A Lattice-Theoretic Framework for Metabolic Pathway Analysis

Constraint-based analysis of metabolic networks has become a widely used approach in computational systems biology. In the simplest form, a metabolic network is represented by a stoichiometric matrix and thermodynamic information on the irreversibility of certain reactions. Then one studies the set of all steady-state flux vectors satisfying these stoichiometric and thermodynamic constraints. We introduce a new lattice-theoretic framework for the computational analysis of metabolic networks, which focuses on the support of the flux vectors, i.e., we consider only the qualitative information whether or not a certain reaction is active, but not its specific flux rate. Our lattice-theoretic view includes classical metabolic pathway analysis as a special case, but turns out to be much more flexible and general, with a wide range of possible applications. We show how important concepts from metabolic pathway analysis, such as blocked reactions, flux coupling, or elementary modes, can be generalized to arbitrary lattice-based models. We develop corresponding general algorithms and present a number of computational results.