# For Fluorescence-Based Competitive Binding Assays

This web page provides a mathematical equation that is particularly developed to convert IC50 values observed in fluorescence-base competitive binding assays into Ki values. If you are not familiar with our work, please go over the background information first. You are required to cite our work in any resulting publication if you apply the computation on this web page.

### The inputs: How the FP-based binding assay was performed

Total concentration of the protein ([P]T) = (nM)
Total concentration of the fluorescence-labeled ligand ([L]T) = (nM)
Dissociation constant of the protein-ligand complex (Kd) =  (nM)
Total concentration of the inhibitor when 50% inhibition is achieved  (IC50) = (nM)

### 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 Kd denote for the dissociation constant of the PL complex and Ki 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 (FPmax), and a negative control, which contains only the fluorescence-labeled ligand ([L]T) defining the minimal FP signal (FPmin), 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 Ki value of the given inhibitor:

The above equation shows that Ki 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, Kd. 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 Ki: 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).

* This page is constructed and maintained by Dr. Xueliang Fang and Dr. Renxiao Wang. Latest update on 04/12/2004.
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