Dynamic metabolic flux analysis demonstrated on cultures where the limiting substrate is changed from carbon to nitrogen and vice versa

Abstract

The main requirement for metabolic flux analysis (MFA) is that the cells are in a pseudo-steady state, that there is no accumulation or depletion of intracellular metabolites. In the past, the applications of MFA were limited to the analysis of continuous cultures. This contribution introduces the concept of dynamic MFA and extends MFA so that it is applicable to transient cultures. Time series of concentration measurements are transformed into flux values. This transformation involves differentiation, which typically increases the noisiness of the data. Therefore, a noise-reducing step is needed. In this work, polynomial smoothing was used. As a test case, dynamic MFA is applied on Escherichia coli cultivations shifting from carbon limitation to nitrogen limitation and vice versa. After switching the limiting substrate from N to C, a lag phase was observed accompanied with an increase in maintenance energy requirement. This lag phase did not occur in the C- to N-limitation case.

Figure 1

A moving window is run through a time series of data. W₁ is the polynomial fitting window, W₂ is the interpolation window.

Figure 2

Two ways of estimating the derivative in point a: D₁ is calculated by symbolically deriving the function in point a; D₂ is the slope between point a and point b (where a and b are calculated from the curve). Dots represent sample points through which a curve is fitted.

Figure 3

Polynomial fit of some metabolites (expressed in g/L) for the experiment where carbon-limiting medium was replaced with nitrogen-limiting medium. The switch is made at time zero, when the cells are in carbon-limited steady state. Steady state values of five residence times before the switch and five residence times after the switch are not shown.

Figure 4

Polynomial fit of some metabolites (expressed in g/L) for the experiment where nitrogen-limiting medium was replaced with carbon-limiting medium. The switch is made at time zero, when the cells are in nitrogen-limited steady state. Steady state values of five residence times before the switch and five residence times after the switch are not shown.

Figure 5

Fluxes in mol/L/h of the biomass production. Open symbols are the values as derived from the polynomials with formula 4; closed symbols are values obtained after flux balancing (top). The growth rate in 1/h of the cells during the transients (bottom). Left: C-limitation to N-limitation; right: N-limitation to C-limitation. The first point left of each figure is the steady state value before the medium switch. The last point right on each figure is the steady state value after at least 50 hours. Error bars represent the standard deviations.

Figure 6

Amount of oxygen consumed (top) and carbon dioxide produced (bottom). Left: C-limitation to N-limitation; right: N-limitation to C-limitation. The first point left of each figure is the steady state value before the medium switch. The last point right on each figure is the steady state value after at least 50 hours. Error bars represent the standard deviations.

Figure 7

Fluxes through the ATP hydrolysis reaction (ATPHY reaction): it can be considered as a measure for the maintenance requirement of the cells, as it combines all the futile cycles and ATP hydrolysed in nonspecific reactions. Left: C-limitation to N-limitation; right: N-limitation to C-limitation. The first point left of each figure is the steady state value before the medium switch. The last point right on each figure is the steady state value after at least 50 hours. Error bars represent the standard deviations.

Figure 8

Fluxmap of the glycolysis, penthose phosphate pathway, and citric acid cycle for the experiment where carbon-limiting medium is changed to nitrogen-limiting medium at time zero. The ordinate on each graph represents the flux expressed in mol/mol Biomass/h while the abscissa represents time. The first point left of each figure is the steady state value before the medium switch. The last point right on each figure is the steady state value after at least 50 hours. Error bars represent the standard deviations.

Figure 9

Fluxmap of the glycolysis, penthose phosphate pathway, and citric acid cycle for the experiment where nitrogen-limiting medium is changed to carbon-limiting medium at time zero. The ordinate on each graph represents the flux expressed in mol/mol Biomass/h while the abscissa represents time. The first point left of each figure is the steady state value before the medium switch. The last point right on each figure is the steady state value after at least 50 hours. Error bars represent the standard deviations.