Fig 1.
A universal central metabolic pathway for bacteria.
The central carbon metabolic pathway is simplified into 29 fluxes, used as the outputs of our model.
Fig 2.
The flowchart of MFlux algorithm.
Fig 3.
Overview of central metabolic fluxes collected in our dataset.
“Flux range” represents the variation of each flux in the 13C-MFA dataset. “95% confidence interval” indicates that 95% of flux data were within a small range. “Average flux value” is the average value in each flux based on all data in our 13C-MFA dataset.
Fig 4.
A comparison of three ML algorithms: SVM, k-NN, and decision tree.
The best cross-validation results on 29 fluxes are compared. All tests in this step were performed on the WT dataset only.
Fig 5.
Best results by SVM on WT and WP datasets.
Grid searches are performed on both linear and RBF kernels. The results from WP dataset are much better than those from the WT dataset. The result indicated that the size of the dataset is an important factor affecting the predictive power of machine learning models.
Fig 6.
A comparison between linear-kernel SVM and RBF-kernel SVM.
The best cross-validation results of linear kernel and RBF kernel after grid searches on WP dataset are very similar. The RBF kernel is employed in the final model for flux prediction.
Fig 7.
Summary of root mean squared error (RMSE) from 20 case studies: averaged flux from 13C-MFA dataset, ML-only, and MFlux (ML + quadratic programming).
The average RMSE is 7.7 from ML-only, and 5.6 from MFlux. Detailed information is in S1 and S2 Tables.
Table 1.
Glc, glucose; Xyl, xylose; Lac, lactate; Ace, acetate; KO, knockout.
Fig 8.
A comparison of the 13C-MFA flux, the flux predicted by ML only, and the flux predicted by MFlux in Case 8.
B. subtilis was incubated in a shake flask (37 C, 300 rpm, aerobic condition), and supplied with labeled succinate and glutamate as carbon sources in M9 minimal medium. Detailed information is in S1 Table.
Fig 9.
A comparison of the 13C-MFA flux, the flux predicted by ML only, and the flux predicted by MFlux in Case 16.
G. thermoglucosidasius M10EXG was incubated in sealed bottles (micro-aerobic condition), supplied with glucose as a carbon source. Detailed information is in S2 Table.
Fig 10.
A comparison of the 13C-MFA flux, the flux predicted by MFlux, and the flux predicted by FBA.
FBA analysis is simulated by an E. coli iJO1366 model (latest version) with default boundary settings from the reference [54]. The default values of growth associated maintenance energy (GAM) and non-growth associated maintenance energy (NGAM) were adopted. A) E. coli fluxome of glucose metabolism was precisely measured via parallel labeling experiments (a recent paper not in our dataset) [12]. B) E. coli fluxome of glycerol and glucose co-metabolism as measured by Drs. Yao and Shimizu (unpublished data). The E. coli strain was cultured in chemostat fermentor with a working volume of 1 L(37 C). The dilution rate in the continuous culture was 0.35 h−1. [1-13C] glucose and [1, 3-13C] glycerol were used for tracer experiments. The flux calculation is based on a previous method [42]. The RMSE from FBA is 22.5, while the RMSE from MFlux (this work) is 5.1. The COBRA toolbox running on MATLAB R2012b was employed for FBA/pFBA/geometricFBA simulation, and Gurobi 5.5 was used for linear programming. Detailed information is included in S2 Table.