Author for correspondence: Kevin J Flynn Tel: +44 (0)1792 295726 Fax: +44 (0)1792 295447 Email: email@example.com
• A mathematical model is described that simulates the major features of the interactions between different nitrogen (N)-sources in the nonheterocystous diazotrophic cyanobacterium Gloeothece.
• The interaction between ammonium and nitrate is related to the intracellular concentration of glutamine (GLN), which in turn is representative of cellular N-status. Development of nitrogenase activity is related to N-limitation but, once developed, continues for as long as there is sufficient glucan (carbon-reserve) in order to support N2 fixation and the assimilation of the resultant ammonium into amino acids.
• Nitrogenase activity decreases in response to elevated N-status and also to increased net oxygen evolution, in keeping with biochemical reality. The model describes the diel cycle of C and N2 fixation as seen under alternating 12 h light and 12 h darkness, and also the N2 fixation cycle of about 40 h duration seen in cells cultured in continuous illumination.
• This model has the potential to be adapted to describe N2 fixation in heterocystous cyanobacterium and in Trichodesmium.
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Availability of nitrogen (N) is an important potential growth-limiting factor in aquatic systems. Diazotrophic (N2-fixing) cyanobacteria have a competitive advantage over organisms that have a more restricted range of inorganic nitrogen sources when the availability of fixed-N becomes rate limiting. The activity of these organisms is important not only in freshwater but, as is being increasingly recognized (Capone, 2001), in the marine environment. Until recently nitrate upwelled from deep waters has been considered as the main source of nitrogen for new oceanic, primary production, with prokaryotic N2 fixation regarded as relatively insignificant. However the realization that N2-fixing organisms are present in greater abundances in the ocean than has been previously believed has led to a re-evaluation of the oceanic nitrogen cycle (Falkowski, 1997; Herbert, 1999; Capone, 2001; Fuhrman & Capone, 2001; Zehr et al., 2001).
In this study, we simulate the interaction between the three main forms of inorganic nitrogen used for assimilation into cellular material, namely ammonium, nitrate and N2. Generally a ‘preference’ is shown (Flynn et al., 1997; Cheng et al., 1999) for the N source with the assimilatory pathway that costs least in terms of energy required to assimilate the same quantity of inorganic nitrogen into amino acids. Ammonium, although requiring transportation into the cell, is already at the appropriate redox state for assimilation into amino acids and hence requires the least energy. In the absence of sufficient NH4+ to give an intracellular N-status that represses other N source acquisitions, autotrophic microbes typically assimilate nitrate. Nitrate requires transportation and subsequent reduction to ammonium through the combined actions of nitrate and nitrite reductase. These reduction processes require energy derived ultimately from photosynthesis. In diazotrophs, the absence of ammonium and nitrate causes a decrease in cellular N-status that leads to the synthesis of nitrogenase, allowing N2 fixation to occur. Although N2 can diffuse freely across the cytoplasmic membrane its nitrogenase catalysed reduction to ammonium requires a considerable input of energy.
Nitrogenase, the enzyme that catalyses N2 fixation, is inactivated by oxygen (Gallon, 1981). Since cyanobacterial photosynthesis produces O2, the processes of photosynthesis and N2 fixation therefore conflict. Both CO2 fixation and N2 fixation are, however, ultimately dependent on reductant generated by the light reactions of photosynthesis. Diazotrophic cyanobacteria generally employ one of two strategies in order to separate the activities of their O2-evolving photosystem 2 (PS2) from nitrogenase. In heterocystous cyanobacteria, N2 fixation is confined to a separate PS2-deficient cell type, the heterocyst. In most nonheterocystous cyanobacteria, however, N2 fixation and photosynthetic O2 production are separated in time, with maximum rates of N2 fixation occurring during periods where net O2 production is low or zero. This behaviour is most obvious in cultures growing under alternating light and darkness. Here, N2 fixation occurs during the dark period supported by the catabolism of C reserves that were synthesized during the previous light period. This C reserve is typically, glucan (Gallon et al., 1988). The unicellular cyanobacterium, Gloeothece, which is the subject of this study, exhibits this kind of behaviour. The diel pattern of N2 fixation seen under alternating 12 h light and 12 h darkness is considered here to be due to metabolic changes (Gallon, 1992) rather than to an endogenous cellular rhythm, as has been suggested for some unicellular cyanobacteria (Mitsui et al., 1986, 1987; Huang & Grobbelaar, 1995). It is important to note that N2 fixation in Gloeothece reverts to a rhythm with a 40-h period when cultures are maintained under continuous illumination (Mullineaux et al., 1981).
The aims of this work are to generate a mechanistic mathematical model capable of reproducing the results found in experimental studies on Gloeothece. These models are not empirical curve-fitting exercises but employ the essence of biochemical interactions to attain simulation output mimicking the behaviour of the real organism. The primary reason for constructing the model is to act as a dynamic review of our knowledge of the biological system. Construction of such models is not only a test of our knowledge but also has a practical application following the development and subsequent application of models of environmentally important diazotrophs.
Gloeothece is a non-heterocystous unicellular cyanobacterium capable of aerobic N2 fixation. Being well studied there is an abundance of data and literature describing the physiology and biochemistry of this organism, providing information and test scenarios for the development of models. A successful model should be able to replicate the patterns of nitrogenase activity found in cultures of Gloeothece grown in the absence of combined nitrogen under a variety of light regimes. The model should also be able to mimic the transition from ammonium to nitrate and then to N2 as the assimilatory source of inorganic nitrogen (Flynn et al., 1997; Cheng et al., 1999). Finally the model should be able to simulate the behaviour of nitrogenase activity observed when a culture is grown under anaerobic conditions (Du & Gallon, 1993).
Description of the Model
The model was based on ammonium–nitrate interaction model (ANIM) described by Flynn et al. (1997) to which had been added the photoacclimatization components of Flynn (2001). The full mathematical model, described as a schematic in Fig. 1 with further details in Table 1, is available on request from the corresponding author; only details pertinent to the description of N2 fixation are described here.
Table 1. State variables and external variables used in the description of the model, the units for each quantity and a brief description
g N g−1C
Internal ammonium pool
g N l−1
Total nitrogen assimilated via N2 fixation
g C l−1
Cell C in culture
g Chl g−1 C
Chlorophyll a C quota
g Fe l−1
External Iron included for future work
g Fe g−1 C
Internal iron pool
g N g−1 C
Glutamine C quota
g N g−1 C
Internal nitrate pool
g N g−1 C
Cellular organic N : C (excluding GC)
g N l−1
g N g−1 C d−1
Nitrate/nitrite reductase activity
g N l−1
g N g−1 C d−1
The N-sources enter the cell and accumulate as pools of dissolved inorganic-N (DIN), as ammonium and nitrate. The maximum rates of DIN transport are related to the N-status of the cell, with transport enhanced when the organism is starved of N. Although details of this relationship are known for a few organisms, this is not the case for Gloeothece. We have therefore employed the default relationship in ANIM (Flynn et al., 1997).
Nitrate is reduced to ammonium through the activity of an inducible nitrate–nitrite reductase system (NNiR) and the pool of ammonium is consumed for the synthesis of glutamine (GLN) as the first organic product of N assimilation. Glutamine is, in turn, used in the synthesis of all other cellular nitrogenous components. The intracellular GLN, and the total cellular N : C ratio (indicative of general N status) feed back on the transport of DIN and on the synthesis of NNiR. A higher concentration of GLN is required to terminate ammonium assimilation than to terminate that of nitrate (Flynn & Fasham, 1997).
The ANIM model also contains components representing the process of photosynthesis and respiration (Flynn, 2001). These regulate the availability of carbon for biosynthetic activity via the description of a quotient for the availability of storage C (Cresv). The form of this relationship is shown in Fig. 2, with the equation in Table 2. A photoacclimative component, which simulates the synthesis of chlorophyll, interacts with the current N-status of the cell, with irradiance and hence with the need for carbon fixation (Flynn, 2001).
Table 2. Additional and updated auxiliaries to those listed in Flynn et al. (1997); dl represents a dimensionless quantity
= NCm × Um
Maximum rate of amino acid synthesis
g N g−1 C d−1
Removal of GLN from GC for amino acid synthesis
g N g−1 C d−1
= C × (GC + AC + NO3C + NC)
Cyanobacterial N in suspension
g N l−1
= C × N2fix
N assimilated by the culture through N2 fixation
g N l−1
Basal respiration rate, including term to halt respiration at high NC
g C g−1 C d−1
Availability of C to support amino acid synthesis
Availability of C for metabolism
= PS − RS
C-specific growth rate
g N g−1 C d−1
= (NTR > 0) × (NTR × NTRred)
Rate of N2 fixation as a function of the availability of nitrogenase activity and reductant
Respiration accounting for the use of carbon by all cellular processes (see Flynn, 2001).
g C g−1 C d−1
= SIN(FRAC(TIME) × π × 2)
Sun representing the illumination regime, varies between −1 and +1
To this ANIM model we have added the N2 fixation submodel. By contrast to the accumulation of NH4+ and NO3−, N2 fixation does not require a transporter but as in other diazotrophs the synthesis of nitrogenase in cyanobacteria appears to be controlled by an early product of organic-N synthesis (which we assume here to be GLN, or a compound that is metabolically linked to GLN) (Flynn, 1991). Since nitrogenase is an unstable enzyme, its activity is affected by turnover, representing a balance between the synthesis and decay of the enzyme. In addition, the presence of O2 (a byproduct of net photosynthesis) is detrimental to nitrogenase activity as well as stimulating degradation of the enzyme itself. These new additional controls are indicated within Fig. 1 and are described in detail below. Updated equations and parameters are summarized in Tables 1, 2 and 3.
Table 3. Additional and updated constants to those listed in Flynn et al. (1997) for the ammonium–nitrate interaction model (ANIM)
Size of GC pool that supports half of the maximum amino acid synthesis rate
g N g−1 C
Chl-specific slope of photosynthesis – irradiance curve
Constant for rate of synthesis of nitrogenase relevant to the maximum possible
g N g−1 C d−1
C respired in order to support the reduction of N2 to intracellular ammonium
g C g−1 N
C respired in order to support the reduction of nitrate to intracellular ammonium
g C g−1 N
Maximum growth rate
0.277 × 2
g C g−1 C d−1
Nitrogen fixation is described through the addition of a flow of N into the intracellular ammonium pool controlled by the availability of nitrogenase enzyme activity and by the availability of reductant. The rate of N2 fixation, N2fix, is described by Eqn (1),
N2fix = NTR × NTRred(Eqn 1)
(NTR is the activity of the nitrogenase enzyme and NTRred is a quotient describing the relative availability of reductant to support N2 fixation). The amount of N2 fixed, atNfx, can then be accounted for as a function of biomass, C (Eqn 2).
atNfix = C × N2red(Eqn 2)
The availability of reductant for N2 fixation (NTRred) is described by an equation similar to that previously developed to calculate the availability of reductant for other processes such as nitrate/nitrite reduction (Flynn et al., 1997). This relates the availability of C to cellular N : C by a sigmoidal equation (Eqn 3). The availability of reductant for N2 fixation is thus linked to the catabolism of carbon reserves and is not supported directly by photosynthesis. This is consistent with observed data (Maryan et al., 1986).
(NC is the N : C mass ratio; Cres1 is the maximum NC value under conditions where there is no stored C to support respiratory processes; Cres2 is a constant that allows the shape of the sigmoidal curve represented by Eqn (3) to be altered as in Fig. 2). In the model as used here, the same curve is used to control N2 fixation (NTRred) as is used to control ammonium assimilation in darkness (Cresv).
Nitrogen fixation is regulated through the activity of nitrogenase (NTR) which, in turn, is controlled by two functions describing the synthesis and decay of enzyme activity (Fig. 3). It should be noted that the state variable NTR describes activity and not mass of enzyme (Table 1). In cultures of Gloeothece growing under alternating 12 h light and 12 h darkness, the appearance of nitrogenase activity occurs approximately 10 h after the onset of the light period (Reade et al., 1999). In order to grow diazotrophically, cultures of Gloeothece require a minimum of 4 h illumination per day (H. S. Khamees, unpubl. data). Thus, 4 h of illumination may be considered to be required to accumulate sufficient storage products to sustain subsequent N2 fixation (Gallon et al., 1988). The further period of 6 h before nitrogenase appears in cultures is believed to represent the period needed to synthesize nitrogenase once suitable conditions have been established (Reade et al., 1999). The basic conditions favouring N2 fixation are therefore linked to the nitrogen and carbon status (N : C) of the cell. However once initiated, activity is not solely controlled by NC (cellular N : C ratio). For example, synthesis of nitrogenase and activity of the enzyme cannot be sustained in the absence of appropriate carbon reserves, while nitrogenase is adversely affected by exposure to O2.
Synthesis of nitrogenase, as described in Eqn 4, is therefore activated by a low NC value and allowed to continue until nitrogenase activity falls below a predetermined minimum.
where the synthesis of nitrogenase activity (NTRs) is a function of a maximal rate of synthesis (NTRms) and the availability of sufficient carbon storage products represented by a low value of NC. Limitation or cessation of this synthesis occurs when enzyme activity (NTR) reaches a maximum (NTRmax) or once N2 fixation halts because of lack of reductant (carbon reserves) or as a result of O2 inhibition. The first part of this equation is a Boolean logic term (value 1 if true, or 0 if false) that enables nitrogenase synthesis only if cellular N-status falls below some predetermined value (N : C < 0.155) or if N2 fixation is already occurring at a set rate.
Decay of nitrogenase activity (NTRd) (Eqn 5) is regulated by two functions; a term for the proteolytic degradation of the nitrogenase enzyme (Reade et al., 1999), plus another representing inhibition of nitrogenase by oxygen.
The decay of nitrogenase activity (NTRd) is a function of current activity (NTR), which is affected by the proteolytic degradation of the enzyme (NTRdr), a correction due to growth and hence increased C (Cu), and a function representing oxygen repression (O2in). O2in is related to the net growth rate, Cu, and hence the net evolution of O2. A scalar (× 100) is used to increase the inhibition by O2 of nitrogenase activity to values that achieve the rates of inhibition seen experimentally.
O2in = 100 × Cu(Eqn 6)
Catabolism of glucan supports N2 fixation (Schneegurt et al., 1994). In the model glucan is not represented per se. Rather, excess C over the minimum required to define the highest NC is used via Eqn 3. Consumption of C, plus the assimilation of fixed N, results in an elevation of NC and hence the cessation of N2 fixation due to inadequate C. However, in reality, C catabolism not only provides reductant for N2 fixation but, by supporting respiration generates ATP and consumes O2, thereby providing an O2-deficient environment, limiting inactivation of nitrogenase.
Results and Discussion
The primary test for the model is whether it can reproduce the features of Gloeothece physiology detailed in Table 4. Our findings show how this mechanistically determined model can, through feedback control, not only demonstrate a preference for ammonium over nitrate (Flynn et al., 1997) but also controls the fixation of N2 (Table 4i). The model mimics the findings of a number of studies involving Gloeothece and reacts well in tests involving changing environmental conditions. Figure 4(a), displaying data from a simulation, mimics an experiment in which a culture of Gloeothece is grown in a medium containing a mixture 2.8 mg N l−1 (= 200 m) each of NH4+ and NO3−. Ammonium is used first, followed by nitrate and only when both these sources are exhausted do cultures use N2 as a nitrogen source. During growth on nitrate, cultures exhibit nitrate reductase and nitrite reductase activity, and produce nitrogenase activity during growth on N2 (Fig. 4b). The model can also simulate the cessation of N2 fixation on addition of nitrate, and the cessation of both N2 fixation and nitrate assimilation on the introduction of sufficient ammonium (Fig. 5).
Table 4. Summary of those aspects of N2 fixation displayed by cultures of Gloeothece that must be accommodated by a functional model
Preference for inorganic nitrogen. Ammonium > nitrate > N2
Figure 6 displays the steady-state relationships between external NH4+ and NO3− concentrations and N2 fixation. As would be expected, a lower concentration of NH4+ is required to repress N2 fixation than that of NO3−. Information concerning the actual relationship between N2 fixation and DIN is not available for Gloeothece or any similar cyanobacterium at present and requires further investigation. The concentration values in Fig. 6, in the sub-m range are, however, consistent with the range at which ammonium and nitrate uptakes interact with each other in other microalgae (Flynn et al., 1997).
The control of nitrogen source interactions, as seen in Figs 4–6, is via the N-C status of the cell. Although feedback control has been theorized to occur via the presence of GLN, it was found that the model operated in a more stable fashion when control was achieved by regulating N2 fixation via the intracellular N : C ratio (NC). The authors do not contest that feedback control could involve the intracellular concentration of GLN but note that this reflects the cellular N : C status. Attempts to use direct regulation by GLN were complicated by the sensitivity of the regulatory transportation into and out of the GLN pool. Moreover, it may not be the intracellular concentrations of GLN but the availability of 2-oxoglutarate (the carbon compound required to assimilate the resulting GLN from the GS-GOGAT pathway) that is responsible for regulation of the genes associated with nitrogen metabolism in cyanobacteria (Tanigawa et al., 2002). The intracellular concentration of these metabolites, however, should also reflect N : C status (NC), so the model would remain valid irrespective of whether regulation is exerted through GLN, and/or through 2-oxoglutarate.
A mathematical component that successfully describes the activity of the nitrogenase enzyme has been developed. Regulation is in conjunction with another component representing the availability of reductant derived from carbohydrate storage products (NTRred). Mechanistic in construction, nitrogenase activity is initiated once sufficient previously accumulated carbon is available and following a suitable period of delay for enzyme synthesis. This has been found to occur approximately 2 h before the onset of the dark period of a 12-h light/dark cycle with maximal activity occurring around 4 h into the dark period (Reade et al., 1999). This is reflected in the rate of N2 fixation described by the model in Fig. 7.
Shorter doubling times and hence increased growth rates are typically associated with the preferred inorganic nitrogen source (N. Stephens, unpubl. data). This is indeed the case, with the model predicting growth rates of 0.255 d−1, 0.197 d−1 and 0.132 d−1 for growth of Gloeothece on ammonium, nitrate and N2, respectively. Some workers (Cheng et al., 1999; Reade et al., 1999) have reported contrary results, with growth on ammonium being relatively poor. These results, however, probably reflect limitation from some other environmental factor, or because those experiments often employ concentrations (mm) of ammonium that are toxic.
Under conditions of constant illumination, N2-fixing cultures of Gloeothece exhibit an asynchronous cycle of nitrogenase activity. In simulations with decreased photosynthetic activity, analogous to the low irradiance conditions under which Gloeothece cells are cultured, this asynchronous rhythm can be found to tend towards a period of 40 h (Mullineaux et al., 1980). The model did not initially give a precise value of 40 h (1.66 d) for the period between peaks of nitrogenase activity (Fig. 8); however, the slowing of cellular processes and hence growth led to an extended period of approximately 40 h between successive peaks of nitrogenase activity. Decreased acetylene reduction and hence a decline in growth rate has been measured in cells grown in continuous illumination (Gallon et al., 1975). Optimal growth occurs in conjunction with 12 h light and 12 h darkness (H. S. Khames unpubl. data).
Growth of cultures of Gloeothece under anaerobic conditions should result in a peak of nitrogenase activity occurring in the light phase of a cycle of an alternating 12 h light and 12 h dark, rather than in the dark (Du & Gallon, 1993). The model reproduces this response (Fig. 9, cf. Fig. 7). Although the low concentration of O2 will protect the O2 labile nitrogenase enzyme from inactivation, it will also limit a cell's ability to carry out respiration, which would now be entirely dependent on photosynthetic O2 production. Thus, in N2-fixing cells incubated anaerobically the abundance of nitrogenase would be expected to remain high, with N2 fixation being regulated not only by the availability of carbon but also by ATP to support the reduction reactions. The ATP would result from the breakdown of reductant in an O2-dependent reaction that, under anaerobic conditions, must be photosynthetically derived.
Availability of reductant is an important regulatory feature in the model. A decrease in the amount of carbon available for respiration (via the NTRred term) leads to the cessation of cellular activity and growth (data not shown) and can be mimicked in the model by decreasing the availability of carbon. Suspension of cellular processes as a consequence of the limitation of reductant also occurred during the periods of darkness.
The model also suggests that the peak in nitrogenase activity in a culture of Gloeothece grown under alternating 12 h light and 12 h darkness using low irradiance occurs later in the dark period. This is a consequence of the longer period needed to accumulate sufficient carbon reserves (glucan) in order to achieve the critical N : C ratio (poor N-status) that triggers nitrogenase synthesis. This suggestion is consistent with observed findings (J. R. Gallon, unpubl. data). Once a sufficient excess of carbon is present, the model predicts that, under low irradiance conditions that are typically associated with normal Gloeothece growing conditions, a culture would fix N2 only every alternate dark period (Fig. 10a). In a batch culture containing a large number of cells dividing at slightly different times, this could be expressed in data as an underlying 40 h rhythm, as suggested by data in the studies by Mullineaux et al. (1980). However, using the model we can define a lower concentration of carbon reserve at which N2 fixation will be initiated and, by setting a higher threshold NC value for synthesis of nitrogenase activity (NTRs), we can still achieve an overall diurnal pattern of nitrogen fixation (Fig. 10b). If the model is correct, cultures expressing synchronized cell division under appropriate conditions for growth should fix N2 only every other dark period when grown under 12 h light and 12 h of darkness. However, this remains to be tested experimentally.
Our model not only satisfies the initial aims of the study but presents a number of opportunities for further development. The mechanistic approach to modelling algal physiology (Flynn et al., 1997; Flynn & Martin-Jézequel, 2000; Flynn, 2001) has been advanced significantly by the introduction of the N2 fixation submodel described here. We are currently extending this work to include the implications of the increased requirements for iron to support photosynthesis under conditions of low illumination (developing from the work of Flynn & Hipkin, 1999) and the additional requirements for iron in N2 fixation. This development, together with the inclusion of a phosphorus-submodel (Flynn, 2001) will enable us to consider the implications of P and iron limitation in the world's oceans and of iron fertilization experiments (Martin et al., 1989; Martin et al., 1994) on diazotrophic activity. It has also been shown that sulphate limitation can significantly affect the diazotrophic growth of Gloeothece (Ortegacalvo & Stal, 1994) and an increase in growth can be associated with increased phosphorus (Flynn, 2002). The release and subsequent recovery of ammonium and amino acids by N2-fixing cyanobacteria (Flynn & Gallon, 1990; Bronk et al., 1994; Mulholland & Capone, 2000) have apparent physiological and ecological consequences that may be considered using the model approach in Flynn and Berry (1999). As more nutrients are discovered to affect the growth of cyanobaterial and algal cells the role of mechanistic models as a predictive and quantitative tool can only increase.
This work was supported by the Natural Environment Research Council, UK, through a studentship to N. S. and by the Leverhulme Trust/Royal Society through a Fellowship to K. J. F.