It can be tricky to get a good fit to the 5PL.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 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. If your goal is to obtain meaningful best-fit parameters, then you'll need lots of high quality data.If S is distinct than 1.0, then the curve is asymmetric as shown below. If S=1, the curve is symmetrical and identical to the standard dose-response equation. Consider constraining it to equal 1.0 (stimulation) or -1 (inhibition). HillSlope is the unitless slope factor or Hill slope. Note that the logEC50 is not the same as logXb.

LogEC50 is the concentrations that give half-maximal effects, in the same units as X. LogXb = LogEC50 + (1/HillSlope)*Log((2^(1/S))-1)ĭenominator = (1+10^((LogXb-X)*HillSlope))^Sīottom and Top are the plateaus at the left and right ends of the curve, in the same units as Y. Then choose Asymmetrical (five parameter), X is log(concentration).Ĭonsider constraining the Hill Slope to a constant value of 1.0 (stimulation) or -1 (inhibition).Īlso consider whether Bottom or Top should be fixed to constant values, or shared between data sets. Enter response into Y in any convenient units.įrom the data table, click Analyze, choose nonlinear regression, and choose the panel of equations: Dose-Response - Special, X is log(concentration). Enter the logarithm of the concentration of the agonist into X.

This equation is sometimes referred to as a five-parameter logistic equation, abbreviated 5PL. To extend the model to handle curves that are not symmetrical, the Richards equation adds an additional parameter, S, which quantifies the asymmetry.

This curve is symmetrical around its midpoint. It fits four parameters: the bottom and top plateaus of the curve, the EC50 (or IC50), and the slope factor (Hill slope). The standard dose-response curve is sometimes called the four-parameter logistic equation. Use a related equation when X values are concentrations or doses. This equation is used when X values are logarithms of doses or concentrations.

Graphpad prism 4 parameter fit