PREDPP for MM Elimination

Earlier I posted this $DES block for the 2-compartment model with depot and M-M elimination: C2 = A(2)/S2 DADT(1) = -K12*A(1) DADT(2) = K12*A(1) -K23*A(2) +K32*A(3) -C2*VM/(KM+C2) DADT(3) = K23*A(2) -K32*A(3) Joachim Grevel says: Since she defines the CENTRAL compartment as DEFOBS, the line > C2 = A(2)/S2 in $DES is redundant ...in my opinion. It is true that the predictions computed by PREDPP are always concentrations, or more accurately, scaled compartment amounts. Thus, in the $ERROR block, F is in fact A(2)/S2 when the prediction is from the central compartment, and in a table or scatter, a value of PRED obtained from the central compartment is also A(2)/S2. But within the $DES block, unscaled compartment amounts are present in the variables A(1), A(2), A(3), etc. This is why A(2)/S2 (a concentration) was computed for use in the M-M elimination term -C2*VM/(KM+C2). It would not be incorrect to use -A(2)*VM/(KM+A(2)) here. It simply changes the units of KM and VM. In fact, ADVAN10 uses amounts rather than concentrations in its computations. Here are some remarks on the units of KM and VM from Lew Sheiner and Stuart Beal, from some private correspondence. -- The MM model as derived in Biochemistry, just like the one you use in ADVAN10, deals in amounts: VmC/(Km+C) has units amount/time because Vm does, and C/(Km+C) is dimensionless. So it is not a question of correct diff e's - both formulations will be correct for dA/dt; it is a question of parameterization and mechanistic modeling. Kinetically, an enzyme can only know the chemical activity of species near it, not amounts in compartments, so that A50 (the MM parameter you use, as opposed to C50) is physically meaningless. In Biochem and PK, Km has units of (molar) concentration. For undoubtedly good reasons that I now forget, you chose to write your MM model in terms of A50, hence the rest follows. ADVAN6, however, allows one to use the standard formulation, and that is what I generally prefer. ADVAN10 as well allows what you term the standard formulation (I agree with the term "standard"). One simply redefines Km.