Quantitative study of adverse effects of chemicals on living systems: dose–response, mechanisms of injury, xenobiotic metabolism, risk assessment. Substrate of regulatory science (EPA, EFSA, FDA safety files).
toxicology
Dose–response curve
Relation between administered dose and biological effect; typically sigmoidal E = E_max · C^n/(EC₅₀^n + C^n) (Hill).…
LD₅₀ / LC₅₀
Dose (or environmental concentration) killing 50% of a test population. Standard (if blunt) acute-toxicity ranking: LD₅₀ < 5 mg/kg…
Xenobiotic metabolism
Phase I oxidation/reduction/hydrolysis (CYP450 family) introduces polar groups; Phase II conjugation with glucuronide, sulfate, GSH,…
Carcinogen
Agent causing or promoting cancer. IARC 1 (known human: benzene, asbestos, formaldehyde), 2A (probable), 2B (possible), 3 (inadequate), 4…
Endocrine disruptor
Chemical interfering with hormone signalling (agonist, antagonist, biosynthesis/clearance modulator). BPA, phthalates, PCBs, PFAS.…
Hepatotoxicity
Liver injury from intrinsic (dose-dependent, predictable: acetaminophen) or idiosyncratic (host-dependent, unpredictable: flucloxacillin)…
NOAEL / benchmark dose
Highest tested dose producing no statistically or biologically significant adverse effect (NOAEL). Modern refinement: benchmark-dose BMD,…
Risk assessment framework
Four-step NRC (1983): hazard identification, dose–response assessment, exposure assessment, risk characterisation. Produces margin of…
Haber's rule: C·t = k (constant-C toxicity); time-integrated dose D = ∫C(s) ds
Haber's rule framework — the canonical time-integrated-dose model for acute inhalation toxicity (Haber 1924 WWI chemical-warfare-agent…
Weibull: F(D) = 1−exp(−(D/α)^β); shape β, scale α; LD_50 = α·log(2)^{1/β}
Weibull dose-response framework — the canonical parametric quantal-response-curve family in acute toxicology (Weibull 1951 reliability…
Probit LD_50: P(death | log D) = Φ((log D − μ)/σ); LD_50 = 10^μ; slope 1/σ normal
Probit LD_50 framework — the canonical log-normal quantal-response-curve model in classical toxicology (Bliss 1934 probit transformation;…
Haber: t_eff=k/C; 2C halves t_eff; D(t)=C·t; exp-decay D(t)=C_0/λ·(1−e^{−λt}); D(∞)=C_0/λ
Sympy-exact symbolic witness of Haber's rule time-to-effect canonical form and the exponentially-decaying-exposure generalisation. Setup:…
Weibull: F=1−exp(−(D/α)^β); LD_50=α·log(2)^{1/β}; at β=1: LD_50=α·ln2; F(α)=1−1/e
Sympy-exact symbolic witness of the Weibull dose-response canonical form, LD_50 identity, and characteristic-dose anchor. Setup: D, α, β —…
Probit: P = 1/2 − erf(√2(μ−x)/(2σ))/2; P(μ)=1/2; slope@LD_50 = √2/(2√π·σ)
Sympy-exact symbolic witness of the probit dose-response canonical form and its LD_50 and slope anchors. Setup: x (log-dose), μ…
Dose makes poison (Paracelsus 1538)
Paracelsus 1538 'sola dosis facit venenum'; foundational text in toxicology.
LD50 (Trevan 1927)
J Trevan 1927 LD50 standard; modern OECD-GHS + 1996 acute-toxicity-assessment alternatives.
Benchmark dose (Crump 1984)
K Crump 1984 BMD; modern EPA benchmark-dose-modeling + replaces NOAEL/LOAEL approach.
AOP (Ankley 2010)
Ankley 2010 + Vinken 2013 adverse-outcome-pathway framework; modern OECD + ECHA risk-assessment standard.
Microplastic toxicity (Lehner 2019)
Lehner 2019 + Leslie 2022 blood-microplastic + Ragusa 2021 placental; modern emerging contaminant of concern.
Paracelsus (1538)
Paracelsus 1538 'sola dosis facit venenum'; foundational text in toxicology; modern dose-response Hill-coeff + safe-low-dose.
LD50 (Trevan 1927)
J Trevan 1927 LD50 probit-method; modern OECD-up-down + non-animal NAMs alternatives + 2024 EPA-cosmetic-cruelty-free.
Haber's rule (1924)
F Haber 1924 toxic-dose c×t=k; modern AEGL Acute-Exposure-Guideline-Levels + chemical-warfare emergency-response thresholds.
Biotransformation (Müller 1948)
R Williams 1948 + Brodie 1950s detoxification phase-I/II; modern CYP450 + UGT + GST + drug-drug-interaction predictions.
Thalidomide (McBride 1961)
W McBride-W Lenz 1961 thalidomide-phocomelia; modern teratology + Kefauver-Harris 1962 + R/S-thalidomide racemization.
Toxicogenomics (Fielden 2002)
M Fielden 2002 + Hamadeh 2002 toxicogenomics; modern Tox21 + 10k-cmpd HTS + ToxCast 2007 + ML predictivity.