Table 4 The algorithm for the automated calculation of reaction rates (column "rate") and time derivatives for all the isotopomers (shown in left column) of pyruvate (d_pyr /dt) and accoa (d_accoa /dt) exemplified for pdh reaction (pyr → accoa).

000 → 00

u₀₀₀= v₀C₀₀₀/C_pyr

D₀₀₀= -u₀₀₀

D₀₀= u₀₀₀

001 → 01

u₀₀₁= v₀C₀₀₁/C_pyr

D₀₀₁= -u₀₀₁

D₀₁= u₀₀₁

010 → 10

u₀₁₀= v₀C₀₁₀/C_pyr

D₀₁₀= -u₀₁₀

D₁₀= u₀₁₀

011 → 11

u₀₁₁= v₀C₀₁₁/C_pyr

D₀₁₁= -u₀₁₁

D₁₁= u₀₁₁

100 → 00

u₁₀₀= v₀C₁₀₀/C_pyr

D₁₀₀= -u₁₀₀

D₀₀= u₀₀₀+u₁₀₀

101 → 01

u₁₀₁= v₀C₁₀₁/C_pyr

D₁₀₁= -u₁₀₁

D₀₁= u₁₀₁+u₀₀₁

110 → 10

u₁₁₀= v₀C₁₁₀/C_pyr

D₁₁₀= -u₁₁₀

D₁₀= u₁₁₀+u₀₁₀

111 → 11

u₁₁₁= v₀C₁₁₁/C_pyr

D₁₁₁= v₀-u₁₁₁

D₁₁= u₁₁₁+u₀₁₁