The assays discriminating for individual isozyme activity (discrimination assays) are based on isozyme-selective metal ion dependence. The reference assay mixture (0.4 mL final volume) contained 30 mM HEPES/KOH, pH 7.5, 0.6 mg/mL BSA, 25 mM MgCl2, 20 mM NaF, 1 mM DDT, 1 mM both NMN and ATP, and either ∼1 mg/mL protein tissue extract or 0.15–2.5 µg/mL each pure recombinant isozyme. The above assay, referred as “A”, was used to measure total NMNAT activity, i.e. the “reference” activity value for all different mNMNAT isoforms. For isozyme discrimination, the additional mixtures “B”, “C”, and “D” were set replacing 25 mM MgCl2 with either 50 µM MgCl2 (B) or 1.5 mM ZnCl2 (C) or 4 mM CoCl2 (D). The assays under condition “D” were carried out in the absence of DTT. Suitable parameters for subsequent calculation were obtained by parallel assaying of each recombinant isozyme under the four conditions above. Then, reaction rates obtained from “B”, “C”, and “D” were divided each by the reference activity value obtained from “A”. The resulting reaction rate ratios, i.e. the coefficients b1, b2, b3; c1, c2, c3; d1, d2, d3, were substituted in the following system of three linear equations:
Tissue NMNAT activity (condition assay “B”) = (b1·X)+(b2·Y)+(b3·Z).
Tissue NMNAT activity (condition assay “C”) = (c1·X)+(c2·Y)+(c3·Z).
Tissue NMNAT activity (condition assay “D”) = (d1·X)+(d2·Y)+(d3·Z).
where X, Y, and Z represent the true enzymatic activities of mNMNAT1, mNMNAT2, and mNMNAT3, respectively, in the complex mixture. Solution of the matrix based on the Cramer’s rule [38] yields the actual activity values X, Y, and Z as if they were measured under reference condition “A”. Matrix calculation was carried out by Microsoft Excel and, specifically, by using the functions MDETERM(array), MINVERSE(array) and MMULT(array-1,array2), were “array” is the matrix of coefficients b1, b2, b3; c1, c2, c3; d1, d2, d3; “array-1“ is the transposed matrix of “array” obtained by the function MINVERSE(array), and “array2” is the vector obtained from tissue NMNAT activity values under conditions “B”, “C”, and “D”. The whole procedure including a numerical example of the matrix substitution calculation is detailed in Supporting Information files: