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Glossary of Pharmacology 

Cheng-prusoff equation

Definition: 

The Cheng-Prusoff equation defines the theoretical relationship between the IC50 and Ki of an inhibitory ligand. This is useful since the IC50 changes depending on the amount of substrate in a reaction, however Ki does not change as it is a direct measure of the relationship between the inhibitory ligand and its binding partner.  Note: the Cheng-Prosoff relationship assumes no cooperativity occurs in the receptor-ligand interaction. 

The Cheng-Prusoff equation is K=  IC50/(1+ [S]/Km)

where, 

Ki = the inhibitory constant, defined as the equilibrium concentration of an inhibitory ligand when 50% of the receptor sites are occupied if no competing substrate is present.   

IC50 = The concentration at which the inhibitory ligand displaces 50% of the substrate.   

[S] = The concentration of the substrate used in the binding assay.  

Km = the affinity constant of the substrate, defined as the equilibrium concentration that results in substrate occupying 50% of the receptor sites in the absence of competition.   

Relevance:

This equation allows for the calculation of a Ki value for a specific inhibitory ligand. Both IC50 and Ki can be thought of as a measure of the potency of inhibition. Importantly, IC50 values are calculated based on experimental binding assays and are sensitive to the amount of substrate present and therefore, IC50 values cannot be compared unless all conditions were equal. However, Ki values can be compared as they are a measure of the direct property of the binding  affinity of the inhibitory ligand to its binding partner. 


Experimentally, it is easier to calculate the IC50 by measuring the reduction in activity observed by increasing concentrations of the inhibitory ligand. However, by also measuring the amount of labelled substrate in an assay and its Km, it is possible to then calculate the Ki of the inhibitory ligand and this value can be used to compare the inhibition potency of several compounds for a specific binding partner regardless of the experimental differences in substrate levels. 

Linked terms: IC50, Ki, substrate, binding affinity, ligand, potency

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