In response to impending anoxic conditions, denitrifying bacteria sustain respiratory metabolism by producing enzymes for reducing nitrogen oxyanions/-oxides (NOx) to N2 (denitrification). Since denitrifying bacteria are non-fermentative, the initial production of denitrification proteome depends on energy from aerobic respiration. Thus, if a cell fails to synthesise a minimum of denitrification proteome before O2 is completely exhausted, it will be unable to produce it later due to energy-limitation. Such entrapment in anoxia is recently claimed to be a major phenomenon in batch cultures of the model organism Paracoccus denitrificans on the basis of measured e−-flow rates to O2 and NOx. Here we constructed a dynamic model and explicitly simulated actual kinetics of recruitment of the cells to denitrification to directly and more accurately estimate the recruited fraction (). Transcription of nirS is pivotal for denitrification, for it triggers a cascade of events leading to the synthesis of a full-fledged denitrification proteome. The model is based on the hypothesis that nirS has a low probability (, h−1) of initial transcription, but once initiated, the transcription is greatly enhanced through positive feedback by NO, resulting in the recruitment of the transcribing cell to denitrification. We assume that the recruitment is initiated as [O2] falls below a critical threshold and terminates (assuming energy-limitation) as [O2] exhausts. With = 0. 005 h−1, the model robustly simulates observed denitrification kinetics for a range of culture conditions. The resulting (fraction of the cells recruited to denitrification) falls within 0. 038–0. 161. In contrast, if the recruitment of the entire population is assumed, the simulated denitrification kinetics deviate grossly from those observed. The phenomenon can be understood as a ‘bet-hedging strategy’: switching to denitrification is a gain if anoxic spell lasts long but is a waste of energy if anoxia turns out to be a ‘false alarm’.
Denitrification is a key process in the global nitrogen cycle and is also a major source of atmospheric N2O [2]. A plethora of biogeochemical models have been developed for understanding the ecosystem controls of denitrification and N2O emissions [3]. A common feature of these models is that the denitrifying community of the system (primarily soils and sediments) in question is treated as one homogenous unit with certain characteristic responses to O2 and concentrations. This simplification is fully legitimate from a pragmatic point of view, but in reality any denitrifying community is composed of a mixture of organisms with widely different denitrification regulatory phenotypes [4]. Modelling has been used to a limited extent to analyse kinetic data for various phenotypes (See [5] and references therein) and for understanding the accumulation of intermediates [6]. To our knowledge, however, no attempts have been made to model the regulation during transition from aerobic to anaerobic respiration in individual strains, despite considerable progress in the understanding of their regulatory networks. It would be well worth the effort, since the regulatory phenomena at the cellular level provide clues as to how denitrification and NO and N2O emissions therefrom are regulated in intact soils [7]. Explicit modelling of the entire denitrification regulatory network, however, would take us beyond available experimental evidence, with numerous parameters for which there are no empirical values. Considering this limitation, here we have constructed a simplified model to investigate if a stochastic transcriptional initiation of key denitrification genes (nirS) could possibly explain peculiar kinetics of e−-flow as Paracoccus denitrificans switch from aerobic to anaerobic respiration [4], [8]. Although denitrification is widespread among bacteria, the α-proteobacterium Pa. denitrificans is the ‘paradigm’ model organism in denitrification research. Recent studies [4], [8], [9] have indicated a previously unknown phenomenon in this species that, in response to O2 depletion, only a marginal fraction () of its entire population appears to successfully switch to denitrification. In these studies, however, is inferred from rates of consumption and production of gases (O2, NOx, and N2), and a clear hypothesis as to the underlying cause of the low is also lacking. To fill these gaps, we formulated a refined hypothesis addressing the underlying regulatory mechanism of the cell differentiation in response to O2 depletion. On its basis, we constructed a dynamic model and explicitly simulated the actual kinetics of recruitment of the cells from aerobic respiration to denitrification. The model adequately matches batch cultivation data for a range of experimental conditions [4], [8] and provides a direct and refined estimation of. The exercise is important for understanding the physiology of denitrification in general and of Pa. denitrificans in particular and carries important implications for correctly interpreting various denitrification experiments. Generally, the transcription of genes encoding denitrification enzymes is inactivated in the presence of O2. A population undertaking denitrification typically responds to full aeration by completely shutting down denitrification and immediately initiating aerobic respiration [10]. Thus, O2 controls denitrification at transcriptional as well as metabolic level, and both have a plausible fitness value. The transcriptional control minimises the energy cost of producing denitrification enzymes, and the metabolic control maximises ATP (per mole electrons transferred) because the mole ATP per mole electrons transferred to the terminal e−-acceptor is ∼50% higher for aerobic respiration than for denitrification [10]. Denitrification enzymes produced in response to an anoxic spell are likely to linger within the cells under subsequent oxic conditions (although, this has not been studied in detail), ready to be used if O2 should become limiting later on. However, these enzymes will be diluted by aerobic growth, since the transcription of their genes is effectively inactivated by O2. Hence, a population growing through many generations under fully oxic conditions will probably be dominated by the cells without intact denitrification proteome. When confronted with O2 depletion, such a population will have to start from scratch, i. e. , transcribe the relevant genes, translate mRNA into peptide chains (protein synthesis by ribosomes) and secure that these chains are correctly folded by the chaperones, transport the enzymes to their correct locations in the cell, and insert necessary co-factors (e. g. , Cu, Fe, or Mo). In E. coli grown under optimal conditions, the whole process from the transcriptional activation to a functional enzyme takes ≤20 minutes [11] and costs significant amount of energy (ATP). Synthesis of denitrification enzymes is rewarding if anoxia lasts long and NOx remains available, but it is a waste of energy if anoxia is brief. Since the organisms cannot sense how long an impending anoxic spell will last, a ‘bet-hedging strategy’ [12] where one fraction of a population synthesises denitrification enzymes while the other does not may increase overall fitness. Most, if not all, denitrifying bacteria are non-fermentative and completely rely on respiration to generate energy [13], [14]. This implies that their metabolic machinery will run out of energy whenever deprived of terminal e−-acceptors. When [O2] falls below some critical threshold, the cells will ‘sense’ this and start synthesising denitrification proteome, utilising energy from aerobic respiration [10]. However, if O2 is suddenly exhausted or removed, the lack of a terminal e−-acceptor will create energy limitation, restraining the cells from enzyme synthesis, hence, entrapping them in anoxia. This was clearly demonstrated by Højberg et al. [15], who used silicone immobilised cells to transfer them from a completely oxic to a completely anoxic environment. Such a rapid transition is unlikely to occur in nature; however, the experiment illustrates one of the apparent perils in the regulation of denitrification: the cells that respond too late to O2 depletion will be entrapped in anoxia, unable to utilise alternative electron acceptors for energy conservation and growth. Højberg et al.' s [15] observations have largely been ignored in the research on the regulation of denitrification, and it is implicitly assumed that, in response to O2 depletion, all cells in cultures of denitrifying bacteria will switch to denitrification. Contrary to this, however, Bergaust et al. [4], [8], [16] followed by Nadeem et al. [9] proposed that in batch cultures of Pa. denitrificans, only a small fraction of all cells is able to switch to denitrification. During transition from oxic to anoxic conditions, they observed a severe depression in the total e−-flow rate (i. e. , to O2+NOx, see Fig. 1), which was estimated on the basis of measured gas kinetics. Had all of the cells switched to denitrification as O2 exhausted, the total e−-flow rate would have carried on increasing, without such a depression. The depression was followed by an exponential increase in the e−-flow rate, which was tentatively ascribed to anaerobic growth of a small (fraction recruited to denitrification). It was postulated that this fraction escaped entrapment in anoxia by synthesising initial denitrification proteins within the time-window when O2 was still present, whereas the majority of the cells () failed to do so, thus remained unable to utilise NOx. To represent the batch cultivation conducted by Bergaust et al. [4], [8], the model explicitly simulates growth of two sub-populations, one with denitrification enzymes () and the other without (); both equally consume O2, but cannot reduce NOx to N2. Once oxygen concentration in the liquid falls below a critical level [22], the cells within are assumed to initiate nirS transcription (and thereby ensure recruitment to) with a rate described by a probabilistic function: (cells h−1), where is assumed to be an dependent probability (h−1) for any cell within to initiate nirS transcription (leading to a full denitrification capacity). When falls below, triggers and holds a constant value as long as is above a critical minimum. For, is zero (assuming the inactivation of NNR by O2); is also zero for (assuming the lack of energy for protein synthesis). The recruitment of to is simulated as an instantaneous event; thus, the model does not take into account the time-lag between the initiation of nirS transcription and the time when the transcribing cell has become a fully functional denitrifier. This simplification is based on the evidence that this lag is rather short. Experiments with E. coli [11] under optimal conditions suggest lags of ∼20 minutes between the onset of transcription and the emergence of a functional enzyme. In Pa. denitrificans [8], [22], the lag observed between the emergence of denitrification gene transcripts and the subsequent gas products suggests that the time required for synthesising the enzymes is within the same range. In a series of experiments with denitrifying bacteria (Pseudomonas denitrificans, Pseudomonas fluorescens, Alcaligenes eutrophus and Paracoccus pantotrophus) [24]–[26], oxic cultures were sparged with N2 to remove O2 and were monitored by measuring optical density (OD550). All the strains except Ps. fluorescens went through a conspicuous ‘diauxic lag: a period of little or no growth’ [26]; the OD remained practically constant during the lag period, lasting 4–30 hours, which was eventually followed by anaerobic growth. To understand the diauxic lag, Liu et al. [24] used the common assumption that all cells would eventually switch to denitrification. They constructed a simulation model based on the assumption that all the cells contained a minimum of denitrification proteome (even after many generations under oxic conditions). This minimum would allow them to produce more denitrification enzymes when deprived of O2, albeit very slowly due to energy limitation. The time taken to effectively produce adequate amounts of denitrification enzymes (= the diauxic lag) was taken to be a function of the initial amounts of these enzymes per cell. Although their model may possibly explain short time-lags, it appears unrealistic for lag phases as long as 10–30 hours [25] because to produce such long lags, conceivably, the initial enzyme concentration would be less than one enzyme molecule per cell, which is mathematically possible but biologically meaningless. The model presented in this paper provides an alternative explanation for the apparent diauxic lags: a sudden shift from fully oxic to near anoxic conditions (by sparging with N2) would leave the medium with only traces of O2, which would be quickly depleted due to aerobic respiration. As a consequence, the available time for initiating the synthesis of denitrification proteome would be marginal, allowing only a tiny fraction () of the cells to switch to denitrification. This marginal fraction would grow exponentially from the very onset of anoxic conditions, but it would remain practically undetectable as measured (OD) for a long time, creating the apparent 4–30 h lag. The length of the lag depends on the fraction of the cells switching to denitrification. To demonstrate this alternative explanation, we adjusted our model to the reported conditions and simulated the experiment of Liu et al [24]. The model produced qualitatively similar ‘diauxic lags’ in the simulated cell density (OD), although the time length of the lag could be anything (depending on assumptions regarding the residual O2 after sparging, which was not measured).
Bergaust et al. [4], [8] studied aerobic and anaerobic respiration rates in Paracoccus denitrificans (DSM413). The cells were incubated (at 20°C) as stirred batches in 120 mL gastight vials, containing 50 mL Sistrom' s medium [27] (Fig. 3). The medium was supplemented with various concentrations of KNO3 or KNO2. Prior to inoculation, air in the headspace was replaced with He to remove O2 and N2 (He-washing), followed by the injection of no, 1, or 7 headspace-vol. % O2. Finally, each vial was inoculated with ∼3×108 aerobically grown cells. The model effectively represents the physical phenomena mentioned above, so as to ensure that the simulation results match the measured data for the right reasons. Net effect of sampling (dilution and leakage) is included in the simulation of O2 kinetics at the reported sampling times. Transport of O2 between the headspace and the liquid is modelled using an empirically determined transport coefficient and the solubility of O2 in water at 20°C. To simulate the metabolic activity (O2 consumption and N2 production) and growth, the model divides the cells into two sub-populations: one without and the other with denitrification enzymes (and pools, respectively, see Fig. 3). Both equally consume O2 if present, but cannot reduce to N2. Those cells that, in response to O2 depletion, are able to initiate nirS transcription (see Fig. 2) are recruited to the pool, where = 0 prior to the recruitment. The recruitment rate () is modelled according to a probabilistic function described below (Eqs. 7–8). The model ignores sampling effect on N2 (leakage and loss), thus calculating the cumulative N2 production as if no sampling took place. That is because the experimentally determined N2 accumulation (which is to be compared with the model predictions) was already corrected for the net sampling effect. The model is developed in Vensim DSS 6. 2 Double Precision (Ventana Systems, Inc. http: //vensim. com/) using techniques from the field of system dynamics [29]. The model is divided into three sectors: I. O2 kinetics, II. Population dynamics of and, and III. Denitrification kinetics (Fig. 4). Structural-basis for the O2 kinetics is mapped in Fig. 4A: the squares represent the state variables, the circles the rate of change in the state variables, the shaded ovals the auxiliary variables, the arrows mutual dependencies between the variables, and the edges represent flows into or out of the state variables. Briefly, Fig. 4A (left to right) shows that O2 in the vial' s headspace () is transported () to the liquid-phase (), where it is consumed () by both the and populations (lacking and carrying denitrification enzymes, respectively) in proportion to an identical cell-specific velocity of O2 consumption (). represents net marginal changes in due to sampling. Below we present equations and a detailed explanation of the structural components shown for this sector. Fig. 4B represents the structure governing the population dynamics of and. Briefly, the figure shows that both the populations are able to grow by aerobic respiration (and, respectively). Initially, = 0 and is populated through recruitment () of the cells from the pool, where the recruitment is a product of and an [O2] dependent specific-probability (h−1) of the recruitment (, see Eqs. 7–8). The growth rate of is primarily based on denitrification (), but the cells that are recruited before O2 is completely exhausted also grow by consuming the remaining traces of O2. Below we present equations and a detailed explanation of the structural components shown for this sector. The structure controlling the denitrification kinetics is mapped in Fig. 4C. Briefly, the figure shows that the cells with denitrification proteome () control the consumption rate of (), recovered as, in proportion to a cell-specific velocity of consumption (). The denitrification intermediates NO and N2O are not explicitly modelled, as they accumulated to miniscule concentrations only [4], [8]. Most of the parameter values used in the model are well established in the literature (See Table 2). However, somewhat uncertain parameters include, , , and the assumed parameter:
To test the assumption of a single homogeneous population, we forced our model to achieve 100% recruitment to denitrification by setting = 1 h−1. In consequence, the simulated N2 accumulation (molN vial−1) showed gross overestimation as compared to the measured for all the treatments (as illustrated for some randomly selected ones in Fig. 6). To find a more adequate value, was calibrated to produce the best possible match between the simulated and measured N2 through optimisation. (The optimisation was carried out in Vensim DSS 6. 2 Double Precision, http: //vensim. com/). Table 4 presents the optimal for each treatment; no consistent effect of initial [O2] and [] was found on the optimal results. The average for all the treatments = 0. 0052, which appears to give reasonable fit between the simulated and measured N2 (See Figs. 7,8, and 9). This indicates that the simulations with = 0. 0052 should provide a reasonable approximation of (the fraction recruited to denitrification) during the actual experiment. To investigate whether the recruitment of a small fraction of the cells to denitrification could explain the ‘diauxic lag’ observed by Liu et al. [24], we used our model to simulate the conditions they reported for their experiment. In short, Liu et al. [24] incubated Ps. denitrificans (ATCC 13867) in oxic batch cultures, which were sparged with N2 as the cultures had reached different cell densities (OD550 = 0. 05–0. 17). The sparging resulted in apparent diauxic lags, i. e. , periods with little or no detectable growth. The length of such lags increased with the cell density present at the time of sparging. Two sensitivity analyses were run to investigate the system' s response to initial O2 in the headspace, : one corresponding to a range of initial [O2] in the liquid-phase below (see Eqs. 7–8) and the other for a range much higher than. All other model parameters and initial values remained as listed in Tables 2 and 3, respectively. The exercise helps illustrate the relative importance of aerobic growth versus the recruitment () in determining the time taken to deplete the pool. The prevailing wisdom in denitrification research is that, under impending anoxic conditions, all cells in a batch culture of denitrifying bacteria will switch to denitrification. However, recent experiments with batch cultures of Pa. denitrificans have provided evidence that, in response to O2 depletion, only a small fraction () of the entire population is able to switch to denitrification [4], [8], [9]. The evidence is based on indirect analyses of e−-flow rates to O2 and NOx during the transition of the cells from aerobic to anaerobic respiration. To provide a direct and refined estimation of, we constructed a dynamic model and directly simulated kinetics of recruitment of the cells to denitrification. We first formulated a hypothesis as to the underlying regulatory mechanism of cell differentiation under approaching anoxia. Briefly, it is that the low is due to a low probability of initiating transcription of the nirS genes, but once initiated, the transcription is greatly enhanced through autocatalytic positive feedback by NO, resulting in the recruitment of the transcribing cell to denitrification. Then, as we implemented this hypothesis in the model, the simulation results showed that the specific-probability () of 0. 0052 (h−1) for a cell to switch to denitrification is sufficient to robustly simulate the measured denitrification gas kinetics. The model estimated the resultant between 3. 8–16. 1% only (average = 8. 2%). The phenomenon may be considered as a ‘bet-hedging’ regulation ‘strategy’ [12]: the fraction switching to denitrification benefits if the anoxic spell is long and NOx remains available, whereas the non-switching fraction benefits, by saving energy required for the protein synthesis, if the anoxic spell is short. The strategy has important implications for the interpretation of numerous experiments on Pa. denitrificans and other denitrifying organisms, as this study has illustrated by presenting a more plausible explanation of the apparent diauxic lags [24] on the basis of the low.
In response to oxygen-limiting conditions, denitrifying bacteria produce a set of enzymes to convert / to N2 via NO and N2O. The process (denitrification) helps generate energy for survival and growth during anoxia. Denitrification is imperative for the nitrogen cycle and has far-reaching consequences including contribution to global warming and destruction of stratospheric ozone. Recent experiments provide circumstantial evidence for a previously unknown phenomenon in the model denitrifying bacterium Paracoccus denitrificans: as O2 depletes, only a marginal fraction of its population appears to switch to denitrification. We hypothesise that the low success rate is due to a) low probability for the cells to initiate the transcription of genes (nirS) encoding a key denitrification enzyme (NirS), and b) a limited time-window in which NirS must be produced. Based on this hypothesis, we constructed a dynamic model of denitrification in Pa. denitrificans. The simulation results show that, within the limited time available, a probability of 0. 005 h−1 for each cell to initiate nirS transcription (resulting in the recruitment of 3. 8–16. 1% cells to denitrification) is sufficient to adequately simulate experimental data. The result challenges conventional outlook on the regulation of denitrification in general and that of Pa. denitrificans in particular.
bacteriology
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nitrogen metabolism
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pseudomonas fluorescens
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Low Probability of Initiating nirS Transcription Explains Observed Gas Kinetics and Growth of Bacteria Switching from Aerobic Respiration to Denitrification