Equation: Gaddum/Schild EC50 shift

Introduction

A competitive inhibitor competes for agonist binding to a receptor, and shifts the dose-response curve to the right without changing the maximum response. By fitting all the curves globally, you can determine the affinity of the competitive inhibitor.

Step by step

Create an XY data table. Enter the logarithm of the concentration of the agonist ligand into X. Enter response into Y in any convenient units. Enter data with no inhibitor into column A. Enter data collected with a constant concentration of inhibitor into column B. Repeat, if you have data, for column C, D, E, ..., each with a different concentration of inhibitor. Enter the inhibitor concentration (in molar so 1nM is entered as '1e-9') into the column titles. Don't forget to enter '0' as the column title for data set A.

From the data table, click Analyze, choose nonlinear regression, and choose the panel of equations:  Dose-Response -- Special. Then choose Gaddum/Schild EC50 shift.

Consider constraining the parameters HillSlope and SchildSlope to their standard values of 1.0. This is especially useful if you don't have many data points, and therefore cannot fit these parameters.

Model

EC50=10^LogEC50

Antag=1+(B/(10^(-1*pA2)))^SchildSlope

LogEC=Log(EC50*Antag)

Y=Bottom + (Top-Bottom)/(1+10^((LogEC-X)*HillSlope))

Interpret the parameters

EC50 is the concentration of agonist that gives half maximal response in the absence of inhibitor. Prism reports both the EC50 and its log.

pA2 is the negative logarithm of the concentration of antagonist needed to shift the dose response curve by a factor of 2. If the HillSlope and SchildSlope are fixed to 1.0, it is the pKb, the negative log of the equilibrium dissociation constant (Molar) of inhibitors binding to the receptors.

HillSlope describes the steepness of the family of curves. A HillSlope of 1.0 is standard, and you should consider constraining the Hill Slope to a constant value of 1.0.

SchildSlope quantifies how well the shifts correspond to the prediction of competitive interaction. If the competitor is competitive, the SchildSlope will equal 1.0. You should consider constraining SchildSlope to a constant value of 1.0. antagonist term, [B], is now raised to the power S, where S denotes the Schild slope factor. If the shift to the right is greater than predicted by competitive interactions, S will be greater than 1. If the rightward shift is less than predicted by competitive interaction, then S will be less than 1.

Top and Bottom are plateaus in the units of the Y axis.