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 Equation: One site -- Total, accounting for ligand depletion

Introduction

You don't have to measure nonspecific binding directly. Instead, you can determine Bmax and Kd by fitting only total binding by assuming that the amount of nonspecific binding is proportional to the concentration of radioligand.

If only a small fraction of radioligand binds, you can use a simpler model.

This equation allows for a substantial fraction of the added ligand to bind. This only works with radioactive ligands, so the assessment of added ligand and bound ligand are in the same counts-per-minute units. This method doesn't work with fluorescent ligands.

Step by step

Create an XY data table. Enter radioligand concentration into X, and total binding into Y. If you have several experimental conditions, place the first into column A, the second into column B, etc.

Enter both X and Y in CPM units. This is essential for the analysis to work.

From the table of total binding, click Analyze, choose nonlinear regression, choose the panel of Saturation Binding equations, and choose One site -- Total, accounting for ligand depletion.

You must constrain two parameters to constant values based on your experimental design:

SpAct is the specific radioactivity in cpm/fmol

Vol is the reaction volume in ml

Model

KdCPM=KdnM * Vol * 1000 * SpecAct

; (nm/L * mL * 0.001 L/ml * 1000000 fmol/nmol * cpm/fmol)

a=-1-NS

b=KdCPM + NS*KdCPM + X + 2*X*NS + Bmax

c=-1*X*(NS*KdCPM + X*NS+Bmax)

Y=(-b+sqrt(b*b-4*a*c) )/(2*a) ;Y is in cpm Interpret the parameters

Bmax is the maximum specific binding in cpm.

KdnM is the equilibrium dissociation constant in nM.

NS is the slope of nonspecific binding in Y units divided by X units.

Notes

This analysis accounts for the fact that a large fraction of the added radioligand binds to the receptors. If you are able to assume that only a small fraction of radioligand binds, which means that the concentration you added is virtually identical to the free concentration, use an alternative analysis.

Reference

This equation came from S. Swillens (Molecular Pharmacology, 47: 1197-1203, 1995)