
The dose–response relationship, or exposure–response relationship, describes the magnitude of the
response of an
organism
An organism is any life, living thing that functions as an individual. Such a definition raises more problems than it solves, not least because the concept of an individual is also difficult. Many criteria, few of them widely accepted, have be ...
, as a
function of exposure (or
doses) to a
stimulus or
stressor
A stressor is a chemical or biological agent, environmental condition, external stimulus or an event seen as causing stress to an organism. Psychologically speaking, a stressor can be events or environments that individuals might consider dema ...
(usually a
chemical
A chemical substance is a unique form of matter with constant chemical composition and characteristic properties. Chemical substances may take the form of a single element or chemical compounds. If two or more chemical substances can be combin ...
) after a certain exposure time. Dose–response relationships can be described by dose–response curves. This is explained further in the following sections. A stimulus response function or stimulus response curve is defined more broadly as the response from any type of stimulus, not limited to chemicals.
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 other
organism
An organism is any life, living thing that functions as an individual. Such a definition raises more problems than it solves, not least because the concept of an individual is also difficult. Many criteria, few of them widely accepted, have be ...
s are exposed. These conclusions are often the basis for public policy. The
U.S. Environmental Protection Agency has developed extensive guidance and reports on dose–response modeling and assessment, as well as software. The
U.S. Food and Drug Administration also has guidance to elucidate dose–response relationships during
drug development
Drug development is the process of bringing a new pharmaceutical drug to the market once a lead compound has been identified through the process of drug discovery. It includes preclinical research on microorganisms and animals, filing for regu ...
. Dose-response relationships may be used in individuals or in populations. The adage "
the dose makes the poison" reflects how a small amount of a toxin can have no significant effect, while a large amount may be fatal. 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 particular
sensory receptor
Sensory neurons, also known as afferent neurons, are neurons in the nervous system, that convert a specific type of stimulus, via their receptors, into action potentials or graded receptor potentials. This process is called sensory transduc ...
, for instance the nicotinic acetylcholine receptor for nicotine, or the
mechanoreceptor
A mechanoreceptor, also called mechanoceptor, is a sensory receptor that responds to mechanical pressure or distortion. Mechanoreceptors are located on sensory neurons that convert mechanical pressure into action potential, electrical signals tha ...
for 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).
Analysis and creation of dose–response curves
Construction of dose–response curves
A dose–response curve is a
coordinate graph relating the magnitude of a dose (stimulus) to the response of a biological system. A number of effects (or
endpoints) 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 the
logarithm
In mathematics, the logarithm of a number is the exponent by which another fixed value, the base, must be raised to produce that number. For example, the logarithm of to base is , because is to the rd power: . More generally, if , the ...
of the dose that is plotted on the X axis. The curve is typically
sigmoidal, 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 a
threshold dose when in fact there is none.
Statistical analysis of dose–response curves may be performed by regression methods such as the
probit model
In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word is a portmanteau, coming from ''probability'' + ''unit''. The purpose of the model is to es ...
or
logit model
In statistics, the logit ( ) function is the quantile function associated with the standard logistic distribution. It has many uses in data analysis and machine learning, especially in data transformations.
Mathematically, the logit is the ...
, 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 are
organ bath preparations,
ligand binding assay A ligand binding assay (LBA) is an assay, or an analytic procedure, which relies on the binding of ligand molecules to receptors, antibodies or other macromolecules. A detection method is used to determine the presence and amount of the ligand-rece ...
s,
functional assays, and
clinical drug trials.
Specific to response to doses of radiation the Health Physics Society (in the United States) has published
documentary serieson the origins of the linear no-threshold (LNT) model though the society has not adopted a policy on LNT."
Hill equation
Logarithmic dose–response curves are generally
sigmoidal-shape and monotonic and can be fit to a classical
Hill equation. The Hill equation is a
logistic function
A logistic function or logistic curve is a common S-shaped curve ( sigmoid curve) with the equation
f(x) = \frac
where
The logistic function has domain the real numbers, the limit as x \to -\infty is 0, and the limit as x \to +\infty is L.
...
with respect to the logarithm of the dose and is similar to a
logit model
In statistics, the logit ( ) function is the quantile function associated with the standard logistic distribution. It has many uses in data analysis and machine learning, especially in data transformations.
Mathematically, the logit is the ...
. A generalized model for multiphasic cases has also been suggested.
The
Hill equation is the following formula, where
is the magnitude of the response,
/chem> is the drug concentration (or equivalently, stimulus intensity) and is the drug concentration that produces a 50% maximal response and is the Hill coefficient.
:
The parameters of the dose response curve reflect measures of potency (such as EC50, IC50, ED50, etc.) and measures of efficacy (such as tissue, cell or population response).
A commonly used dose–response curve is the EC50 curve, the half maximal effective concentration, where the EC50 point is defined as the inflection point of the curve.
Dose response curves are typically fitted to the Hill 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, undesired side effects
In medicine, a side effect is an effect of the use of a medicinal drug or other treatment, usually adverse but sometimes beneficial, that is unintended. Herbal and traditional medicines also have side effects.
A drug or procedure usually used ...
appear 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 in ). 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. ligand
In coordination chemistry, a ligand is an ion or molecule with a functional group that binds to a central metal atom to form a coordination complex. The bonding with the metal generally involves formal donation of one or more of the ligand's el ...
concentration.
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.
Emax model
The Emax model 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:
:
Compare with a rearrangement of Hill:
:
The Emax model 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 often monotonic
In mathematics, a monotonic function (or monotone function) is a function between ordered sets that preserves or reverses the given order. This concept first arose in calculus, and was later generalized to the more abstract setting of ord ...
, in some cases non-monotonic dose response curves can be seen.[Roeland van Wijk et al., Non-monotonic dynamics and crosstalk in signaling pathways and their implications for pharmacology. Scientific Reports 5:11376 (2015) ]
Limitations
The concept of linear dose–response relationship, thresholds, and all-or-nothing responses may not apply to non-linear situations. A threshold model or linear no-threshold model may 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 analysis may also provide insights into the effect of drugs.
See also
* Arndt–Schulz rule
* Ceiling effect (pharmacology)
* Certain safety factor
* Hormesis
* Pharmacodynamics
Pharmacodynamics (PD) is the study of the biochemistry, biochemical and physiology, physiologic effects of drugs (especially pharmaceutical drugs). The effects can include those manifested within animals (including humans), microorganisms, or comb ...
* Spatial epidemiology
Spatial epidemiology is a subfield of epidemiology focused on the study of the spatial distribution of health outcomes; it is closely related to health geography.
Specifically, spatial epidemiology is concerned with the description and examinat ...
* Weber–Fechner law
The Weber–Fechner laws are two related scientific law, scientific laws in the field of psychophysics, known as Weber's law and Fechner's law. Both relate to human perception, more specifically the relation between the actual change in a physica ...
* Dose fractionation
References
External links
Online Tool for ELISA Analysis
Online IC50 Calculator
Ecotoxmodels
A website on mathematical models in ecotoxicology
Ecotoxicology is the study of the effects of toxic chemicals on biological organisms, especially at the population biology, population, biological community, community, ecosystem, and biosphere levels. Ecotoxicology is a multidisciplinary field, ...
, with emphasis on toxicokinetic-toxicodynamic models
CDD Vault, Example of Dose-Response Curve fitting software
{{DEFAULTSORT:Dose-response relationship
Pharmacodynamics
Toxicology