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 Equation: Two sites -- Fit total and nonspecific binding

Introduction

In a saturation binding experiment, you vary the concentration of radioligand and measure binding. The goal is to determine the Kd (ligand concentration that binds to half the receptor sites at equilibrium) and Bmax (maximum number of binding sites).

The ligand binds not only to receptors sites, but also to nonspecific sites. There are three approaches to dealing with nonspecific binding.

Subtract off the nonspecific, and analyze only the specific binding.

Analyze the total binding only, inferring the amount of nonspecific binding from the shape of the total binding curve. This approach doesn't work well when the ligand binds to two sites

Globally analyze the total and nonspecific binding at one time. This is the best approach, and the details are explained below.

Step by step

Create an XY data table. Enter radioligand concentration into X, total binding into Y, and nonspecific binding into column B.

Use any convenient units for X. The Kd will be reported in those same concentration units. Use the same units for total and nonspecific binding. The Bmax will be reported in those same units.

From the data table, click Analyze, choose nonlinear regression, choose the panel of Saturation Binding equations, and choose Two sites -- Total and nonspecific binding.

The parameter Background is the measured 'binding' when there is no radioligand binding added, so represents the counter background, if there is any. Consider constraining it to a constant value of zero.

Model

Specific1=BmaxHi*X/(X+KdHi)

Specific2=BmaxLo*X/(X+KdLo)

Nonspecific=NS*X + Background

<A>Y=Specific1 + Specific2 + Nonspecific

<B>Y=Nonspecific

The <A> and <B> syntax means that the fourth line is only used for data set A (total binding) while the fifth line is used only for data set B (nonspecific).

The parameters NS and Background are shared between the two data sets.

Interpret the parameters

BmaxHi and BmaxLo are the maximum specific bindings to the two sites in the same units as Y.

KdHi and KdLo are the equilibrium dissociation constants, in the same units as X. It is the radioligand concentration needed to achieve a half-maximum binding at equilibrium.

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

Background is the amount of nonspecific binding with no added radioligand. This represents counter background. If your counter automatically subtracts off the background signal, you can constrain Background to a constant value of zero.