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Optimization models in metabolic engineering and systems biology focus typically on optimizing a unique criterion, usually the synthesis rate of a metabolite of interest or the rate of growth. Connectivity and non-linear regulatory effects, however, make it necessary to consider multiple objectives in order to identify useful strategies that balance out different metabolic issues. This is a fundamental aspect, as optimization of maximum yield in a given condition may involve unrealistic values in other key processes. Due to the difficulties associated with detailed non-linear models, analysis using stoichiometric descriptions and linear optimization methods have become rather popular in systems biology. However, despite being useful, these approaches fail in capturing the intrinsic nonlinear nature of the underlying metabolic systems and the regulatory signals involved. Targeting more complex biological systems requires the application of global optimization methods to non-linear representations. In this work we address the multi-objective global optimization of metabolic networks that are described by a special class of models based on the power-law formalism: the generalized mass action (GMA) representation. Our goal is to develop global optimization methods capable of efficiently dealing with several biological criteria simultaneously. In order to overcome the numerical difficulties of dealing with multiple criteria in the optimization, we propose a heuristic approach based on the epsilon constraint method that reduces the computational burden of generating a set of Pareto optimal alternatives, each achieving a unique combination of objectives values. To facilitate the post-optimal analysis of these solutions and narrow down their number prior to being tested in the laboratory, we explore the use of Pareto filters that identify the preferred subset of enzymatic profiles. We demonstrate the usefulness of our approach by means of a case study that optimizes the ethanol production in the fermentation of Saccharomyces cerevisiae.
The authors wish to acknowledge support of this research work from the Spanish Ministry of Education and Science (projects DPI2008-04099, PHB2008-0090-PC, BFU2008-00196 and CTQ2009-14420-C02), the Spanish Ministry of External Affairs (projects HS2007-0006 and A/023551/09), the Spanish Ministry of Science and Innovation (ENE2011-28269-C03-03), the Generalitat de Catalunya (FI programs; http://www10.gencat.net/agaur_web/AppJava/a_beca.jsp?categoria=predoctorals&id_beca=16701) and the Spanish Ministry of Education, Culture and Sport (FPU programs; http://www.educacion.gob.es/educacion/universidades/convocatorias/titulados-doctores-profesores/fpu/convocatoria.html). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. |
