DUALITY-THEORY FOR THERMODYNAMIC BOTTLENECKS IN BIOREACTION PATHWAYS

The thermodynamic evaluation of reaction feasibility, based on the sta ndard Gibbs energies of reaction, faces difficulties when, instead of isolated reactions, we are examining whole pathways. For pathways, we seek not only to decide whether they are feasible but also to pinpoint the pathway segment that causes thermodynamic difficulties. The obstr ucting pathway-segment may either be a single reaction (localized bott leneck) or a sequence of reactions (distributed bottleneck) which cann ot take place simultaneously. We present a duality theory that convert s the primal problem of selecting concentrations of species to make a pathway feasible to its dual problem of selecting linear combinations of reactions that make the pathway infeasible. The dual problem leads to an algorithm that can determine the thermodynamic feasibility of an y chemical reaction system. The method involves the analysis of indivi dual reactions and the selective construction of larger subpathways; i t uncovers localized and distributed thermodynamic bottlenecks of a pa thway. The method is applicable to reaction systems of any origin or t opology, provided that concentrations of species are restricted to pos itive intervals.