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Constraint-based modeling techniques have become a standard tool for the  in silico  analysis of metabolic networks. To further improve their accuracy, recent methodological developments focused on integration of thermodynamic information in metabolic models to assess the feasibility of flux distributions by thermodynamic driving forces. Here we present  OptMDFpathway , a method that extends the recently proposed framework of Max-min Driving Force (MDF) for thermodynamic pathway analysis. Given a metabolic network model,  OptMDFpathway  identifies both the optimal MDF for a desired phenotypic behavior as well as the respective pathway itself that supports the optimal driving force.  OptMDFpathway  is formulated as a mixed-integer linear program and is applicable to genome-scale metabolic networks. As an important theoretical result, we also show that there exists always at least one elementary mode in the network that reaches the maximal MDF. We employed our new approach to systematically identify all substrate-product combinations in  Escherichia coli  where product synthesis allows for concomitant net CO 2  assimilation via thermodynamically feasible pathways. Although biomass synthesis cannot be coupled to net CO 2  fixation in  E .  coli  we found that as many as 145 of the 949 cytosolic carbon metabolites contained in the genome-scale model  i JO1366 enable net CO 2  incorporation along thermodynamically feasible pathways with glycerol as substrate and 34 with glucose. The most promising products in terms of carbon assimilation yield and thermodynamic driving forces are orotate, aspartate and the C4-metabolites of the tricarboxylic acid cycle. We also identified thermodynamic bottlenecks frequently limiting the maximal driving force of the CO 2 -fixing pathways. Our results indicate that heterotrophic organisms like  E .  coli  hold a possibly underestimated potential for CO 2  assimilation which may complement existing biotechnological approaches for capturing CO 2 . Furthermore, we envision that the developed  OptMDFpathway  approach can be used for many other applications within the framework of constrained-based modeling and for rational design of metabolic networks.

plos computational biology/plos computational biology

OptMDFpathway: Identification of metabolic pathways with maximal thermodynamic driving force and its application for analyzing the endogenous CO2 fixation potential of Escherichia coli