Fig 1.
Labelling curves in a linear non-reversible pathway.
(a) A linear non-reversible pathway subjected to a step label input. (b) Label propagation curves for a linear non-reversible pathway of 5 randomly sized metabolites. Circles indicate the position of “label shock wave”, i.e. the time points at which the first derivative of each labeling curve reaches maximum. The values of the pool sizes Mi and the shock wave positions are given in the legend.
Fig 2.
Comparison between estimated and real LSW positions.
We now compare three randomly generated linear non-reversible pathways of length 10. Estimations were based on formula (17). Real values were obtained by numerically solving . The solid line corresponds to y = x.
Fig 3.
Examples of label propagation in the pathway of Fig 1 after applying a sinusoidal Eq (19) label input.
(a) Pathway scheme subjected to a sinusoidal label input; (b) A high frequency input wave (T = 2π/ω = 1 s) leads to a rapid reduction in amplitude through propagation via the pathway. (c) A low frequency (T = 2 s) preserves the wave amplitude at the end of the pathway better and leaves the wave delay almost unchanged compared to case T = 1 s. The same wave delay explains the impression that this graph is merely stretched out compared to graph b) (abstraction made of the change in amplitude).
Fig 4.
Examples of label propagation in the previously considered linear pathway subjected to an RPP label input.
The labeling curves of metabolites ranked 3 or above closely resemble the labeling curves obtained with a plain sinusoidal wave input. (a) Pathway subjected to an RPP label input; (b) Like in sinusoidal wave input, applying an RPP with high frequency (T = 1 s) leads to a rapid reduction in amplitude as the signal moves along the pathway. (c) The same observation as for sinusoidal wave applies to the low frequency RPP (T = 2 s): it preserves the wave amplitude at the end of the pathway better and leaves the wave delay observed for T = 1 s almost unchanged.
Fig 5.
Comparison of estimated and true fluxes in a simulated RPP experiment.
(a) Scheme of RPP experiment on E. coli. Fully labeled glucose is fed to the culture in RPP form. Several aminoacids are measured by GC-MS. (b) Only statistically and structurally identifiable free and dependent fluxes (distinguished by “f” and “d” at the beginning of the flux names) are reported (17 of 70). The prefixes “n” and “x” in flux names correspond to net and exchange fluxes respectively. Exchange fluxes are mapped on [0, 1] intervals. Error bars correspond to 95% CI estimated by linearized statistics. The solid line indicates y = x positions. This example shows that in an RPP experiment, we can expect a good agreement between true and estimated values for identifiable fluxes.