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 Equation: Biphasic dose-response

This equation is used when X values are logarithms of doses or concentrations. Use a related equation when X values are concentrations or doses.

## Introduction

A common deviation from the standard monotonic sigmoid shape is the biphasic sigmoid shape.

## Step by step

Create an XY data table. Enter the logarithm of the concentration of the agonist into X. Enter response into Y in any convenient units.

From the data table, click Analyze, choose nonlinear regression, and choose the panel of equations:  Dose-Response -- Special, X is log(concentration). Then choose Biphasic dose-response, X is log(concentration).

Consider constraining nH1 and nH2 to constant values of 1.0 (stimulation) or -1 (inhibition).

Also consider whether Bottom or Top should be fixed to constant values, or shared between data sets.

## Model

Span=Top-Bottom

Section1=Span*Frac/(1+10^((LogEC50_1-X)*nH1))

Section2=Span* (1-Frac)/(1+10^((LogEC50_2-X)*nH2))

Y=Bottom + Section1 +Section2 ## Interpret the parameters

Bottom and Top are the plateaus at the left and right ends of the curve, in the same units as Y.

LogEC50_1 and LogEC50_2 are the concentrations that give half-maximal stimulatory and inhibitory effects in the same units as X.

nH1 and nH2 are the unitless slope factors or Hill slopes. Consider constraining these to equal 1.0 (stimulation) and -1 (inhibition).

Frac is the proportion of maximal response due to the more potent phase.