Modeling the dynamic regulation of nitrogen fixation in the cyanobacterium Trichodesmium sp

APPLIED AND ENVIRONMENTAL MICROBIOLOGY, May 2006, p. 3217–3227 Vol. 72, No. 50099-2240/06/$08.00�0 doi:10.1128/AEM.72.5.3217–3227.2006Copyright © 2006, American Society for Microbiology. All Rights Reserved.

Modeling the Dynamic Regulation of Nitrogen Fixationin the Cyanobacterium Trichodesmium sp.

Sophie Rabouille,* Marc Staal, Lucas J. Stal, and Karline SoetaertCentre for Estuarine and Marine Ecology, Netherlands Institute of Ecology, KNAW, Yerseke, The Netherlands

Received 28 December 2005/Accepted 21 February 2006

A physiological, unbalanced model is presented that explicitly describes growth of the marine cyanobacte-rium Trichodesmium sp. at the expense of N2 (diazotrophy). The model involves the dynamics of intracellularreserves of carbon and nitrogen and allows the uncoupling of the metabolism of these elements. The resultsshow the transient dynamics of N2 fixation when combined nitrogen (NO3

�, NH4�) is available and the

increased rate of N2 fixation when combined nitrogen is insufficient to cover the demand. The daily N2 fixationpattern that emerges from the model agrees with measurements of rates of nitrogenase activity in laboratorycultures of Trichodesmium sp. Model simulations explored the influence of irradiance levels and the length ofthe light period on fixation activity and cellular carbon and nitrogen stoichiometry. Changes in the cellular C/Nratio resulted from allocations of carbon to different cell compartments as demanded by the growth of theorganism. The model shows that carbon availability is a simple and efficient mechanism to regulate the balanceof carbon and nitrogen fixed (C/N ratio) in filaments of cells. The lowest C/N ratios were obtained when thelight regime closely matched nitrogenase dynamics.

In marine waters, nitrogen generally controls primary pro-duction (16). In such environments, N2-fixing organisms have acompetitive advantage over organisms that rely on the avail-ability of combined nitrogen. In the tropical oceans, N2-fixingcyanobacteria can be extremely abundant in surface waters andaccount for a considerable input of combined nitrogen into theupper mixed layer (11, 28), with a strong impact on localcommunity production (9).

At ocean basin scales, N2-fixing cyanobacteria affect the cou-pling of C-N-P cycles and contribute considerably to the netoceanic sequestration of atmospheric carbon dioxide (28). Forinstance, a global-scale estimate made by Lee et al. (31) of netCO2 fixation in the absence of measurable nitrate led to theconclusion that 20 to 40% of the total new primary productionin tropical and subtropical oceans could be attributed to N2-fixing organisms. The quantitative impact of N2-fixing organ-isms on nutrient cycling in the oceans and on the global carbonbudget is widely acknowledged (14, 16, 26, 36, 51). Biogeo-chemical models have been developed to offer a dynamic viewof biological and biochemical systems. At global scales, thesemodels aim to provide estimates of the main oceanic biogeo-chemical fluxes, such as total, new, and regenerated production(17). Others describe the global nitrogen cycle at the ecosystemlevel (18, 25, 35). At smaller scales, phytoplankton growthmodels describe time-dependent changes in biomass or num-bers as a function of one or several limiting factors, therebyoffering support to hypotheses about biological and physiolog-ical processes. However, these models do not account for thephysiological and regulatory mechanisms of N2 fixation in cyano-bacteria, since there is still very little knowledge about the factorsthat control them.

In this paper we focus on the marine nonheterocystous cyano-bacterium Trichodesmium sp., identified as one of the mostsignificant N2-fixing organisms in oceans (6). Because nitroge-nase, the enzyme complex responsible for the reduction of N2,is very sensitive to inactivation by O2, cyanobacteria haveevolved various strategies to separate N2 fixation from O2-generating photosynthesis (2, 4, 21). It has been hypothesizedthat Trichodesmium separates N2 fixation spatially from oxy-genic photosynthesis, allowing it to fix N2 during the day (1). Inthis respect, Trichodesmium has adopted a protective strategysimilar to that of heterocystous cyanobacteria (4). Since C/Nratios in natural populations of Trichodesmium remain rela-tively constant (10), it is expected that Trichodesmium willshow balanced growth.

This paper presents a model designed to assess the mecha-nisms that control physiological processes, in particular pri-mary production. This model explicitly describes unbalancedgrowth and N2 fixation in Trichodesmium spp. and their controlby environmental factors. Different numerical simulationswere performed under various conditions to test the effects oflight and nutrient availability on growth and N2 fixation underboth transient and steady-state conditions. We aimed to pin-point (i) whether light intensity and the temporal distributionof light would have an effect on the pattern and rate of N2

fixation and (ii) the analysis of the role of carbon availability onN2 fixation. We also analyze, in qualitative terms, the role ofthe nitrogen supply in (i) the interaction between nitrogenlimitation and N2 fixation and (ii) N2 fixation dynamics. Theresults of these simulations are compared to measurements ofnitrogenase activity carried out on exponentially growing cul-tures of Trichodesmium.

MATERIALS AND METHODS

Laboratory experiments. Trichodesmium sp. strain IMS101 was grown at 27°Cin modified YCBII medium (12) in 250-ml Erlenmeyer flasks under a 12-hlight/12-h dark (L12) regime in an incubator without shaking. YCBII medium

* Corresponding author. Present address: Ocean Sciences Depart-ment, University of California—Santa Cruz, 1156 High Street, SantaCruz, CA 95064. Phone: (831) 459-5152. Fax: (831) 459-4882. E-mail:[email protected].

3217

on January 8, 2015 by guesthttp://aem

.asm.org/

Dow

nloaded from

http://aem.asm.org/

was modified by the addition of 15.9 g liter�1 Na2CO3 and 1.6 � 10�9 MNa2SeO3 and was devoid of combined nitrogen. The pH of the medium was�8.2. Light was provided by cool white 15-W fluorescent tubes at an incidentphoton irradiance of 70 �mol · m�2 · s�1. The cultures were swirled daily by hand

in order to prevent the formation of large aggregates or wall growth. N2 fixationwas monitored by using the acetylene reduction technique. Only exponentiallygrowing cultures were used for our experiments. Samples of 50 ml of culturewere filtered on a GF/F glass fiber filter (diameter, 47 mm) under a moderatevacuum. Subsequently, the filter was placed in the incubation chamber for anonline acetylene reduction assay (47). Filter incubation was preferred to liquidincubation, because it has been shown to be superior (47). The gas flow over thefilter with Trichodesmium was 2 liters · h�1 and was composed of 20% O2, 70%N2, and 10% C2H2. The incubation chamber was kept at 25°C and at the samelight regime and photon flux density as in the culture. The gas flow was in linewith a gas chromatograph (Chrompack-CP9000; Varian, The Netherlands)equipped with a flame ionization detector and a 500-�l sample loop for auto-mated injections. The conditions of the gas chromatograph and other detailswere those described by Staal et al. (47).

N2 fixation model. (i) Internal pools. Depending on their structure, growthmodels can or cannot represent fluctuations in cellular composition and thus theadaptation of the organism to its environment. The Trichodesmium N2 fixationmodel is a physiological growth model that explicitly includes reserves of carbonand nitrogen whose dynamics are unbalanced. The model describes the interac-tion between nitrogen and carbon metabolism and emphasizes the biotic andabiotic conditions that control N2 fixation rates. The model is described below,and a flow diagram is given in Fig. 1. The model variables are listed in Table 1;see Table 2 for the model formulation, Table 3 for the modeled processes, andTable 4 for parameter values.

The cellular carbon components are decomposed as described by Lancelot andBillen (29). Cellular carbon is represented by the pool of low-molecular-weightcarbon molecules (photosynthate) (Csm), the internal carbon reserves (glycogen)(Cr), and the structural biomass (Cs). Csm has a short turnover time, allowing fastchanges of process rates. In the model this pool served as the intermediate for allmetabolic processes. The Csm consumption terms can be either (i) storage in theform of carbon reserves (Cr), (ii) incorporation in structural biomass (Cs), (iii)dissimilation, or (iv) consumption for maintenance. An exchange thus occurs be-tween the intracellular carbon reserves (Cr) and Csm. Similarly, internal storage ofnitrogen (Nr) is included in the model in order to account for temporal variations inN2 fixation. This nitrogen reserve groups glutamine (the early product of N2 fixation

FIG. 1. Schematic representation of the four compartments in themodel and their related mass fluxes. Solid arrows, C flux; dashedarrows, N flux; dotted arrows, losses due to mortality (M) and main-tenance costs (R). The units (C and/or N) used to describe the contentof each compartment are circled.

TABLE 1. Model variables

Variable Unita Description

State variablesCsm mmol C · m�3 Concentration of small metabolites in TrichodesmiumCr mmol C · m�3 Concentration of carbon reserves in TrichodesmiumCs mmol C · m�3 Concentration of the structural and functional biomass in TrichodesmiumNr mmol N · m�3 Concentration of nitrogen as first N products and N reserve in TrichodesmiumNit mol N · mol C�1 · h�1 Nitrogenase activityN1 mmol N · m�3 Nitrate concentration in the environmentN2 mmol N · m�3 Ammonium concentration in the environmentDet mmol C · m�3 DetritusDt h�1 Dilution rate (turbidostat only)

Ordinary variablesN mmol N · m�3 Total dissolved inorganic nitrogen (DIN) in the culture mediumCtot mmol C · m�3 Total Trichodesmium carbonNs mmol N · m�3 Cs expressed as nitrogenNtot mmol N · m�3 Total Trichodesmium nitrogenC:N mol C · mol N�1 C/N ratio of TrichodesmiumpCsm Proportion of carbon in the small-metabolite pool Csm with regard to total cellular carbonpCr Proportion of carbon stored in Cr with regard to total cellular carbonpCs Proportion of carbon in the structural biomass (Cs) with regard to total cellular carbonpNr Proportion of nitrogen stored in Nr with regard to total cellular nitrogen (expressed as

carbon units)at g Chl · m�3 Trichodesmium chlorophyll contentaC g Chla · g C�1 Chla/C ratio of TrichodesmiumCe mol C · mol C�1 Excess of Csm over the cellular quota QClC Limitation factor due to the availability of carbon in CsmNe mol N · mol N�1 Excess of N reserves over the cellular quota QNIN Limitation factor due to the availability of nitrogen in Nrel m�1 Light extinction coefficientI� �mol phot · m�2 · s�1 Average irradiance in the culture

a phot, photons.

3218 RABOUILLE ET AL. APPL. ENVIRON. MICROBIOL.


.asm.org/

Dow

nloaded from

http://aem.asm.org/

[7]) and the pool of nitrogen reserve components (e.g., cyanophycin and phycobili-proteins). This pool represents intracellular nitrogen available for the synthesis ofstructural biomass (Cs) (structural carbon and nitrogen). The uptake of externalcombined nitrogen also feeds into the nitrogen reserve pool.

The structural biomass (Cs) pool sets the maximum rates of all processes. Theuncoupling between carbon and nitrogen metabolism allows processes to bemodulated (limited or inhibited) by both the carbon status and the nitrogenstatus of cells (Ce and Ne, respectively), which represent the availability of thesetwo elements for metabolism. Carbon status is calculated as the relative propor-tion of the photosynthate (Csm) to total carbon, excluding the minimum cellularcarbon quota; nitrogen status is the relative proportion of the nitrogen reserves(Nr) to total N, excluding the minimum cellular nitrogen quota (Table 2). Hence,growth can occur independently of the periods of photosynthesis, provided thatsufficient nitrogen and carbon are available to cells. The limitation functions(lC and lN) associated with the internal states follow a type III (sigmoid) response(Table 2). Inhibition by internal status is expressed as 1 minus sigmoid.

(ii) Formulations of photosynthesis and growth. The carbon-specific photo-synthesis rate (P) depends on the chlorophyll a (Chla) content. Light depen-dence [g1(I)] is described using the exponential saturation function from refer-ence 41, including a photoinhibition term. The actual photosynthesis rate isfurther limited by the extent of carbon reserves in cells (1 � lC). The maximumrate of photosynthesis, Pm (expressed as mol of C · g of Chla�1 · h�1), wasrecalculated from Kana’s measurements (27) on Trichodesmium thiebautii. Therate of carbon storage in Cr (g3) is assumed to be proportional to the carbonstatus following a saturation function. The consumption rate of this reserve (g2)is linearly related to the reserve concentration (Cr). Growth (G) is the produc-tion of structural biomass at the expense of photosynthate and nitrogen reserves.We considered a maximum theoretical specific growth rate of Trichodesmium of0.9 day�1. The actual growth rate results from the limitation by carbon andnitrogen internal states, following Liebig’s law of the minimum. Phosphorus isnot limiting in our model, and the effect of temperature is not taken into account.

(iii) Effects of nitrogen substrates and associated growth costs. Trichodes-mium is a facultative diazotroph and can take up combined inorganic nitrogencompounds (38). In the model, combined nitrogen is preferred over N2, acondition based on the absence or lower rates of N2 fixation when Trichodes-mium is grown on NH4

� or NO3� (24). The uptake and assimilation of combined

nitrogen are described by one equation, in which the rates of consumption ofNH4

� (U1) and NO3� (U2) are proportional to their concentrations. The rate of

consumption follows Michaelis-Menten kinetics and is modulated by the deple-tion of internal nitrogen reserves. As Stephens et al. (49) proposed, we simulatethe potential activity of N2 fixation as the result of a balance between an increase(g4) and a decrease (g8) in the potential activity rather than as a turnover of theenzyme itself. Nitrogenase activity is dependent on N2, ATP, and reducingequivalents. The increase in the potential rate of N2 fixation is assumed to becontrolled by the nitrogen (g6) and energy status of the cells. It is also sensitiveto the concentration of NO3

� (40). The actual rate of N2 fixation results fromcarbon availability and the cellular nitrogen status as well as the potential rate ofnitrogenase activity.

ATP pools are not modeled sensus stricto; the energy gained from photosyn-

TABLE 2. Model formulation

Variable Equation

Rate of change of thestate variablesa

dCsm/dt..........................�P � g2 (Cr) � g3 (Csm) � G � (m � rb)� Csm � ra � Csm � Dt

dCr/dt ............................�g3 (Csm) � g2 (Cr) � (m � rb) � Cr� Cr � Dt

dCs/dt ............................�G � (m � rb) � Cs � Cs � DtdNr/dt ............................�F � U1 � U2 � G � (N:C)Cs � (m � rb)

� Nr � Nr � DtdNit/dt...........................�g4 � g8 � Nit � DtdN1/dt ...........................�U1 � N1 � DtdN2/dt ...........................�U2 � N2 � DtdDet/dt..........................�m � Ctot � Det � DtdDt/dt ............................c13 � Dt � (Ieq � I�)

Ordinary variablesN ...................................N1 � N2Ctot ................................Csm � Cr � Cs � Nr/(N:C)NrNs ..................................Cs � (N:C)CsNtot................................Ns � NrC:N ...............................Ctot/NtotpCsm..............................Csm/CtotpCr ................................Cr/CtotpCs ................................Cs/CtotpNr ................................[Nr/(N:C)Nr]/Ctotat....................................Cs � (N:C)Cs � aNaC ..................................at/(Ctot � 12)Ce ..................................Csm/Ctot � QClC ...................................Ce

2/(kC2 � Ce

2)Ne..................................Nr/Ntot � QNlN ...................................Ne

1.2/(kN1.2 � Ne

1.2)el ....................................c9 � c10 � at � c11 � at

c12

I� .....................................I/zm � {[�1/el] � [exp(�el � zm) � 1]}

a When the model is run as a continuous culture, the dilution rate becomes aconstant: Dt � D.

TABLE 3. Modeled processes

Process Equation Unit Description

P g1 (I�) � (1 � lC) � aC � 12 � Csmmol C · m�3 · h�1 Actual gross photosynthesis rate

g1(I�) Pm � [1 � exp(�I�/Ik)] � exp(�I�/�l) mol C · g Chla�1 · h�1 P-I curve (41)g2(Cr) c1 � Cr mmol C · m�3 · h�1 Carbon flux from Cr to Csm (catabolism)g3(Csm) c2 � lC � Cs mmol C · m�3 · h�1 Carbon flux from Csm to Cr (storage)g4 c3 � MIN {[1 � g5(N1)], [1 � g6(Ne)]} � g7(Ce) mol N · mol C�1 · h�1 · h�1 Synthesis of nitrogenase activityg5(N1) N1/(N1 � kd) Limitation due to presence of nitrateg6(Ne) Ne

6/(kN6 � Ne

6) Limitation due to Neg7(Ce) Ce

6/(kCn6 � Ce

6) Limitation due to Ceg8 c4 � g9(Nit) � g7(Ce) mol N · mol C�1 · h�1 · h�1 Breakdown of nitrogenase activityg9(Nit) Nit/(Nit � c5) Decay scaled to nitrogenase activityF Nit � (1 � lN) � g10(Ce) � Cs mmol N · m�3 · h�1 Actual N2 fixation rateg10(Ce) Ce

6/(kCf6 � Ce

6) Limitation due to availability of DINU1 c6 � lC � g11(N) � (1 � lN) � Cs � N1/N mmol N · m�3 · h�1 Actual nitrogen uptake rateU2 c6 � lC � g11(N) � (1 � lN) � Cs � (1 � N1/N) mmol N · m�3 · h�1 Actual ammonium uptake rateg11(N) N/(N � kd) Limitation due to availability of DING gm � MIN(lC, lN) � Cs mmol C · m�3 · h�1 Actual gross production of structural

biomass Csra1 if N � 10�5, c7; otherwise, c8 � (c7 � c8) � (1 � N1/N) Minimum fraction of the gross growth (Cs

production) lost as respiration activityra ra1 � (ra2 � ra1) � [1 � g11(N)] � G mmol C · m�3 · h�1 Actual loss due to respiration activity

VOL. 72, 2006 MODELING THE DYNAMIC REGULATION OF NITROGEN FIXATION 3219


.asm.org/

Dow

nloaded from

http://aem.asm.org/

thesis is represented as the accumulation of fixed carbon. Thus, the energy forany metabolic process is provided by the dissimilation of the carbon reserves. Forthe model, we assume that N2 fixation is limited by electrons originating from themobilization of the carbon metabolites (Csm). Respiration accounts for differ-ences in energy costs that result from the use of different nitrogen sources. Whengrowth cannot be sustained by the uptake of combined nitrogen, N2 fixation isinduced in order to meet nitrogen demand. The transition to N2 fixation willmoderately increase the energy cost for N assimilation, which is reflected in ahigher rate of respiration. The higher energy cost of growth on NO3

� than onNH4

� is also taken into account. The minimum maintenance rate increases whenthe concentration of NH4

� decreases.(iv) Physical setting. The modeled system can be run either as a well-stirred

continuous culture or as a turbidostat. We emphasize that the term chemostatdoes not apply here, since that term usually refers to cultures in steady statecontrolled by a growth-limiting nutrient (often but not exclusively nitrogen) andrequires a continuous light regime. In this study a light-dark regime was applied,and Trichodesmium growth was light limited and not nutrient limited.

Biomass generates an extinction of light (eI). Hence, the higher the biomass,

the lower the resultant average irradiance (I�) within the vessel becomes, loweringthe specific photosynthesis rate. Biomass is considered to be well mixed and as aresult homogeneously distributed. Growth will be light limited at the equilibriumstate. Dilution removes part of the biomass and prevents culture senescence,since light is never completely extinguished. When the model reaches equilib-rium, the daily average of all the specific rates becomes constant and the daily netspecific growth rate equals the dilution rate. To qualify this equilibrium, we donot use here the term “steady state,” which refers to a perfect constancy ofvariables in time. In the model, the light regime induces a periodicity in themetabolism, and at equilibrium, variables are still fluctuating within 24 h buttheir daily average is constant from one day to another. Such an equilibriumis called “dynamic equilibrium.” In this model, the dynamic equilibrium isdetermined by light conditions and by the dilution rate. When the model isrun as a turbidostat, the dilution rate becomes a state variable that fluctuatesuntil the average irradiance (I�) in the culture reaches a chosen value, Ieq

(Table 2). Ieq characterizes the light regime reached in the turbidostat at theequilibrium.

TABLE 4. Parameter values

Parameter Value Unita Description

PhotosynthesisPm 3.1438 mol C · g Chla�1 · h�1 Maximum gross photosynthesis rate in Trichodesmium (from

Kana [27])aN 1.5 g Chl · mol N�1 Chlorophyll a-to-nitrogen ratioIk 100 �mol phot · m�2 · s�1 Saturation irradiance for photosynthesis�1 350 �mol phot · m�2 · s�1 Photoinhibition coefficient for photosynthesisc1 0.12 h�1 Catabolism rate of Crc2 0.2 h�1 Maximum carbon storage ratekC 0.06 mol C · mol C�1 Half-saturation Csm/Ctot ratio for carbon storage

N2 fixation and uptakec3 10 � gm � 24�1 mol N · mol C�1 · h�2 Maximum rate of increase of nitrogenase activity related to

the maximum specific growth rate (gm)c4 8 � gm � 24�1 mol N · mol C�1 · h�2 Maximum rate of decay of nitrogenase activity related to the

maximum specific growth rate (gm)c5 0.0005 mol N · mol C�1 · h�1 Coefficient of the decay function g8c6 0.0272 mol N · mol C�1 · h�1 Maximum carbon-specific rate of nitrogen uptakekCn 0.045 mol C · mol C�1 Half-saturation Csm/Ctot ratio for the allocation of carbon to

nitrogenase synthesiskCf 0.05 mol C · mol C�1 Half-saturation Csm/Ctot ratio for the allocation of carbon to

N2 fixationkd 0.5 mmol N · m�3 Half-saturation constant for DIN uptakekN 0.1 mol N · mol N�1 Half-saturation Nr/Ntot ratio for nitrogen storage

Growthgm 0.9 � 24�1 h�1 Maximum specific growth rate of Trichodesmium(N:C)Nr 0.4 mol N · mol C�1 N-to-C ratio in nitrogen reserves (Nr)(N:C)Cs 0.3 mol N · mol C�1 N-to-C ratio in structural biomass (Cs)QC 0.03 mol C · mol C�1 Minimum cellular C quota (Csm-to-Cs ratio)QN 0.00 mol N · mol N�1 Minimum cellular N quota (Nr-to-Cs ratio)c7 0.4 Highest value in the range of the minimum respiration activityc8 0.2 Lowest value in the range of the minimum respiration activityra2 0.45 Maximum fraction of the gross growth (Cs production) lost as

respiration activityrb 0.02 � 24�1 h�1 Rate of the maintenance costm 0.002 � 24�1 h�1 Natural mortality rate

Forcing functionsI 120.0 �mol phot · m�2 · s�1 Incident solar irradiance during light hoursIeq Variable �mol phot · m�2 · s�1 Avg irradiance in the culture at the dynamic equilibriumc9 0.04 m�1 Background light extinction due to suspended materialc10 0.0088 Extinction parameterc11 0.054 Extinction parameterc12 0.667 Extinction parameterzm 1 m Maximum depth of the water columnD 0.0085 h�1 Dilution rate in the culturec13 0.001 Adjustment coefficient for the dilution rate in the turbidostat

a phot, photons.



.asm.org/

Dow

nloaded from

http://aem.asm.org/

(v) Implementation. The model is formulated as a system of ordinary differ-ential equations. It is implemented in the FORTRAN language, in the FEMMEsimulation environment (44), running on Windows. The model is available fordownload from the FEMME website (http://www.nioo.knaw.nl/cemo/femme/).

Simulations. The model was run as a continuous culture and as a turbidostat.In the continuous-culture runs, the daily average of the net specific growth rateequaled the dilution rate when the model reached the dynamic equilibrium. Theturbidostat allowed better control of the light intensity in the culture. In eachturbidostat simulation, the average desired irradiance in the culture at equilib-rium (Ieq) was set as a parameter. The dilution rate was not constant in theseexperiments but changed at each time step, resulting in a constant daily averageof the biomass concentration that created the light conditions in the vessel equalto Ieq.

(i) Transient behavior experiments. The first two simulations consisted of awell-mixed continuous culture in which the initial concentration of combinednitrogen in the culture vessel was 10 �M and the initial total biomass was 6.8mmol of C · m�3. The medium supply did not contain combined nitrogen. Theculture was exposed to a constant incident photon irradiance of 120 �mol · m�2 · s�1

during the light period.In the L12 simulation, the on-off light rhythm applied was 12 h of light and 12 h

of darkness (hence, the daily average was 60 �mol · m�2 · s�1). The model wasfirst run as a continuous culture with a dilution rate set to 0.0085 h�1. Then,under the same conditions, the model was run as a turbidostat, with an Ieq of 12.5�mol · m�2 · s�1 during the light period.

In the L16 simulation, the length of the light period was changed to 16 h oflight and 8 h of darkness. The same incident photon irradiance was applied (120�mol · m�2 · s�1 during the 16 h of light), and the model was run as a turbidostat,with an Ieq of 9.375 �mol · m�2 · s�1 during the light period. The total averagedaily light dose experienced by the turbidostat culture at the dynamic equilibriumwas then the same as that in the turbidostat culture in the L12 simulation.

(ii) Equilibrium state analysis. One hundred simulations were performed inorder to investigate the influence of the average light intensity in the culturevessel on the stoichiometry of cellular carbon and nitrogen. The model was runas a turbidostat, and Ieq was uniformly varied between predefined ranges.

Series 1 consisted of 100 simulations similar to the L12 experiments (i.e., undera 12-h light/12-h dark cycle) with Ieq values ranging from 5 to 100 �mol · m�2 ·s�1. The incident photon irradiance applied during the light phase was againconstant in all runs (120 �mol · m�2 · s�1); the total daily light dose remainedthe same.

Series 2 consisted of 100 simulations to analyze the coinfluence of the averagelight intensity and the length of the light period on cell metabolism. Both Ieq (5 to100 �mol · m�2 · s�1) and the length of the light period (8 h to 18 h) werechanged during these simulations, while the incident photon irradiance appliedduring the light phase was again constant in all runs (120 �mol · m�2 · s�1).

RESULTS

Figure 2 displays experimental data; Fig. 3 shows simulationresults with the model run as a continuous culture; and Fig. 4to 6 show results of the simulation with the model run as aturbidostat.

Dynamics of nitrogenase activity. Figure 2 depicts the daily

pattern of nitrogenase activity in a culture of Trichodesmiumsp. strain IMS101, measured by the online acetylene reductiontechnique. Nitrogenase activity was observed essentially duringthe light period of the light-dark cycle. The rate of N2

fixation increased throughout the first half of the light pe-riod and reached its maximum 4 to 5 h after the onset of thelight period. During the second half of the light period,activity decreased steadily, and activity quickly ceased whenit became dark.

Transient dynamics of nitrogen concentration, rate of N2

fixation, and consumption of nitrogen in a simulated experi-ment (L12 experiment). The model behaved qualitatively inthe same way whether it was run in the light-limited continu-ous-culture mode or in the turbidostat mode. This was true forthe transient phase as well as for the equilibrium phase (datanot shown). This was because the system was limited by light inboth modes. The only difference was the resultant light inten-sity in the culture vessel. The results of the L12 continuousculture run are depicted in Fig. 3. The dilution experimentexhibited a progressive shift from growth at the expense ofcombined nitrogen to diazotrophic growth when the externalcombined nitrogen levels fell below the semisaturation concen-tration for nitrogen uptake. Nitrogen uptake and N2 fixationoccurred during the transition period. When available, com-bined nitrogen was preferred. Subsequently, when uptake de-creased, N2 fixation became progressively more important(Fig. 3). During this transient phase, both dissolved inorganicnitrogen (DIN) uptake and N2 fixation were strongly stimu-lated when the light was switched on. A gradual and slightdecrease in DIN uptake was then observed during the lightphase (due to inhibition by the nitrogen reserves [Nr]), whileN2 fixation continued to increase due to the increasing poten-tial activity of the nitrogenase. After the light was switched off,DIN uptake, which is dependent on energy from the catabo-lism of carbon reserves, dropped to half the value obtainedduring the light period, while N2 fixation dropped to zerobecause nitrogenase broke down during the night. Several dayswere required for the population to deplete the DIN from theenvironment, because the inoculum was small.

FIG. 2. Measurement of nitrogenase activity in Trichodesmium sp.strain IMS101 over 24 h. FIG. 3. Simulation of the successive use of different nitrogen

sources in a continuous culture of Trichodesmium sp. strain IMS101grown under a regime consisting of 12 h of light and 12 h of darkness.Shown are the concentration of DIN in the medium, the DIN uptakerate, and the N2 fixation rate. Horizontal black bars on the x axis showthe dark period.



.asm.org/

Dow

nloaded from

http://aem.asm.org/

Influence of the photoperiod on the daily pattern (L12 ver-sus L16 run). In the turbidostat as well as in the continuous-culture experiment, the model displayed a daily pattern of N2

fixation with increasing activity during the first half of the lightperiod and a decrease during the second half. The daily be-havior at equilibrium is depicted comparatively for the twolight regimes in Fig. 4. Nitrogenase synthesis was activated atthe beginning of the day by the depletion of the nitrogenreserves (Fig. 4a and b). When energy became available, therate of N2 fixation increased, and so did the nitrogen reserves

(Fig. 4b). Eventually, the cellular nitrogen status caused adecay of active nitrogenase in the middle of the light period,thus decreasing the N2 fixation potential (Fig. 4a). N2 fixationcontinued during the rest of the light period but decreased (i)because the “synthesis” of nitrogenase decreased as the inter-nal nitrogen reserves became replete during the course of theday and (ii) due to the decay of nitrogenase. The decay ofnitrogenase is proportional to the nitrogenase activity as wellas to the shortage of available carbohydrates in cells (Fig. 4a).When the light was switched off, carbon (Csm) was no longer

FIG. 4. L12 (left panels) and L16 (right panels) turbidostat experiments. Shown are daily dynamics when the model has reached the dynamicequilibrium, for simulations run with a regime consisting of 12 h of light and 12 h of darkness (L12) or 16 h of light and 8 h of darkness (L16).(a) Availability of carbon reserves, and synthesis and decay of nitrogenase activity. (b) Nitrogenase activity, rate of N2 fixation, and availability ofnitrogen reserves. (c) Resultant average irradiance (Ieq) in the vessel and C/N ratio. Horizontal black bars represent the duration of the darkperiod.



.asm.org/

Dow

nloaded from

http://aem.asm.org/

supplied by photosynthesis and net consumption led to a de-crease of the available Csm reserves.

The resultant average irradiance in the vessel chosen in L16was such that the total daily average light experienced by col-onies was the same as that in the L12 turbidostat. Due to thelower average irradiance (Ieq) experienced by colonies in theL16 culture, a lower carbon-specific maximum rate of Cs syn-thesis was observed. However, photosynthesis occurred for alonger period, so that the daily net Cs synthesis rate was higherin L16. As a result, L16 showed higher total intracellular car-bon and nitrogen contents (in structural biomass as well as inreserves) than L12 (data not shown).

Figure 4 shows that N2 fixation activity occurred as long asthe culture was exposed to light. Biomass-specific nitrogenaseactivity still showed a maximum approximately halfway into thelight period, but this maximum value was lower than that in theL12 experiment. The daily N2 fixation rate was higher in L16than in L12. Cells in L16 accumulated more carbon and nitro-gen than cells in L12. However, proportionally, more carbonwas stored in Cr and Csm reserves in L16, while more wasallocated to Nr and Cs in L12. As a result, the C/N ratioobserved in L16 was somewhat higher than that in L12.

Influence of the available irradiance on cell metabolism(series 1). In the series 1 runs, the average irradiance (Ieq) inthe culture at the equilibrium was set and the dilution rateprogressively changed until the amount of biomass gave thedesired value Ieq. Beyond a critical dilution rate, which equalsthe maximum growth rate, washout occurs. An unbalancedgrowth rate was achieved by changes in the cellular carbon andnitrogen contents, which were expressed as the relative pro-portions of the different molecules (Table 2). Thus, we definethe relative proportion of structural carbon, pCs, as its contentrelative to total intracellular carbon: pCs � [Cs]/Ctot (Table 2).The relative content of the carbon reserve, pCr, was calculatedin the same way. The relative proportion of stored nitrogen,pNr, is the content of Nr, expressed as carbon, versus totalcarbon content. In Fig. 5 the daily average of different variablesat equilibrium is plotted as a function of the daily averagephoton flux density (I�). Because at dynamic equilibrium thebiomass dilution equaled the net growth rate, a higher imposedirradiance provoked a higher growth rate and therefore higherdilution rates at equilibrium (Fig. 5a). With increasing irradi-ances, more carbon was fixed and stored in Csm and Cr. Hence,the proportion of carbon storage (pCsm and pCr) increased,while the proportion of carbon in structural biomass (Cs) de-creased (Fig. 5b and c). N2 fixation is regulated by the avail-ability of Csm and therefore increased with light, as did theproportion of nitrogen stored (Nr) (Fig. 5c). Although growthdecreased the cellular carbon content (because of losses due tocarbon dissimilation), carbon assimilation increased fasterthan nitrogen assimilation. As a result, the C/N ratio increasedwith the average irradiance (Fig. 5a).

Coinfluence of the average irradiance in the culture and theduration of the light period (series 2). Figure 6 displays thefluctuations of the C/N ratio for different light periods. Threelines were drawn that represent, respectively, L8, L12, and L16.These curves show that higher C/N ratios resulted from theextra carbon assimilated during longer day lengths. This phe-nomenon is attributed to the saturation in the photosynthesis-light relationship. In this experiment, the total daily amount oflight in the culture vessel (Ieq � day length) was equal in all

FIG. 5. Overview of 100 simulations similar to the L12 experiments(series 1), except that the dilution rate changes. The daily averages ofvariables at the equilibrium state are plotted as a function of the dailyaverage irradiance in the vessel. (a) Average dilution rate and C/Nratio. (b) pCs and pCr. (c) pCsm and pNr. Rates are given per volumeof medium.

FIG. 6. Combined influences of the average irradiance (Ieq) in theculture and the length of the light period at the dynamic equilibrium(series 2). Daily averages of variables at the equilibrium state areplotted as a function of the resultant daily average irradiance in thevessel. Lines represent changes in the daily average C/N ratio for agiven light period: 8 h (L8), 12 h (L12), or 16 h (L16). Note that the xaxis gives the irradiance (Ieq) averaged over 24 h.



.asm.org/

Dow

nloaded from

http://aem.asm.org/

runs. Hence, when the light period was short, light intensitywas high. This resulted in a maximum rate of photosynthesis,but not all energy was used. In contrast, when the light periodwas long, incident irradiance was lower and photosynthesis wassubmaximal. Last, the relative increase in the C/N ratio withirradiance is slightly higher at long day lengths (Fig. 6). Forinstance, the C/N ratio at 34.8 �mol · m�2 · s�1 is 113.8% ofthe value at 3.7 �mol · m�2 · s�1 in L8, while it is 119% of thatvalue in L16.

DISCUSSION

Little is known about the regulatory mechanisms of N2 fix-ation in Trichodesmium. Nitrogenase concentrations in popu-lations are rarely quantified, and even when they are, the activeand inactive forms of this enzyme complex are not easily dis-tinguished from each other (12, 22, 54). Furthermore, thenumber of N2-fixing cells in a trichome of Trichodesmium ismostly unknown. Therefore, it seems almost impossible toquantify the nitrogenase content or its potential activity inindividual nitrogen-fixing cells. Due to these uncertainties, ni-trogenase content is not a suitable state variable for the model.Therefore, we chose to model nitrogenase activity (potentialand actual rates of N2 fixation) rather than the enzyme content.N2 fixation is an energy-costly process and therefore is notpreferred when combined nitrogen is sufficiently available. Asemphasized by Gallon (21), use of N2 instead of DIN entailssome extra costs, associated with (i) the synthesis of nitroge-nase and (ii) the maintenance of anaerobic or microaerobicconditions to protect nitrogenase from inactivation by O2.High respiration rates have been observed in Trichodesmiumpopulations during periods of N2 fixation (4, 8, 27, 42), and ithas been suggested that additional O2-consuming reactions areenhanced when N2 fixation and photosynthesis occur simulta-neously (2). In addition, combined nitrogen availability in theenvironment seems to elicit a down-regulation of the synthesisand activity of nitrogenase (40). A representation of intracel-lular reserves of both carbon and nitrogen is essential in orderto accurately describe the dynamics of N2 fixation and its reg-ulation by the environment. To date, different physiologicallybased models already describe the uncoupling of carbon andnitrogen assimilation in the phytoplankton. In such unbalancedmodels, internal reserves consisting of either energy reserves(carbon) or intracellular nitrogen are included as an interme-diate between photosynthesis and growth (15, 29, 50). Theseformulations have proved their accuracy in models related tocultures (23) as well as to natural environments (19, 30, 45, 52).Stephens et al. (49) devised a model that simulates the inter-action between the different nitrogen sources in the nonhet-erocystous diazotrophic cyanobacterium Gloeothece. In thismodel, uncoupling of carbon and nitrogen assimilation wasachieved through the description of the intracellular concen-tration of a nitrogen reserve (glutamine) and included thedescription of nitrogenase activity. Thus, in the Gloeothecemodel, the changes in the C/N ratio were driven by fluctuationsof the glutamine pool (nitrogen reserve), while the accumula-tion of storage carbon (and hence energy reserves) was notexplicitly included. Therefore, the representation of the inter-actions led to a complex set of equations. In order to be ableto more easily interpret the analysis of the model behavior and

to consider N2 fixation from a mechanistic point of view, wehave chosen to use a simpler formulation. We included decom-position of cellular carbon components as proposed by Lancelotand Billen (29) in which an intermediary pool of low-molecular-weight carbon molecules (Csm), the product of photosynthesis,is described in addition to the internal reserves of carbon. TheCsm pool is an important component of the model, since itsrapid turnover allows fast fluctuations of the cellular processes.Added to that description, an internal storage of nitrogenreserves was included to account for N2 fixation. Hence, thesimulated mechanisms include a down-regulation of active ni-trogenase by available combined nitrogen in the environment,while the actual fixation rate is further regulated by the inter-nal nitrogen and carbon status. Carbon is allocated differentlyaccording to fluctuations in the environment. This model has aflexible structure, resulting in a dynamic response of cells toexternal forcing. Since both photosynthesis and N2 fixationdepend on light and on the internal status of cells, it is possibleto analyze whether differences in the light patterns can result indifferent carbon acquisition and growth.

Diurnal dynamics of N2 fixation in Trichodesmium. BecauseTrichodesmium fixes N2 during the day, the energy required fordiazotrophy is provided mainly by photosynthesis. Such a re-lation has been clearly pointed out for heterocystous cyanobac-teria (46) and for Trichodesmium (26, 48). Trichodesmiumshowed a rapid decline in the N2 fixation rate when photosyn-thesis ceased, suggesting that an immediate shortage of energyoccurred after darkness (Fig. 2). Hence, our results confirm thedependence of Trichodesmium sp. strain IMS101 on ATP pro-vided by photosynthesis, highlighting the importance of thedifferent substrates required for N2 fixation (N2, ATP, andreducing equivalents). In the model, the lowering of the avail-able Csm reserves in cells at the end of the day resulted in anincreased decay of active nitrogenase during the dark (Fig. 4b).The actual N2 fixation rate drops to zero at the end of the daywhile nitrogenase is still active, indicating that activity is lim-ited by the shortage of carbohydrates in the form of Csm. N2

fixation, driven by the “small-metabolite” pool (Csm) in themodel, shows a fast response to light. The role of this com-partment is to take into account fast exchanges of carbon torepresent, for instance, the steep decline in N2 fixation whenthe light is turned off. However, this decline is less steep thanthat measured in the laboratory culture. Furthermore, Csm

content originates both from photosynthesis and from storage/catabolism. When cells are exposed to the dark, Csm is fuellednot by photosynthesis but only by catabolism of cellular car-bohydrates. Provided that the Csm reserve is available to meetthe energy demand, the model also shows that diazotrophy inTrichodesmium can occur during part of the night (Fig. 4b).These results disagree with observations by Mulholland andBernhardt (37), who did not observe any night N2 fixation incultures of Trichodesmium sp. strain IMS101. On the otherhand, our results are in accordance with the behavior of cul-tured populations of Trichodesmium sp. strain GBRTRLI101(20) and with studies of natural Trichodesmium populationsfrom the Pacific (32), supporting the idea that nitrogenaseactivity is not strictly restricted to the light period in Tricho-desmium.

Although photosynthesis and N2 fixation both occur duringthe day, unbalanced growth leads to a fluctuation of the C/N



.asm.org/

Dow

nloaded from

http://aem.asm.org/

ratio in cells at a diel scale (Fig. 4c). The maximum hourly N2

fixation rate [expressed in mol of N · (g of Chla)�1 · h�1] andcarbon fixation rate [expressed in mol of C · (g of Chla)�1 ·h�1] calculated by the model were, respectively, 0.043 and 0.24in L12 and 0.036 and 0.19 in L16 cultures. These values are inthe range reported for different studies on Trichodesmium,listed by Mulholland and Bernhardt (37). The daily averages ofthe molar C/N2 fixation ratio were 22 in the L12 culture (wherethe daily average of the dilution rate is 0.28 day�1) and 18.7in the L16 culture (where the daily average of the dilution rateis 0.29 day�1), consistent with results from acetylene reduc-tion assays reported from continuous-culture experimentswith Trichodesmium (37).

Influence of the light rhythm. Fluctuations of the C/N ratioas a function of light indicate that both the irradiance and theday length affect N2 fixation and cellular elemental composi-tion in Trichodesmium (Fig. 6). L12 and L16 simulations re-ceived the same total daily light dose (Ieq � day length) butexperienced different light regimes. When the day length in-creased, nitrogenase was active in cells for a longer periodduring the day, and although it was progressively down-regu-lated by the increasing nitrogen reserves, activity proceededtoward the end of the light period because carbon was stillavailable to fuel N2 fixation. Light energy is more efficientlyused by photosynthesis at long day lengths: more carbon isfixed per cell and Cs production is higher at the daily scale (andso is pCr), but cells proportionately allocate less nitrogen totheir structural biomass. Hence, at shorter day lengths, photo-synthesis was better synchronized to nitrogenase requirementsand resulted in a lower C/N ratio. In contrast, with longer lightperiods, an imbalance occurred between photosynthesis andbiomass production, and cells redirected the extra carbon fixedinto storage. The higher diurnal accumulation of carbon inreserves in L16 also indicates that much less energy was usedby the N2 fixation process at the beginning and end of theperiod of activity. Because nitrogenase activity is not constantduring the day, our model simulations emphasize the impor-tance of energy availability when nitrogenase approaches itsmaximum potential activity, i.e., mainly before midday. Thetemporal light patterns may thus be part of the factors thatinfluence the proliferation of Trichodesmium populations. Themodel suggests that cell C/N stoichiometry is tightly regulated,and the range of C/N ratios calculated by the model is inagreement with field observations of natural Trichodesmiumpopulations (3).

Regulation in the modeled system versus laboratory culture.With the model, we could generate a daily N2 fixation patternqualitatively similar to the daily patterns measured by us in alaboratory culture of Trichodesmium (Fig. 2) and patternsknown from natural populations and other cultures (39).

A special feature of Trichodesmium is that it fixes N2 duringthe day, concomitantly with photosynthesis. N2 fixation ratesare related to photosynthetic activity on a short time scale.Incident irradiance was kept constant during the light period inboth the laboratory culture and the model simulations. Theobserved diel pattern of N2 fixation is not correlated withincident irradiance, suggesting that the process of N2 fixation isnot linearly related to light. Rather, the daily pattern hadmodulations, indicating the occurrence of internal regulatorymechanisms that result from cell history. In the laboratory

culture, the increase in the rate of N2 fixation observed in themorning can be due either to (i) an increase in the fixationpotential within N2-fixing cells, (ii) an increase in the numberof cells that actually fix N2, or (iii) an increase in availability ofthe substrate (carbon) limiting the N2 fixation rate. The firsttwo possibilities agree with the modeled increase in nitroge-nase activity (whether in one cell or in several cells), whereasthe third is the modulation of the N2 fixation rate by carbonavailability. In the same way, declining rates in the afternoonfollow deactivation of the enzyme but could also reflect adecrease in numbers of N2-fixing cells.

Because N2 fixation in the model depends only on physio-logical factors, enzymatic activities are not confined to the lightperiod. Rather, we assume that diazotrophic activity is deter-mined by nitrogen limitation and cell C/N stoichiometry. Thisassumption is based on two main ideas: (i) the synthesis anddecay of the enzyme are activated and modulated by the in-ternal nutrient and energy states of the cells and (ii) the po-tential fixation rate is enhanced by nitrogen starvation butlimited by electrons originating from the small carbon metab-olites or ATP produced by respiration or photosynthesis. As aresult, the onset of enzyme activity starts before the onset ofthe light, and the activity varies along the light period althoughthe applied irradiance is constant. Daily fluctuations calculatedby the model proved to be in good agreement with the dynam-ics of N2 fixation observed in Trichodesmium populations (3),as well as with our own measurements (Fig. 2). Hitherto, mod-els available in the literature have displayed patterns of nitro-genase activity that were most often directly related to lightintensity (26, 33, 34). However the synthesis and activity ofnitrogenase are probably under the control of a circadian clock(12, 43). In Synechococcus sp. strain Rf-1, the cyclic nitroge-nase activity resulted from de novo synthesis of nitrogenaseduring the dark (13). In Trichodesmium, part of the enzymaticcomplex is destroyed during the afternoon and synthesized denovo toward the end of the night and the beginning of the daythrough genetic regulatory mechanisms (5, 53, 54). This tran-scriptional regulation cannot be described explicitly within ourmodel, because it occurs at different scales than the processeswe have focused on. However, regulation is still exerted by themetabolism in the model, which integrates processes at lowerlevels. In particular, the gene transcriptional level is implicitlyinvolved in the calculation of the potential activity of nitroge-nase through the feedback regulation exerted by the internalnitrogen status and a presumed regulatory mechanism basedon the Csm and Nr stoichiometry (Fig. 4a and 5a). The modelis then able to reproduce the daily patterns of the metabolismthat result from these coupled influences of the environmentand the internal status of cells.

Finally, the model shows that carbon availability is a simpleand efficient mechanism for regulating the balance of carbonand nitrogen fixed (C/N ratio) in cells with a spatial separationof N2 fixation. We conclude that N2 fixation is ultimately de-termined by substrate availability and that this direct controlprevents high fluctuations on a daily basis.

Conclusions. The dynamics of N2 fixation are complex be-cause they involve the influence of external as well as internalfactors. The mathematical model presented here aimed toprovide a scientific reflection tool conceptualizing the ecolog-ical determinants of the N2 fixation process in Trichodesmium.



.asm.org/

Dow

nloaded from

http://aem.asm.org/

The combined representation of intracellular reserves of car-bon and nitrogen and the description of the activity of nitro-genase are essential parts of the model formulation. The mod-eling is unconventional in that it precedes observations thatcould be used to test, validate, or falsify its assumptions. How-ever, where available, the model simulation results agree qual-itatively with observations. The model generates a correct tim-ing of the onset of enzyme activity synthesis. Moreover, it alsoproved to represent the co-occurrence and transition betweennitrogen uptake and N2 fixation, and we were able to repro-duce a daily pattern of nitrogenase activity as observed innature. This model is suitable for exploring the influence ofenvironmental factors on the metabolism of this importantcyanobacterium and the conditions promoting N2 fixation. Inparticular, we emphasize the strong relation between N2 fixa-tion and carbon availability. The C/N ratio appeared to bedependent on the light regime. Fluctuations in cell C/N stoi-chiometry resulted from changes in carbon uptake, assimila-tion into the different cellular compartments, and energy con-sumption, according to growth requirements. With the simplemechanism of carbon-limited N2 fixation, the C/N ratio wasbalanced over days in the model. This modeling exercise thusemphasizes the need for acquisition of data on nitrogenaseactivity under various environmental conditions, as it may besubstrate (carbon) limited. Substrate limitation can directlycontrol C/N ratios and could thus precede the delayed geneticregulatory mechanisms based on the cellular C/N status.

ACKNOWLEDGMENTS

We are very grateful to J. Zehr for his contructive comments on themanuscript.

This work was funded by a grant from the European Commission,contract MEIF-CT-2003-500516.

REFERENCES

1. Bergman, B., and E. J. Carpenter. 1991. Nitrogenase confined to randomlydistributed trichomes in the marine cyanobacterium Trichodesmium thiebau-tii. J. Phycol. 27:158–165.

2. Bergman, B., J. R. Gallon, A. N. Rai, and L. J. Stal. 1997. N2 fixation bynon-heterocystous cyanobacteria. FEMS Microbiol. Rev. 19:139–185.

3. Berman-Frank, I., J. T. Cullen, Y. Shaked, R. M. Sherrell, and P. G.Falkowski. 2001. Iron availability, cellular iron quotas, and nitrogen fixationin Trichodesmium. Limnol. Oceanogr. 46:1249–1260.

4. Berman-Frank, I., P. Lundgren, Y.-B. Chen, H. Kupper, Z. Kolber, B. Bergman,and P. Falkowski. 2001. Segregation of nitrogen fixation and oxygenic pho-tosynthesis in the marine cyanobacterium Trichodesmium. Science 294:1534–1537.

5. Capone, D. G., J. M. O’Neil, J. Zehr, and E. J. Carpenter. 1990. Basis for dielvariation in nitrogenase activity in the marine planktonic cyanobacteriumTrichodesmium thiebautii. Appl. Environ. Microbiol. 56:3532–3536.

6. Capone, D. G., J. P. Zehr, H. W. Paerl, B. Bergman, and E. J. Carpenter.1997. Trichodesmium, a globally significant marine cyanobacterium. Science276:1221–1229.

7. Carpenter, E. J., B. Bergman, R. Dawson, P. J. A. Siddiqui, E. Soderback,and D. G. Capone. 1992. Glutamine-synthetase and nitrogen cycling in col-onies of the marine diazotrophic cyanobacteria Trichodesmium spp. Appl.Environ. Microbiol. 58:3122–3129.

8. Carpenter, E. J., and T. Roenneberg. 1995. The marine planktonic cyanobac-teria Trichodesmium spp.—photosynthetic rate measurements in the SWAtlantic Ocean. Mar. Ecol. Prog. Ser. 118:267–273.

9. Carpenter, E. J., and K. Romans. 1991. Major role of the cyanobacteriumTrichodesmium in nutrient cycling in the North Atlantic Ocean. Science254:1356–1358.

10. Carpenter, E. J., A. Subramaniam, and D. G. Capone. 2004. Biomass andprimary productivity of the cyanobacterium Trichodesmium spp. in the trop-ical N Atlantic Ocean. Deep-Sea Res. Pt. I 51:173–203.

11. Cavender-Bares, K. K., D. M. Karl, and S. W. Chisholm. 2001. Nutrientgradients in the western North Atlantic Ocean: relationship to microbialcommunity structure and comparison to patterns in the Pacific Ocean. Deep-Sea Res. Pt. I 48:2373–2395.

12. Chen, Y. B., J. P. Zehr, and M. Mellon. 1996. Growth and nitrogenfixation of the diazotrophic filamentous nonheterocystous cyanobacte-rium Trichodesmium sp. IMS 101 in defined media: evidence for a circa-dian rhythm. J. Phycol. 32:916–923.

13. Chow, T. J., and F. R. Tabita. 1994. Reciprocal light-dark transcriptionalcontrol of Nif and Rbc expression and light-dependent posttranslationalcontrol of nitrogenase activity in Synechococcus sp. strain Rf-1. J. Bacteriol.176:6281–6285.

14. Coles, V. J., R. R. Hood, M. Pascual, and D. G. Capone. 2004. Modeling theimpact of Trichodesmium and nitrogen fixation in the Atlantic Ocean. J.Geophys. Res. Oceans 109:C06007. doi:10.1029/2002JC001754.

15. Droop, M. R. 1973. Some thoughts on nutrient limitation in algae. J. Phycol.9:264–272.

16. Falkowski, P. G. 1997. Evolution of the nitrogen cycle and its influence onthe biological sequestration of CO2 in the ocean. Nature 387:272–275.

17. Faugeras, B., M. Levy, L. Memery, J. Verron, J. Blum, and I. Charpentier.2003. Can biogeochemical fluxes be recovered from nitrate and chlorophylldata? A case study assimilating data in the Northwestern Mediterranean Seaat the JGOFS-DYFAMED station. J. Mar. Syst. 40:99–125.

18. Fennel, K., Y. H. Spitz, R. M. Letelier, M. R. Abbott, and D. M. Karl. 2002.A deterministic model for N2 fixation at stn. ALOHA in the subtropicalNorth Pacific Ocean. Deep-Sea Res. Pt. II 49:149–174.

19. Flynn, K. J., and M. J. R. Fasham. 2003. Operation of light-dark cycleswithin simple ecosystem models of primary production and the consequencesof using phytoplankton models with different abilities to assimilate N indarkness. J. Plankt. Res. 25:83–92.

20. Fu, F. X., and P. R. F. Bell. 2003. Factors affecting N2 fixation by thecyanobacterium Trichodesmium sp. GBR-TRLI101. FEMS Microbiol. Ecol.45:203–209.

21. Gallon, J. R. 2001. N2 fixation in phototrophs: adaptation to a specializedway of life. Plant Soil 230:39–48.

22. Gallon, J. R., J. J. Cheng, L. J. Dougherty, V. A. Gallon, H. Hilz, D. M.Pederson, H. M. Richards, S. Ruggeberg, and C. J. Smith. 2000. A novelcovalent modification of nitrogenase in a cyanobacterium. FEBS Lett. 468:231–233.

23. Geider, R. J., H. L. MacIntyre, and T. M. Kana. 1998. A dynamic regulatorymodel of phytoplanktonic acclimation to light, nutrients, and temperature.Limnol. Oceanogr. 43:679–694.

24. Holl, C. M., and J. P. Montoya. 2005. Interactions between nitrate uptakeand nitrogen fixation in continuous cultures of the marine diazotrophTrichodesmium (Cyanobacteria). J. Phycol. 41:1178–1183.

25. Hood, R. R., N. R. Bates, D. G. Capone, and D. B. Olson. 2001. Modeling theeffect of nitrogen fixation on carbon and nitrogen fluxes at BATS. Deep-SeaRes. Pt. II 48:1609–1648.

26. Hood, R. R., A. Subramaniam, L. R. May, E. J. Carpenter, and D. G.Capone. 2002. Remote estimation of nitrogen fixation by Trichodesmium.Deep-Sea Res. Pt. II 49:123–147.

27. Kana, T. M. 1993. Rapid oxygen cycling in Trichodesmium thiebautii. Limnol.Oceanogr. 38:18–24.

28. Karl, D., A. Michaels, B. Bergman, D. Capone, E. Carpenter, R. Letelier, F.Lipschultz, H. Paerl, D. Sigman, and L. Stal. 2002. Dinitrogen fixation in theworld’s oceans. Biogeochemistry 57/58:47–98.

29. Lancelot, C., and G. Billen. 1985. Carbon-nitrogen relationships in nutrientmetabolism of coastal marine ecosystems. Adv. Aquat. Microbiol. 3:263–321.

30. Lancelot, C., G. Billen, C. Veth, S. Becquevort, and S. Mathot. 1991. Mod-eling carbon cycling through phytoplankton and microbes in the Scotia-Weddell Sea area during sea ice retreat. Mar. Chem. 35:305–324.

31. Lee, K., D. M. Karl, R. Wanninkhof, and J.-Z. Zhang. 2002. Global estimatesof net carbon production in the nitrate-depleted tropical and subtropicaloceans. Geophys. Res. Lett. 29:1907. doi:10.1029/2001GL014198.

32. Letelier, R. M., and D. M. Karl. 1996. Role of Trichodesmium spp. in theproductivity of the subtropical North Pacific Ocean. Mar. Ecol. Prog. Ser.133:263–273.

33. Levine, S. N., and W. M. Lewis, Jr. 1984. Diel variation of nitrogen fixationin Lake Valencia, Venezuela. Limnol. Oceanogr. 29:887–893.

34. Levine, S. N., and W. M. Lewis, Jr. 1987. A numerical model of nitrogenfixation and its application to Lake Valencia. Freshwat. Biol. 17:265–274.

35. Moore, J. K., S. C. Doney, D. M. Glover, and I. Y. Fung. 2002. Iron cyclingand nutrient-limitation patterns in surface waters of the World Ocean. Deep-Sea Res. Pt. II 49:463–507.

36. Moore, J. K., S. C. Doney, J. A. Kleypas, D. M. Glover, and I. Y. Fung. 2002.An intermediate complexity marine ecosystem model for the global domain.Deep-Sea Res. Pt. II 49:403–462.

37. Mulholland, M. R., and P. W. Bernhardt. 2005. The effect of growth rate,phosphorus concentration, and temperature on N2 fixation, carbon fixation,and nitrogen release in continuous cultures of Trichodesmium IMS101. Lim-nol. Oceanogr. 50:839–849.

38. Mulholland, M. R., and D. G. Capone. 1999. Nitrogen fixation, uptake andmetabolism in natural and cultured populations of Trichodesmium spp. Mar.Ecol. Prog. Ser. 188:33–49.

39. Mulholland, M. R., and D. G. Capone. 2000. The nitrogen physiology of the



.asm.org/

Dow

nloaded from

http://aem.asm.org/

marine N2-fixing cyanobacteria Trichodesmium spp. Trends Plant Sci. 5:148–153.

40. Mulholland, M. R., K. Ohki, and D. G. Capone. 2001. Nutrient controls onnitrogen uptake and metabolism by natural populations and cultures ofTrichodesmium (Cyanobacteria). J. Phycol. 37:1001–1009.

41. Platt, T., C. L. Gallegos, and W. G. Harrison. 1980. Photoinhibition ofphotosynthesis in natural assemblages of marine phytoplankton. J. Mar. Res.38:687–701.

42. Roenneberg, T., and E. J. Carpenter. 1993. Daily rhythm of O2-evolution inthe cyanobacterium Trichodesmium thiebautii under natural and constantconditions. Mar. Biol. 117:693–697.

43. Schneegurt, M. A., D. L. Tucker, J. K. Ondr, D. M. Sherman, and L. A.Sherman. 2000. Metabolic rhythms of a diazotrophic cyanobacterium,Cyanothece sp. strain ATCC 51142, heterotrophically grown in continu-ous dark. J. Phycol. 36:107–117.

44. Soetaert, K., V. deClippele, and P. Herman. 2002. FEMME, a flexible envi-ronment for mathematically modelling the environment. Ecol. Model. 151:177–193.

45. Soetaert, K., P. M. J. Herman, J. J. Middelburg, C. Heip, C. L. Smith, P.Tett, and K. Wild-Allen. 2001. Numerical modelling of the shelf breakecosystem: reproducing benthic and pelagic measurements. Deep-Sea Res.Pt. II 48:3141–3177.

46. Staal, M., S. T. L. Hekkert, P. Herman, and L. J. Stal. 2002. Comparison ofmodels describing light dependence of N2 fixation in heterocystous cya-nobacteria. Appl. Environ. Microbiol. 68:4679–4683.

47. Staal, M., S. T. Lintel-Hekkert, F. Harren, and L. Stal. 2001. Nitrogenaseactivity in cyanobacteria measured by the acetylene reduction assay: a com-parison between batch incubation and on-line monitoring. Environ. Micro-biol. 3:343–351.

48. Staal, M., F. J. R. Meysman, and L. J. Stal. 2003. Temperature excludesN2-fixing heterocystous cyanobacteria in the tropical oceans. Nature 425:504–507.

49. Stephens, N., K. J. Flynn, and J. R. Gallon. 2003. Interrelationships betweenthe pathways of inorganic nitrogen assimilation in the cyanobacteriumGloeothece can be described using a mechanistic mathematical model. NewPhytol. 160:545–555.

50. Tett, P. 1998. Parameterising a microplankton model. Napier University,Edinburgh, United Kingdom.

51. Tyrrell, T. 1999. The relative influences of nitrogen and phosphorus onoceanic primary production. Nature 400:525–531.

52. Van den Meersche, K., J. J. Middelburg, K. Soetaert, P. van Rijswijk,H. T. S. Boschker, and C. H. R. Heip. 2004. Carbon-nitrogen coupling andalgal-bacterial interactions during an experimental bloom: modeling a C-13tracer experiment. Limnol. Oceanogr. 49:862–878.

53. Wyman, M., J. P. Zehr, and D. G. Capone. 1996. Temporal variability innitrogenase gene expression in natural populations of the marine cyanobac-terium Trichodesmium thiebautii. Appl. Environ. Microbiol. 62:1073–1075.

54. Zehr, J. P., M. Wyman, V. Miller, L. Duguay, and D. G. Capone. 1993.Modification of the Fe protein of nitrogenase in natural populations ofTrichodesmium thiebautii. Appl. Environ. Microbiol. 59:669–676.



.asm.org/

Dow

nloaded from

http://aem.asm.org/

Documents

Modeling the dynamic regulation of nitrogen fixation in the cyanobacterium Trichodesmium sp