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.