interrelationships between the pathways of inorganic nitrogen assimilation in the cyanobacterium...

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Research

Blackwell Publishing Ltd.

Interrelationships between the pathways of inorganic nitrogen assimilation in the cyanobacterium

Gloeothece

can be described using a mechanistic mathematical model

Nicholas Stephens, Kevin J. Flynn and John R. Gallon

School of Biological Sciences, University of Wales Swansea, Singleton Park, Swansea SA2 8PP, UK

Summary

• A mathematical model is described that simulates the major features of the inter-actions between different nitrogen (N)-sources in the nonheterocystous diazo-trophic cyanobacterium

Gloeothece

.• The interaction between ammonium and nitrate is related to the intracellular con-centration 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 supportN

2

fixation and the assimilation of the resultant ammonium into amino acids.• Nitrogenase activity decreases in response to elevated N-status and also toincreased net oxygen evolution, in keeping with biochemical reality. The modeldescribes the diel cycle of C and N

2

fixation as seen under alternating 12 h light and12 h darkness, and also the N

2

fixation cycle of about 40 h duration seen in cells cul-tured in continuous illumination.• This model has the potential to be adapted to describe N

2

fixation in hetero-cystous cyanobacterium and in

Trichodesmium

.

Key words:

Assimilation, cyanobacteria,

Gloeothece

, model, N

2

fixation,ammonium, nitrate.

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Author for correspondence:

Kevin J Flynn

Tel: +44 (0)1792 295726

Fax: +44 (0)1792 295447

Email: [email protected]

Received:

29 April 2003

Accepted:

11 August 2003

doi: 10.1046/j.1469-8137.2003.00901.x

Introduction

Availability of nitrogen (N) is an important potential growth-limiting factor in aquatic systems. Diazotrophic (N

2

-fixing)cyanobacteria have a competitive advantage over organismsthat have a more restricted range of inorganic nitrogen sourceswhen the availability of fixed-N becomes rate limiting. Theactivity of these organisms is important not only in freshwaterbut, as is being increasingly recognized (Capone, 2001), in themarine environment. Until recently nitrate upwelled fromdeep waters has been considered as the main source ofnitrogen for new oceanic, primary production, withprokaryotic N

2

fixation regarded as relatively insignificant.However the realization that N

2

-fixing organisms are presentin greater abundances in the ocean than has been previouslybelieved has led to a re-evaluation of the oceanic nitrogencycle (Falkowski, 1997; Herbert, 1999; Capone, 2001;Fuhrman & Capone, 2001; Zehr

et al

., 2001).

In this study, we simulate the interaction between the threemain forms of inorganic nitrogen used for assimilation intocellular material, namely ammonium, nitrate and N

2

. Gener-ally a ‘preference’ is shown (Flynn

et al

., 1997; Cheng

et al

.,1999) for the N source with the assimilatory pathway thatcosts least in terms of energy required to assimilate the samequantity of inorganic nitrogen into amino acids. Ammonium,although requiring transportation into the cell, is already atthe appropriate redox state for assimilation into amino acidsand hence requires the least energy. In the absence of sufficientNH

4+

to give an intracellular N-status that represses other Nsource acquisitions, autotrophic microbes typically assimilatenitrate. Nitrate requires transportation and subsequent reduc-tion to ammonium through the combined actions of nitrateand nitrite reductase. These reduction processes requireenergy derived ultimately from photosynthesis. In diazo-trophs, the absence of ammonium and nitrate causes adecrease in cellular N-status that leads to the synthesis of


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nitrogenase, allowing N

2

fixation to occur. Although N

2

candiffuse freely across the cytoplasmic membrane its nitrogenasecatalysed reduction to ammonium requires a considerableinput of energy.

Nitrogenase, the enzyme that catalyses N

2

fixation, is inac-tivated by oxygen (Gallon, 1981). Since cyanobacterial photo-synthesis produces O

2

, the processes of photosynthesis andN

2

fixation therefore conflict. Both CO

2

fixation and N

2

fix-ation are, however, ultimately dependent on reductant gener-ated by the light reactions of photosynthesis. Diazotrophiccyanobacteria generally employ one of two strategies in orderto separate the activities of their O

2

-evolving photosystem 2(PS2) from nitrogenase. In heterocystous cyanobacteria, N

2

fixation is confined to a separate PS2-deficient cell type, theheterocyst. In most nonheterocystous cyanobacteria, how-ever, N

2

fixation and photosynthetic O

2

production are sepa-rated in time, with maximum rates of N

2

fixation occurringduring periods where net O

2

production is low or zero. Thisbehaviour is most obvious in cultures growing under alternat-ing light and darkness. Here, N

2

fixation occurs during thedark period supported by the catabolism of C reserves thatwere synthesized during the previous light period. This Creserve is typically, glucan (Gallon

et al

., 1988). The unicellu-lar cyanobacterium,

Gloeothece

, which is the subject of thisstudy, exhibits this kind of behaviour. The diel pattern of N

2

fixation seen under alternating 12 h light and 12 h darknessis considered here to be due to metabolic changes (Gallon,1992) rather than to an endogenous cellular rhythm, as hasbeen suggested for some unicellular cyanobacteria (Mitsui

et al

., 1986, 1987; Huang & Grobbelaar, 1995). It is impor-tant to note that N

2

fixation in

Gloeothece

reverts to a rhythmwith a 40-h period when cultures are maintained under con-tinuous illumination (Mullineaux

et al

., 1981).The aims of this work are to generate a mechanistic mathe-

matical model capable of reproducing the results found inexperimental studies on

Gloeothece

. These models are notempirical curve-fitting exercises but employ the essence of bio-chemical interactions to attain simulation output mimicking

the behaviour of the real organism. The primary reason for con-structing the model is to act as a dynamic review of our know-ledge of the biological system. Construction of such models isnot only a test of our knowledge but also has a practical appli-cation following the development and subsequent applicationof models of environmentally important diazotrophs.

Gloeothece

is a non-heterocystous unicellular cyanobacte-rium capable of aerobic N

2

fixation. Being well studied thereis an abundance of data and literature describing the physiol-ogy and biochemistry of this organism, providing informa-tion and test scenarios for the development of models. Asuccessful model should be able to replicate the patterns ofnitrogenase activity found in cultures of

Gloeothece

grown inthe absence of combined nitrogen under a variety of lightregimes. The model should also be able to mimic the transitionfrom ammonium to nitrate and then to N

2

as the assimilatorysource of inorganic nitrogen (Flynn

et al

., 1997; Cheng

et al

.,1999). Finally the model should be able to simulate thebehaviour of nitrogenase activity observed when a culture isgrown under anaerobic conditions (Du & Gallon, 1993).

Description of the Model

The model was based on ammonium–nitrate interactionmodel (ANIM) described by Flynn

et al

. (1997) to which hadbeen added the photoacclimatization components of Flynn(2001). The full mathematical model, described as aschematic in Fig. 1 with further details in Table 1, is availableon request from the corresponding author; only detailspertinent to the description of N

2

fixation are described here.The N-sources enter the cell and accumulate as pools of

dissolved inorganic-N (DIN), as ammonium and nitrate. Themaximum rates of DIN transport are related to the N-statusof the cell, with transport enhanced when the organism isstarved of N. Although details of this relationship are knownfor a few organisms, this is not the case for

Gloeothece.

We havetherefore employed the default relationship in ANIM (Flynn

et al

., 1997).

Fig. 1 Routes of entry for different inorganic nitrogen sources and their relationship to the main cellular processes. The state variable definitions and units are listed in Table 1.

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Nitrate is reduced to ammonium through the activity of aninducible nitrate–nitrite reductase system (NNiR) and thepool of ammonium is consumed for the synthesis ofglutamine (GLN) as the first organic product of N assimila-tion. Glutamine is, in turn, used in the synthesis of all othercellular nitrogenous components. The intracellular GLN, andthe total cellular N : C ratio (indicative of general N status)feed back on the transport of DIN and on the synthesis ofNNiR. A higher concentration of GLN is required to termi-nate ammonium assimilation than to terminate that of nitrate(Flynn & Fasham, 1997).

The ANIM model also contains components representingthe process of photosynthesis and respiration (Flynn, 2001).These regulate the availability of carbon for biosyntheticactivity via the description of a quotient for the availability ofstorage C (Cresv). The form of this relationship is shown inFig. 2, with the equation in Table 2. A photoacclimative com-ponent, which simulates the synthesis of chlorophyll, inter-acts with the current N-status of the cell, with irradiance and

hence with the need for carbon fixation (Flynn, 2001).To this ANIM model we have added the N

2

fixation sub-model. By contrast to the accumulation of NH

4+

and NO

3–

,N

2

fixation does not require a transporter but as in other dia-zotrophs the synthesis of nitrogenase in cyanobacteria appearsto be controlled by an early product of organic-N synthesis(which we assume here to be GLN, or a compound that ismetabolically linked to GLN) (Flynn, 1991). Since nitroge-nase is an unstable enzyme, its activity is affected by turnover,representing a balance between the synthesis and decay of theenzyme. In addition, the presence of O

2

(a byproduct of netphotosynthesis) is detrimental to nitrogenase activity as wellas stimulating degradation of the enzyme itself. These newadditional controls are indicated within Fig. 1 and aredescribed in detail below. Updated equations and parametersare summarized in Tables 1, 2 and 3.

Nitrogen fixation is described through the addition of aflow of N into the intracellular ammonium pool controlled bythe availability of nitrogenase enzyme activity and by theavailability of reductant. The rate of N

2

fixation, N

2

fix, isdescribed by Eqn (1),

N

2

fix

=

NTR

×

NTRred

Eqn 1

(NTR is the activity of the nitrogenase enzyme and NTRredis a quotient describing the relative availability of reductant tosupport N

2

fixation). The amount of N

2

fixed, atNfx, canthen be accounted for as a function of biomass, C (Eqn 2).

atNfix

=

C

×

N

2

red

Eqn 2

The availability of reductant for N

2

fixation (NTRred) isdescribed by an equation similar to that previously developedto calculate the availability of reductant for other processessuch as nitrate/nitrite reduction (Flynn

et al

., 1997). Thisrelates the availability of C to cellular N : C by a sigmoidalequation (Eqn 3). The availability of reductant for N

2

fixationis thus linked to the catabolism of carbon reserves and is notsupported directly by photosynthesis. This is consistent withobserved data (Maryan

et al

., 1986).

Eqn 3

(NC is the N : C mass ratio; Cres1 is the maximum NC valueunder conditions where there is no stored C to supportrespiratory processes; Cres2 is a constant that allows theshape of the sigmoidal curve represented by Eqn (3) to bealtered as in Fig. 2). In the model as used here, the same curveis used to control N

2

fixation (NTRred) as is used to controlammonium assimilation in darkness (Cresv).

Nitrogen fixation is regulated through the activity of nitro-genase (NTR) which, in turn, is controlled by two functionsdescribing the synthesis and decay of enzyme activity (Fig. 3).

Table 1 State variables and external variables used in the description of the model, the units for each quantity and a brief description

Parameter Units Description

AC g N g−1C Internal ammonium poolatN2 µg N l−1 Total nitrogen assimilated via N2 fixationC µg C l−1 Cell C in cultureChlC g Chl g−1 C Chlorophyll a C quotaF µg Fe l−1 External Iron included for future workFC g Fe g−1 C Internal iron poolGC g N g−1 C Glutamine C quotaNO3C g N g−1 C Internal nitrate poolNC g N g−1 C Cellular organic N : C (excluding GC)NH4 µg N l−1 External NH4

+

NNiR g N g−1 C d−1 Nitrate/nitrite reductase activityNO3 µg N l−1 External NO3

–

NTR g N g−1 C d−1 Nitrogenase activity

Fig. 2 Relationship between NC (the intracellular N : C ratio) and the availability of carbon reserves (Cresv).

NTRredNC Cres

NC Cres Cres

( / )

( / ) =

−− +

1 1

1 1 2

4

4

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Table 2 Additional and updated auxiliaries to those listed in Flynn et al. (1997); dl represents a dimensionless quantity

Auxiliary Description Units

AAsm = NCm × UmMaximum rate of amino acid synthesis g N g−1 C d−1

AAs

Removal of GLN from GC for amino acid synthesis g N g−1 C d−1

ALG_N = C × (GC + AC + NO3C + NC)Cyanobacterial N in suspension µg N l−1

atNfx = C × N2fixN assimilated by the culture through N2 fixation µg N l−1

basres

Basal respiration rate, including term to halt respiration at high NC g C g−1 C d−1

CAAs

Availability of C to support amino acid synthesis dl

Cresv

Availability of C for metabolism dlCu = PS − RS

C-specific growth rate g N g−1 C d−1

N2fix = (NTR > 0) × (NTR × NTRred )Rate of N2 fixation as a function of the availability of nitrogenase activity and reductant g N g−1 C d−1

NCu

Updated quota control term (see Flynn, 2001) dlNTRd = (NTR > 0) × NTR × (Cu × NTRdr × O2in)

Rate of loss of nitrogenase activity (NTR) is a function of protein decay and inhibition by O2 g N g−1 C d−1 d−1

NTRdr = (Cu > 0) × 1.2 × UmRate of decay for nitrogenase activity scaled to Um g N g−1 C d−1

NTRm = Um × NCm × 4Maximum activity of nitrogenase scaled to maximum growth rate Um and maximum N quota NCm g N g−1 C d−1

NTRms = 1.2 × UmMaximum rate of increase of nitrogenase activity related to maximum growth rate Um g N g−1 C d−1 d−1

NTRred = CresvQuotient for availability of C for N2 fixation dl

NTRs

Rate of nitrogenase synthesis as a function of carbon reserve availability (NC), current value of NTR, and thesynthesis of nitrogenase (measured as nitrogenase activity) g N g−1 C d−1 d−1

O2in = (Cu > 0) × (100 × Cu)O2 inhibition function d−1

PFD = IF(SIGN(SUN) = 1, sun × maxPFD,0)Photon flux density µmol photons m−2 d−1

Pqm = (Um + basres + NCu × Um × (redcoNO3t + redcoN2F + 1.5)) × NCuMaximum potential photosynthetic rate g C g−1 C d−1

PS

Gross photosynthesis rate g C g−1 C d−1

RS = redcoNO3t × NO3t + redcoN2F × N2fix + AAs × 1.5 + basresRespiration accounting for the use of carbon by all cellular processes (see Flynn, 2001). g C g−1 C d−1

SUN = SIN(FRAC(TIME) × π × 2)Sun representing the illumination regime, varies between −1 and +1 dl

= > × × × −−−

×+

× ( )

GC AAsm NCu

NC NCo

NCm NCoGC

GC AAsmGLNCAAs0 2

= × × ×− −

− − .

Um NC NCmNCm NC NCm NCo

NCm NC NCm NCo0 05 ( < )

( )/( )( )/( ) + 0.01

= +

<

× +

+ +

≥

PSPqm

CresvPS

PqmCresv

PSPqm

Cresv1 1

=−

− +

/

/

( )

( )4

1 1

1 1 2

4NC Cres

NC Cres Cres

=+ × −

− + × −

( ) ( C )( C ) ( C )

1 kqN N NCoN NCo kqN N m NCo

= < > ×−

− +× . .

(( C ) ( )) max

max 2N OR N fixNTR NTR

NTR NTR NTRksNTRms0 155 0 01

= × × ×

Pqm TANH alpha PFDChlCPqm

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It should be noted that the state variable NTR describes activ-ity and not mass of enzyme (Table 1). In cultures of Gloeothecegrowing under alternating 12 h light and 12 h darkness, theappearance of nitrogenase activity occurs approximately 10 hafter the onset of the light period (Reade et al., 1999). In orderto grow diazotrophically, cultures of Gloeothece require a min-imum of 4 h illumination per day (H. S. Khamees, unpubl.data). Thus, 4 h of illumination may be considered to berequired to accumulate sufficient storage products to sustainsubsequent N2 fixation (Gallon et al., 1988). The furtherperiod of 6 h before nitrogenase appears in cultures is believedto represent the period needed to synthesize nitrogenase oncesuitable conditions have been established (Reade et al., 1999).The basic conditions favouring N2 fixation are thereforelinked to the nitrogen and carbon status (N : C) of the cell.However once initiated, activity is not solely controlled byNC (cellular N : C ratio). For example, synthesis of nitroge-nase and activity of the enzyme cannot be sustained in theabsence of appropriate carbon reserves, while nitrogenase isadversely affected by exposure to O2.

Synthesis of nitrogenase, as described in Eqn 4, is thereforeactivated by a low NC value and allowed to continue untilnitrogenase activity falls below a predetermined minimum.

Eqn 4

where the synthesis of nitrogenase activity (NTRs) is afunction of a maximal rate of synthesis (NTRms) and theavailability of sufficient carbon storage products representedby a low value of NC. Limitation or cessation of this synthesisoccurs when enzyme activity (NTR) reaches a maximum(NTRmax) or once N2 fixation halts because of lack ofreductant (carbon reserves) or as a result of O2 inhibition. Thefirst part of this equation is a Boolean logic term (value 1 iftrue, or 0 if false) that enables nitrogenase synthesis only ifcellular 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 regulatedby two functions; a term for the proteolytic degradation of thenitrogenase enzyme (Reade et al., 1999), plus another repre-senting inhibition of nitrogenase by oxygen.

NTRd = (NRT > 0) × NTR × (Cu + NTRdr = O2in) Eqn 5

The decay of nitrogenase activity (NTRd) is a function ofcurrent activity (NTR), which is affected by the proteolyticdegradation of the enzyme (NTRdr), a correction due togrowth and hence increased C (Cu), and a functionrepresenting oxygen repression (O2in). O2in is related to thenet growth rate, Cu, and hence the net evolution of O2. A

Table 3 Additional and updated constants to those listed in Flynn et al. (1997) for the ammonium–nitrate interaction model (ANIM)

Constant Definition Value Unit

AAsmGLN Size of GC pool that supports half of 0.001 g N g−1 Cthe maximum amino acid synthesis rate

Alpha Chl-specific slope of photosynthesis – irradiance curve 2 × 10−6 m2 g−1 Chl g C µmol−1 photonCres1 Value of N:C when there are no C-reserves 0.2 g N g−1 CCres2 Constant for computing C-reserve 0.001 dlkqN Shape controlling constant (Flynn, 2001) 1 dlLD Light/dark switch. LD = 1; constant illumination = 0 1 dlM Scalar for controlling photoacclimatization 3 dlmaxPFD Maximum value for PFD when sun = 100% 43.2 × 106 µmol photons m−2 d−1

NCm Max Q const 0.2 g N g−1 CNCo Minimum cell quota 0.15 g N g−1 CNTRks Constant for rate of synthesis of nitrogenase 0.01 g N g−1 C d−1

relevant to the maximum possibleredcoN2F C respired in order to support the reduction 6.17 g C g−1 N

of N2 to intracellular ammoniumredcoNO3t C respired in order to support the reduction 1.71 g C g−1 N

of nitrate to intracellular ammoniumUm Maximum growth rate 0.277 × 2 g C g−1 C d−1

Fig. 3 Flow representation showing synthesis and decay functions affecting the nitrogenase activity (NTR).

NTRs NC OR N fixNTR NTR

NTR NTR NTRksNTRms

( . ) ( . )

max

max

= < >

×−

− +×

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scalar (× 100) is used to increase the inhibition by O2 ofnitrogenase activity to values that achieve the rates ofinhibition 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 NCis used via Eqn 3. Consumption of C, plus the assimilation offixed N, results in an elevation of NC and hence the cessationof N2 fixation due to inadequate C. However, in reality, Ccatabolism not only provides reductant for N2 fixation but, bysupporting respiration generates ATP and consumes O2,thereby providing an O2-deficient environment, limitinginactivation of nitrogenase.

Results and Discussion

The primary test for the model is whether it can reproduce thefeatures of Gloeothece physiology detailed in Table 4. Ourfindings show how this mechanistically determined modelcan, through feedback control, not only demonstrate apreference for ammonium over nitrate (Flynn et al., 1997)but also controls the fixation of N2 (Table 4i). The modelmimics the findings of a number of studies involvingGloeothece and reacts well in tests involving changingenvironmental conditions. Figure 4(a), displaying data from asimulation, mimics an experiment in which a culture ofGloeothece is grown in a medium containing a mixture2.8 mg N l−1 (= 200 µ) each of NH4

+ and NO3–.

Ammonium is used first, followed by nitrate and only whenboth these sources are exhausted do cultures use N2 as anitrogen source. During growth on nitrate, cultures exhibitnitrate reductase and nitrite reductase activity, and producenitrogenase activity during growth on N2 (Fig. 4b). Themodel can also simulate the cessation of N2 fixation onaddition of nitrate, and the cessation of both N2 fixation andnitrate assimilation on the introduction of sufficientammonium (Fig. 5).

Figure 6 displays the steady-state relationships betweenexternal 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 con-

cerning the actual relationship between N2 fixation and DINis not available for Gloeothece or any similar cyanobacteriumat present and requires further investigation. The concentra-tion values in Fig. 6, in the sub-µ range are, however, con-sistent with the range at which ammonium and nitrateuptakes interact with each other in other microalgae (Flynnet al., 1997).

The control of nitrogen source interactions, as seen inFigs 4–6, is via the N-C status of the cell. Although feedbackcontrol has been theorized to occur via the presence of GLN,it was found that the model operated in a more stable fashionwhen control was achieved by regulating N2 fixation via theintracellular N : C ratio (NC). The authors do not contestthat feedback control could involve the intracellular concen-tration of GLN but note that this reflects the cellular N : Cstatus. Attempts to use direct regulation by GLN were com-plicated by the sensitivity of the regulatory transportation intoand out of the GLN pool. Moreover, it may not be the intra-cellular concentrations of GLN but the availability of 2-oxoglutarate (the carbon compound required to assimilate theresulting GLN from the GS-GOGAT pathway) that is res-ponsible for regulation of the genes associated with nitrogenmetabolism in cyanobacteria (Tanigawa et al., 2002). The intra-cellular concentration of these metabolites, however, shouldalso reflect N : C status (NC), so the model would remainvalid irrespective of whether regulation is exerted throughGLN, and/or through 2-oxoglutarate.

A mathematical component that successfully describes theactivity of the nitrogenase enzyme has been developed. Regu-lation is in conjunction with another component representingthe availability of reductant derived from carbohydrate storageproducts (NTRred). Mechanistic in construction, nitrogenaseactivity is initiated once sufficient previously accumulatedcarbon is available and following a suitable period of delay forenzyme synthesis. This has been found to occur approxi-mately 2 h before the onset of the dark period of a 12-h light/

Table 4 Summary of those aspects of N2 fixation displayed by cultures of Gloeothece that must be accommodated by a functional model

Reference

Preference for inorganic nitrogen. Ammonium > nitrate > N2 Flynn et al. (1997); Cheng et al. (1999)Dynamics of N2 fixation Gallon et al. (1988); Mullineaux (1981)Regulation of N metabolism via an early assimilatory product, hypothesized to be glutamine

Flynn (1991)

Nitrogenase synthesis, degradation and activity Reade et al. (1999)Inhibition of nitrogenase by O2 Gallon (1981); Gallon & Hamadi (1984)Effect of light regimes on growth of Gloeothece Ortegacalvo & Stal (1991)Interactions between photosynthesis and respiration with N2 fixation Maryan et al. (1986); Scherer et al. (1988); Scherer (1990)Carbohydrate accumulation Mullineaux et al. (1980); Gallon (1981); Schneegurt et al. (1994)Release of intracellular ammonium and amino acids Bronk et al. (1994); Flynn & Gallon (1990)


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dark cycle with maximal activity occurring around 4 h intothe dark period (Reade et al., 1999). This is reflected in therate of N2 fixation described by the model in Fig. 7.

Shorter doubling times and hence increased growth ratesare typically associated with the preferred inorganic nitrogensource (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 growthon ammonium being relatively poor. These results, however,probably reflect limitation from some other environmental

factor, or because those experiments often employ concen-trations (m) of ammonium that are toxic.

Under conditions of constant illumination, N2-fixing cul-tures of Gloeothece exhibit an asynchronous cycle of nitroge-nase activity. In simulations with decreased photosyntheticactivity, analogous to the low irradiance conditions underwhich Gloeothece cells are cultured, this asynchronous rhythmcan be found to tend towards a period of 40 h (Mullineauxet al., 1980). The model did not initially give a precise valueof 40 h (1.66 d) for the period between peaks of nitrogenaseactivity (Fig. 8); however, the slowing of cellular processes andhence growth led to an extended period of approximately 40 h

Fig. 4 Derepression of N2 fixation. Simulation of the hierarchical use of different N-sources under 12 h light and 12 h dark regime, showing (a) the decrease in external ammonium (NH4

+), nitrate (NO3–) and then

N2 fixation, and (b) the activities of nitrate/nitrite reductase (NNiR) and nitrogenase (NTR). The dark phase is the latter half of each day.


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between successive peaks of nitrogenase activity. Decreasedacetylene reduction and hence a decline in growth rate has beenmeasured in cells grown in continuous illumination (Gallonet al., 1975). Optimal growth occurs in conjunction with12 h light and 12 h darkness (H. S. Khames unpubl. data).

Growth of cultures of Gloeothece under anaerobic condi-tions should result in a peak of nitrogenase activity occurringin the light phase of a cycle of an alternating 12 h light and12 h dark, rather than in the dark (Du & Gallon, 1993). Themodel reproduces this response (Fig. 9, cf. Fig. 7). Althoughthe low concentration of O2 will protect the O2 labile nitro-genase enzyme from inactivation, it will also limit a cell’sability to carry out respiration, which would now be entirely

Fig. 5 Repression of N2 fixation. Continuation from Fig. 4 showing the consequences of subsequent additions of NO3

– and then NH4+

repressing first N2 fixation and then nitrate/nitrite assimilation, respectively. Line types showing nitrogen source uptakes as per Fig. 4.

Fig. 6 Interaction between external NO3– or NH4

+ concentration and the 24-h averaged N2 fixation rate from steady-state simulations in a 12-h light and 12 h dark light regime.

Fig. 7 Extract from a simulation of N2 fixation in cultures of Gloeothece when no other forms of nitrogen are present. Note that N2 fixation starts before the end of each light period.

Fig. 8 Simulation of the assimilation of ammonium, nitrate and N2 under conditions of constant illumination. The insert provides an enlarged view, the axes being the same as the main figure. Lines types showing nitrogen source uptakes as per Fig. 4.

Fig. 9 Simulation of N2 fixation under anaerobic conditions. Note that maximal N2 fixation occurs during the light periods.


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dependent on photosynthetic O2 production. Thus, in N2-fixing cells incubated anaerobically the abundance of nitroge-nase would be expected to remain high, with N2 fixationbeing regulated not only by the availability of carbon but alsoby ATP to support the reduction reactions. The ATP wouldresult from the breakdown of reductant in an O2-dependentreaction that, under anaerobic conditions, must be photosyn-thetically derived.

Availability of reductant is an important regulatory featurein the model. A decrease in the amount of carbon availablefor respiration (via the NTRred term) leads to the cessationof cellular activity and growth (data not shown) and can bemimicked in the model by decreasing the availability ofcarbon. Suspension of cellular processes as a consequence of

the limitation of reductant also occurred during the periods ofdarkness.

The model also suggests that the peak in nitrogenase activ-ity in a culture of Gloeothece grown under alternating 12 hlight and 12 h darkness using low irradiance occurs later inthe dark period. This is a consequence of the longer periodneeded to accumulate sufficient carbon reserves (glucan) inorder to achieve the critical N : C ratio (poor N-status) thattriggers nitrogenase synthesis. This suggestion is consistentwith observed findings ( J. R. Gallon, unpubl. data). Once asufficient excess of carbon is present, the model predicts that,under low irradiance conditions that are typically associatedwith normal Gloeothece growing conditions, a culture wouldfix N2 only every alternate dark period (Fig. 10a). In a batch

Fig. 10 Simulation of the assimilation of ammonium, nitrate and N2 where the synthesis of nitrogenase activity is initiated by (a) NC (internal N : C ratio) < 0.155 and (b) NC < 0.159. These results were obtained with a decreased maximum growth rate (Um = 0.277) in the model, this being representational of decreased growth rates at low irradiance. The inserts provide an enlarged view, the axes being the same as the main figures. Lines types showing nitrogen source uptakes as per Fig. 4.


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culture containing a large number of cells dividing at slightlydifferent times, this could be expressed in data as an underly-ing 40 h rhythm, as suggested by data in the studies by Mul-lineaux et al. (1980). However, using the model we can definea lower concentration of carbon reserve at which N2 fixationwill be initiated and, by setting a higher threshold NC valuefor synthesis of nitrogenase activity (NTRs), we can stillachieve an overall diurnal pattern of nitrogen fixation(Fig. 10b). If the model is correct, cultures expressing syn-chronized cell division under appropriate conditions forgrowth should fix N2 only every other dark period whengrown under 12 h light and 12 h of darkness. However, thisremains to be tested experimentally.

Our model not only satisfies the initial aims of the studybut presents a number of opportunities for further develop-ment. The mechanistic approach to modelling algal physi-ology (Flynn et al., 1997; Flynn & Martin-Jézequel, 2000;Flynn, 2001) has been advanced significantly by the introduc-tion of the N2 fixation submodel described here. We are cur-rently extending this work to include the implications of theincreased requirements for iron to support photosynthesisunder conditions of low illumination (developing from thework of Flynn & Hipkin, 1999) and the additional require-ments for iron in N2 fixation. This development, togetherwith the inclusion of a phosphorus-submodel (Flynn, 2001)will enable us to consider the implications of P and ironlimitation in the world’s oceans and of iron fertilizationexperiments (Martin et al., 1989; Martin et al., 1994) ondiazotrophic activity. It has also been shown that sulphatelimitation can significantly affect the diazotrophic growth ofGloeothece (Ortegacalvo & Stal, 1994) and an increase ingrowth can be associated with increased phosphorus (Flynn,2002). The release and subsequent recovery of ammoniumand amino acids by N2-fixing cyanobacteria (Flynn & Gallon,1990; Bronk et al., 1994; Mulholland & Capone, 2000) haveapparent physiological and ecological consequences that maybe considered using the model approach in Flynn and Berry(1999). As more nutrients are discovered to affect the growthof cyanobaterial and algal cells the role of mechanistic modelsas a predictive and quantitative tool can only increase.

Acknowledgements

This work was supported by the Natural EnvironmentResearch Council, UK, through a studentship to N. S. and bythe Leverhulme Trust/Royal Society through a Fellowship toK. J. F.

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