Prediction of metabolic flux distribution from gene expression data based on the flux minimization principle

Abstract

Prediction of possible flux distributions in a metabolic network provides detailed phenotypic information that links metabolism to cellular physiology. To estimate metabolic steady-state fluxes, the most common approach is to solve a set of macroscopic mass balance equations subjected to stoichiometric constraints while attempting to optimize an assumed optimal objective function. This assumption is justifiable in specific cases but may be invalid when tested across different conditions, cell populations, or other organisms. With an aim to providing a more consistent and reliable prediction of flux distributions over a wide range of conditions, in this article we propose a framework that uses the flux minimization principle to predict active metabolic pathways from mRNA expression data. The proposed algorithm minimizes a weighted sum of flux magnitudes, while biomass production can be bounded to fit an ample range from very low to very high values according to the analyzed context. We have formulated the flux weights as a function of the corresponding enzyme reaction's gene expression value, enabling the creation of context-specific fluxes based on a generic metabolic network. In case studies of wild-type Saccharomyces cerevisiae, and wild-type and mutant Escherichia coli strains, our method achieved high prediction accuracy, as gauged by correlation coefficients and sums of squared error, with respect to the experimentally measured values. In contrast to other approaches, our method was able to provide quantitative predictions for both model organisms under a variety of conditions. Our approach requires no prior knowledge or assumption of a context-specific metabolic functionality and does not require trial-and-error parameter adjustments. Thus, our framework is of general applicability for modeling the transcription-dependent metabolism of bacteria and yeasts.

Figure 1. Schematic description of the E-Fmin framework.

The algorithm was implemented through the following procedures. The first step was to obtain absolute gene expression profiles in a given condition from microarray, RNA-seq, or other high-throughput methods. Second, gene expression profiles were mapped onto individual reactions using gene-reaction associations. Third, the mapped expression data were integrated with the network model, and the optimization problem is solved to predict the flux distribution. Finally, model predictions were validated by comparison with experimentally measured flux data. The performance of model prediction can be gauged using standard measures, such as correlation coefficients (denoted by ρ) and sum of squared error (SSE).

Figure 2. Toy example illustrating an implementation of the E-Fmin algorithm.

The network model includes nine reactions (r ₁ to r ₉) but only five available stoichiometric constraints among the five intracellular metabolites under the steady-state assumption. E-Fmin determines the full flux vector for this undetermined system by solving a linear programming problem such that a weighted sum of flux magnitudes is minimized while biomass production (i.e., r ₉ in this example) carries nonzero flux. Given two sets of transcriptomic data, E-Fmin generates different flux distributions (denoted by thick arrows). The weight to the i ^th reaction (w_i) is formulated as a decreasing function of the associated gene expression level (g_i), i.e., w_i = 1 – g_i. The weights highlighted in red represent the reactions for which no associated gene expression data are available.

Figure 3. Exometabolome data of Saccharomyces cerevisiae and model predictions.

Bars represent experimental and predicted values of exchange fluxes when the glucose uptake was A) 16.5 and B) 11.0 mmol/(gDW⋅h). Capital letters on the x-axis denote the production rates of extracellular metabolites, i.e., E: ethanol production, C: CO₂ production, G: glycerol production, A: acetate production, T: trehalose production, L: lactose production, and B: biomass production. GIMME, Gene Inactivity Moderated by Metabolism and Expression; FBA, flux balance analysis; iMAT, integrative metabolic analysis tool.

Figure 4. E-Fmin predictions of intracellular metabolic fluxes in wild-type Escherichia coli.

Shown is a comparison of the metabolic fluxes at varied dilution rates (D; x-axis) as measured using ¹³C-metabolic flux analysis (¹³C-MFA; y-axis) and predicted by E-Fmin (z-axis). In all cases, flux comparisons were made using their relative values normalized with the glucose uptake flux of 100 mmol/(gDW⋅h).