Large Scale Methods to Enumerate Extreme Rays and Elementary Modes

A major challenge in systems biology is to improve the understanding of complex metabolic networks. Here, we focus on structural analysis since it requires mainly reaction stoichiometries, in contrary to detailed dynamic methods that are often limited by insufficient knowledge on mechanisms and parameters. Thermodynamic reaction constraints and the steady state assumption reduce the solution space for valid reaction fluxes to a convex polyhedral cone. Pathway analysis methods aim at finding a unique generating set for the flux cone---called extreme rays or elementary modes. We describe critical aspects for an efficient implementation of the double description method for large scale application. The efficiency of introduced techniques is demonstrated with large application examples from combinatorics and systems biology.