Elementary vectors and autocatalytic sets for computational models of cellular growth

Traditional models of cellular growth involve an approximative biomass 99reaction99 which specifies biomass composition in terms of precursor metabolites (such as amino acids and nucleotides). On the one hand, biomass composition is often not known exactly and may vary drastically between extreme conditions; on the other hand, the predictions of computational models crucially depend on biomass. Even elementary flux modes (EFMs) depend on the biomass reaction. (To be specific: not just the numerical values of the EFMs, but also their supports and their number.) To better understand cellular phenotypes across conditions, we introduce and analyze new classes of elementary vectors for more comprehensive models of cellular growth, involving explicit synthesis reactions for all macromolecules. Growth modes (GMs) are given by stoichiometry, and elementary growth modes (EGMs) are GMs that cannot be decomposed without cancellations. Unlike EFMs, EGMs need not be support-minimal. Most importantly, every GM can be written as a sum of EGMs. In models with additional (capacity) constraints, growth vectors (GVs) and elementary growth vectors (EGVs) also depend on growth rate. In any case, EGMs/EGVs do not depend on the biomass composition. In fact, they cover all possible biomass compositions and can be seen as unbiased versions of elementary flux modes/vectors (EFMs/EFVs) used in traditional models. To relate the new concepts to other branches of theory, we define autocatalytic GMs and the corresponding autocatalytic sets of reactions. Further, we illustrate our results in a small model of a self-fabricating cell, involving glucose and ammonium uptake, amino acid and lipid synthesis, and the expression of all enzymes and the ribosome itself. In particular, we study the variation of biomass composition as a function of growth rate. In agreement with experimental data, low nitrogen uptake correlates with high carbon (lipid) storage.