Large-scale dynamic models of metabolic networks
The development and application of methods quantifying the metabolic fluxes such as Flux Balance Analysis (FBA) has been one of the driving forces behind the successful growth of metabolic engineering. However, applications of FBA have been limited by the fact that FBA does not take into account kinetic properties of the network and therefore it cannot be used to identify rate-limiting steps and comprehend time course evolutions of the system. Dynamic mathematical descriptions of the metabolism offer a large advantage compared to constraint-based stoichiometric models, but unfortunately their development comes with inevitable difficulties due to: (i) structural uncertainties, such as incomplete knowledge about stoichiometry or about kinetic laws of the enzymes, and (ii) quantitative/parametric uncertainties such as lack of knowledge concerning kinetic parameters. Recent developments and vast resources of curated genome scale metabolic networks address to a great extent the issues around stoichiometric uncertainty. However, the knowledge about kinetic rate laws and in particular their parameters is to these days still limited. In this contribution, starting from large-scale stoichiometric models we use the ORACLE (Optimization and Risk Analysis of Complex Living Entities) framework that integrates available information in a set of stable log-linear kinetic models sharing the same steady state. These models are used to compute kinetic parameters of the enzymatic mechanisms in the metabolic network, e.g. the maximal velocities, Vmax, and Michaelis constants, Km. Using these kinetic parameters, we systematically develop populations of stable dynamic models having the same steady-state as the log-linear ones. The estimated parameters are comparable to the experimental information as seen in BRENDA and other databases. These non-linear estimations about the stable state can be therefore used to analyze properties of the system upon large perturbations and investigate time course evolutions in and around this steady state. We demonstrate the capabilities of the proposed approach by building a dynamic E. coli core model that includes ca. 200 metabolites and more than 400 reactions. We discuss the strengths and limitations of this approach and possible avenues for development.