The Dose Makes the Poison
Paracelsus established the foundational principle of toxicology in the 16th century: every substance is toxic at some dose, and the dose alone determines whether it acts as a remedy or a poison. Modern toxicology quantifies this through the dose-response relationship — a sigmoidal curve relating the administered dose to the probability of an adverse effect, with the LD50 marking the dose lethal to half the exposed population.
The Sigmoidal Curve
The dose-response curve follows a characteristic S-shape (sigmoid) when plotted on linear axes, or a straight line when mortality is expressed as probits (probability units) against log dose. The Hill equation captures this shape with two key parameters: the LD50 (the curve's midpoint) and the Hill slope b (its steepness). A steep slope means a narrow range between harmless and lethal doses — critical information for setting safety margins.
From LD50 to Safety Margins
Regulatory toxicology uses the LD50 as a starting point for risk assessment, but the full dose-response curve matters more than the midpoint alone. The safety margin — the ratio of toxic dose to therapeutic or expected exposure dose — determines how much buffer exists between normal use and danger. Substances with steep slopes and narrow safety margins (like warfarin) require careful dose monitoring.
Beyond Lethality
Modern toxicology recognizes that death is a crude endpoint. Sub-lethal effects — organ damage, reproductive toxicity, carcinogenicity, endocrine disruption — may occur at doses far below the LD50. The No Observed Adverse Effect Level (NOAEL) and Benchmark Dose (BMD) approaches capture these subtler endpoints, forming the basis for establishing acceptable daily intakes and occupational exposure limits.