AP® Environmental Science review sheet from Aim for Five (aimforfive.com/enviro/units/8/8-13)
Unit 8 · Topic 8.13
8.13 Dose Response Curve
A dose-response curve shows how a group of organisms responds as the dose of a substance increases. From it you can read the threshold dose, the ED50 and the LD50, which together describe how toxic a substance is and at what levels it starts to cause harm.
Key terms
- dose-response curve
- threshold dose
- ED50
- LD50
- toxicant
Reading the curve
A dose-response curve plots dose on the x-axis (often on a logarithmic scale, where each step is ten times the last) and the percent of the test population showing a response on the y-axis. The response might be death, a specific symptom or a measurable effect.
The curve usually has an S shape (it is called sigmoidal). At low doses it is flat near 0%, because no individual responds. It then rises steeply through the middle doses and levels off near 100% at high doses, once nearly every individual responds. The steep middle shows that individuals vary in sensitivity: some respond at lower doses, some only at higher ones.
Key points on the curve
- Threshold dose: the highest dose that causes no detectable effect. On the graph, it is the last point before the curve starts to rise above zero; any higher dose begins to cause a measurable response.
- ED50 (effective dose 50%): the dose at which 50% of the population shows a specific, non-lethal effect, such as a symptom or a desired drug effect.
- LD50 (lethal dose 50%): the dose at which 50% of the population dies. Read it by going across from 50% on the y-axis to the curve, then down to the x-axis.
- For the same substance, the ED50 is normally lower than the LD50: you see effects at doses well below those that kill.
Using ED50 and LD50 together
When a substance is a medicine, you want a big gap between the dose that works and the dose that kills. If a drug's ED50 for relieving pain is 10 mg/kg and its LD50 is 1,000 mg/kg, normal doses are far from dangerous. If the two values were close together, small dosing mistakes could be deadly. The same logic applies to pesticides: you want a low dose to affect the pest and a very high dose to harm people or wildlife.
Where the data come from, and the limits
Deliberately dosing people with toxic substances would be unethical, so dose-response data usually come from animal studies on rats, mice or other species, plus observations of people accidentally exposed at work or in disasters. Scientists then estimate safe human limits, usually setting them far below the animal threshold using safety factors to allow for differences between species and between individuals, such as children.
Some substances, especially some carcinogens (cancer-causing substances), may not have a clear threshold; regulators often assume that any dose adds some risk. And as with LD50, a curve describes one kind of response from one kind of exposure, so it doesn't capture every possible harm.
Worked examples
Try each one yourself first, then open the solution.
- Example 1
Reading values from dose-response data
In a test, groups of mice received a chemical at different doses (mg/kg), with these percentages dying: 0 → 0%; 5 → 0%; 10 → 4%; 20 → 18%; 40 → 50%; 80 → 86%; 160 → 100%. (a) Estimate the threshold dose. (b) What is the LD50? (c) Describe the shape of the curve.
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- Step 1: (a) The threshold is the highest dose with no effect. No mice died at 5 mg/kg, but some died at 10 mg/kg, so the threshold is at least 5 mg/kg and below 10 mg/kg. With these data, the best estimate is 5 mg/kg, the highest tested dose with no deaths.
- Step 2: (b) The LD50 is the dose with 50% mortality: 40 mg/kg.
- Step 3: (c) Plotted, the points are flat near 0% at low doses, rise steeply between about 10 and 80 mg/kg, and level off at 100%: an S-shaped (sigmoidal) curve.
Answer: (a) About 5 mg/kg (somewhere from 5 up to just under 10 mg/kg). (b) 40 mg/kg. (c) S-shaped: flat, then steep rise, then leveling off at 100%.
- Example 2Calculator allowed
Trap: comparing two curves
On one dose-response graph, Chemical P's curve rises steeply at low doses and reaches 50% at 8 mg/kg. Chemical Q's curve is shifted to the right and reaches 50% at 120 mg/kg. Both measure death. Which is more toxic, and by how much?
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- Step 1: Both curves measure death, so the 50% points are LD50 values: P = 8 mg/kg, Q = 120 mg/kg.
- Step 2: A curve farther to the left means a lower dose produces the same response, so P is more toxic.
- Step 3: Ratio: 120 ÷ 8 = 15.
Answer: Chemical P is more toxic, about 15 times more, because its curve sits farther left and its LD50 is lower.
Common mistakes
- Guessing the LD50 from the middle of the x-axis. Find 50% on the y-axis, go across to the curve, then straight down to read the dose.
- Thinking a curve farther to the right is more toxic. Farther right means higher doses are needed, so it is less toxic.
- Confusing the threshold with the LD50. The threshold is the highest dose with no detectable effect, just before effects appear; the LD50 is where half the population dies.
On the exam
- Expect a described dose-response graph or data table. Practice identifying the threshold, ED50 and LD50 and explaining what each means.
- If asked why animal data are used, mention that testing toxic doses on humans would be unethical.
Connected topics
Videos
Check yourself
5 questions on 8.13 Dose Response Curve. Pick an answer to see if you got it, and why.
| Dose (mg/kg) | Fish swimming abnormally, Chemical A (%) | Fish swimming abnormally, Chemical B (%) |
|---|---|---|
| 0 | 0 | 0 |
| 5 | 0 | 10 |
| 10 | 0 | 30 |
| 20 | 10 | 50 |
| 40 | 30 | 75 |
| 80 | 50 | 90 |
| 160 | 85 | 100 |
Hypothetical data from groups of 40 fish per dose
Based on the data, what is the ED50 of Chemical A?
Which statement correctly compares the two chemicals?
Toxicity data for setting limits on chemicals in people usually come from studies like this one on animals. Which statement best describes how regulators handle this?
| Dose (mg/kg body weight) | Mice that died (%) |
|---|---|
| 0 | 0 |
| 10 | 0 |
| 20 | 5 |
| 40 | 25 |
| 60 | 50 |
| 80 | 80 |
| 100 | 95 |
Hypothetical data from a toxicity test on groups of 40 mice
Based on the data, what is the LD50 of the chemical for these mice?
Which dose is the threshold dose in this study?
0 of 5 answered