Application of Doehlert uniform shell designs for selecting optimal amounts of internal standards in the analysis of prostaglandins and leukotrienes by liquid chromatography–tandem mass spectrometry

A protocol for the analysis of multiple prostaglandins and leukotrienes in cell culture media by using multiple internal standards was validated. A two-factor Doehlert design was used to determine the behaviour of the relationship analyte/internal standard (namely: PGE2/PGE2-d4, PGE3/PGE2-d4, LTB4/LTB4-d4 and LTB5/LTB4-d4) and to select the optimal amounts of deuterated internal standards for quantifying simultaneously the prostaglandins and leukotrienes in cell culture media by LC–MS/MS. The selection of optimal amounts of internal standards was based on mathematical models that allow visualizing concentration regions where the response factors remain constant over a wide range of analytical concentrations. The linearity of the calibration curves for each analyte at the optimal levels suggested by the mathematical models was statistically confirmed by means of the ratio lack-of-fit to pure error. The validated protocol was successfully applied in the simultaneous quantification of pro- and anti-inflammatory eicosanoids in stimulated cod head kidney cell culture media. The two-factor Doehlert design has permitted to estimate the experimental response as a function of six variables (PGE2, PGE3, LTB4, LTB5, PGE2-d4 and LTB4-d4) which represents a substantial reduction of resources, time and experiments of approximately 84% (7 × 3 experiments) when compared with the full six-factor Doehlert design (43 × 3 experiments).