Impact of Stoichiometry Representation on Simulation of Genotype-Phenotype Relationships in Metabolic Networks

Abstract

Genome-scale metabolic networks provide a comprehensive structural framework for modeling genotype-phenotype relationships through flux simulations. The solution space for the metabolic flux state of the cell is typically very large and optimization-based approaches are often necessary for predicting the active metabolic state under specific environmental conditions. The objective function to be used in such optimization algorithms is directly linked with the biological hypothesis underlying the model and therefore it is one of the most relevant parameters for successful modeling. Although linear combination of selected fluxes is widely used for formulating metabolic objective functions, we show that the resulting optimization problem is sensitive towards stoichiometry representation of the metabolic network. This undesirable sensitivity leads to different simulation results when using numerically different but biochemically equivalent stoichiometry representations and thereby makes biological interpretation intrinsically subjective and ambiguous. We hereby propose a new method, Minimization of Metabolites Balance (MiMBl), which decouples the artifacts of stoichiometry representation from the formulation of the desired objective functions, by casting objective functions using metabolite turnovers rather than fluxes. By simulating perturbed metabolic networks, we demonstrate that the use of stoichiometry representation independent algorithms is fundamental for unambiguously linking modeling results with biological interpretation. For example, MiMBl allowed us to expand the scope of metabolic modeling in elucidating the mechanistic basis of several genetic interactions in Saccharomyces cerevisiae.

Author Summary

One of the challenging tasks in systems biology is to quantitatively predict the metabolic behavior of the cell under given genetic and environmental constraints. To this end, genome-scale metabolic reconstructions and simulation tools are indispensable. The choice of the objective function to be used for simulating genome-scale metabolic models is dependent on the biological context and one of the most relevant parameters for successful modeling. Formulation of the intended objective function often requires the use of multiple fluxes, e.g. the sum of fluxes through ATP-producing reactions. We demonstrate that the existing tools confound biological interpretation of the simulations due to undesired dependence on the representation of stoichiometry and propose a new tool – Minimization of Metabolites Balance (MiMBl). MiMBl allows casting of the desired biological objective functions into linear optimization models and gives consistent simulation results when using numerically different but biochemically equivalent stoichiometry representations. We demonstrate relevance of MiMBl for addressing biological questions through improved predictions of genetic interactions within the yeast metabolic network. Genetic interactions imply functional relationship between the genes and therefore allow assessing different hypotheses for the underlying biological principles. MiMBl explains several of the genetic interactions as outcome of flux re-routing for minimal metabolite turnover adjustments.