(679c) A Bi-Level Optimisation Approach for the Productivity and the Thermodynamic Performance in Metabolic Systems

A bi-level optimisation strategy has been proposed to predict the pathways in a metabolic system for the maximum productivity and the operating conditions based on the thermodynamic performance of the system. A metabolic network is most often interpreted and modeled in terms of a collection of enzyme-catalyzed reactions that utilise substrate metabolites to generate final products. The complexity in metabolic systems necessitates the development of the integrated approaches to analyse and interpret the systemic properties of cellular metabolism, which shifts the emphasis from single metabolic reactions to systemic pathways defined by the elementary flux mode analysis. In addition, metabolic systems need to attain the desired operability, which is directly related to the thermodynamic performance of these systems. In this work a methodology is developed to establish a rational metabolic engineering strategy for the elucidation and optimisation of metabolic systems such that the maximum productivity and the optimal operating conditions are achieved. A bi-level optimisation is performed that combines the metabolic flux analysis and pathway identification with the thermodynamic analysis of metabolic systems. In the first level, a systematic enumeration of pathways of a metabolic system is described by the elementary flux mode analysis, which uses a mathematical tool to comprehensively analyse and identify all the metabolic routes in the system that are both stoichiometrically and thermodynamically feasible for a set of enzymes. The optimal metabolic flux distribution and the corresponding pathways are identified for the maximum yield of desired products by LP optimisation. This is subject to the stoichiometric flux balance analysis and the negative inequality constraint on the Gibbs free energy change of a system. In the second level, thermodynamic optimisation in terms of the minimisation of the Gibbs free energy change of a metabolic system is carried out for the best performance of the system. The Gibbs free energy change from the metabolites to products during a production is predicted for the stoichiometrically balanced pathways that are energetically coupled through sequence of metabolites. The Gibbs free energy of formation of metabolites in a system using which the Gibbs free energy change of the system is predicted is presented as a function of temperature, pressure, pH and metal ions concentrations in this model. Hence the minimization of the Gibbs free energy change optimises these operating conditions, for the optimal pathways that achieve the desired productivity. These optimisation levels are integrated through the flux balance analysis, the elementary flux mode analysis and the Gibbs free energy change predictions. This integrated optimisation procedure thus generated ensures the maximisation of the external flux capacities and the minimisation of the Gibbs free energy change and hence derives the optimal pathways and the operating conditions for achieving the desired objectives. The methodology is effectively demonstrated by a case study on synthesis of pentose phosphate pathways (PPP) and the glycolysis cycle of the insilico Escherichia coli. The yield of amino acid is maximised, while the minimisation of the Gibbs free energy change during the process optimises the operating conditions required for the process. Thus the optimal flux distributions as well as the optimal conditions on the pH and ion concentrations are achieved.