From Escherichia coli mutant 13C labeling data to a core kinetic model: A kinetic model parameterization pipeline

Abstract

Kinetic models of metabolic networks offer the promise of quantitative phenotype prediction. The mechanistic characterization of enzyme catalyzed reactions allows for tracing the effect of perturbations in metabolite concentrations and reaction fluxes in response to genetic and environmental perturbation that are beyond the scope of stoichiometric models. In this study, we develop a two-step computational pipeline for the rapid parameterization of kinetic models of metabolic networks using a curated metabolic model and available 13C-labeling distributions under multiple genetic and environmental perturbations. The first step involves the elucidation of all intracellular fluxes in a core model of E. coli containing 74 reactions and 61 metabolites using 13C-Metabolic Flux Analysis (13C-MFA). Here, fluxes corresponding to the mid-exponential growth phase are elucidated for seven single gene deletion mutants from upper glycolysis, pentose phosphate pathway and the Entner-Doudoroff pathway. The computed flux ranges are then used to parameterize the same (i.e., k-ecoli74) core kinetic model for E. coli with 55 substrate-level regulations using the newly developed K-FIT parameterization algorithm. The K-FIT algorithm employs a combination of equation decomposition and iterative solution techniques to evaluate steady-state fluxes in response to genetic perturbations. k-ecoli74 predicted 86% of flux values for strains used during fitting within a single standard deviation of 13C-MFA estimated values. By performing both tasks using the same network, errors associated with lack of congruity between the two networks are avoided, allowing for seamless integration of data with model building. Product yield predictions and comparison with previously developed kinetic models indicate shifts in flux ranges and the presence or absence of mutant strains delivering flux towards pathways of interest from training data significantly impact predictive capabilities. Using this workflow, the impact of completeness of fluxomic datasets and the importance of specific genetic perturbations on uncertainties in kinetic parameter estimation are evaluated.

Fig 1. Pictorial representation of the kinetic parameterization pipeline for constructing kinetic models of metabolic networks.

(1A): A set of isotopic labeling data across a range of genetic and/or environmental conditions must be generated or procured. (1B): A stoichiometric model must be constructed. (2): ¹³C-MFA is performed, and flux ranges are elucidated using the procured isotopic labeling data across all strains from step 1A and the stoichiometric model constructed in step 1B. (3): The flux distributions that were generated in step 2 are used as training data for parameterizing the kinetic model using the stoichiometric model constructed in step 1B and the K-FIT algorithm.

Fig 2. k-ecoli74 metabolic network.

Reaction and metabolite abbreviations provided in S4 File.

Fig 3. k-ecoli74 regulatory network.

Reaction and metabolite abbreviations provided in S4 File.

Fig 4. k-ecoli74 fitness to mutant flux distributions used for kinetic parameterization.

Fig 5. Comparison of k-ecoli74-predicted flux values with ¹³C-MFA flux values.

Fig 6. Number of k-ecoli74-predicted fluxes from each strain used for parameterization falling with one, two, three, or four SDs of the corresponding ¹³C-MFA value.

Fig 7. Comparison of mutant strain predicted scaled metabolite concentrations with wild-type metabolite concentration (all values scaled by wild-type absolute metabolite concentration).

(A) Δpgi relative concentration (B) Δrpe relative concentration (C) Δeda relative concentration (D) Δedd relative concentration (E) Δfbp relative concentration (F) Δzwf relative concentration (G) Δgnd relative concentration. Error bars denote range of a single standard deviation from mean scaled concentration value.

Fig 8. Comparison of overproducing strain metabolite yield ranges when top three models are used to evaluate target metabolite yields with experimental ranges and k-ecoli457 yield values.

Fig 9. Leave-one-out cross-validation comparison with full parameterization.

(A) Predicted cross-validation SSR vs. full parameterization SSR per-strain comparison (B) Predicted cross-validation glucose uptake rate vs. full parameterization glucose uptake rate per-strain comparison.

Fig 10. Regulatory mechanisms that are dispensable and indispensable to k-ecoli74 fitness.