The ETFL formulation allows multi-omics integration in thermodynamics-compliant metabolism and expression models

Pierre Salvy,Vassily Hatzimanikatis

doi:10.1038/s41467-019-13818-7

Pierre Salvy, Vassily Hatzimanikatis

Open Access

https://doi.org/10.1038/s41467-019-13818-7

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Abstract

Systems biology has long been interested in models capturing both metabolism and expression in a cell. We propose here an implementation of the metabolism and expression model formalism (ME-models), which we call ETFL, for Expression and Thermodynamics Flux models. ETFL is a hierarchical model formulation, from metabolism to RNA synthesis, that allows simulating thermodynamics-compliant intracellular fluxes as well as enzyme and mRNA concentration levels. ETFL formulates a mixed-integer linear problem (MILP) that enables both relative and absolute metabolite, protein, and mRNA concentration integration. ETFL is compatible with standard MILP solvers and does not require a non-linear solver, unlike the previous state of the art. It also accounts for growth-dependent parameters, such as relative protein or mRNA content. We present ETFL along with its validation using results obtained from a well-characterized E. coli model. We show that ETFL is able to reproduce proteome-limited growth. We also subject it to several analyses, including the prediction of feasible mRNA and enzyme concentrations and gene essentiality.

Highlights

ETFL is robust to missing data, as missing enzymes and their composition can be approximated using average enzyme characteristics
We provide in the Supplementary Note 2 a standardized procedure to produce ETFL models from genomescale models
Integration with platforms like KBase[30] can be envisioned to automatically draft ETFL reconstructions parametrized by curated organism-specific data

Summary

Results

We showed with ETFL that an uptake increase does not yield a proportional growth rate increase as with FBA and that ETFL provides a maximal uptake rate that is unmodeled in FBA, more effectively modeling growth-dependent biomass yield in E. coli This allows for more realistic predictions for phenotypes that are limited by the expression capabilities of the cell as well as captures the variability of the biomass composition in different growth regimens. Because ETFL contains integer variables, it is not compatible with traditional sampling methods in its current formulation It is possible, though, to make the model convex, and amenable to sampling, by fixing the integers to their values at a given growth rate and, if applicable, TFA directionality. Parameters for which this has been observed include catalytic rate constants, molecular weights, and concentrations

Conclusions

Methods

Apply the catalytic constraints to the FBA

Code availability