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Dose Response
Curve

Understand how organisms respond to increasing concentrations of a substance: from no observable effect to the lethal dose and everything in between.

AP Environmental Science

What Is a Dose Response Curve?

A dose response curve is a graph that shows the relationship between the dose of a substance (chemical, drug, pollutant) and the magnitude of effect it produces in an organism or population. The x-axis represents dose (often on a logarithmic scale), and the y-axis represents the percentage of a population showing a specific response.

Key Terminology

Dose
The amount of substance an organism is exposed to, measured in \(\text{mg/kg}\) body weight
Response
The measurable biological effect: death, illness, enzyme inhibition, or behavioral change
Threshold
The minimum dose below which no detectable adverse effect occurs in the population

Critical Dose Values

\(\text{LD}_{50}\)
The lethal dose that kills 50% of a test population. Lower \(\text{LD}_{50}\) means more toxic.
\(\text{ED}_{50}\)
The effective dose that produces a desired therapeutic effect in 50% of a population.
\(\text{TD}_{50}\)
The toxic dose that produces a toxic (non-lethal) effect in 50% of a population.

Anatomy of the S-Curve

Dose (log scale) % Response 0 25 50 75 100
\(\text{LD}_{50}\)
 50% Threshold No effect Steep rise zone Plateau

The Threshold Model

For most toxic substances, there exists a threshold dose: below this level, the body can detoxify or repair any damage, so no adverse effects are observed. Above the threshold, effects increase with dose.

1
Below threshold: The body's repair mechanisms neutralize the substance. No observable harm.
2
At threshold: The first detectable adverse effects begin to appear in the most sensitive individuals.
3
Above threshold: Response increases rapidly along the steep portion of the S-curve.

Threshold vs. Non-Threshold

Dose Response Threshold Threshold model Non-threshold (LNT)
Threshold
Safe dose exists below threshold. Applies to most non-carcinogenic toxins and pharmaceuticals.
Non-Threshold (LNT)
No safe dose: risk begins at any exposure. Used for radiation, carcinogens, mutagens.

The Therapeutic Index

When a substance is used as a drug, we care about the gap between the effective dose and the toxic dose. The therapeutic index (TI) quantifies this margin of safety:

High TI
Wide safety margin. Example: common vitamins may have TI > 100.
Low TI
Narrow safety margin. Example: warfarin (blood thinner) has TI close to 1: requires careful dosing.

How to Read a Dose Response Curve

1
Identify the axes: x-axis is dose (often log-transformed), y-axis is % of population responding.
2
Locate the threshold: The dose where the curve first rises above the baseline (0% response).
3
Find the \(\text{LD}_{50}\) / \(\text{ED}_{50}\): Draw a horizontal line from 50% on the y-axis to the curve, then drop down to the x-axis.
4
Assess the slope: A steeper curve means small dose increases cause large jumps in response.
5
Compare curves: A curve shifted left is more potent (lower dose for the same effect).

Distinguish intrinsic hazard from exposure-dependent risk.

Use this illustration to explore the concept described in its caption.

A steel storage tank and groundwater well appear in a section through layered porous ground. The foreground bund wall and soil are deliberately omitted by the cutaway; the modeled containment wall is continuous. Blue pore-space highlights indicate saturation. A separate diagram distinguishes blocked contact from a conditional release, transport and contact pathway.
The modeled baseline assumes continuous, intact containment. The foreground bund wall and ground are cut away for visibility, not shown as a breach. Blue highlights indicate water in pore spaces, not pollutant concentration or measured flow. Hazard alone does not establish exposure; the companion shows a conditional failure pathway without inferring an actual leak, probability or dose. The omitted front wall is a cutaway convention; the containment structure is continuous.
Two pathways contrast blocked contact under intact containment with a conditional release–transport–contact sequence after failure.
Intact containment can block exposure; failure permits release, transport and contact only if each pathway stage occurs.

Example: Comparing Substance A vs. Substance B

Dose (\(\text{mg/kg}\))
 % Mortality 0 50 100 10 100 Substance A Substance B

Example: Finding \(\text{LD}_{50}\) from Data

A lab exposes 10 groups of 20 rats each to increasing doses of Pesticide X. Here are the mortality results:

Dose (\(\text{mg/kg}\)) Deaths / 20 % Mortality
100%
5210%
10525%
20840%
301050%
501680%

Example: Calculating the Therapeutic Index

A new anti-inflammatory drug has the following dose response data:

\(\text{ED}_{50}\)
\(20~\text{mg/kg}\): the dose producing pain relief in 50% of subjects
\(\text{TD}_{50}\)
\(200~\text{mg/kg}\): the dose producing liver damage in 50% of subjects

Factors Affecting Dose Response

Body Size
Larger organisms require higher absolute doses. Dose is normalized to \(\text{mg/kg}\) body weight.
Age
Children and elderly are often more susceptible due to immature or weakened detoxification systems.
Genetic Variation
Individuals may metabolize toxins faster or slower, shifting their personal dose response.
Synergistic Effects
Combined exposure to multiple chemicals can amplify effects beyond what each alone would cause.

Bioaccumulation and Biomagnification

Dose response is not just about a single exposure event. Many pollutants accumulate in organisms over time, shifting the effective dose upward even at low environmental concentrations.

Bioaccumulation
A substance builds up in an individual organism faster than it can be metabolized or excreted (e.g., mercury in fish tissue).
Biomagnification
Concentration increases at each trophic level of a food chain, so top predators receive the highest doses.

Common Mistakes

✕ Confusing \(\text{LD}_{50}\) direction
A lower \(\text{LD}_{50}\) means more toxic, not less. Students often reverse this because "lower number = less dangerous" feels intuitive.
✕ Ignoring the log scale
Dose response x-axes are often logarithmic. Equal spacing on the graph does NOT mean equal dose increments.
✕ Assuming all substances have thresholds
Carcinogens and radiation use the linear no-threshold model: there is no "safe" dose. Not all toxins behave the same way.

Summary Comparison

Concept Definition Key Detail
\(\text{LD}_{50}\) Lethal dose killing 50% Lower = more toxic
\(\text{ED}_{50}\) Effective dose for 50% Desired therapeutic effect
\(\text{TD}_{50}\) Toxic dose harming 50% Non-lethal adverse effect
Therapeutic Index \(\text{TD}_{50} / \text{ED}_{50}\) Higher = safer drug
Threshold Minimum dose for effect Exists for most non-carcinogens
LNT Model No safe dose exists Used for carcinogens, radiation

Question 1 of 5

Substance X has an \(\text{LD}_{50}\) of \(5~\text{mg/kg}\) and Substance Y has an \(\text{LD}_{50}\) of \(500~\text{mg/kg}\). Which statement is correct?

Question 2 of 5

A drug has an \(\text{ED}_{50}\) of \(10~\text{mg/kg}\) and a \(\text{TD}_{50}\) of \(50~\text{mg/kg}\). What is its therapeutic index?

Question 3 of 5

The linear no-threshold (LNT) model is most appropriately applied to which type of substance?

Question 4 of 5

On a dose response graph, Substance A's curve is shifted to the left of Substance B's curve. What does this indicate?

Question 5 of 5

DDT concentration was measured at \(0.04~\text{ppm}\) in lake water but \(25~\text{ppm}\) in osprey (a fish-eating bird). This increase through the food chain is an example of: