Metabolism is defined as the full complement of chemical transformations in living systems. In this talk, we will discuss a number of mathematical problems arising in the analysis and redesign of metabolic networks and highlight optimization-inspired solutions we have arrived. In particular, we will discuss the optStoic procedure which is a two-stage MILP-based computational procedure wherein the first step, optStoic, explores the maximum extent of converting carbon substrate(s) to desired product(s) through a non-intuitive combination of co-reactants and co-products while maintaining overall thermodynamic feasibility and mass balances. In the subsequent step, the algorithm identifies the minimal network of reactions to perform the overall conversion. To further expand our pathway designing capabilities beyond the known repertoire of enzymatic reactions, we incorporate hypothetical reactions predicted using reaction rules. Reaction rules expand our solution space and allow us to explore enzymatic capabilities which are yet to be identified (i.e., due to substrate promiscuity) or those that could be designed through protein engineering. First, we track and codify as rules, all reaction centers using a novel prime factorization based encoding technique (rePrime). An MILP based algorithm novoStoic then allows for the efficient integration of both reaction rules and reaction in the search for pathways that carry out the efficient conversion of source to target molecules.

rePrime is also used to efficiently trace the origin and destination of all atoms in all reactions present in a database. This capability is leveraged for constructing genome-scale atom mapping models for two organisms E. coli and Synechocystis 6803. We subsequently perform a meta-analysis of 13C isotope labeling data (i.e. 13C-MFA) to assess the impact on prediction fidelity of scaling-up core bacterial and cyanobacterial mapping models to a genome-scale carbon mapping (GSCM) models. imEco726 (668 reaction and 566 metabolites) and imSyn711 (731 reactions, 679 metabolites) for E. coli and Synechocystis, respectively. Flux ranges obtained with GSCM models are compared with those obtained upon projecting core model ranges on to a genome-scale metabolic model to elucidate the loss of information and erroneous biological inferences about pathway usage arising from assumptions contained within core models, reaffirming the importance of using mapping models with global carbon path coverage in 13C metabolic flux analysis.

Bio:
Costas Maranas is a computational biologist whose research interests include metabolic network reconstruction, analysis and redesign, synthetic biology and microbial strain design for bio-renewables and biofuels production, computational enzyme and antibody design and bioinformatics.  Many of his problems are solved using numerical optimization and involve ordinary and partial differential equation constraints.