Calculation of biochemical net reactions and pathways by using matrix operations

Pathways for net biochemical reactions can be calculated by using a computer program that solves systems of linear equations. The coefficients in the linear equations are the stoichiometric numbers in the biochemical equations for the system. The solution of the system of linear equations is a vector of the stoichiometric numbers of the reactions in the pathway for the net reaction; this is referred to as the pathway vector. The pathway vector gives the number of times the various reactions have to occur to produce the desired net reaction. Net reactions may involve unknown numbers of ATP, ADP, and P-i molecules. The numbers of ATP, ADP, and P-t in a desired net reaction can be calculated in a two-step process. In the first step, the pathway is calculated by solving the system of linear equations for an abbreviated stoichiometric number matrix without ATP, ADP, P-i, NAD(red), and NAD(ox). In the second step, the stoichiometric numbers in the desired net reaction, which includes ATP, ADP, P-i, NAD(red), and NAD(ox), are obtained by multiplying the full stoichiometric number matrix by the calculated pathway vector.