Fig 1.
Panel A shows an example network in the Systems Biology Graphical Notation format (SBGN, www.sbgn.org) [20] to illustrate the basic principle of ScalaFlux. The flux models (and associated datasets) required to quantify the flux through reaction r16 using classical non-stationary 13C-MFA and ScalaFlux are compared in panel B. The ScalaFlux model, the set of measurements required for the flux calculation, and the flux calculation workflow are shown in panel C.
Fig 2.
Network decomposition to construct flux models.
The metabolic network shown in Fig 1A can be decomposed into 17 minimal subsystems (panel A) which are sufficient to simulate the labeling dynamics of metabolic intermediates (green circles) from the local label input(s) (red circles). Each minimal subsystem is self-consistent and can be used for independent flux calculations. These minimal subsystems can also be combined to analyze larger subsystems, as shown in panels B and C.
Fig 3.
Fluxes through each reaction of the example network (Fig 1A) estimated by analyzing all minimal subsystems.
Fluxes were estimated independently in all the minimal subsystems shown in panel A. The estimated fluxes are in good agreement with the true values (R2 = 0.98, p-value = 1.10−14, panel B). The distribution of fluxes estimated from 200 noisy datasets are shown in panel C, with the true value used for simulation shown as a red dot and the median of the estimated fluxes shown as a white dot.
Fig 4.
Demonstration of the scalability of ScalaFlux.
The absolute flux through the pathway r10-r16 (orange reactions in panel A) can be quantified in 29 different subsystems (columns in panel B), each of which i) include different reactions (in blue) and ii) exploit different sets of measurements (labeling of local label inputs in red, and concentrations and labeling of metabolic intermediates in green). The fluxes estimated for each subsystem are shown in panel C and are compared to the true value (1.0 μmol/gDW/h, horizontal line).
Fig 5.
13C-metabolic flux analysis of prenyl pyrophosphate biosynthesis in Saccharomyces cerevisiae (wild type, S037 and S023 strains).
The yeast prenyl pyrophosphate pathway contains five reactions for the successive condensation of IPP (in grey) onto each intermediate (DMAPP, FPP, GPP and GGPP) (A). The labeling dynamics of IPP were fitted with a double logistic function, which was used as the local label input. Fluxes were estimated by fitting the metabolite concentrations and transient 13C-enrichments of GPP, FPP and GGPP. Experimental and fitted data are shown for each strain in panel B for the labeling dynamics (dots: experimental values; lines: best fit) and in panel C for the metabolite concentrations. The fluxes estimated in each strain are given with their standard deviations in panel D. The GGPP demand calculated from phytoene accumulation in strain S023 is shown in grey for comparison. The GGPP turnover rate estimated in each strain is shown in panel E.