Section3:Determination of EC50-IC50

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Models and Curve Fitting Guidelines

For competition binding assays and functional antagonist assays the most common summary measure of the dose-response curve is the IC50, the concentration of substance that provides 50% inhibition. For agonist/stimulator assays the most common summary measure is the EC50, the concentration giving 50% of that compound’s maximal response. Substantial variation in the methodology used to derive these values exists, and this variation has been shown to substantially impact overall assay variability. This section discusses important issues to consider and provides some guidelines on how to proceed. They are a based on the rdsData Standardization for Results Management document (Section XI of this manual). Consult that section for the specifics of each assay type. Consult a statistician to see if these guidelines are appropriate for your assay, and if other outcomes such as AUC or a threshold dose should be used.

Before fitting a dose-response curve to obtain the EC/IC50, each well should be converted to either percent activity or percent inhibition with respect to positive and negative controls

	Bottom	Top	Rel IC50	Slope
4-Param	2.01	128.32	0.015	-0.58
% Fit Err	202.85	14.82	57.54	-22.56
Bottom=0	0.00	134.33	0.014	-0.53
% Fit Err		12.42	57.21	-12.91
Top=100	6.21	100.00	0.034	-0.87
% Fit Err	57.08		21.55	-16.09

Example 3 is best fit by a fixed bottom (3PLFB) model. Note that the data does not define the bottom asymptote, and the fitted bottom (41.54) and fitted slope (-1.83) from the 4PL are inappropriate for binding data. The fixed bottom model reduces the fitting error from 80.19% to 20.85%, while the IC50 increases by more than two-fold. The fitted IC50 (20.88nM) is inside the dose-range (0.001-25nM), and so it is appropriate to report this value. Note in this case Activity Base was unable to fit a fixed top model.

	Bottom	Top	Rel IC50	Slope
4-Param	41.54	106.79	10.17	-1.83
% Fit Err	81.91	2.90	80.19	-95.59
Bottom=0	0.00	106.94	22.88	-1.25
% Fit Err		2.77	20.85	-30.49
Top=100
% Fit Err

Example 4 illustrates the definition and effect of outliers (left panel). Outliers are single, vertically isolated points that are clearly inappropriate. The point is “obviously” erroneous. The effect of the outlier in this case is to bias the estimate of the bottom upwards, pulling it away from the other points of the data. In general, outliers can bias either the top, bottom or slope parameter depending upon where they occur in the dose-response. It is appropriate to remove the outlier (right panel) and refit the points. Fixing top or bottom did not materially improve the curve fit (not shown).

All Data	Bottom	Top	Rel IC50	Slope
4-Param	32.62	97.21	0.056	-1.31
% Fit Err	40.09	20.73	114.10	-132.18
Outlier Rem	Bottom	Top	Rel IC50	Slope
4-Param	2.25	104.78	0.130	-0.63
% Fit Err	611.06	11.29	53.38	-40.98

Example 5 illustrates the effect of high assay variation. No single point stands out as “obviously erroneous”, and therefore it would be inappropriate to remove any points from the curve fit. Fixing top or bottom does not materially improve the curve fit, and so the 4PL model should be used. Note that the estimates themselves are not implausible, but the fitting error is 33.83%, which is caused by the relatively high assay variation.

	Bottom	Top	Rel IC50	Slope
4-Param	8.12	91.76	0.117	-1.86
% Fit Err	84.04	8.30	33.83	-58.17
Bottom=0	0.00	92.98	0.130	-1.51
% Fit Err		8.94	34.55	-44.50
Top=100	7.62	100.00	0.093	-1.40
% Fit Err	92.45		33.77	-40.93

Notes

1. This equation can be fit to the data using Activity/Base, Bravo/Curve fit, JMP, Graphpad/Prism or Sigma/Plot. Note that the form of the equation varies from one software package to the next. Some, such as Graphpad/Prism, fit Log-IC50 instead of IC50, and the equation looks quite different, but the results are the same as that shown above.
2. The terms absolute and relative IC50 are not universal. Both are usually just called the “IC50”, and it’s left unstated which value is actually used.
3. If the software tool you are using reports Log-IC50 then you must convert both the estimate and the % fitting error (%FE) according to the formulas
4. There should be at least one point on both sides of the reported IC50, i.e. the reported IC50 should lie inside the dose-range used in the assay. The intent of this rule is to make the IC50 estimate an interpolation of generated data and not an extrapolation of generated data. Cases not satisfying this rule should not have an IC50 reported or reported with a comment that indicates the value is extrapolated. If a value is reported, it should be “<X” or “>Y”, as appropriate, where X is the lowest concentration and Y is the largest concentration included in the analysis.
5. The fitting error of the IC50 should be no more than 40% of the IC50. Estimates not satisfying this rule should be flagged in the database. A fitting error of 40% of the IC50 corresponds to an MSR of 3-fold.
6. It is a good idea to remove obvious outliers and then refit the curve without the outliers. Note that if it isn’t obvious, it isn’t an outlier. See examples 4 and 5 above to distinguish high variability from outliers.
7. For competition assays, such as radioligand binding assays and competitive inhibition assays, the fitted slope should be within 2 (slope) fitting errors of the value 1, and slope estimates outside this range indicate assay problems that need to be investigated.