: Iris, hey — I have to tell you, I had the strangest moment at the pharmacy yesterday, standing there holding a bottle of fish oil and genuinely not knowing if the dose on the label was, like, a suggestion or a ceiling.

Iris Holm: And you couldn't tell from the bottle.

Hana Field: Nothing. Just "take two softgels daily" and a picture of a salmon. And that's — okay, so that's actually exactly where we're going today, because there is a principle that should answer that question, and it's so old and so fundamental and somehow we still manage to ignore it completely.

Iris Holm: Dose makes the poison.

Hana Field: Paracelsus. 1493 to 1541. A Swiss physician who said, essentially, every substance will kill you — the only variable is how much. And we have spent five centuries building the math to prove him right, and people are still buying supplements that could genuinely harm their liver because the label says "natural."

Iris Holm: Right, but here's what makes it concrete — aspirin. Five hundred milligrams, you get pain relief. You push past roughly 150 milligrams per kilogram of body weight, you're in toxicity. Past 500 milligrams per kilogram, you're looking at potential lethality. Same molecule. Nothing changed but the number.

Hana Field: Same molecule. And the one that really stopped me — water. Hyponatremia. Endurance athletes have actually died from drinking too much water, documented cases, because the sodium in their blood diluted past the point of function. Water.

Iris Holm: Which means the question isn't "is this thing safe" — it's what dose is safe for which body. And that's the thing we don't have a clean answer to.

Hana Field: And that's the thing that I keep tripping over — like, we know it's not on/off, we know it scales, but I don't think most people actually have a picture of what that scaling looks like.

Iris Holm: Dimmer switch. That's the whole thing. Not a light switch — a dimmer. Below a certain point, the room stays dark. No effect at all. Then there's a range in the middle where small turns produce real, useful light. Crank it too high, the bulb burns out.

Hana Field: Oh, that's — yeah, that lands.

Iris Holm: The actual shape is called sigmoidal — S-shaped on a log-dose axis. Three phases. Flat at the bottom, that's sub-threshold, your body literally doesn't register the substance. Then a steep climb, the therapeutic zone, where small dose changes produce massive effect changes. Then it plateaus — and the plateau tips into harm.

Hana Field: So the middle section, the steep part — that's the therapeutic window. And I've heard that phrase, but what makes one window narrow and another wide? Like, what's actually different?

Iris Holm: That's the therapeutic index — it's a ratio. Toxic dose divided by therapeutic dose. And if that number is, say, two, you're in trouble. You double the effective dose and you're already in danger. A wide window means the ratio is large — you've got room. A narrow one means the gap is basically nothing.

Hana Field: And aspirin actually sits in that narrow zone for certain people.

Iris Holm: Right — which is exactly why the 20th century had to put numbers on this. EC50, the dose that gets you fifty percent of the maximum effect, that's what made Paracelsus's intuition into something you can actually compare across drugs. But the complication is that EC50 isn't a fixed constant. It shifts with age, liver function, body weight. The number that clears the steep part of the curve for one person might already be on the plateau for someone else.

Hana Field: So the curve is universal as a shape — but where any individual sits on it, that's a completely different question.

Iris Holm: And that's exactly where 'natural' breaks down — because the curve doesn't check the label. Turmeric, fish oil, vitamin A — all of them have toxic thresholds. The curve doesn't care what aisle you bought it in.

Hana Field: Which is — I mean, that's the thing that actually gets me. Paracelsus figured this out in the 1500s, and we have five centuries of math behind it now, and someone is still standing in the pharmacy reading 'natural' on a fish oil bottle and thinking, okay, I'm exempt. Like the word 'natural' is doing this enormous load-bearing work that physics simply doesn't allow it to do.

Iris Holm: It's emotional categorization. 'Natural' gets filed in a different mental folder than 'drug.' Same curve, different folder.

Hana Field: And the folder is wrong.

Iris Holm: Here's the part that sharpens it — potency versus efficacy. Two supplements, say turmeric and fish oil, both marketed for inflammation, both claiming roughly the same benefit. Same efficacy on the label, functionally. But their EC50 values could be completely different — meaning one might require a far higher dose to get you to that same effect. And the bottle doesn't tell you that.

Hana Field: Wait — so you could be taking more than you think just to hit the marketed effect, and that excess is exactly what pushes you up the curve toward harm.

Iris Holm: Toward the plateau, yes. And the plateau isn't neutral — it tips into toxicity. The FDA doesn't set reference thresholds for salicylate for fun. Blood concentrations above 300 micrograms per milliliter — that's their clearly toxic marker for aspirin. That number exists because the curve demanded a number.

Hana Field: And you know what none of that population data accounts for — and this is actually where it gets worse before it gets better — is where any one person actually sits on the curve. Because population ranges are approximations, and we haven't even touched what happens when individual variation shifts your threshold entirely.

Iris Holm: That's the next layer. And it complicates everything we just said.

Hana Field: And the shift can happen without anyone noticing — that's the part that actually keeps me up. I keep thinking about a nephrology clinic, a patient on standard aspirin for heart protection, and they finally check her creatinine after two years. The number comes back wrong. Wrong toward danger. And nobody had told her her curve had moved.

Iris Holm: Because the 150 milligrams per kilogram threshold — that's a population number. It doesn't know her kidney function declined.

Hana Field: She's taking the instructions she has.

Iris Holm: Which is why therapeutic drug monitoring exists — TDM. You actually measure blood concentrations. You don't estimate from population tables, you pull the number from this specific patient and you ask: are we inside the window, or have we drifted past it? The FDA's 300 micrograms per milliliter marker for salicylate toxicity — TDM is how you find out if she's already there.

Hana Field: So TDM is basically the admission that population ranges aren't enough.

Iris Holm: It is. And it's still not universally accessible — which, frankly, is a separate problem. But even TDM assumes the curve is a single sigmoid. And that assumption, actually, is where hormesis walks in and breaks things.

Hana Field: Wait — a biphasic curve? Like beneficial at very low doses, then harmful?

Iris Holm: For some substances, yes. A stimulatory effect at low doses before inhibition kicks in. That's not the simple threshold model — it's a different shape entirely. And there's actually an open-source tool called CurveCurator that applies a recalibrated F-statistic just to classify which type of curve a substance is following, because the computational problem of fitting these curves reliably is still unsolved. That's not historical. That's current research.

Hana Field: So we're handing patients population averages, and the underlying math for individual curves is still — I mean, that's the thing nobody in the pharmacy aisle knows.

Iris Holm: And nobody has mapped the collision. That's the part that actually breaks the Paracelsian promise — not because Paracelsus was wrong, but because he was describing one substance. The moment you're taking three things simultaneously, the graded response you'd predict from any single curve becomes something else. A population-level risk you didn't sign up for.

Hana Field: And that's — I mean, that's most people, right? Not one drug. Three things, a supplement, a prescription, maybe an over-the-counter. And the curve that was mapped for each one individually just doesn't account for what they do to each other. Five hundred years of 'the dose makes the poison,' and the clean single-substance rule quietly falls apart the minute someone's Tuesday morning looks like most people's Tuesday mornings.

Iris Holm: The honest version is this — the curve is universal. Your position on it is yours alone. And we've barely started building systems that treat it that way.

Hana Field: That's where I keep landing. Paracelsus gave us the question in the 1500s, the 20th century gave us EC50 and TDM, and most people are still navigating dose by reading a label written for a population they may not belong to. That's not a failure of science. It's a failure of translation.

Iris Holm: Good place to stop. Genuinely.