

The standard doseresponse curve is sometimes called the fourparameter logistic equation. It fits four parameters: the bottom and top plateaus of the curve, the EC50 (or IC50), and the slope factor (Hill slope). This curve is symmetrical around its midpoint. To extend the model to handle curves that are not symmetrical, the Richards equation adds an additional parameter, S, which quantifies the asymmetry. This equation is sometimes referred to as a fiveparameter logistic equation, abbreviated 5PL.
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: DoseResponse  Special. Then choose Asymmetrical (five parameter).
Consider constraining the Hill Slope to a constant value of 1.0 (stimulation) or 1 (inhibition).
Also consider whether Bottom or Top should be fixed to constant values, or shared between data sets.
LogXb = LogEC50 + (1/HillSlope)*Log((2^(1/S))1)
Numerator = Top  Bottom
Denominator = (1+10^((LogXbX)*HillSlope))^S
Y = Bottom + (Numerator/Denominator)
Bottom and Top are the plateaus at the left and right ends of the curve, in the same units as Y.
LogEC50 is the concentrations that give halfmaximal effects, in the same units as X. Note that the logEC50 is not the same as logXb..
HillSlope is the unitless slope factor or Hill slope. Consider constraining it to equal 1.0 (stimulation) or 1 (inhibition).
S is the unitless symmetry parameter. If S=1, the curve is symmetrical and identical to the standard doseresponse equation. If S is distinct than 1.0, then the curve is asymmetric as shown below.
•If your goal is to obtain meaningful bestfit parameters, then you'll need lots of high quality data. It is very hard to fit both slope and asymmetry with tight confidence intervals. If your goal is just to interpolate unknowns from a standard curve, the width of the confidence intervals of the parameters doesn't really matter. What you want is a curve that follows the data, and in some cases an asymmetrical five parameter model does so better than a four parameter model.
•It can be tricky to get a good fit to the 5PL. See this discussion.
•Other formulations of asymmetrical doseresponse curves have been developed. For example, Ricketts and Head developed a model for use in baroreflex studies.
•Bindslev has written a lengthy online text, DrugAcceptor Interactions. Chapter 10, Hill in Hell discusses many models of doseresponse curves, including asymmetrical ones.
•Liao and Liu have done simulations that show the advantage of fitting the EC50 rather Xb.
•Gottschalk and Dunn review the properties of the 5Pl.
•The equation builtin to Prism is only one of several ways to express a five parameter concentrationresponse curve.
Bindslev, DrugAcceptor Interactions. Chapter 10, Hill in Hell
Giraldo, J., Vivas, N. M., Vila, E. & Badia, A. Assessing the (a)symmetry of concentrationeffect curves: empirical versus mechanistic models. Pharmacol Ther 95, 21–45 (2002).
Gottschalk, P. G. & Dunn, J. R. The fiveparameter logistic: a characterization and comparison with the fourparameter logistic. Anal Biochem 343, 54–65 (2005).
Liao, J.J.Z, Liu, R., Reparameterization of fiveparameter logistic function, Journal of Chemometrics, 23:248253 (2009)
Ricketts, J. H. and Head, G.A. A fiveparameter logistic equation for investigating asymmetry of curvature in baroreflex studies. Am. J. Physiology, 277: R44154 (1999)