Cheng-Prusoff equation

The half maximal inhibitory concentration (IC₅₀) is a measure of the potency of a substance in inhibiting a specific biological or biochemical function. IC₅₀ is a quantitative measure that indicates how much of a particular inhibitory substance (e.g. drug) is needed to inhibit, ''in vitro'', a given biological process or biological component by 50%. The biological component could be an enzyme, cell, cell receptor or microorganism. IC₅₀ values are typically expressed as molar concentration.

IC₅₀ is commonly used as a measure of antagonist drug potency in pharmacological research. IC₅₀ is comparable to other measures of potency, such as EC₅₀ for excitatory drugs. EC₅₀ represents the dose or plasma concentration required for obtaining 50% of a maximum effect ''in vivo''.

IC₅₀ can be determined with functional assays or with competition binding assays.

Sometimes, IC₅₀ values are converted to the pIC₅₀ scale.

:$\ce = -\log_ \ce$

Due to the minus sign, higher values of pIC₅₀ indicate exponentially more potent inhibitors. pIC₅₀ is usually given in terms of molar concentration (mol/L, or M), thus requiring IC₅₀ in units of M.

The IC₅₀ terminology is also used for some behavioral measures in vivo, such as a two bottle fluid consumption test. When animals decrease consumption from the drug-laced water bottle, the concentration of the drug that results in a 50% decrease in consumption is considered the IC₅₀ for fluid consumption of that drug.

Functional antagonist assay

The IC₅₀ of a drug can be determined by constructing a dose-response curve and examining the effect of different concentrations of antagonist on reversing agonist activity. IC₅₀ values can be calculated for a given antagonist by determining the concentration needed to inhibit half of the maximum biological response of the agonist. IC₅₀ values can be used to compare the potency of two antagonists.

IC₅₀ values are very dependent on conditions under which they are measured. In general, ''a higher concentration of inhibitor leads to lowered agonist activity.'' IC₅₀ value increases as agonist concentration increases. Furthermore, depending on the type of inhibition, other factors may influence IC₅₀ value; for ATP dependent enzymes, IC₅₀ value has an interdependency with concentration of ATP, especially if inhibition is competitive.

IC₅₀ and affinity

Competition binding assays

In this type of assay, a single concentration of radioligand (usually an agonist) is used in every assay tube. The ligand is used at a low concentration, usually at or below its K_d value. The level of specific binding of the radioligand is then determined in the presence of a range of concentrations of other competing non-radioactive compounds (usually antagonists), in order to measure the potency with which they compete for the binding of the radioligand. Competition curves may also be computer-fitted to a logistic function as described under direct fit.

In this situation the IC₅₀ is the concentration of competing ligand which displaces 50% of the specific binding of the radioligand. The IC₅₀ value is converted to an absolute inhibition constant K_i using the Cheng-Prusoff equation formulated by Yung-Chi Cheng and William Prusoff (see K_i).

Cheng Prusoff equation

IC₅₀ is not a direct indicator of affinity, although the two can be related at least for competitive agonists and antagonists by the Cheng-Prusoff equation. For enzymatic reactions, this equation is:

:$K_i = \frac\ce$

where K_i is the binding affinity of the inhibitor, IC₅₀ is the functional strength of the inhibitor, is fixed substrate concentration and K_m is the Michaelis constant i.e. concentration of substrate at which enzyme activity is at half maximal (but is frequently confused with substrate affinity for the enzyme, which it is not).

Alternatively, for inhibition constants at cellular receptors:

:$K_i = \frac\ce$

where is the fixed concentration of agonist and EC₅₀ is the concentration of agonist that results in half maximal activation of the receptor. Whereas the IC₅₀ value for a compound may vary between experiments depending on experimental conditions, (e.g. substrate and enzyme concentrations) the K_i is an absolute value. K_i is the inhibition constant for a drug; the concentration of competing ligand in a competition assay which would occupy 50% of the receptors if no ligand were present.

The Cheng-Prusoff equation produces good estimates at high agonist concentrations, but over- or under-estimates K_i at low agonist concentrations. In these conditions, other analyses have been recommended.

See also

* Certain safety factor
* EC₅₀ (half maximal effective concentration)
* LD₅₀ (median lethal dose)
* K_i (equilibrium constant)

References

External links

AAT Bioquest Online IC50 Calculator

Online IC50 calculator
(www.ic50.tk) based on the C programming language and gnuplot

Alternative online IC50 calculator
(www.ic50.org) based on Python, NumPy, SciPy and Matplotlib

ELISA IC50/EC50 Online Tool
(link seems broken)



Online tool for analysis of in vitro resistance to antimalarial drugs

IC50-to-Ki converter
of an inhibitor and enzyme that obey classic Michaelis-Menten kinetics.

{{pharmacology, state=collapsed

Concentration indicators
Pharmacodynamics