Click here to download

BACKGROUND INFORMATION

We assume a typical case of fluorescence-based competitive binding assay. Let P denote for the protein molecule, L for the fluorescence-labeled ligand molecule, I for the competitive inhibitor, PL for the protein-ligand complex, and PI for the protein-inhibitor complex.

Let [P], [L], [I], [PL], and [PI] denote for the concentrations of these five species, respectively. Let [P]_T, [L]_T, and [I]_T denote for the total concentration of the protein, the ligand, and the inhibitor, respectively. Let K_d denote for the dissociation constant of the PL complex and K_i for the one of the PI complex.

Basic assumptions:

Please make sure that your binding assay meets the following basic assumptions before you apply the equation below.

(1) We assume that I inhibits the binding of L to P competitively and both L and I bind to P with a stoichiometry of 1:1.

(2) We assume that L and PL are the only two species in the system that can generate FP signals.

(3) We assume that a positive control, which is a mixture of fluorescence-labeled ligand ([L]_T) with the protein ([P]_T) defining the maximal FP signal (FP_max), and a negative control, which contains only the fluorescence-labeled ligand ([L]_T) defining the minimal FP signal (FP_min), are used in the assay. And, the inhibition ratio at any point is defined as following:

Mathematic equation:

The equation below will be used to compute the K_i value of the given inhibitor:

The above equation shows that K_i can be expressed as a function of the concentration of the free inhibitor at 50% inhibition, [I]₅₀, the concentration of the free labeled ligand at 50% inhibition, [L]₅₀, the concentration of the free protein at 0% inhibition, [P]₀, and the dissociation constant of the protein-ligand complex, K_d. Derivation of this equation is described in details in the following references.

References:

[1] Renxiao Wang, Zaneta Nikolovska-Coleska, Xueliang Fang and Shaomeng Wang, "From IC₅₀ to K_i: A General Mathematical Solution for Fluorescence-Based Competitive Binding Assays", (to be submitted).

[2] Zaneta Nikolovska-Coleska, Renxiao Wang, Xueliang Fang, Hongguang Pan, York Tomita, Peng Li, Peter P. Roller, Krzysztof Krajewski, Naoyuki Saito, Jeanne Stuckey and Shaomeng Wang, "Development and Optimization of a Binding Assay for the XIAP BIR3 Domain Using Fluorescence Polarization", Analytical Biochemistry, 2004, (accepted for publication).

Known problems:

We have observed that, when the IC₅₀ value of the given inhibitor reaches a very low level, e.g. nanomolar or sub-nanomolar, our equation sometimes generates a zero value as the final K_i value. A reasonable explanation is that in such cases the uncertainties in experimental measurement are comparable to the absolute value of K_i. Our equation however requires mathematically accurate inputs in order to get correct results. So if the above problem indeed occurs in your case, a good idea is to optimize your binding assay to get results as reliable as possible.

* This page is constructed and maintained by Dr. Xueliang Fang and Dr. Renxiao Wang. Latest update on 04/12/2004.
** This page has been visited [Put a counter here!] times.