Modeling Dynamics of Coupled Nitrification and Aerobic Denitrification
Modeling Dynamics of Coupled Nitrification and Aerobic Denitrification
Conventional biological NH3 removal consists of two distinct steps: nitrification by autotrophs under aerobic conditions, and denitrification by heterotrophs under anaerobic conditions . Recently, microbes e.g. Pseudomonas spp. have been discovered coupling heterotrophic nitrification to aerobic denitrification (HNAD). These bacteria can complete the conversion of ammonia (NH3) to dinitrogen gas (N2). To further our understanding of microbial nitrogen conversion pathways, a dynamic model based on a system of ordinary differential equations was built (Figure 1).
The model was collectively fit to agree to time series data of two closely related P. stutzeri strains: P. stutzeri YZN-001 , and P. stutzeri XL-2 . The best model qualitatively described the data for the N-species and population volume.
With the model, relative dynamics of the system could be studied, pathway bottlenecks could be identified, and hypotheses about HNAD could be generated. Furthermore, only minor manipulations of the model are required to qualitatively describe HNAD data from a different species P .putida ZN1 . Moreover, this model can predict nitrogen dynamics for both ammonia dependent growth and nitrate dependent growth. This allowed us to forecast nitrogen conversion for Pseudomonas cells exposed to a combination of nitrogen sources. A conceptual understanding of microbial nitrogen dynamics laid the foundation for our experimental design to synthetically engineer ammonia conversion in Pseudomonas putida.
For Cattlelyst, we wanted to convert ammonia (NH3) into dinitrogen gas (N2). We learned that NH3 bioremediation in wastewater systems relies upon two types of bacteria, nitrifiers and denitrifiers. The overall process is very complex and therefore not applicable to our biofilter. Yet, over the past decades, bacteria capable of converting NH3 into N2 have been isolated; Pseudomonas stutzeri , Paracoccus denitrificans , Paracoccus pantotrophus (formerly known as Thiospaera pantotrophus) , Bacillus Licheniformis  and Rhodococcus spp. . These bacteria couple nitrification to denitrification in a process referred to as heterotrophic nitrification aerobic denitrification (HNAD). HNAD organisms are characterized by (1) their high growth rates and (2) their ability to realize this conversion aerobically . These features make the HNAD mechanism interesting for its application in our biofilter.
However, these natural bacteria have evolved to remove ammonia in completely different conditions to ours. Therefore we wanted to make our own bacterium fit to the biofilter conditions. To synthetically establish the ammonia conversion pathway, we needed to understand the HNAD mechanism. Unfortunately, at this moment, the exact mechanisms explaining this phenotype are not fully understood, although suggestions have been made by Wehrfritz et al.  and Joo et al. . filter.
Visual representation of the pathwaysarrow_downward
To explain the coupling of nitrification and denitrification in one organism, Wehrfritz et al.  proposed the following biochemical mechanism.
To prevent confusion, the uptake and export rates will be described as specific reaction rates, and the bioprocess engineering definition for fluxes will be adopted in this work. The flux vector and intracellular fluxes used in FBA will be referred to as the metabolic flux vector and intracellular metabolic fluxes (Table 1).
Figure 1: Proposed biochemical mechanism for HNAD based on the ‘classical’ HNAD organism Paracoccus pantotrophus (formerly known as Thiospaera pantotrophus) .
HNAD starts with the oxidation of ammonia to hydroxylamine (NH2OH) facilitated by ammonia monooxygenase (AMO). NH2OH is subsequently oxidized to nitrite (NO2-) by hydroxylamine oxidoreductase (HAO). These two enzymatic steps overlap with the classical nitrification pathway employed by autotrophic nitrifiers, e.g. Nitrosomas europaea. The aforementioned oxidation steps are followed by the reduction of NO2- to nitric oxide (NO) by nitrite reductase (Nir). NO is then reduced to nitrous oxide (N2O) by the nitric oxide reductase (Nor) enzyme. Lastly, N2O is reduced to dinitrogen gas (N2) by nitrous oxide reductase (Nos). S The three-step nitrite reduction to dinitrogen gas overlaps with the classical denitrification pathway utilized by, e.g. P. denitrificans , , .
Joo et al.  found that Alcaligenes faecalis No. 4 could not use nitrite Nor nitrate when each of them was supplied as the nitrogen source. This indicated that the strain lacks the ability to denitrify from nitrite. Therefore, a different biochemical mechanism explaining the NH3-N2 conversion has been proposed by the authors .
Figure 2: Proposed biochemical mechanism for HNAD based on HNAD organism Alcaligenes faecalis No. 4.
Similar to the classical HNAD mechanism, is the initial oxidation and final reduction step. Dissimilar is that in A. faecalis No. 4. NH2OH is directly converted to N2O.
What became clear from the suggested biochemical mechanisms is that nitrite is not the only product formed by hydroxylamine oxidase. Something we took into account in our modeling.
To further untangle the HNAD mechanism, we built a dynamic metabolic model. Dynamic models describe how system properties change over time and are invaluable as they allow us to understand dynamics of systems that are too complex to be understood intuitively . Additionally, they allow us to make forecasts that cannot be made strictly by extrapolating data . To our knowledge, no dynamic models metabolic had been built for this mechanism specifically. Therefore we found that mathematical and computational analyses could be a valuable tool to gain understanding in the HNAD phenomenon and improve our experimental design.
To build a model for the HNAD metabolic network, knowledge about enzyme mechanisms and published experimental data were gathered first. Based on this knowledge, the HNAD system was represented mathematically by a system of ordinary differential equations (ODEs). These ODEs describe the change of metabolite concentrations over time and contain values for initial metabolite concentrations, reaction rate equations and kinetic parameters . Time series data of two closely related P. stutzeri strains: YZN-001  and XL-2  was used to guide parameter estimation. Consequently, numerous model simulations were performed of which the best ‘fitting’ models were selected. Selection relied on minimization of an objective function that quantified the difference between the simulation and the data. With our final model, we go on to simulating nitrogen dynamics in mixed conditions, identify most influential parameters affecting nitrous oxide production, study dynamics of ammonia uptake in low [ammonia] conditions.
Establishing the HNAD model structure
The general backbone for the HNAD system is based on the hypotheses made by Wehrfritz et al.  and Joo et al. . As published experimental data for two P. stutzeri strains   was used to guide model development. For instance, nitrate and nitrite exchange with the medium was added to the model structure.
Curious about the published experimental data we used for our model?arrow_downward
To gain insight in the dynamics of the HNAD system, data for nitrogen removal for two closely related P. stutzeri strains: YZN-001  and XL-2  was used to guide model development.
Figure 4: Time series data for Pseudomonas stutzeri YZN-001 . Changes in NH3 (♦), NO3- (•), NO2- (*), OD600 (◊), O2 (■), N2 (□) over the course of 72 hours is shown. Y-axis: O2 (mg.L-1) for O2, Y-axis OD600 for OD600, Y-axis Concentration (mg.L-1) for NH3, NO3-, NO2- , N2. Not measured are the dynamics of other medium constituents. Important to note is that strain YZN-001 is grown on succinate (carbon source), ammonia (nitrogen source) and trace elements .
Figure 5: Time series data for Pseudomonas stutzeri XL-2 . Top left panel: OD600 for strain XL-2 grown on acetate (carbon source), nitrate (NO3-) (nitrogen source) and trace elements. Top right panel: Change in nitrate (NO3-) concentration over time. Lower left panel: Change in ammonia (NH3) concentration over time. Lower right panel: change in nitrite (NO2- ) over time. Total timespan was 36 hours. Important to note is that this experiment was conducted to study the effect of different shaking velocities (rpm). Rpm affects the dissolved oxygen concentration (DO). Orange lines: results for 90 rpm, Purple lines: results for 120 rpm, Midnight green lines: results for 150 rpm. Data corresponding to 150 rpm was used for the model .
P. stutzeri YZN-001 was selected because of its ability to couple heterotrophic nitrification to aerobic denitrification. Ammonia is taken up and converted into dinitrogen gas over time. There is no accumulation of intermediates nitrite or nitrate in the medium and, throughout the time-course, the OD600 (reflecting cell population size) increases (Figure 4). However, using these observables alone were not sufficient to study the full dynamics of the system. Therefore, additional time series data for aerobic denitrifier P. stutzeri XL-2 was used because among the observables are nitrate and nitrite. The dynamics of these nitrogen species could not be studied with the data for P. stutzeri YZN-001.
Strain XL-2 takes up nitrate over time. Nitrite accumulates in the medium during the initial time period and after approximately 15 hours nitrite is taken back up by the cells. Moreover, negligible amounts of ammonia accumulate in the medium and the OD600 increases over time (Figure 5).
How can we use data for two different experiments?
In this study, time series data for different organisms was used to build one model. It was proven that the strains are closely related since a phylogenetic study conducted by Zhao et al.  revealed that P. stutzeri YZN-001 was 99.9% identical to P. stutzeri XL-2. Nonetheless, a plethora of external effects could influence the HNAD efficiency, which makes generalization complex. Thus, before using the data (Figure 4-5), culture conditions were compared (Table 2).
Except for the carbon source, all other culture conditions were similar for the two strains. Given that (1) the strains are highly identical and (2) that both acetate and succinate are preferred carbon sources for HNAD , it was assumed that the effect of the different carbon source was negligible.
Curious about the logic behind the proposed reactions?arrow_downward
The general backbone for the intracellular reactions is based on the aforementioned biochemical mechanisms (Figure 1 -2). R1 denotes the ammonia conversion to hydroxylamine. R3 symbolizes the direct conversion of hydroxylamine to nitrous oxide. R4a denotes the reduction of nitrite to nitric oxide. R6 corresponds to the reduction of nitric oxide to nitrous oxide. Lastly, R7 denotes the final reduction step that converts nitrous oxide to dinitrogen gas.
The rationale behind including R3 was that we could not exclude the possibility that partial oxidation of hydroxylamine to nitrous oxide did not occur. Additionally, studies on the nitrogen removal capacities of P. stutzeri strains: YG-24 , GEP-01 , and UFV5 , did not reveal whether the Wehrfritz et al.  mechanism or the Joo et al.  mechanism was predominant in the species.
The reaction overview (Figure 3) includes recent findings . For instance, Caranto and Lancaster  have shown that NO, rather than NO2- is the product of HAO. This conversion is denoted by R_2. Additionally, they hypothesize that under aerobic conditions NO is oxidized to NO2- by means of a nitrite reductase which is symbolized by R4b. Moreover, R5b was added to reflect nitrite oxidation to nitrate. According to Caranto and Lancaster , this conversion is facilitated by a nitrate oxidoreductase.
To establish the link between the intracellular population volume and the extracellular medium, six transport reactions (T’s) were added to complete the system. At physiological pH, for which the time series data was collected, 99% of ammonia is in the form of ammonium (NH4+) . Ionic species, such as NH4+, NO3-, NO2- cannot passively diffuse over the cell membrane . T1 denotes the ammonia transport system. P. stutzeri XL-2 is capable of taking up nitrate from the environment. Additionally, it can reduce nitrate to nitrite (nitrate reductase Nar) and eventually to nitrogenous gasses . To capture this behavior, nitrate transport (T2) and nitrate reduction (R5a) are included in the reaction overview. Moreover, P. stutzeri XL-2 exchanges nitrite with the environment, which is denoted by T3. Lastly, cell membranes are generally permeable for small, uncharged molecules such as gasses like NO, N2O and N2 . Therefore, the exchange of these intermediates between the population volume and the medium was believed to be diffusion-mediated and modelled accordingly (T4,T5,T6).
Translation of the model to mathematical terms
To describe the change in nitrogen species, ODEs detailing the change in metabolite concentration and population volume were set up. The Michealis-Menten (MM) rate law was used to describe the enzymatic conversions. The MM rate law relates production formation P to substrate concentration S in the following way:
where Km (mmol.L-1) is the Michaelis constant and Vmax (mmol.L-1min-1) is the maximum reaction rate, [P] (mmol.L-1) is the concentration of the product, and [S] concentration of the substrate.
Given that the data for P. stutzeri YZN-001 and XL-2 show that the cell population increases over time, we needed to include these dynamics in our model. This is because the concentration of a metabolite and the volume in which it exists are interrelated.
First we needed a term that describes the increase in population volume over time:
Where Vc (l) is the non-segregated population volume, (min-1) is the bacterial growth rate constant.
Given that the bacteria do not grow constantly over time, the bacterial growth rate is time-dependent and is related to the growth medium the bacteria exist in. To reflect this time dependency we used the empirical Monod equation . The equation relates the bacterial growth rate to the concentration of a limiting nutrient. Extracellular nitrate and ammonia were used as ‘limiting’ nutrients for P. stutzeri strains XL-2 and YZN-001 respectively.
Where μmax (min-1) is the maximum growth rate, Kn (mmol.L-1) is the Monod constant, [N] is the concentration of a nitrogen compound (mmol.L-1).
But, how does the population affect the concentration of metabolites? To include this effect, we rewrote the ODEs as illustrated by Jong et al. :
Where [N] (mmol.L-1) is the concentration of a nitrogen species. (n ) ̇(mmol) is the dynamic quantity of a nitrogen species. Vc is the population volume. μ is the growth rate.
If N stays constant (n= 0) and the population volume increases, [N] decreases due to the dilution term: μ[N]. We used the MM rate law to describe the dynamics of the nitrogen species. However, to fit the mathematical description illustrated by Jong et al. , the MM rate equations were rescaled following
Where [N] (mmol.L-1) is the concentration of a nitrogen species. (n ) ̇(mmol) is the dynamic quantity of a nitrogen species. Vc is the population volume. μ is the growth rate.
By multiplying the concentration by the volume in which it exists, we arrived at quantity.
Lastly, the bacteria are able to exchange nitrogen compounds with the medium, Our proposed pathway includes two types of transport, both described differently. Gasses nitric oxide, nitrous oxide and dinitrogen gas readily diffuse through cell membranes. We used Fick’s law, which relates diffusion rate to difference in concentration, to mathematically describe the transport of these gasses:
Where kd is the volumetric flux (L.min-1).
Of course, to relate the intracellular concentration change to the extracellular concentration change, we made sure to divide the ODEs for extracellular N species the volume of the medium (Vv) and ODEs for intracellular species were divided by population volume (Vc), as illustrated by Jong et al. .
We also added two further reactions to our model. First, to reflect that some of the ammonia is ‘poached’ by assimilatory reactions unrelated to HNAD, we introduced a factor kg (min-1) that represents a metabolite sink. Second, one of the major differences between the data for Pseudomonas stutzeri XL-2 (Figure 5) and Pseudomonas stutzeri YZN-001 (Figure 4) is that for strain XL-2, nitrite accumulates in the medium after which it is taken up rapidly. To incorporate sudden nitrite excretion and uptake into the model, a hypothetical metabolic switch was added to the ODEs for intracellular and extracellular NO2- . The switch was modeled by means of a discontinuous Heaviside function.
Curious about the model equations?arrow_downward
In this section, the model equations are represented in more detail. T’s are transport reactions, R’s are enzymatic reactions, Vm is the volume of the medium, and μ is the bacterial growth rate. Kinetic expressions for T’s and R’s can be found in a separate table below.
To complete the model, parameter values needed to be estimated. Over 50,000 parameter sets were generated, according to these bounds,
by means of Latin Hypercube Sampling (LHS). These parameter sets were used to simulate the system. To assess the simulations, the following objective functions were defined:
P. STUTZERI YZN-001
P. STUTZERI XL-2
Where D stands for data, subscript specifies N-species or Vc. ti is time point of measurement. S denotes simulation, subscript specifies N-species or Vc. The model score was obtained by Normalizing the total score. This was achieved by dividing the sum of the YZN-001 and XL-2 scores by the total amount of measured datapoints.
The score function quantifies the discrepancy between the data and the simulation at measured time-points. In order to directly compare simulations and the data, the datasets were converted from units of mg/L to mmol.L-1, hours to minutes, OD600 to L.. The 25 best parameter sets could describe the data quite well,
but to even further decrease the score multiple simulated annealing rounds were performed. Simulated annealing is a global optimization algorithm that, by making small parameter perturbations, tries to reduce the score even further. The best-scoring parameter set was used for further model validation.
Want to see the final model parameters?arrow_downward
Check out the initial conditions herearrow_downward
The ODEs were solved by the stiff ode15s solver (MATLAB R2020a). The time, initial conditions, medium volume for simulations of YZN-001 and XL-2 were:
The final model describes the data well, it can describe the change in extracellular nitrogen species, connected to population growth. With the model we gained insights in the intracellular dynamics of the nitrogen species, which cannot be measured directly. Additionally, we further validated the model for different conditions and a different HNAD strain, P. putida ZN1 , and found that the model can predict the nitrogen dynamics well. We used the final model to pinpoint important parameters for ensuring no accumulation of intermediates. In essence, we uncovered which enzymatic steps need to be optimized in vivo to limit the risk of nitrous oxide (N2O) release. Moreover, the model was used to project what would happen to the dynamics in low [ammonia].
The model can describe the HNAD nitrogen dynamics well
The final model describes the change in extracellular nitrogen species, connected to population growth. Below you can find the results of the final model simulations. We observe that the model describes the data. For strain YZN-001 (Figure 8) which takes up ammonia and subsequently converts it into dinitrogen gas, without accumulation of intermediates nitrate, nitrite, nitric oxide or nitrous oxide. Moreover, the simulated population volume qualitatively describes the data, yet the fit is not perfect. For strain XL-2 (Figure 9), inclusion of the Heaviside function allowed for describing the nitrite peak between t = 10-20 hours. The nitrate reduction is simulated fairly well, however, the initial delayed uptake is not captured fully by the model. For this condition specifically, nitrous oxide accumulates significantly in the medium. Given that nitrous oxide is harmful for the environment, we identified the most important parameters to prevent this accumulation event (read more about this in Limit Nitrous oxide production). However, given that there is no data for these compounds specifically, we do not know whether these projections reflect reality. Lastly, also for strain Xl-2, the simulated population volume could not completely construe the sigmoidal curve depicted by the data. Although the fit to the population volume is not perfect for both conditions, the essence of the nitrogen dynamics can be captured well by the model.
Given the good fit we decided to validate this model further with different published experimental data. We used published data for P. putida ZN1  to validate our model. This dataset was chosen as the experimental conditions are more complex than our other datasets, and that initially two nitrogen sources are available. By conceptualizing the bacterial nitrogen-switch, and slightly altering Tmax1a to 2.7*10-4 mmol.min-1,
we were able to describe the nitrogen dynamics for P. putida ZN1 quite well (Figure 10). As for strain YZN-001 and XL-2 (Figure 8-9), the fit to population volume could only be approximated roughly. Nonetheless, the final population volume estimated does not differ much from the data. Interestingly, the model predicts that more nitrite accumulates in the medium when grown on nitrate and ammonia simultaneously, compared to cells exposed to either one of the N-species. Moreover, almost no NO and N2O accumulate under these conditions, which is different from growth on NO3- alone (Figure 9). Also for this complex condition, the N-dynamics can be described with our model.
Given that the model can capture the HNAD nitrogen dynamics well, we felt confident to use the model to further guide our wetlab ammonia removal design. The HNAD pathway passes through multiple nitrogen intermediates, which are either toxic to the cell or harmful for the environment. Nitrous oxide specifically is an important compound to keep an eye on as it is a greenhouse gas, 300 times more potent than CO2, and it has the potential to damage the ozone layer .
Limit Nitrous oxide production
Nitrous oxide is the penultimate intermediate in the HNAD pathway. Given its harmful properties, its accumulation and subsequent diffusion out of the cells should be prevented. To be able to pinpoint the critical parameters and pathway bottlenecks for production, N2O accumulation was studied in more detail. This was done by isolating the parameters that impacted N2O accumulation. With this initial analysis, we found that growth on ammonia has a lower risk of N2O production than growth on NO3-. Given that Cattlelyst is designed for ammonia removal, this could be beneficial for us. To take the analysis a step further, the effect of pairwise parameter perturbations on the cumulative amount of N2O excreted was obtained. By doing so we could find the most interesting parameter pair: Vmax7 and Tmax3b. Vmax7 is the maximum conversion rate for the Nos enzyme, converting nitrous oxide into dinitrogen gas. And Tmax3b is the maximum excretion rate of nitrite. Figure 11 shows that when Vmax7 is increased and Tmax3b is as well, the cumulative amount of nitrous oxide is kept to a minimum.
We learned that only the Vmax7 can be optimized in vivo. At this moment, no dedicated machinery that excretes nitrite has been found for Pseudomonas spp, thus laboratory optimization for increasing Tmax3b is out of the question. For Vmax7¬ the engineering approach is more straightforward. The only enzyme known to reduce N2O is respiratory N2O reductase (N2OR) . To increase Vmax7, the total enzyme concentration could be increased. To achieve this, we carefully engineered our synthetic denitrification pathway to be as optimal. Read more about this in Synthetic denitrification + limit nitrous oxide production.
What happens in lower ammonia concentrations
Cattlelyst will be operated in open cattle sheds, which means that released ammonia gas will be diluted by the air before it enters the biofilter. Thus, the initial ammonia concentration will most likely be lower compared to the YZN-001 condition (Fig. 4) To quantify the effect of low ammonia concentrations on the HNAD model, we simulated the system for different initial [NH3] concentrations: 0.25, 0.5, 1, 2, 3, 5 mM as system inputs.
The model forecasts that the rate of ammonia uptake is unaffected by the initial ammonia concentration. This implies that ammonia is depleted rapidly when operated under low ammonia concentrations, and when the system is exposed to high ammonia concentrations the depletion takes more time. Depending on [NH3] in the biofilter, duration of depletion of ammonia could be estimated with the model, which further aids the design of the biofilter. There are reports of HNAD bacteria for which the rate of ammonia uptake increases with higher initial ammonia concentrations , . However, the relationship between uptake rate and ammonia concentration has not been studied in detail Pseudomonas strains with low ammonia concentrations. If this were studied, the estimated parameter values for ammonia uptake could be revised and optimized to describe these dynamics.
Another interesting result from this analysis was that the initial ammonia concentration relates almost linearly to the final amount of dinitrogen gas produced.
The final [N2] linearly relates to the initial [NH3], even at low concentrations. This suggests that over the timespan simulated, accumulation of intermediates is not altered and that the branching ratio of HNAD-ammonia: growth-ammonia is constant.
For most HNAD bacteria, intracellular ammonia ends up either as biomass nitrogen or denitrification products in a ratio of 40-50% and 60-50%, respectively , . Does the linear relationship between initial [NH3] and final [N2] reflect reality, and is this ratio conserved, even at low [NH3] in the biofilter? As mentioned before HNAD bacteria are researched for their nitrogen removal abilities at high ammonia/nitrate/nitrite loads, and time series data for low [NH3] is rare . For Bacillus strain N31 converted 40% of the initial low [NH3] (20 mg.L-1=1.18 mmol.L-1) into biomass . This suggests that the ratio biomass-N and denitrification is fixed, even for low ammonia concentrations, and that the linear relationship predicted by the model is true. However, without more data for HNAD bacteria at low [NH3], we could not fully confirm this hypothesis yet.
All in all, the final model can forecast nitrogen removal dynamics coupled to population dynamics. Given the fit to the time series data we used, we can conclude that the model can explain the essence of the HNAD phenomenon in Pseudomonas spp. It allows us to study intracellular dynamics, which are difficult to study experimentally, and difficult to understand intuitively. Moreover, our findings suggest that the proposed underlying pathway can explain the HNAD system, and with that the conversion of ammonia to dinitrogen gas. For Cattlelyst we wanted to establish this conversion in one organism. Hence, our wetlab projects: synthetic nitrification and denitrification, to establish this pathway, are built on the premises of this model. Lastly, the model simulations showed us that there is a significant risk of producing nitrous oxide, which should be prevented due to its intrinsic harmful properties. Therefore, we dedicated another wetlab project to limit nitrous oxide production.
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