Calculation of All Possible Stoichiometric Coefficients and Theoretical Yields of Microbial Global Reactions

Stoichiometric analysis is a crucial step in biochemical processes because it allows us to find the proportions in which the substrates and products react. A system of algebraic equation is obtained from an elemental balance of the participating substances and determined, overdetermined or underdetermined systems can result depending on the number of substances and elements. Underdetermined systems are the most common ones as there are, generally, more substances than elemental balances. However, such systems have been poorly studied and a straightforward way to establish the solution space has not yet been reported. In this work a novel approach for finding all the possible solutions to such underdetermined systems is reported for the first time. The solutions space is expressed as a set of vectors which are here referred as extreme stoichiometries. To illustrate the general applicability and some uses of the proposed approach, three different fermentation systems are analyzed: growth of Chlamydomonas reinhardtii, a mixed culture for hydrogen production, and the growth of Saccharomyces cerevisiae. It is shown how the full stoichiometric spaces can be calculated for heterotrophy, autotrophy, mixotrophy, growth of mixed cultures in mixed substrates and how the experimental results should be contained in such spaces, what permits a consistency analysis. With the proposed method, it is now possible to estimate the maximum yields for any given microbial growth reaction and to assess the congruence of experimental data, even when the system is underdetermined.