Hybrid metabolic flux analysis: combining stoichiometric and statistical constraints to model the formation of complex recombinant products

Abstract

Background: Stoichiometric models constitute the basic framework for fluxome quantification in the realm of metabolic engineering. A recurrent bottleneck, however, is the establishment of consistent stoichiometric models for the synthesis of recombinant proteins or viruses. Although optimization algorithms for in silico metabolic redesign have been developed in the context of genome-scale stoichiometric models for small molecule production, still rudimentary knowledge of how different cellular levels are regulated and phenotypically expressed prevents their full applicability for complex product optimization.

Results: A hybrid framework is presented combining classical metabolic flux analysis with projection to latent structures to further link estimated metabolic fluxes with measured productivities. We first explore the functional metabolic decomposition of a baculovirus-producing insect cell line from experimental data, highlighting the TCA cycle and mitochondrial respiration as pathways strongly associated with viral replication. To reduce uncertainty in metabolic target identification, a Monte Carlo sampling method was used to select meaningful associations with the target, from which 66% of the estimated fluxome had to be screened out due to weak correlations and/or high estimation errors. The proposed hybrid model was then validated using a subset of preliminary experiments to pinpoint the same determinant pathways, while predicting the productivity of independent cultures.

Conclusions: Overall, the results indicate our hybrid metabolic flux analysis framework is an advantageous tool for metabolic identification and quantification in incomplete or ill-defined metabolic networks. As experimental and computational solutions for constructing comprehensive global cellular models are in development, the contribution of hybrid metabolic flux analysis should constitute a valuable complement to current computational platforms in bridging the metabolic state with improved cell culture performance.

Figure 1

Sensitivity analysis of viral production and biomass production fluxes. Sensitivity analysis of biomass or product synthesis estimations was performed when the measured value of each of these fluxes was individually omitted from the complete model, yielding an overdetermined system of equations (see text and Methods section). The estimation of fractional sensitivities was achieved by factoring the appropriate average value of measured metabolite consumption/production rates and average value of measured cell growth rate or productivity, respectively, from all available culture conditions (see Table 2). Horizontal axis marks indicate computed sensitivities are zero.

Figure 2

Data-driven framework for predictive metabolic flux analysis. (A) Schematic representation of a metabolic network with an unknown or ill-defined portion corresponding to the synthesis of a complex recombinant product. These poorly defined pathways are substituted by a statistical sub-model bridging the known well-defined stoichiometry with the target product formation rate. (B) Given a set of measured fluxes (V_m - usually exchange fluxes of metabolic consumption and production), metabolic flux analysis is used to estimate the entire flux distribution (V_e) in a predefined metabolic network. Then, PLS is performed to find a linear regression model between the estimated fluxome and the vector of a measured target such as productivity, V_t. As a result, a list of regression coefficients representing how strongly each flux correlates with the target is obtained (B), making it possible to predict the productivity of independent cultures after metabolic manipulation.

Figure 3

Functional metabolic decomposition of baculovirus-producing S. frugiperda's cells. (A) Performance of predictive MFA in describing baculovirus productivity based on metabolic data from 13 independent cultures (see Table 2). In all cases, Sf9 insect cells were infected with a low multiplicity of infection in serum-free medium. A total of 3 latent variables were used to describe the data. Productivity is expressed in 10³ infectious particles × (10⁶ cells × h)^-1. (B) In order to estimate confidence intervals for the model regression coefficients, Monte Carlo sampling was used to generate 1000 data matrices based on the error variances of all predictor and target variables (see Methods section for details). The strength of association (α) was defined as the confidence interval to regression coefficient ratio, allowing the exclusion of those fluxes with α values lower than 1. (C) After hierarchical clustering, the TCA cycle and mitochondrial respiration naturally arised as a closely connected group of fluxes strongly correlated with high productivities. With lighter association strengths, one additional cluster corresponds to the catabolization fluxes of the essential amino acids phenylalanine, methionine and histidine. Abbreviations: ACoA (acetyl-coenzyme A), Cit (citrate), Fum (fumarate), His (histidine), Mal (malate), Met (methionine), OAA (oxaloacetate), Phe (phenylalanine), Pyr (pyruvate), Suc (succinate), SuCoA (succinyl-coenzyme A), αKG (α-ketoglutarate).

Figure 4

Validation of predictive MFA for metabolic engineering. (A) To validate our framework as a powerful tool to assign targets for metabolic engineering, the complete set of 13 experiments was purposefully split into calibration and validation subsets in two manners. In strategy 1, experiments 6, 7, 8, 9 and 13, which have been rationally designed to manipulate the cellular energetic state, were left aside for validation. In strategy 2, the top three producers (experiments 1, 6 and 7) were chosen as validation cultures to avoid data interpolation. The number of latent variables used to build the calibration models in each case was 1 and 3, respectively. Productivity is expressed in 10³ infectious particles × (10⁶ cells × h)^-1. (B) Metabolic decomposition for each validation strategy, showing the common selection of TCA cycle/respiration as important pathways for viral replication. Also for validation strategy 1, the catabolism of phenylalanine, methionine and histidine had α values higher than 1, as well as other fluxes with lighter correlations with the target (other: catabolism of maltose, proline and tyrosine, formation of alanine).