# EC50

Half maximal effective concentration (${\displaystyle {\ce {EC_{50}}}}$) refers to the concentration of a drug, antibody or toxicant which induces a response halfway between the baseline and maximum after a specified exposure time.[1] ${\displaystyle {\ce {EC_{50}}}}$ is also written as ${\displaystyle {\ce {[A]_{50}}}}$.[2] It is commonly used as a measure of a drug's potency, and the use of ${\displaystyle {\ce {EC_{50}}}}$is preferred over that of 'potency', which has been criticised for its vagueness.[3] ${\displaystyle {\ce {EC_{50}}}}$is a measure of concentration, expressed in molar units (M), where 1 M is equivalent to 1 mol/L.

The ${\displaystyle {\ce {EC_{50}}}}$of a graded dose response curve therefore represents the concentration of a compound where 50% of its maximal effect is observed.[4] The ${\displaystyle {\ce {EC_{50}}}}$of a quantal dose response curve represents the concentration of a compound where 50% of the population exhibit a response,[5] after a specified exposure duration.[clarification needed]

The ${\displaystyle {\ce {EC_{50}}}}$is also related to IC50 which is a measure of a compound's inhibition (50% inhibition). For competition binding assays and functional antagonist assays IC50 is the most common summary measure of the dose-response curve. For agonist/stimulator assays the most common summary measure is the ${\displaystyle {\ce {EC_{50}}}}$.[6]

The ${\displaystyle {\ce {EC_{50}}}}$should not be confused with the affinity constant. While the former reflects the drug the drug concentration needed for a level of tissue response, the latter reflects the drug concentration needed for an amount of receptor binding.

The ${\displaystyle {\ce {[A]}}}$ at which ${\displaystyle {\ce {E}}}$ is 50% of ${\displaystyle {\ce {E_{max}}}}$ is termed the half maximal effective concentration and is abbreviated ${\displaystyle {\ce {EC_{50}}}}$, or rarely ${\displaystyle {\ce {[A]_{50}}}}$. The term "potency" refers to the ${\displaystyle {\ce {EC_{50}}}}$ value. The lower the ${\displaystyle {\ce {EC_{50}}}}$, the less the concentration of a drug is required to produce 50% of maximum effect and the higher the potency. The ${\displaystyle {\ce {EC_{10}}}}$ and ${\displaystyle {\ce {EC_{90}}}}$ concentrations to induce 10% and 90% maximal responses are defined similarly.

## Calculation of ${\displaystyle {\ce {EC_{50}}}}$

Biological responses to ligand concentrations typically following a sigmoidal function. The inflection point at which the increase in response with increasing ligand concentration begins to slow is the ${\displaystyle {\ce {EC_{50}}}}$ , which can be mathematically determined by derivation of the best-fit line. While relying on a graph for estimation is more convenient, this typical method yields less accurate results and less precise.[7]

## Relationship to Affinity

A drug's potency is dependent on the drug's affinity and efficacy. Affinity describes how well a drug can bind to a receptor. Faster or stronger binding is represented by a higher affinity, or equivalently a lower dissociation constant. Efficacy is the relationship between receptor occupancy and the ability to initiate a response at the molecular, cellular, tissue or system level. The response or effect, ${\displaystyle {\ce {E}}}$ , is dependent on both the binding of the drug and the drug-bound receptor. The agonist that binds to the receptor and initiates the response is usually abbreviated ${\displaystyle {\ce {A}}}$  or ${\displaystyle {\ce {D}}}$ . At low agonist concentrations, ${\displaystyle {\ce {[A]}}}$ , the response, ${\displaystyle {\ce {E}}}$  is immeasurably low but at higher ${\displaystyle {\ce {[A]}}}$ , ${\displaystyle {\ce {E}}}$  becomes measurable. ${\displaystyle {\ce {E}}}$  increases with ${\displaystyle {\ce {[A]}}}$  until at sufficiently high ${\displaystyle {\ce {[A]}}}$ , when ${\displaystyle {\ce {E}}}$  plateaus towards an asymptotic maximum attainable response, ${\displaystyle {\ce {E_{max}}}}$ .

## Relation to the Hill Equation

Many different equations can be used to derive an EC50.[citation needed] One possible function of the agonist concentration, [A], is the Hill equation, a special case of a rectangular hyperbola:

${\displaystyle E={\frac {E_{\mathrm {max} }}{1+\left({\frac {{\ce {EC50}}}{{\ce {[A]}}}}\right)^{n_{H}}}}}$ [8]

where E is the observed response or effect above baseline, and nH, the Hill coefficient reflects the slope of the curve.[9]

The EC50 represents the point of inflection of the Hill equation, beyond which increases of [A] have less impact on E. In dose response curves, the logarithm of [A] is often taken, turning the Hill equation into a sigmoidal logistic function. In this case, the EC50 represents the rising section of the sigmoid curve.

## Limitations

The effects of a stressor or drug generally depend on the exposure time. Therefore, the ${\displaystyle {\ce {EC_{50}}}}$ (and similar statistics) will be a function of exposure time. The exact shape of this time function will depend upon the stressor (e.g., the specific toxicant), its mechanism of action, the organism exposed, etc. This time dependency hampers the comparison of potency or toxicity between compounds and between different organisms.

A drug will not have a single value of ${\displaystyle {\ce {EC_{50}}}}$  due to different tissues having different sensitivities to the drug (in part due to tissue specific receptor expression).[citation needed] Furthermore, ${\displaystyle {\ce {EC_{50}}}}$ is dependent on many factors including species, tissue and cell type and genetics.[citation needed]

## pEC50

Morphine is a strong agonist at mu opioid receptors, which is reflected in its ${\displaystyle {\ce {EC_{50}}}}$ of 50-100 nM at retinoic acid treated human neuroblastoma cells.[10] Conversely, acetylcholine at the human M3 muscarinic receptor is comparatively weaker, as it has an ${\displaystyle {\ce {EC_{50}}}}$ of 219 nM.[11] This indicates the wide range of EC50s of drugs; they are typically in the nM to mM range. Hence, it is often more practical to refer to the logarithmically transformed ${\displaystyle {\ce {pEC_{50}}}}$ values: in this case, 7-7.30 for morphine and 6.66 for acetylcholine. Although these values demonstrate the possible range of ${\displaystyle {\ce {EC_{50}}}}$ , they may not be directly compared as they are from different cell and tissue types. Hence, the EC50 is often expressed as ${\displaystyle {\ce {pEC_{50}}}}$ instead of ${\displaystyle {\ce {EC_{50}}}}$ , where: ${\displaystyle {\ce {pEC50}}=-\log _{10}({\ce {EC50}})}$ .

## References

1. ^ Introducing dose response curves Archived 2007-02-19 at the Wayback Machine, Graphpad Software
2. ^ https://www.guidetopharmacology.org/pdfs/termsAndSymbols.pdf
3. ^ https://www.guidetopharmacology.org/pdfs/termsAndSymbols.pdf
4. ^ EC50 definition
5. ^ "definition of EC50 for quantal dose response curve". Archived from the original on 2007-02-20. Retrieved 2019-04-16.
6. ^ Assay Operations for SAR Support Archived 2006-11-29 at the Wayback Machine NIH Chemical Genomics Center
7. ^ Assay Operations for SAR Support Archived 2006-11-29 at the Wayback Machine NIH Chemical Genomics Center
8. ^ https://www.guidetopharmacology.org/pdfs/termsAndSymbols.pdf
9. ^ EC50 equation Archived 2012-04-17 at the Wayback Machine - see page 5
10. ^ https://www.ncbi.nlm.nih.gov/pubmed/2834542
11. ^ http://drugcentral.org/drugcard/65