dose–response relationship

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 organisms 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.{{cite book |author= Lockheed Martin |publisher= United States Environmental Protection Agency, Office of Environmental Information |title=Benchmark Dose Software (BMDS) Version 2.1 User's Manual Version 2.0 |edition= Draft |issue= Doc No.: 53–BMDS–RPT–0028|year=2009|location=Washington, DC |url= http://nepis.epa.gov/Exe/ZyPDF.cgi/P1006XT8.PDF?Dockey=P1006XT8.PDF|author-link= Lockheed Martin }} The U.S. Food and Drug Administration also has guidance to elucidate dose–response relationships{{cite web|url=https://www.fda.gov/regulatory-information/search-fda-guidance-documents/exposure-response-relationships-study-design-data-analysis-and-regulatory-applications|title=Exposure-Response Relationships — Study Design, Data Analysis, and Regulatory Applications|website=Food and Drug Administration|date=26 March 2019}} during drug development. 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.

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).

{{clear right}}

{{clear left}}

File:Dose_response_antagonist.jpgs of 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.]]

{{missing information|section|All the other models in drug development like "Emax"; try {{doi|10.1007/0-387-33706-7_10}} § 10.2|date=April 2023}}

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.{{citation needed|reason=this seems wrong|date=April 2019}}

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–Kärber method.{{cite journal |last1= Hamilton |first1= MA |last2= Russo |first2= RC |last3= Thurston |first3= RV |title= Trimmed Spearman–Karber method for estimating median lethal concentrations in toxicity bioassays |journal= Environmental Science & Technology |volume= 11 |issue= 7 |year= 1977 |pages= 714–9 |doi= 10.1021/es60130a004|bibcode= 1977EnST...11..714H }} Empirical models based on nonlinear regression are usually preferred over the use of some transformation of the data that linearizes the dose-response relationship.{{cite book |last1= Bates |first1= Douglas M. |last2= Watts |first2= Donald G. |title= Nonlinear Regression Analysis and its Applications |year= 1988 |publisher= Wiley |isbn= 9780471816430 |page= 365}}

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 [https://hps.org/hpspublications/historylnt/episodeguide.html documentary series] on the origins of the linear no-threshold (LNT) model though the society has not adopted a policy on LNT."

{{Main article|Hill equation (biochemistry)}}

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 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.{{cite journal |last1=Di Veroli |first1=Giovanni Y. |last2=Fornari |first2=Chiara |last3=Goldlust |first3=Ian |last4=Mills |first4=Graham |last5=Koh |first5=Siang Boon |last6=Bramhall |first6=Jo L. |last7=Richards |first7=Frances M. |last8=Jodrell |first8=Duncan I. |title=An automated fitting procedure and software for dose-response curves with multiphasic features |journal=Scientific Reports |date=1 October 2015 |volume=5 |issue=1 |pages=14701 |doi=10.1038/srep14701 |pmid=26424192 |bibcode=2015NatSR...514701V |doi-access=free |pmc=4589737 }}

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

: $\backslash frac\{E\}\{E\_\{\backslash mathrm\{max\}\}\}=\backslash frac\{[A]^n\}\{\backslash text\{EC\}\_\{50\}^n+[A]^n\}=\backslash frac\{1\}\{1+\backslash left(\backslash frac\{\backslash mathrm\{EC\}\_\{50\}\}\{[A]\}\backslash right)^\{n\}\}${{cite journal |last1=Neubig |first1=Richard R. |last2=Spedding |first2=Michael |last3=Kenakin |first3=Terry |last4=Christopoulos |first4=Arthur |last5=International Union of Pharmacology Committee on Receptor Nomenclature and Drug |first5=Classification. |title=International Union of Pharmacology Committee on Receptor Nomenclature and Drug Classification. XXXVIII. Update on Terms and Symbols in Quantitative Pharmacology |journal=Pharmacological Reviews |date=December 2003 |volume=55 |issue=4 |pages=597–606 |doi=10.1124/pr.55.4.4 |pmid=14657418 |s2cid=1729572 }}

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.{{cite journal|title=Single Channel Properties of P2X2 Purinoceptors |last1=Ding|first1=S|last2=Sachs|first2=F|publisher= The Rockefeller University Press |year=1999|journal=J. Gen. Physiol.|volume=113|issue=5|pages=695–720|pmc=2222910|pmid=10228183|doi=10.1085/jgp.113.5.695}}

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.

The E_max 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:{{cite book |last1=Macdougall |first1=James |chapter=Analysis of Dose–Response Studies—Emax Model |title=Dose Finding in Drug Development |series=Statistics for Biology and Health |date=2006 |pages=127–145 |doi=10.1007/0-387-33706-7_9|isbn=978-0-387-29074-4 }}

: $E\; =\; E\_0\; +\; \backslash frac\{\{[A]\}^n\; \backslash times\; \{E\_\{\backslash mathrm\{max\}\}\}\}\{\{\{[A]\}^n\; +\; \backslash mathrm\{EC\}\_\{50\}^n\}\}$

Compare with a rearrangement of Hill:

: $E\_\{\backslash mathrm\{hill\}\}\; =\; \backslash frac\{\{[A]\}^n\; \backslash times\; \{E\_\{\backslash mathrm\{max\}\}\}\}\{\{\{[A]\}^n\; +\; \backslash mathrm\{EC\}\_\{50\}^n\}\}$

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

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 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) {{doi|10.1038/srep11376}}

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.{{cite journal |last1=Vandenberg |first1=Laura N. |last2=Colborn |first2=Theo |last3=Hayes |first3=Tyrone B. |last4=Heindel |first4=Jerrold J. |last5=Jacobs |first5=David R. |last6=Lee |first6=Duk-Hee |last7=Shioda |first7=Toshi |last8=Soto |first8=Ana M. |last9=vom Saal |first9=Frederick S. |last10=Welshons |first10=Wade V. |last11=Zoeller |first11=R. Thomas |last12=Myers |first12=John Peterson |title=Hormones and Endocrine-Disrupting Chemicals: Low-Dose Effects and Nonmonotonic Dose Responses |journal=Endocrine Reviews |date=2012 |volume=33 |issue=3 |pages=378–455 |doi=10.1210/er.2011-1050 |pmid=22419778 |pmc=3365860 }}

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.{{fact|date=March 2020}}

{{Expand section|date=April 2019}}

Schild analysis may also provide insights into the effect of drugs.

{{div col|colwidth=30em}}

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

{{div col end}}

{{Reflist}}

• [http://www.readerfit.com Online Tool for ELISA Analysis]
• [https://www.aatbio.com/tools/ic50-calculator Online IC₅₀ Calculator]
• [http://www.ecotoxmodels.org Ecotoxmodels] A website on mathematical models in ecotoxicology, with emphasis on toxicokinetic-toxicodynamic models
• [http://info.collaborativedrug.com/dose-response-curve CDD Vault, Example of Dose-Response Curve fitting software]

{{Pharmacology|state=collapsed}}

{{DEFAULTSORT:Dose-response relationship}}

Category:Pharmacodynamics

Category:Toxicology