. 2010 Oct 6;4:135. doi: 10.1186/1752-0509-4-135

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).

reaction	rate	d_pyr/dt	d_accoa/dt
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