Dose–response relationship

"Dose-response" redirects here. For the academic journal, seeDose–Response.

Thedose–response relationship,orexposure–response relationship,describes the magnitude of theresponseof anorganism,as afunctionof exposure (ordoses) to astimulusorstressor(usually achemical) after a certain exposure time.Dose–response relationships can be described bydose–response curves.This is explained further in the following sections. Astimulus response functionorstimulus response curveis defined more broadly as the response from any type of stimulus, not limited to chemicals.

A dose response curve showing the normalised tissue response to stimulation by anagonist.Low doses are insufficient to generate a response, while high doses generate a maximal response. The steepest point of the curve corresponds with anEC₅₀of 0.7molar

Motivation for studying dose–response relationships

Studying dose response, and developing dose–response models, is central to determining "safe", "hazardous" and (where relevant) beneficial levels and dosages for drugs, pollutants, foods, and other substances to which humans or otherorganismsare exposed. These conclusions are often the basis for public policy. TheU.S. Environmental Protection Agencyhas developed extensive guidance and reports on dose–response modeling and assessment, as well as software.TheU.S. Food and Drug Administrationalso has guidance to elucidate dose–response relationshipsduringdrug development.Dose response relationships may be used in individuals or in populations. The adageThe dose makes the poisonreflects how a small amount of a toxin has no significant effect, while a large amount may be fatal. This reflects how dose–response relationships can be used in individuals. In populations, dose–response relationships can describe the way groups of people or organisms are affected at different levels of exposure. Dose response relationships modelled by dose response curves are used extensively in pharmacology and drug development. In particular, the shape of a drug's dose–response curve (quantified by EC50, nH and ymax parameters) reflects the biological activity and strength of the drug.

Example stimuli and responses

Some example measures for dose–response relationships are shown in the tables below. Each sensory stimulus corresponds with a particularsensory receptor,for instance the nicotinic acetylcholine receptor for nicotine, or themechanoreceptorfor mechanical pressure. However, stimuli (such as temperatures or radiation) may also affect physiological processes beyond sensation (and even give the measurable response of death). Responses can be recorded as continuous data (e.g. force of muscle contraction) or discrete data (e.g. number of deaths).

Example Stimulus		Target
Drug/Toxindose	Agonist (e.g.nicotine,isoprenaline)	Biochemical receptors, Enzymes, Transporters
	Antagonist (e.g.ketamine,propranolol)
	Allosteric modulator (e.g.Benzodiazepine)
Temperature		Temperature receptors
Sound levels		Hair cells
Illumination/Light intensity		Photoreceptors
Mechanical pressure		Mechanoreceptors
Pathogen dose (e.g.LPS)		n/a
Radiationintensity		n/a

System Level	Example Response
Population(Epidemiology)	Death,loss of consciousness
Organism/Whole animal (Physiology)	Severity of lesion,blood pressure,heart rate, extent of movement, attentiveness,EEGdata
Organ/Tissue	ATP production, proliferation, muscle contraction, bile production, cell death
Cell(Cell biology,Biochemistry)	ATP production, calcium signals, morphology, mitosis

Analysis and creation of dose–response curves

Semi-log plotsof the hypothetical response to agonist, log concentration on the x-axis, in combination with different antagonist concentrations. The parameters of the curves, and how the antagonist changes them, gives useful information about the agonist's pharmacological profile. This curve is similar but distinct from that, which is generated with the ligand-bound receptor concentration on the y-axis.

Construction of dose–response curves

Adose–response curveis acoordinate graphrelating the magnitude of a dose (stimulus) to the response of a biological system. A number of effects (orendpoints) can be studied. The applied dose is generally plotted on the X axis and the response is plotted on the Y axis. In some cases, it is thelogarithmof the dose that is plotted on the X axis. The curve is typicallysigmoidal,with the steepest portion in the middle. Biologically based models using dose are preferred over the use of log(dose) because the latter can visually imply athreshold dosewhen in fact there is none.

Statistical analysis of dose–response curves may be performed by regression methods such as theprobit modelorlogit model,or other methods such as the Spearman–Kärber method.Empirical models based on nonlinear regression are usually preferred over the use of some transformation of the data that linearizes the dose-response relationship.

Typical experimental design for measuring dose-response relationships areorgan bathpreparations,ligand binding assays,functional assays,andclinical drug trials.

Specific to response to doses of radiation the Health Physics Society (in the United States) has published adocumentary serieson the origins of the linear no-threshold (LNT) model though the society has not adopted a policy on LNT. "

Hill equation

Main article:Hill equation (biochemistry)

Logarithmic dose–response curves are generallysigmoidal-shapeand monotonic and can be fit to a classicalHill equation.The Hill equation is alogistic functionwith respect to the logarithm of the dose and is similar to alogit model.A generalized model for multiphasic cases has also been suggested.

TheHill equationis the following formula, where$E$is the magnitude of the response,${\ce {[A]}}$is the drug concentration (or equivalently, stimulus intensity) and$\mathrm {EC} _{50}$is the drug concentration that produces a 50% maximal response and$n$is theHill coefficient.

${\frac {E}{E_{\mathrm {max} }}}={\frac {[A]^{n}}{{\text{EC}}_{50}^{n}+[A]^{n}}}={\frac {1}{1+\left({\frac {\mathrm {EC} _{50}}{[A]}}\right)^{n}}}$

The parameters of the dose response curve reflect measures ofpotency(such as EC50, IC50, ED50, etc.) and measures of efficacy (such as tissue, cell or population response).

A commonly used dose–response curve is theEC₅₀curve, the half maximal effective concentration, where the EC₅₀point is defined as the inflection point of the curve.

Dose response curves are typically fitted to theHill equation.

The first point along the graph where a response above zero (or above the control response) is reached is usually referred to as a threshold dose. For most beneficial or recreational drugs, the desired effects are found at doses slightly greater than the threshold dose. At higher doses, undesiredside effectsappear and grow stronger as the dose increases. The more potent a particular substance is, the steeper this curve will be. In quantitative situations, the Y-axis often is designated by percentages, which refer to the percentage of exposed individuals registering a standard response (which may be death, as inLD₅₀). Such a curve is referred to as a quantal dose–response curve, distinguishing it from a graded dose–response curve, where response is continuous (either measured, or by judgment).

The Hill equation can be used to describe dose–response relationships, for example ion channel-open-probability vs.ligandconcentration.

Dose is usually in milligrams,micrograms,or grams per kilogram of body-weight for oral exposures or milligrams per cubic meter of ambient air for inhalation exposures. Other dose units include moles per body-weight, moles per animal, and for dermal exposure, moles per square centimeter.

E_maxmodel

The E_maxmodel is a generalization of the Hill equation where an effect can be set for zero dose. Using the same notation as above, we can express the model as:

$E=E_{0}+{\frac {{[A]}^{n}\times {E_{\mathrm {max} }}}{{[A]}^{n}+\mathrm {EC} _{50}^{n}}}$

Compare with a rearrangement of Hill:

$E_{\mathrm {hill} }={\frac {{[A]}^{n}\times {E_{\mathrm {max} }}}{{[A]}^{n}+\mathrm {EC} _{50}^{n}}}$

The E_maxmodel is the single most common model for describing dose-response relationship in drug development.

Shape of dose-response curve

The shape of dose-response curve typically depends on the topology of the targeted reaction network. While the shape of the curve is oftenmonotonic,in some cases non-monotonic dose response curves can be seen.

Limitations

The concept of linear dose–response relationship, thresholds, and all-or-nothing responses may not apply to non-linear situations. Athreshold modelorlinear no-threshold modelmay be more appropriate, depending on the circumstances. A recent critique of these models as they apply to endocrine disruptors argues for a substantial revision of testing and toxicological models at low doses because of observed non-monotonicity,i.e. U-shaped dose/response curves.

Dose–response relationships generally depend on the exposure time and exposure route (e.g., inhalation, dietary intake); quantifying the response after a different exposure time or for a different route leads to a different relationship and possibly different conclusions on the effects of the stressor under consideration. This limitation is caused by the complexity of biological systems and the often unknown biological processes operating between the external exposure and the adverse cellular or tissue response.

Schild analysis

Schild analysismay also provide insights into the effect of drugs.

See also

• Arndt–Schulz rule
• Ceiling effect (pharmacology)
• Certain safety factor
• Hormesis
• Pharmacodynamics
• Spatial epidemiology
• Weber–Fechner law
• Dose fractionation

External links

• Online Tool for ELISA Analysis
• Online IC₅₀Calculator
• EcotoxmodelsA website on mathematical models inecotoxicology,with emphasis on toxicokinetic-toxicodynamic models
• CDD Vault, Example of Dose-Response Curve fitting software