Linear programming based gene expression model (LPM-GEM) predicts the carbon source for Bacillus subtilis

Abstract

Background: Elucidating cellular metabolism led to many breakthroughs in biotechnology, synthetic biology, and health sciences. To date, deriving metabolic fluxes by ¹³C tracer experiments is the most prominent approach for studying metabolic fluxes quantitatively, often with high accuracy and precision. However, the technique has a high demand for experimental resources. Alternatively, flux balance analysis (FBA) has been employed to estimate metabolic fluxes without labeling experiments. It is less informative but can benefit from the low costs and low experimental efforts and gain flux estimates in experimentally difficult conditions. Methods to integrate relevant experimental data have been emerged to improve FBA flux estimations. Data from transcription profiling is often selected since it is easy to generate at the genome scale, typically embedded by a discretization of differential and non-differential expressed genes coding for the respective enzymes.

Result: We established the novel method Linear Programming based Gene Expression Model (LPM-GEM). LPM-GEM linearly embeds gene expression into FBA constraints. We implemented three strategies to reduce thermodynamically infeasible loops, which is a necessary prerequisite for such an omics-based model building. As a case study, we built a model of B. subtilis grown in eight different carbon sources. We obtained good flux predictions based on the respective transcription profiles when validating with ¹³C tracer based metabolic flux data of the same conditions. We could well predict the specific carbon sources. When testing the model on another, unseen dataset that was not used during training, good prediction performance was also observed. Furthermore, LPM-GEM outperformed a well-established model building methods.

Conclusion: Employing LPM-GEM integrates gene expression data efficiently. The method supports gene expression-based FBA models and can be applied as an alternative to estimate metabolic fluxes when tracer experiments are inappropriate.

Keywords: Bacillus subtilis; Carbon source; Constraint-based modeling; Flux balance analysis; Mixed-integer linear programming; Thermodynamically infeasible loops; Transcriptomics.

Fig. 1

The workflow.

Fig. 2

The total model mapping discrepancy calculated over all eight conditions (at $\alpha$ = 0.01, the penalty parameter  α is described below) is shown with respect to the number of iterations of the search space reduction algorithm (IFFPR). As the algorithm proceeds to the end of the list of reactions (> 600 iterations), the total model mapping discrepancy does not further decrease.

Fig. 3

a In each panel, the bars show the z-scores of the predictions of the carbon source transporters are shown (of the eight-carbon-sources study). The headers of the panels indicate the true carbon source of the respective condition; b Prediction of the carbon source for the nutritional shift. GM: glucose to glucose plus malate, 90 min after adding malate; MG: malate to malate plus glucose, 90 min after adding glucose. For (a) and (b), a higher z-score indicates a higher probability for a specific carbon source.

Fig. 4

Prediction performance of our approach (LPM-GEM), iMAT, and mCADRE. For all 40 core reactions for which gold standard data (from ¹³C tracer analysis) was available, the Pearson’s correlation coefficients between the predicted fluxes and the fluxes from the gold standard are shown (grey: fluxes are predicted to be zero in every condition); PPP: pentose phosphate pathway, TCA: tricarboxylic acid.

Fig. 5

Comparison of normalized errors from different methods. Normalized errors of LPM-GEM, iMAT, and mCADRE from eight different conditions are shown in the square root scale (the normalized error is the Euclidean distance between ¹³C metabolic flux values and predicted flux values of the specific condition divided by the magnitude of ¹³C metabolic flux values of the same condition [52])