Dose-Response

ENVR430

Oct 13, 2008

Casarett and Doull, Chapter 2, pp. 18-27(6th Edn) Chapter 2, pp. 19-26 (7th Edn)

Timbrell Chapter 2, pp. 7-25 (3rd Edn)

Dose-Response

Increasing Dose

Increasing Response

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The J-shaped curve(hormesis)

Increasing Dose

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Dose-Response

Dose

Increasing Response

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Threshold Dose • No effect level

• Response at low dose is so low as to be insignificant – A SAFE DOSE

• NEL, No Effects Level

• NOEL, No Observed Effects Level

• NOAEL, No Observed Adverse Effects Level

Some Acronyms

The basis for regulation

Food Safety, Environmental • ADI, Acceptable Daily Intake

– AWI, AMI etc• TDI, Tolerable Daily Intake• MCL, Maximum Contaminant Level (SDWA)• SF, UF, MF: safety, uncertainty, modifying factors

• TLV, Threshold Limit Value• TLV-C, ceiling level• STEL, Short-term exposure limit• TWA, Time-Weighted Average (8h day, 40 h week)

Occupational exposure limits

Above the threshold

• Dose-response is linear ? y = ax + b

• Dose-response is not linear

Defining the shape of the dose-response curve

Theoretical treatment: Assume Quantal or dichotomous response

Quantal response Dichotomous response

• Corresponds to “occupied receptor”

• Examples: Mortality, Tumor incidence

• Assumes normal (Gaussian) distribution

• Maximum 100% affected

Basic assumptions• (a) The response is causally related to the

compound administered• (b) The response is a function of the

concentration at the site of action• (c) The concentration at the site of action is

related to the external dose• (d) An interaction at the site of action initiates

a proportional response• (e) The crucial interaction involves reversible

formation of a receptor-toxin complex

Receptors• Usually proteins

– Located on outside of cell wall, or inside cell

– Interact with ligands

Receptors important in Pharmacology– Agonists and antagonists of neurotransmitters:

cholinergic receptors: acetylcholine; nicotinic receptors: skeletal muscle, autonomic ganglia; muscarinic receptors: smooth muscle, heart, exocrine glands

– Adrenergic receptors: dopamine, endorphins, enkephalins, histamine

– Hormone receptors: Insulin, cortisone (glucocorticoids), estrogen, progesterone, testosterone, prostaglandins

– Drug receptors: Benzodiazepines

Receptors important in Toxicology

–Ah (TCDD) receptor

–CAR, PPARα

–Steroid receptors

Reversible formation of a receptor-toxin complex

k1

R + T R-T

k-1

R = receptor

T = toxic compound

R-T = receptor-compound complex

k1 and k-1 are rate constants for formation and dissociation (respectively) of the complex R-T

k1 * [R] * [T] = k-1 * [R-T]

KT is the dissociation constant of the complex,

= k-1/k1 = [R] * [T] / [R-T]

Total concentration of receptors [Rt] = [R] + [R-T], or

[R] = [Rt] - [R-T]

KT = ([Rt] - [R-T])*[T] / [R-T] = ([Rt]*[T] - [R-T]*[T])/[R-T]

Proportion of total receptors that are occupied = [R-T]/[Rt]

[R-T] = ([Rt] - [R-T])* [T] / KT = [Rt]*[T]/KT - [R-T] * [T]/KT

[R-T] + [R-T]*[T]/KT = [Rt] * [T] /KT = [R-T] * (1 + [T]/KT)

[R-T] = ([Rt] * [T]/KT) / (1 + [T]/KT)

[R-T]/[Rt] = [T] / KT * (1 + [T]/KT) = [T] / (KT + KT*[T]/KT)

[R-T]/[Rt] = [T] / (KT + [T]

• Response or effect e is proportional to [R-T]

• Maximum response Emax occurs when all the receptors are occupied

• e / Emax = [R-T] / [Rt]

• [R-T]/[Rt] = [T] / (KT + [T])

• then e / Emax = [T] / (KT + [T])

• and e = Emax * [T] / (KT + [T])

When T = 0, e = 0

When all receptors are occupied:

[R-T] = [Rt]

e = Emax

Dose (mg/kg)

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Other Considerations• Duration of exposure

• Interaction may not be reversible

• Repair or removal of complex R-T may be important

• Response may be multi-step, binding of T to R may not be the rate-limiting step

• Uniform population - no significant inter-individual differences in response

Dose (mg/kg)0.1 1 10 100 1000 10000

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LD50 Lethal dose

LC50 Lethal concentration

ED50 Effective dose

Some Acute Oral LD50 Values

Category Dose Species Chemical(mg/kg body weight)

Practically nontoxic15 000

Slightly toxic 10 000 Mouse Ethanol 5 000

Moderately toxic 4 900 Rat Glyphosate 750 Rat

Atropine 500

Highly toxic 250 Rat Carbaryl 50

Extremely toxic 13 Rat Parathion 5

Supertoxic 3 Rat Warfarin 0.4 Duck

Aflatoxin B1

Species LD50 (ug/kg body wt)

Guinea-pig 0.5-2

Rat 22-100

Mouse 114-284

Rabbit 10-115

Chicken 25-50

Rhesus monkey < 70

Dog >30-100

Hamster 5051

Species differences in the acute toxicity of dioxin*

*Dioxin: 2,3,7,8-tetrachlorobenzdioxin: TCDD

Oral LD50 Values (mg/kg)

Males Females

Mice 127 137

Rats 355 247

Hamsters 230 249

Rabbits 246 224

Test Compound: Caffeine

Other toxic effects

• Acute / chronic

• Reversible / irreversible

• Immediate / delayed

• Idiosyncratic - hypersensitivity

• Local / systemic

• Target organs

WHERE DO WE MEASURE THE DOSE ?

• External dose

• Internal dose

• Dose at target tissue

• Dose of active species at molecular target of action

Do we have to measure the internal dose ?

Mathematical Models

Kinetics