Figure 1.
Data generated by batch cultivation of Pa. denitrificans [4] (redrawn).
As the cells transited from oxic to anoxic conditions (Panel A), Bergaust et al. [4] observed a severe depression in the total e−-flow rate (i.e., to O2+NOx, Panel B), which was taken to indicate that only a fraction of the cells switched to anaerobic respiration (denitrification). Had all of the cells switched, the total e−-flow would have carried on increasing without such a depression. The depression was followed by an exponential increase in the e−-flow rate, which was ascribed to anaerobic growth of a small fraction () of the cells that escaped entrapment in anoxia and carried on growing by denitrification.
Figure 2.
The regulatory network of denitrification in Pa. denitrificans.
In Pa. denitrificans, denitrification is driven by four core enzymes: Nar (nitrate reductase encoded by the nar genes), NirS (nitrite reductase encoded by nirS), cNor (NO reductase encoded by nor), and NosZ (N2O reductase encoded by nosZ). The transcription of these genes is regulated by, at least, three FNR-type proteins, which are sensors for O2 (FnrP), /
(NarR), and NO (NNR). NarR and NNR facilitate product-induced transcription of the nar and nirS genes (see positive-feedback loops), where NNR also counteracts the NO accumulation (negative-feedback loop) [10], [17], [18]. Circumstantial evidence suggests that O2 inactivates NNR (grey dashed link) [20], and NirS is also unlikely to be functional in the presence of high O2 concentrations. Hence, for our modelling we hypothesise that the probability of an autocatalytic transcriptional activation of nirS is zero until O2 falls below a critical concentration
. When O2 falls below
, the initial nirS transcription is possibly mediated through a minute pool of intact NNR, crosstalk with other factors, or through non-biological traces of NO found in an
-supplemented medium. Regardless of the exact mechanism(s), once nirS transcription is initiated, it will be substantially enhanced by spikes of internal NO emitted from the first molecules of NirS (the positive-feedback loop). The activated positive-feedback will also induce nor and nosZ transcription via NNR (although, the latter can also be induced independently by FnrP [19]), facilitating the synthesis of a full-fledged denitrification proteome. Our model assumes that such recruitment to denitrification will occur with a low probability. We further assume that the recruitment will only be possible as long as a minimum of O2
is available because the production of the first molecules of NirS will depend on energy from aerobic respiration.
Table 1.
Figure 3.
An overview of the modelled system: batch incubation in a gas-tight vial.
The experiment: The stirred Sistrom's medium [27] was inoculated with aerobically grown Pa. denitrificans cells, which were provided with different concentrations of O2 and (g or aq with a chemical species-name represents gaseous or aqueous, respectively). O2 is consumed by respiration, driving its transport from the headspace to the liquid. Once the aerobic respiration becomes limited, the cells may switch to denitrification (recruitment), reducing
to N2 via the intermediates NO and N2O (not shown). For monitoring O2, CO2, N2, NO and N2O, a robotised incubation system [28] was used, which automatically takes samples from the headspace by piercing the rubber septum. Each sampling removes a fraction (3–3.4%) of all gases in the headspace, but it also involves a marginal leakage of O2 and N2 into the vial (as indicated by the two-way arrows at the top of the figure). The model: The model operates with two sub-populations: one without and the other with denitrification enzymes (
and
, respectively). Both consume O2 if present, but
cannot reduce NOx. The
cells may be recruited to the
pool as
falls below a critical threshold. The rate of recruitment (
) is modelled as a probabilistic function:
(cells h−1), where
represents an O2 dependent specific-probability (h−1) for any
cell to initiate nirS transcription (leading to the synthesis of a full-fledged denitrification proteome).
Figure 4.
A stock and flow diagram of the model's structure.
The squares represent the state variables, the circles the rate of change in the state variables, the shaded ovals the auxiliary variables, the arrows dependencies between the variables, and the edges represent flows into or out of the state variables. A. The panel represents the structure that governs the O2 kinetics. Briefly, it shows that O2 in the vial's headspace () is transported (
) to the liquid-phase (
), where it is consumed (
) by both
and
populations with an identical cell-specific velocity of O2 consumption (
).
represents net marginal changes in
due to sampling. B. The panel represents the structural basis for population dynamics of the cells without (
) and with (
) denitrification enzymes. Briefly, it shows that both the populations are able to grow by aerobic respiration (
and
, respectively). The growth rate of
, however, is primarily based on denitrification (
). Initially,
= 0 and is populated through recruitment (
) of the cells from
, where the recruitment is a function of
and an [O2] dependent specific-probability of the recruitment
for any
cell. C. The panel represents the structural basis for the
/N2 kinetics. Briefly, it illustrates that
control the consumption rate of
(
), recovered as N2, in proportion to a cell-specific velocity of
consumption (
).
Table 2.
Model parameters.
Figure 5.
Modelling of (h−1) as a function of
.
A. The panel shows the O2 concentration in the liquid-phase falling as a result of aerobic respiration. B. The panel shows the probability for a cell to switch to denitrification (
, h−1) modelled as a function of
.
(Panels A & B) is the concentration below which
is assumed to trigger (due to withdrawal of the transcriptional control of O2 on denitrification [22]), whereas
is assumed to be the concentration below which
terminates (due to lack of energy for enzyme synthesis). The double-headed arrow (at the bottom of Panel A) illustrates the limited time-window (
) available for the cells to switch to denitrification.
Table 3.
Initial values for the state variables.
Figure 6.
Comparison of the measured [4], [8] and simulated data assuming = 1 h−1.
Assuming a single homogeneous population, as we forced our model to achieve 100% recruitment to denitrification by setting the specific-probability of recruitment () to 1 h−1, the simulated N2 accumulation (molN vial−1) showed considerable overestimation as compared to that measured. To illustrate this, the simulated and measured data are compared here for some randomly chosen treatments. Initial vol.% O2 in the headspace and initial
is shown above each panel.
Figure 7.
Simulations of the treatments with ∼0 vol.% using
= 0.0052 h−1.
The figure compares the measured and simulated O2 depletion (mol vial−1) and N2 accumulation (molN vial−1) for the ∼0 vol.% O2 treatments of Bergaust et al. [4], [8], i.e., the vials with near-zero O2 in the headspace () at the time of inoculation. Separate plots are shown for each initial concentration of
(0.2, 1, and 2 mM). The measured initial O2 was somewhat erratic due to episodes of needle clogging and/or high O2 leakage during sampling, so the initial
used in the simulations is chosen somewhat ad lib so that the simulated O2 depletion coincides with that measured. The discrepancy compared to the measured O2 seems to be significant for 2 mM
treatment. That is most likely due to the inhibitory effect of nitrite on aerobic respiration, which is not taken into account; all simulations are run with an identical
. Near exhaustion, the simulated O2 increases slightly at each sampling time; that is due to the leakage of O2 via the injection system exceeding dilution of the headspace (with He) during each sampling.
Figure 8.
Simulations of the treatments with 1 vol.% using
= 0.0052 h−1.
The figure compares the measured and simulated O2 depletion (mol vial−1) and N2 accumulation (molN vial−1) for the treatments with 1 vol.% O2 in the headspace () at the time of inoculation; separate plots are shown for each initial concentration of
(0.2, 1, and 2 mM). At each sampling time, the simulated O2 is visibly reduced; that is because sampling implies 3.4% dilution of the headspace (with He). This contrasts with the simulations of the treatments with low O2 (Fig. 7), where the leakage of O2 into the system is more dominant.
Figure 9.
Simulations of the treatments with 7 vol.% using
= 0.0052 h−1.
The figure compares the measured and simulated O2 depletion (mol vial−1) and N2 production (molN vial−1) for the treatments with 7 vol.% O2 in the headspace () at the time of inoculation; separate plots are shown for each initial concentration of nitrite (0.2, 1, and 2 mM). At each sampling time, the simulated O2 is visibly reduced because of sampling, which results in 3.4% dilution of the headspace (with He).
Table 4.
Specific-probability of recruitment of a cell to denitrification () estimated for each batch culture by optimisation (best match between the simulated and measured N2 kinetics).
Table 5.
The model's and Bergaust et al.'s [16] estimations of the fraction recruited to denitrification ().
Figure 10.
Simulation of the ‘diauxic lags’ observed by Liu et al [24].
A. The panel shows cumulated OD (optical density) of the cells without () and with (
) denitrification enzymes for the simulated experiment of Liu et al. [24], where one treatment was sparged at time = 2.55 h and the other at 1.1 h. The simulations show, qualitatively, similar ‘lags’ in the two ODs as observed by the experimenters. These apparent lags are due to exponential growth of a minute fraction of the cells that successfully switched to denitrification. The growth of this fraction remains practically undetectable (the “lag” phase) until it reaches a level comparable to the large population trapped in anoxia. B. This panel isolates the ODs of
and show them on a logarithmic scale so that the exponential growth of
, right from the onset of anoxic conditions, becomes visible. The graph initially shows a quick recruitment of the cells from the
to the
pool, followed by the exponential growth-phase.
Figure 11.
Sensitivity analysis (1): Varying initial O2 in the headspace within a low range.
The figure shows the impact of varying within a low range on: A. O2 concentration in the liquid-phase
, B. The number of aerobically growing cells (
), which do not possess denitrification enzymes, C. The rate of recruitment of
to denitrification (
), and D. N2 accumulation. Marked in Panel A,
is the
below which
triggers, and
is the
below which
terminates. In Panel C, the spikes of recruitment (following the initial recruitment) are due to spikes of O2 by sampling, causing
to transiently exceed
. The model predicts that reducing
within a low range (Panel A) will lower the number of aerobically grown cells (Panel B) and, thereby, the recruitment rate (Panel C), thus increasing the time taken to deplete
(slower N2 accumulation, Panel D).
Figure 12.
Sensitivity analysis (2): Varying initial O2 in the headspace ((
)) within a high range.
The figure shows the impact of varying within a range much higher than
(the [O2] below which recruitment of the cells to denitrification is assumed to trigger) on: A. O2 concentration in the liquid-phase
, B. The number of aerobically growing cells (
), which do not possess denitrification enzymes, C. The rate of recruitment of
to denitrification (
), D. The number of cells as a result of the recruitment alone (
), i.e., the denitrifying cells (
) but without aerobic and NOx-based growth, and E. Cumulated N2. The cumulated N2 reached stable plateaus at nearly the same time for all the runs (Panel E), despite the fact that the time taken to deplete O2 below
decreased with increasing
(Panel A). Thus, once denitrification was initiated, the rates increased with increasing initial
due to an increasing population of oxygen-grown cells (Panels B–D). The fraction of the cells recruited to denitrification (
) declined with increasing initial O2 concentration (not shown), but this was not sufficient to compensate for the increasing number of oxygen-raised cells.