ETFL: A Formulation of ME-Models Accounting for Expression and Thermodynamics in Constraint-Based Models

Since flux balance analysis (FBA) has been introduced in Systems Biology, several attempts have been made at supplementing it with expression data [1-3]. With the notable exception of O’Brien et al. [1], none of them account directly for the enzyme production as a part of the mathematical programming formulation of the problem. Furthermore, O’Brien et al. propose a bilinear programming formulation that is computationally heavy. We propose a top-down model formulation, from metabolism to RNA synthesis, that allows the simulation of thermodynamics-compliant intracellular fluxes, as well as enzyme and mRNA levels. The formulation results in a mixed integer linear problem (MILP) which enables both relative and absolute metabolite, proteins, and mRNA concentration integration. The proposed formulation does not require any bilinear solver. We present here the results obtained using the Escherischia coli model iJO1366 [4]. We show that the formulation is able to reproduce proteome-limited growth, which flux balance analysis cannot [1], as well as predict feasible mRNA and enzyme concentrations in the cell. O'Brien, E.J., et al., Genome-scale models of metabolism and gene expression extend and refine growth phenotype prediction. Mol Syst Biol, 2013. 9: p. 693. Sánchez, B.J., et al., Improving the phenotype predictions of a yeast genome‐scale metabolic model by incorporating enzymatic constraints. Molecular Systems Biology, 2017. 13(8). Beg, Q.K., et al., Intracellular crowding defines the mode and sequence of substrate uptake by Escherichia coli and constrains its metabolic activity. Proc Natl Acad Sci U S A, 2007. 104(31): p. 12663-8. Orth, J.D., et al., A comprehensive genome-scale reconstruction of Escherichia coli metabolism-2011. Molecular Systems Biology, 2011. 7.