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Application in various fields
Importance in pharmacology
Toxicity measurement
Measuring drug efficacy
Agonists and antagonists
Parameters for curve plotting
Curve characteristics
Mathematical treatment
References 
Further reading 

A dose-response curve is the graphical representation of a dose-response relationship, the magnitude of response of an organism from exposure to drugs and chemical interactors. Usually, dose is concerned with the concentration of the drug applied in in vitro or in vivo experiments, though it may also be manipulated by dosing interval, exposure duration, and various other parameters.

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Application in various fields

Measuring and plotting the response to exposure to non-chemical agents such as radiation is nominally termed a stimulus-response curve. However, it is usually also termed a dose-response curve when applied to therapeutic research.

Any condition that can be applied to an organism and the response measured may be plotted in a dose-response curve, such as the growth rate of plants under exposure to differing magnitudes of light, temperature, and sound.

Given the general applicability of dose-response curves to many areas of investigation, they are used throughout the sciences, in epidemiology for risk assessment purposes, and in materials science for establishing tensile strength, for example.

Importance in pharmacology

However, dose-response curves are perhaps most associated with pharmacology, where they are utilized extensively to establish the safety and efficacy of drugs, therapeutics, environmental toxins, and novel treatments within a wide range of living organisms.

Toxicity measurement

One of the most commonly measured parameters concerning dose-response curves is the toxicity of a chemical, drug, or toxin towards a specific cell line or tissue in vitro, for example, or animal or genetic sub-group in vivo. In this case, the stimulus under investigation is applied to the organism of interest, and the toxicity is directly interpreted from the dose required to kill a proportion of the population.

Pharmacodynamics – Part 2: Dose-response Relationship

In the USA, the FDA lays out the appropriate protocols for determining the median lethal dose (LD50), the quantity of a substance that will, on average, kill half of the population of many commercially available products. This value is inferred from dose-response curves and is useful in determining safe exposure limits to various chemicals for humans and animals.

Measuring drug efficacy

While the LD50 is concerned with the proportion of organisms killed by drug exposure, a more generic measure of drug efficacy is the median effective dose (ED50), the dose required to produce any specified response in 50% of the population.

For chemotherapeutic drugs, these terms may be synonymous during in vitro assays where the experiments aim to measure the magnitude of the cell-killing effect, but most drugs are more concerned with inducing some other therapeutic effect in the organism for which a dose-response curve can plot the influence.

Agonists and antagonists

A chemical stimulus may act as an agonist, which interacts with a receptor belonging to the organism to produce a response, or an antagonist, which blocks access to receptors by an agonist and thereby inhibits response. Generally, cell receptor activation results in chemical and electronic signaling within the cell to produce some measurable effect, such as the production or inhibition of a particular protein or transporter.

Parameters for curve plotting

Depending on the ultimate downstream effects of a stimulant on the organism, one or multiple parameters will be selected to plot a dose-response curve to demonstrate this influence best. For example, if the purpose of an applied drug is to promote the production of a particular enzyme, then fluorescent probes specific to that enzyme could be employed in combination with flow cytometry to provide quantitative information regarding enzyme concentration.

The toxicity of the applied drug could also be simultaneously assessed and plotted in a separate dose-response curve by using a second fluorophore sensitive to cells undergoing apoptosis. In vivo dose-response experiments usually also track a number of physical and biochemical parameters to establish the influence of the applied stimulus. Physical parameters include animal weight, lesion and tumor size, appetite, organ condition, and many others, while blood and tissue samples can track the biochemical response to stimulus exposure.

Curve characteristics

The dose of the applied stimulus is generally plotted on the X axis of the dose-response curve, with the magnitude of response on the Y axis. With these axes, most dose-response curves are sigmoidal, with an exponentially increasing effect per dose unit until a point where increasing the dose has a gradually lesser relative influence on response. Once plotted, the gradient of the dose-response curve can be used to infer the EC50 or other specific metric of interest.

Mathematical treatment

Numerous mathematical protocols have been developed for the treatment of dose-response data, often for highly particular applications, but some of the most common extrapolations include the above-mentioned LD50 and EC50, in addition to median inhibitory concentration (IC50), the concentration required to inhibit a specific function such as protein transcription or cell division, which is perhaps the most commonly reported in determination of drug efficacy.

References

  • Steenland & Deddens (2004) A practical guide to dose-response analyses and risk assessment in occupational epidemiology. Epidemiology, 15(1). https://pubmed.ncbi.nlm.nih.gov/14712148/
  • Huot et al. (2011) The effect of radiation dose on the tensile and impact toughness of highly cross-linked and remelted ultrahigh-molecular weight polyethylenes. J Biomed Mater Res B Appl Biomater, 97(2) https://pubmed.ncbi.nlm.nih.gov/21394903/
  • Goldoni & Johansson (2007) A mathematical approach to study combined effects of toxicants in vitro: Evaluation of the Bliss independence criterion and the Loewe additivity model. Toxicology in vitro, 21(5) https://www.sciencedirect.com/science/article/pii/S0887233307000677
  • WHO (2020) Dose-response assessment and derivation of health-based guidance values. https://cdn.who.int/media/docs/default-source/food-safety/publications/chapter5-dose-response.pdf?sfvrsn=32edc2c6_5

Further Reading

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Last Updated: Sep 8, 2023

Written by

Michael Greenwood

Michael graduated from the University of Salford with a Ph.D. in Biochemistry in 2023, and has keen research interests towards nanotechnology and its application to biological systems. Michael has written on a wide range of science communication and news topics within the life sciences and related fields since 2019, and engages extensively with current developments in journal publications.