Dose–response relationship

Some example measures for dose–response relationships are shown in the tables below. Each sensory stimulus corresponds with a particular sensory receptor, for instance the nicotinic acetylcholine receptor for nicotine, or the mechanoreceptor 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).

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 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 or logit model, or other methods such as the Spearman-Karber method.[5] Empirical models based on nonlinear regression are usually preferred over the use of some transformation of the data that linearizes the dose-response relationship.[6]

Typical experimental design for measuring dose-response relationships are organ bath preparations, ligand binding assays, functional assays, and clinical drug trials.

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

Logarithmic dose–response curves are generally sigmoidal and monotonic and can be fit to a classical Hill equation. The Hill equation is a logistic function with respect to the logarithm of the dose and is similar to a logit model. A generalized model for multiphasic cases has also been suggested.[7]

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

${\displaystyle {\frac {E}{E_{\mathrm {max} }}}={\frac {1}{1+\left({\frac {\mathrm {EC} _{50}}{[A]}}\right)^{n}}}}$[8]

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 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 LD₅₀). 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 concentration.[9]

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.