Cellular inorganic carbon fluxes in Trichodesmium: a combined approach using measurements and modelling

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Combining experimental and theoretical approaches to characterize the carbon acquisition of a cyanobacterium, this paper improves interpretations of C isotope fractionation by accounting for the important role of intracellular C cycling.

Abstract

To predict effects of climate change on phytoplankton, it is crucial to understand how their mechanisms for carbon acquisition respond to environmental conditions. Aiming to shed light on the responses of extra- and intracellular inorganic C (C_i) fluxes, the cyanobacterium Trichodesmium erythraeum IMS101 was grown with different nitrogen sources (N₂ vs NO₃ ^–) and pCO₂ levels (380 vs 1400 µatm). Cellular C_i fluxes were assessed by combining membrane inlet mass spectrometry (MIMS), ¹³C fractionation measurements, and modelling. Aside from a significant decrease in C_i affinity at elevated pCO₂ and changes in CO₂ efflux with different N sources, extracellular C_i fluxes estimated by MIMS were largely unaffected by the treatments. ¹³C fractionation during biomass production, however, increased with pCO₂, irrespective of the N source. Strong discrepancies were observed in CO₂ leakage estimates obtained by MIMS and a ¹³C-based approach, which further increased under elevated pCO₂. These offsets could be explained by applying a model that comprises extracellular CO₂ and HCO₃ ^– fluxes as well as internal C_i cycling around the carboxysome via the CO₂ uptake facilitator NDH-1₄. Assuming unidirectional, kinetic fractionation between CO₂ and HCO₃ ^– in the cytosol or enzymatic fractionation by NDH-1₄, both significantly improved the comparability of leakage estimates. Our results highlight the importance of internal C_i cycling for ¹³C composition as well as cellular energy budgets of Trichodesmium, which ought to be considered in process studies on climate change effects.

Introduction

Cyanobacteria are ancient organisms responsible for oxygenation of the atmosphere during times when CO₂ concentrations were about two orders of magnitude higher than today (cf. Buick, 1992; Kasting and Siefert, 2002). Possibly due to their origin at that time, the CO₂-fixing enzyme RubisCO of cyanobacteria has one of the lowest affinities among all autotrophic organisms (Badger et al., 1998; Tortell, 2000). Consequently, cyanobacteria are dependent on high activities of carbon-concentrating mechanisms (CCM) for increasing the CO₂ concentration in the vicinity of RubisCO. Currently, due to ongoing anthropogenic CO₂ combustion, the availability and speciation of inorganic C (C_i) in seawater is changing at a rapid pace (IPCC, 2007). In view of this ocean acidification (Caldeira and Wickett, 2003), a number of studies in recent years have focused on the mechanisms of C acquisition and CO₂ responses of different groups of phytoplankton (e.g. Rost et al., 2008). Among these studies, the abundant N₂-fixing cyanobacterium Trichodesmium stands out by showing an exceptionally high stimulation of biomass production and N₂ fixation in response to elevated pCO₂ (e.g. Hutchins et al., 2007; Levitan et al., 2007; Kranz et al., 2009). Further studies on the underlying reasons for these CO₂ effects show a decrease in C_i affinity at high pCO₂ (Kranz et al., 2009; Kranz et al., 2010). Given the high energy demand of the CCM in cyanobacteria, a reallocation of energy between C_i acquisition and N₂ fixation was suggested to stimulate production at high pCO₂ (Kranz et al., 2010).

Cellular C_i affinities of Trichodesmium are determined by the interplay of several transporters and structural adaptations composing the CCM. In order to understand pCO₂ responses of the CCM as well as potential changes in energy demand, it is necessary to distinguish between these different components. While CO₂ can diffuse through the cell membrane without energy investments, the low equilibrium concentrations, slow interconversion with HCO₃ ^– (Zeebe and Wolf-Gladrow, 2007), and its tendency to leak out of the cell compromise the use of CO₂ as the predominant C_i source. Therefore, cyanobacteria have evolved energy-dependent transporters for taking up HCO₃ ^–, which can be accumulated in the cell more efficiently (Badger et al., 2006). Trichodesmium has been found to cover ~90% of its C demand using HCO₃ ^– (Kranz et al., 2009; Kranz et al., 2010). Uptake of HCO₃ ^– in this species is catalysed by the Na⁺-dependent transporter BicA, which is fuelled by Na⁺/HCO₃ ^– symport or via an H⁺/Na⁺ antiport mechanism (Price et al., 2008).

Cyanobacterial RubisCO is localized in distinct compartments within the cell, the so-called carboxysomes. The protein shells of these microbodies are permeable to HCO₃ ^– but pose a diffusion barrier for CO₂ (Dou et al., 2008; Espie and Kimber, 2011), allowing significant accumulation of CO₂ in the vicinity of RubisCO. Inside the carboxysomes, transformation of HCO₃ ^– to CO₂ is accelerated by carbonic anhydrase (CA; reviewed by Espie and Kimber, 2011). In addition to direct HCO₃ ^– uptake and CO₂ diffusion, CO₂ uptake in Trichodesmium is facilitated by the NDH-1₄ complex, which converts CO₂ to HCO₃ ^– in the cytoplasm, presumably in a CA-like reaction (Price et al., 2002). The protein complex is thought to be located on the thylakoid membrane and form part of the photosynthetic/respiratory electron transport chain, being fuelled by electrons donated from NADPH or ferredoxin, which are subsequently transferred to the plastoquinone pool (Price et al., 2002). After the hydration of CO₂, a proton is thought to be released into the thylakoid lumen, contributing to the pH gradient necessary for ATP synthesis and making the reaction irreversible in the light (Price et al., 2002).

Conversion of CO₂ to HCO₃ ^– by the NDH complex has been proposed to drive internal C_i recycling to minimize loss via CO₂ efflux (Maeda et al., 2002; Price et al., 2002). Due to the strong CO₂ accumulation required in cyanobacteria, CO₂ efflux is a major challenge in these organisms. Despite the interplay of the carboxysome and proposed recapture of CO₂ by the NDH-1₄ complex, efflux of CO₂ has been shown to equal ~50–90% of gross C_i uptake in Trichodesmium (Kranz et al., 2009; Kranz et al., 2010). Next to the C source (CO₂ vs HCO₃ ^–), leakage (i.e. CO₂ efflux : gross C_i uptake) can strongly affect isotopic composition of organic C produced during photosynthesis (Burkhardt et al. 1999, Sharkey and Berry, 1985), and thus measurements of ¹³C fractionation can provide complementary information on this aspect of CCM regulation (e.g. Laws et al., 1997; Keller and Morel, 1999; Rost et al., 2006; Tchernov and Lipschultz, 2008). In fact, differences in leakage estimates based on membrane inlet mass spectrometry (MIMS; Badger et al., 1994) and C isotope fractionation (Sharkey and Berry, 1985) have been attributed to internal C_i cycling driven by NDH (Kranz et al., 2010).

In a previous study (Eichner et al., 2014), the energy allocation to different physiological processes in Trichodesmium under varying energetic states was addressed by altering the cellular energy budget through addition of different nitrogen sources: while N₂ fixation is a highly energy-demanding process with a high demand for ATP, NO₃ ^– requires very little ATP (only for uptake) but instead has a high electron demand. The study highlighted the dependence of energy reallocation on the stoichiometry in energy demands (ATP vs NADPH) of the different pathways involved. The energy demand of the CCM in Trichodesmium remains uncertain, however, especially because the regulation of internal C_i fluxes is as yet poorly characterized. To shed light on the extra- and intracellular C_i fluxes under the different energetic conditions, Trichodesmium was grown with different pCO₂ levels and N sources (N₂ vs NO₃ ^–), and a combination of different methods, including MIMS and ¹³C fractionation measurements, as well as modelling, was employed. While MIMS provides a useful tool to investigate C_i fluxes across the cell membrane, internal fluxes cannot be directly measured and were therefore modelled. Model calculations of internal C_i fluxes made use of the measured extracellular C_i fluxes and the isotopic composition of particulate organic C (δ¹³C_POC), which reflects the integrated effects of extra- and intracellular C_i fluxes. Hereby, a common model of ¹³C fractionation (Sharkey and Berry, 1985) was extended by including internal fluxes around the carboxysome.

Materials and methods

Culture conditions

Trichodesmium erythraeum IMS101 was grown in semi-continuous batch cultures at 25°C and 150 μmol photons m^–2 s^–1 with a 12 h : 12h light : dark cycle. Cultures were grown in 0.2-μm-filtered artificial seawater (YBCII medium; Chen et al., 1996) and kept in exponential growth phase by regular dilution with culture medium. Culture bottles were continuously bubbled with 0.2-μm-filtered air with pCO₂ levels of 380 and 1400 μatm. Prior to experiments, cells were allowed to acclimate to the respective pCO₂ for at least 2 weeks. Cultures in which pH had drifted by >0.09 units compared to cell-free reference media were excluded from further analysis. In treatments with NO₃ ^– as the N source, 0.2-μm-filtered NaNO₃ was added to achieve mean concentrations of 97±2 µmol l^–1 in the experiments, and these never fell below 65 µmol l^–1. Cultures were acclimated to NO₃ ^– for at least 1 week before measurements. Samples for the analysis of dissolved inorganic C (DIC) were filtered through 0.2 μm filters and measured colourimetrically (QuAAtro autoanalyzer, Seal, Norderstedt, Germany). Average precision was ±5 μmol kg^–1. The pH values of the acclimation media were measured potentiometrically (pH meter pH3110, WTW, Weilheim, Germany). For further details on culture conditions as well as carbonate chemistry parameters, see Eichner et al. (2014).

MIMS measurements

Cellular C_i fluxes (Fig. 1) were obtained using a custom-made MIMS system (Rost et al., 2007), applying a disequilibrium approach described by Badger et al. (1994). Assays were performed in YBCII medium buffered with HEPES (50mM, pH 8.0) at acclimation temperature and light intensity, unless otherwise specified. To account for the diurnal cycle of C_i fluxes in Trichodesmium, measurements were performed three times over the day, during time intervals from 0 to 1.5, 5.5 to 7, and 9 to 10.5h after beginning of the photoperiod. CO₂ and O₂ fluxes were measured as a function of DIC, starting with concentrations close to zero (media bubbled with CO₂-free air), which were subsequently increased by step-wise addition of NaHCO₃ up to concentrations of ~5000 μM. As the assay medium is buffered, unlike the conditions during acclimation of the cells, the HCO₃ ^–:CO₂ ratio stayed constant over the investigated DIC range. DIC-saturated rates of photosynthesis (V_max) and half-saturation concentrations [K_1/2 (DIC)] were obtained by fitting a Michaelis-Menten function to the data. Net O₂ evolution was converted to C fixation (F _fix) assuming a photosynthetic quotient (PQ) of 1.34 (Williams and Robertson, 1991). Net CO₂ uptake (F _{cyt, netCO2}) was calculated from the steady-state rate of CO₂ depletion at the end of the light period and corrected for the CO₂/HCO₃ ^– interconversion in the medium (F _{ext, db}). Using C fixation and net CO₂ uptake, HCO₃ ^– uptake rates (F _{cyt, HCO3–}) could be derived by a mass balance equation:

Fig. 1.

Schematic diagram showing the cellular C_i pools and fluxes characterized by measurements and modelling. Fluxes and concentrations in the external medium and fluxes over the cell membrane as well as C fixation (F _fix) were measured by MIMS, while fluxes in and out of the carboxysome were modelled. Shading intensity denotes δ¹³C values of different cellular C pools (including POC and C_i in the cytosol and carboxysome). (A) Fractionation during C fixation by RubisCO leads to depletion of POC in ¹³C and enrichment of ¹³C in the carboxysomal C_i pool. (B) Fractionation during internal C_i cycling, e.g. via NDH, leads to ¹³C depletion of the carboxysomal C_i pool. Consequently, the POC formed is isotopically lighter than in scenario A. This figure is available in colour at JXB online.

$$F_{cyt,HC{O}_3^{-}}=F_{fix}-F_{cyt,netC{O}_2}$$ (1)

For normalization of the CO₂ and O₂ traces, duplicate samples for chlorophyll a (chl a) analysis were taken after each measurement. Chl a was extracted in acetone for >12h and determined fluorometrically (TD-700 fluorometer, Turner Designs, Sunnyvale, CA, USA; Holm-Hansen and Rieman, 1978).

Leakage estimation

Cellular leakage was estimated by two different methods. Firstly, leakage was determined by MIMS measurements using the disequilibrium approach (Badger et al., 1994). Cellular leakage (L _MIMS) is defined as the ratio of CO₂ efflux (F _{cyt, out}) to gross C_i uptake [i.e. the sum of HCO₃ ^– (F _{cyt, HCO3–}) and gross CO₂ uptake (F _{cyt, CO2})]:

$$L_{MIMS}=\frac{F_{cyt, out}}{F_{cyt, HC{O}_3^{-}}+F_{cyt, C{O}_2^{}}}$$ (2)

F _{cyt, out} was estimated from the initial increase in CO₂ concentration after switching off the light (Badger et al., 1994). These estimates are based on the assumption that the rate of diffusive CO₂ efflux during the light phase is well represented by the rate of CO₂ efflux during the first ~20 s of the subsequent dark phase. As leakage calculated by this approach is based on O₂ measurements that are converted to C fluxes, the sensitivity to different PQ values was tested by varying PQ between 1.0 and 1.7, yielding deviations of not more than 15% of leakage estimates (i.e. 0.06 units).

In the second approach, leakage was estimated from the isotopic fractionation during POC formation (ε _p), which was calculated from the difference in isotopic composition between POC (δ¹³C_POC) and CO₂ (δ¹³C_CO2) in the medium according to Freeman and Hayes (1992). Duplicate samples for analysis of δ¹³C_POC were filtered onto pre-combusted GF/F filters and acidified with 200 μl HCL (0.2M) to remove all C_i prior to analysis. δ¹³C_POC was measured with an EA mass spectrometer (ANCA SL 2020, SerCon Ltd, Crewe, UK). For analysis of the isotopic composition of DIC (δ¹³C_DIC), filtered samples were fixed with HgCl₂ (final concentration 110mg l^–1). Subsequent to acidification of the samples, isotopic composition of CO₂ in the headspace was analysed with an isotope ratio mass spectrometer (GasBench-II coupled to Delta-V advantage, Thermo, Bremen, Germany). The isotopic composition of CO₂ was calculated from δ¹³C_DIC, following a mass balance equation (Zeebe and Wolf-Gladrow, 2007). Leakage (L _13C) was subsequently derived using an extended equation from Sharkey and Berry (1985):

$$L_{13C}=\frac{{\epsilon }_p-(a_{cyt}{\epsilon }_{db})}{{\epsilon }_{Rub}}$$ (3)

where ε _Rub is the intrinsic discrimination of ¹³C by RubisCO (assumed to be +25‰; Roeske and O’Leary, 1984; Guy et al., 1993) and ε _db represents the equilibrium fractionation between CO₂ and HCO₃ ^– (–9‰; Mook et al., 1974). The fractional contribution of HCO₃ ^– to gross C_i uptake (a _cyt), being introduced by Burkhardt et al. (1999), has been determined by MIMS measurements for the respective treatments. These calculations assume an equilibrium situation and further consider the cell as a single compartment.

Results and discussion

General CCM characteristics

MIMS measurements showed a highly efficient CCM with a high capacity for regulation of C_i affinity over the diurnal cycle as well as with different pCO₂ levels, in agreement with previous studies on Trichodesmium (e.g. Kranz et al., 2009; Kranz et al., 2010). Half-saturation DIC concentrations for C fixation (K_1/2) ranged between ~20 and 500 µmol DIC l^–1 (Supplementary Figure S1), which is equivalent to ~0.2 and 4 µmol CO₂ l^–1 and is thus substantially lower than the K_M of cyanobacterial RubisCO (105–185 µmol CO₂ l^–1; Badger et al., 1998). Taking the ratio of K_M to K_1/2 as a measure of CO₂ accumulation in the vicinity of RubisCO (assuming a K_M of 150 µmol CO₂ l^–1), our data suggest accumulation factors between ~35 and 900 and indicate that the degree of RubisCO saturation is always larger than 80%. Accordingly, under the applied external CO₂ concentrations, concentrations in the carboxysome typically exceed 600 µmol CO₂ l^–1. The CCM was primarily based on active HCO₃ ^– uptake, accounting for 82±4% of gross C_i uptake (Table 1). As gross C_i uptake was approximately twice as high as net C fixation at acclimation DIC (~2100 µmol CO₂ l^–1), leakage measured by MIMS ranged between 0.3 and 0.7 (i.e. CO₂ efflux equalled 30–70% of gross C_i uptake; Table 1). As a consequence of the high HCO₃ ^– contribution and the high CO₂ efflux, the net fluxes of CO₂ were generally directed out of the cell (cf. negative values for net CO₂ uptake: Table 1, Fig. 2).

Table 1.

Diurnal cycle of C_i fluxes measured by MIMS under acclimation DIC levels (~2100 µmol l^–1) in Trichodesmium acclimated to two different pCO₂ levels (380 vs 1400 µatm) and N sources (N₂ vs NO₃ ^–)^a

	380 µatm –NO3 –			380 µatm +NO3 –			1400 µatm –NO3 –			1400 µatm +NO3 –
	Morning	Midday	Evening	Morning	Midday	Evening	Morning	Midday	Evening	Morning	Midday	Evening
Net C fixation	91±15	57±14	87±3	95±20	56±22	70±18	80±13	39±14	61±4	91	61±19	63±16
Gross Ci uptake	157±18	144±24	167±17	135±23	128±16	143±25	144±7	124±9	142±6	144	127±22	131±17
HCO3 – uptake	134±18	117±22	133±12	118±21	108±14	113±14	126±11	95±9	112±2	120	97±17	102±12
Gross CO2 uptake	23±4	27±4	34±6	17±3	20±2	30±13	18±4	28±5	30±6	24	30±9	29±6
Net CO2 uptake	–45±10	–60±12	–46±9	–23±2	–52±8	–42±11	–46±5	–56±8	–51±4	–28	–36±8	–39±9
HCO3 –:Ci uptake	0.85±0.03	0.81±0.03	0.80±0.02	0.87±0.01	0.84±0.01	0.80±0.06	0.88±0.03	0.77±0.04	0.79±0.03	0.83	0.76±0.05	0.78±0.01
CO2 efflux	69±12	87±13	79±13	40±3	72±6	72±8	64±7	85±14	81±3	53	66±4	67±10
Leakage	0.44±0.05	0.61±0.05	0.47±0.03	0.30±0.03	0.57±0.11	0.51±0.04	0.45±0.07	0.69±0.10	0.57±0.01	0.37	0.53±0.07	0.52±0.07

^a All C_i fluxes are given in µmol C (mg chl a)^–1 h^–1. Errors are standard deviations for biological replicates (1 SD; n = 3 except 1400 +NO₃ ^– morning with n = 1).

Fig. 2.

Example showing the dependence of C_i fluxes measured by MIMS in Trichodesmium on the DIC concentration in the assay. Data shown were measured in the evening in a culture grown at 380 µatm pCO₂ without NO₃ ^–. The shaded area denotes the range of acclimation DIC levels.

Diurnal changes in C_i fluxes

The diurnal cycle was characterized by low K_1/2 values in the morning and a downregulation of C fixation rates at midday (ANOVA, P < 0.001; Supplementary Figure S1A and B). Leakage estimated by MIMS at acclimation DIC was lowest in the morning, increased towards midday, and decreased again towards the evening (ANOVA, P < 0.05; Table 1). Leakage estimates for DIC levels approaching zero (obtained by curve fits of leakage plotted over DIC concentration; Fig. 2) varied even more over the course of the day, yielding values around 0.3 in the mornings, while at midday and in the evening ratios approached 1.0 (data not shown). These diurnal changes in leakage could be explained by the concurrent changes in the ratio of HCO₃ ^– to CO₂ uptake (Table 1, Supplementary Figure 1C), which were characterized by low CO₂ fluxes in the mornings (ANOVA, P < 0.05; Table 1), while HCO₃ ^– uptake was higher in the morning than at midday, and increased again towards the evening (ANOVA, P < 0.05; Table 1). Over the day, a higher share of HCO₃ ^– uptake, which is less prone to diffuse out of the cell, was thus correlated with lower leakage.

Effects of different pCO₂ levels and N sources

The affinity for C_i was downregulated at elevated pCO₂, as indicated by high K_1/2 values under these conditions (Supplementary Figure 1B). Under acclimation DIC, however, C_i fluxes (C fixation, C_i uptake, and CO₂ uptake and efflux) were not significantly affected by pCO₂ (ANOVA, P > 0.05; Table 1), reflecting the cells’ capacity to achieve similar C fixation over a range of pCO₂ levels by regulating their CCM. Regarding the N source, C fixation rates and CO₂ uptake under acclimation DIC were equally unaffected (ANOVA, P > 0.05; Table 1). Although cells mainly used HCO₃ ^– as a C_i source in all treatments, HCO₃ ^– uptake at acclimation DIC decreased slightly with increasing pCO₂ (~10%; ANOVA, P < 0.05; Table 1, Supplementary Figure 1C), but was not affected by N source (ANOVA, P > 0.05; Table 1). Interestingly, CO₂ efflux was affected by the N source (ANOVA, P < 0.01; Table 1), with ~20% lower efflux in NO₃ ^– users compared to N₂ fixers, possibly due to differences in internal pH caused by the uptake/accumulation of NO₃ ^– vs NH₄ ⁺ in the cell. One could also speculate that growing cells on NO₃ ^– reduces the general membrane permeability, since NH₄ ⁺ transfer between cells is only necessary under N₂-fixing conditions, which could also affect the permeability for CO₂. Leakage at acclimation DIC estimated by MIMS was, however, not significantly affected by pCO₂ or N source at any time of the day (ANOVA, P > 0.05; Table 1).

Offsets in leakage estimates

High leakage values obtained in MIMS measurements reflect the strong C_i accumulation necessary for C fixation in cyanobacteria due to the poor CO₂ affinity of their RubisCO. However, leakage estimates obtained from δ¹³C values (L _13C, eqn 3) even exceeded MIMS-based estimates. Overall fractionation during formation of POC (ε _p) was not significantly affected by N treatment (ANOVA, P > 0.05) but increased with pCO₂ (ANOVA, P < 0.0001), ranging from 14.4±1.0‰ at 380 µatm to 19.9±0.9‰ at 1400 µatm pCO₂. Consequently, leakage estimates based on ε _p (eqn 3) also increased with pCO₂, while estimates from MIMS measurements at acclimation DIC were constant over the range of pCO₂ levels. L _13C was calculated to range between 0.82 and 1.14, exceeding MIMS-based measurements by ~30–60% (Fig. 3) and even reaching theoretically impossible values (>1). A similar discrepancy between these two approaches, which was equally dependent on pCO₂ acclimation, has been observed previously (Kranz et al., 2010). In the following paragraph, possible reasons for the deviations between estimates are outlined.

Fig. 3.

Leakage estimates by MIMS (mean values of measurements conducted at three time points over the day; Badger et al., 1994) and ¹³C fractionation (Sharkey and Berry, 1985) determined in Trichodesmium grown under two pCO₂ levels and N sources (n ≥ 3).

Following the approach by Badger et al. (1994), leakage is directly calculated from the measured CO₂ efflux and gross C_i uptake. As CO₂ efflux cannot readily be determined during the light due to the concurrent C_i uptake, the rise in the CO₂ signal directly after switching off the light is taken as an estimate of CO₂ efflux during the light phase, assuming that the accumulated C_i pool and therewith gross CO₂ efflux are initially at the pre-darkness level (Badger et al., 1994). If active C_i uptake as well as C fixation by RubisCO do not cease immediately upon darkening, leakage estimates could be biased and likely to be underestimated. Despite these potential uncertainties, this is a more direct approach than the alternative method, which infers leakage from the isotopic composition of cells. The ¹³C-based approach makes use of the effect of leakage on ε _p (eqn 3; Sharkey and Berry, 1985). Briefly, while the intrinsic fractionation by RubisCO (ε _Rub) generally causes organic material to be depleted in ¹³C (Fig. 1A), variation in ε _p can be induced by changes in the C_i source and/or leakage. Consequently, any errors in estimates of ε _Rub or a _cyt, but also any unaccounted process affecting ε _p, would cause ¹³C-based leakage estimates to be biased.

Kranz et al. (2010) suggested that internal C_i cycling within the cell may affect ε _p in general. The CO₂ dependence of the offset between MIMS- and ¹³C-based leakage estimates was furthermore suggested to reflect a CO₂ effect on the NDH complex driving this internal C_i cycling (Kranz et al., 2010), in line with early observations of the C_i dependence of CO₂ uptake by the NDH complex (Price and Badger, 1989a,c). In Fig. 1, the effects of internal C_i cycling on isotopic composition are illustrated. While Fig. 1A assumes an equilibrium situation and does not include any internal C_i cycling, Fig. 1B illustrates non-equilibrium situations caused by internal C_i cycling. The degree of ¹³C enrichment in the cytosol and within the carboxysome, according to this concept, would be dependent on the type of kinetic fractionation in the cytosol. This could include complete or incomplete unidirectional fractionation as well as enzymatic fractionation by the NDH complex. Accounting for these processes requires the introduction of a second compartment. The approach taken here can be considered as an extension of the model of Sharkey and Berry (1985), which considers the cell as one compartment. In order to avoid errors being introduced by large uncertainties, e.g. in permeability of the plasma membrane and carboxysome in Trichodesmium, a flux-based model that is independent of these assumptions is employed, rather than a full kinetic model. Our approach is similar to the model of Schulz et al. (2007), but disequilibrium situations are also considered.

Internal C_i fluxes and fractionation—model setup

To test our concept (Fig. 1) and quantitatively describe the possible effect of internal cycling on δ¹³C, intracellular C_i fluxes and their effects on isotopic ratios in different cellular C_i pools were modelled. For parameterizations, HCO₃ ^– and gross CO₂ fluxes measured by MIMS as well as measured fractionation values ε _p were used. The model is based on flux balance equations for the individual isotope species. The flux balance of total C (¹²C + ¹³C) in the cytosol and in the carboxysome, respectively, is given by the following equations:

$$\begin{array}{l}{F}_{cyt, C{O}_2}+F_{cyt, HC{O}_3^{-}}+F_{carb, out}\\ -F_{cyt, out}-F_{carb, C{O}_2}-F_{carb, HC{O}_3^{-}}=0\end{array}$$ (4)

$$F_{carb, HC{O}_3^{-}}+F_{carb, C{O}_2}-F_{carb, out}-F_{fix}=0$$ (5)

As about 99% of C is ¹²C, i.e. $F=F12+F13\equiv F12$, the flux balance equations for ¹³C can be derived by multiplying the fluxes (F) with the isotopic ratio R = ¹³C/¹²C. The isotopic fractionation factor α _db is defined by the isotopic ratio of CO₂ divided by the isotopic ratio of HCO₃ ^–, i.e. ${\alpha }_{db}=R_{C{O}_2}/R_{HC{O}_3^{-}}$. Using the equilibrium fractionation (ε _db), the fractionation factor between CO₂ and HCO₃ ^- can be calculated for the external medium as well as for the cytosol according to:

$${\alpha }_{db, ext}=1+{\epsilon }_{db}/1000$$ (6)

$${\alpha }_{db, cyt}=1+{\epsilon }_{cyt}/1000$$ (7)

While the equilibrium value ε _db is –9‰ (i.e. CO₂ is isotopically lighter than HCO₃ ^–; Mook et al., 1974), ε _cyt can significantly deviate from this value due to kinetic effects. The uncatalysed conversion of HCO₃ ^– to CO₂ shows a kinetic fractionation of –22‰, whereas the formation of HCO₃ ^– from CO₂ is associated with a kinetic fractionation of +13‰ (Marlier and O’Leary, 1984). Hence, the actual value of ε _cyt is determined by the disequilibrium between CO₂ and HCO₃ ^– in the cytosol, which depends on all fluxes in and out of the cytosol, and on the internal CO₂ and HCO₃ ^– concentrations, which cannot be calculated in the framework of a flux-based model. Assuming a unidirectional conversion of CO₂ to HCO₃ ^– in the cytosol, a value of +13‰ for ε _cyt will be adopted. By setting ε _cyt to +30‰, a potential fractionation by the NDH-1₄ complex will be taken into account. The situation where the conversion of CO₂ to HCO₃ ^– in the cytosol is not completely unidirectional will be considered by setting ε _cyt to +8‰.

The R associated with F _fix can be written in terms of the isotopic fractionation against ¹³C by RubisCO described by the factor α _Rub = R _carb / R _POC, where R _carb is the isotopic ratio of CO₂ in the carboxysome and R _POC is the isotopic ratio of POC. The value of α _Rub is calculated from the intrinsic RubisCO fractionation ε _Rub (assuming an intermediate value of +25‰; Roeske and O’Leary, 1984; Guy et al., 1993):

$${\alpha }_{Rub}=1+{\epsilon }_{Rub}/1000$$ (8)

Given the isotopic ratios (R) of CO₂ and the isotopic fractionation factors between HCO₃ ^– and CO₂ expressed as α _bd = 1/α _db, the flux balance equations for ¹³C can be derived from eqns 4 and 5 for the cytosol and the carboxysome, respectively:

$$\begin{array}{l}{R}_{ext}{F}_{cyt, C{O}_2}+{\alpha }_{bd, ext}{R}_{ext}{F}_{cyt, HC{O}_3^{-}}+R_{carb}{F}_{carb, out}\\ -R_{cyt}{F}_{cyt, out}-R_{cyt}{F}_{carb, C{O}_2}-{\alpha }_{bd, cyt}{R}_{cyt}{F}_{carb, HC{O}_3^{-}}=0\end{array}$$ (9)

$$\begin{array}{l}{\alpha }_{bd\text{,} cyt}{R}_{cyt}{F}_{carb, HC{O}_3^{-}}+R_{cyt}{F}_{carb, C{O}_2}\\ -R_{carb}{F}_{carb, out}-R_{carb}{F}_{fix}/{\alpha }_{Rub}=0\end{array}$$ (10)

R _cyt is the isotopic ratio of CO₂ in the cytosol. The overall isotopic fractionation by the cell is defined with respect to the isotopic composition of CO₂ in the external medium (R _ext):

$${\epsilon }_p=\left(\frac{R_{ext}}{R_{POC}}-1\right)\times 1000=\left({\alpha }_{Rub}\frac{R_{ext}}{R_{carb}}-1\right)\times 1000$$ (11)

The ratio R _ext/R _carb reflects the impact of the inner compartment on the isotopic fractionation and can be calculated from flux balance eqns 9 and 10. Eqn 10 can be solved for R _cyt, which in turn is substituted into eqn 9, yielding the ratio:

$$\begin{array}{l}\frac{R_{ext}}{R_{carb}}=\frac{\begin{array}{l}\left(F_{fix}/{\alpha }_{Rub}+F_{carb, out}\right)\left(F_{carb,C{O}_2}+{\alpha }_{bd, cyt}{F}_{carb,HC{O}_3^{-}}+F_{cyt, out}\right)\\ {}_{}\end{array}}{\left(F_{cyt, C{O}_2}+{\alpha }_{bd, ext}{F}_{cyt, HC{O}_3^{-}}\right){\left(F_{carb, C{O}_2}+{\alpha }_{bd, cyt}{F}_{carb, HC{O}_3^{-}}\right)}^{{}^{}}}-\frac{F_{carb, out}}{\left(F_{cyt, C{O}_2}+{\alpha }_{bd, ext}{F}_{cyt, HC{O}_3^{-}}\right)}\\ \\ =\frac{F_{cyt, out}}{{\alpha }_{Rub}\left(F_{cyt, C{O}_2}+{\alpha }_{bd, ext}{F}_{cyt, HC{O}_3^{-}}\right)}\times \left(\frac{F_{fix}}{F_{cyt, out}}+\frac{F_{fix}+{\alpha }_{Rub}{F}_{carb, out}}{F_{carb, C{O}_2}+{\alpha }_{bd, cyt}{F}_{carb, HC{O}_3^{-}}}\right)\end{array}$$ (12)

This solution is valid for arbitrary combinations of fluxes as long as the constraints imposed by flux balance equations 4 and 5 are obeyed:

$$\begin{array}{l}{F}_{fix}=F_{carb, C{O}_2}+F_{carb, HC{O}_3^{-}}-F_{carb, out}\\ =F_{cyt, C{O}_2}+F_{cyt, HC{O}_3^{-}}-F_{cyt, out}\end{array}$$ (13)

Given the fractional contribution of HCO₃ ^– to total C_i uptake into the cytosol (a _cyt) and the carboxysome (a _carb), as well as the leakage out of the cytosol (L _cyt) and the carboxysome (L _carb), eqns 6 to 8 and 11 to 13 can be used to derive the overall isotopic fractionation:

$$\begin{array}{l}{\epsilon }_p=\frac{a_{cyt}{\epsilon }_{db}}{1-a_{cyt}{\epsilon }_{db}/{10}^3}+L_{cyt}\frac{\left(a_{carb}{\epsilon }_{\text{cyt}}+L_{carb}{\epsilon }_{Rub}\right)}{\left(1-a_{cyt}{\epsilon }_{db}/{10}^3\right)\left(1-a_{carb}{\epsilon }_{cyt}/{10}^3\right)}\\ \\ \approx a_{cyt}{\epsilon }_{db}+L_{cyt}\left(a_{carb}{\epsilon }_{cyt}+L_{carb}{\epsilon }_{Rub}\right)\text{.}\end{array}$$ (14)

Solving the approximated solution for L _cyt yields the following:

$$L_{cyt}=\frac{{\epsilon }_p-a_{cyt}{\epsilon }_{db}}{a_{carb}{\epsilon }_{cyt}+L_{carb}{\epsilon }_{Rub}}$$ (15)

The approximate solution can be considered as a generalization of the original function given by Sharkey and Berry (1985), accounting for two compartments. The authors assumed that the cell takes up HCO₃ ^– into a single compartment and subsequently converts it to CO₂; hence there is no HCO₃ ^– inside the cell. The compatibility of our model with the original function can be confirmed by comparing ε _p for L _carb = 1 (i.e. no second compartment) and a _carb = 0 (i.e. only CO₂ uptake into the carboxysome).

As pointed out by Schulz et al. (2007), diffusive CO₂ fluxes generally need to be added to cellular fluxes measured by MIMS (Badger et al., 1994) when relating them to ¹³C fractionation. For membrane permeability exceeding 10^–4 cm s^–1, as proposed for a diatom (~10^–2 cm s^–1; Hopkinson et al., 2011), diffusive CO₂ fluxes are high and internal CO₂ concentrations approach those of the cell’s exterior (Supplementary Figure S2). In this case, gross CO₂ efflux estimated by MIMS would be underestimated, which could explain part of the discrepancy between MIMS-based leakage and estimates based on eqn 4 (Sharkey and Berry, 1985). While there is, to our knowledge, no recent data on the membrane permeability of cyanobacteria available, older studies on cyanobacteria state significantly lower values, approaching 10^–5 cm s^–1 (Badger et al., 1985; Marcus et al., 1986), which are in line with diffusive CO₂ fluxes being low enough to allow for considerable CO₂ accumulation in the cell (Supplementary Figure S2). Using this permeability, the effect of diffusive CO₂ influx on leakage obtained by our model was estimated, yielding maximum changes in the order of a few percent, which were thus neglected. In view of the uncertainties in this parameter, measurements of membrane permeability of cyanobacteria are needed to improve future estimates of internal C fluxes.

Internal C_i fluxes and fractionation—model application

To test the sensitivity of our model, the potential effect of changes in a _cyt on ε _p was quantified, using the maximum variability observed in our study (0.84 vs 0.76) while leaving all other parameters constant. This variability can explain a change in ε _p by not more than 0.7‰. Thus, a _cyt can be excluded as a main driver behind the variability in ε _p (or leakage estimates), even if variability in a _cyt is severely underestimated. Applying the model to our measured fluxes and ε _p values, a range of different possible scenarios for intracellular fluxes and fractionation in the cytosol is obtained (Fig. 4).

Fig. 4.

Interrelationship between L _carb, ε _cyt, and a _carb in the model, depicted for different values of L _cyt and ε _p. The shaded areas mark the range of possible values for L _carb and ε _cyt that could reconcile our measurements of isotopic composition with measured external C_i fluxes. Black and grey lines are based on ε _p measured in cells acclimated to 380 and 1400 µatm pCO₂, respectively.

According to these interrelations, while at L _cyt according to our MIMS measurements (0.5), only a very high fractionation in the cytosol (ε _cyt) can explain our results, at L _cyt ≥ 0.7, there is a large range of possible combinations of parameters (see shaded areas in Fig. 4). As we aim to find parameters that can explain ε _p in both of our pCO₂ treatments, the high ε _p measured in cells grown at 1400 µatm constrains the range of possible values, while ε_p of cells grown at 380 µatm could be explained by a larger range of values for a _carb and L _carb (Fig. 4). High values for a _carb and L _carb (both approaching 1) allow for a larger range of possible values of ε _cyt to explain our measured ε _p (Fig. 4). Due to the high contribution of HCO₃ ^– to C_i uptake and the additional conversion of CO₂ to HCO₃ ^– by the NDH complex, a _carb is likely to be close to 1, most probably exceeding a _cyt measured in our experiment (0.82). Moreover, high diffusive CO₂ influx into the carboxysome seems unlikely in view of the supposed function of the carboxysome as a diffusion barrier to CO₂ (e.g. Reinhold et al., 1989). While comparison experiments with CA knockout mutants with intact and broken carboxysomes confirmed that the carboxysome shell impedes diffusion of CO₂ (Dou et al., 2008), the pores in the hexamer protein subunits of the shell are supposed to be permeable to small, negatively charged molecules such as HCO₃ ^– (Tsai et al., 2007; Klein et al., 2009; Espie and Kimber, 2011). Despite the low CO₂ permeability, high rates of CO₂ efflux, and thus high L _carb, are likely due to the very high accumulation factor (two to three orders of magnitude; this study and Kaplan et al., 1980). A value for L _carb of 0.9 is therefore used in the model scenarios described in the following (Table 2). Using eqn 13, the following expression for the ratio of internal to external C_i fluxes can be derived:

Table 2.

Different scenarios of external and internal C_i fluxes that can reconcile measurements of C_i fluxes by MIMS and ε _p values obtained in this study (scenarios 1, 2 and 4 to 6) and by Kranz et al. (2010, scenario 3)^a

Scenario	pCO2	ε p	a cyt	L MIMS	L 13C	L cyt	L carb	a carb	ε cyt
		Measured				Modelled
1	1400	20	0.8	0.5	1.1	0.8	0.9	1	13
2	380	14	0.8	0.5	0.8	0.6	0.9	1	13
3	180	7	0.8	0.4	0.6	0.4	0.9	1	13
4	1400	20	0.8	0.5	1.1	0.9	0.9	1	8
5	1400	20	0.8	0.5	1.1	0.5	0.9	1	30
6	380	14	0.8	0.5	1.1	0.6	0.9	0.7	20

^a ε _p, a _cyt, and L _MIMS were measured; L _13C was calculated from ε _p according to Sharkey and Berry (1985); remaining values are model input parameters and model results (L _cyt , L _carb, a _carb, and ε _cyt).

$$\frac{F_{carb,C{O}_2}+F_{carb,HC{O}_3^{-}}}{F_{cyt,C{O}_2}+F_{cyt,HC{O}_3^{-}}}=\frac{1-{\text{L}}_{cyt}}{1-{\text{L}}_{carb}}$$ (16)

For the chosen value for L _carb of 0.9 and the measured L _cyt of 0.5, eqn 16 yields a ratio of internal vs external C_i cycling of 5.

Compared to estimates based on Sharkey and Berry (1985), our model significantly improved the compatibility of leakage estimates with those obtained by MIMS measurements (Table 2). The maximum fractionation that could be achieved in an uncatalysed reaction from CO₂ to HCO₃ ^– is +13‰ (O’Leary et al., 1992). With this kinetic fractionation, ε _p values measured for the two pCO₂ levels can be explained by leakage values from the cytosol (L _cyt) of 0.8 and 0.6, respectively (scenarios 1 and 2, Table 2), which are significantly lower than the estimates based on the function by Sharkey and Berry (L _13C = 1.1 and 0.8, respectively). The remaining difference to leakage estimates obtained by MIMS (L _MIMS = 0.5) could be explained by an underestimation of leakage by the MIMS approach, as discussed above. Assuming that the conversion between CO₂ and HCO₃ ^– in the cytosol was not completely unidirectional, ε _cyt could range between +13‰ and –9‰ (equilibrium fractionation; O’Leary et al., 1992). To simulate this intermediate scenario, an ε _cyt of +8‰ is assumed (senario 4, Table 2), yielding an L _cyt of 0.9 for the high CO₂ treatment.

Kinetic fractionation could be achieved by the NDH complex or by creation of a strong disequilibrium in the cytosol, minimizing the back-reaction from HCO₃ ^– to CO₂. Mutants of Synechococcus expressing human CA in the cytosol were unable to accumulate C_i (Price and Badger, 1989b), suggesting that HCO₃ ^– is accumulated in the cytosol, and that a chemical disequilibrium in the cytosol favours the reaction from HCO₃ ^– to CO₂ rather than the opposite direction. This strongly argues for a fractionating enzyme instead of a purely chemical disequilibrium driving unidirectional CO₂ to HCO₃ ^– conversion in the cytosol. Assuming that NDH not only drives the unidirectional conversion of CO₂ to HCO₃ ^– but also discriminates against ¹³C during the reaction, leakage estimates by our model can be further reconciled with MIMS-based estimates. In a scenario assuming an upper estimate for ε _cyt of +30‰ (scenario 5, Table 2), which is within the range of fractionation measured in other enzymes such as RubisCO, our MIMS-measured data can be reproduced even for the high pCO₂ treatment (L _MIMS = L _cyt = 0.5; Table 2). Note that in combination with one of the other factors discussed above, such as an underestimation of L _carb or of MIMS-based leakage estimates, enzymatic fractionation less than +30‰ could also explain our measurements (cf. e.g. scenarios with ε _cyt of 13‰; Table 2). Although CA and NDH have been proposed to have similar reaction mechanisms (Price et al., 2002), our model results suggest that the fractionation by the NDH complex is different from that of CA (1‰ for conversion of CO₂ to HCO₃ ^–; Paneth and O’Leary, 1985). This might be due to the fact that the subunit carrying out the hydration reaction in the NDH-1₄ complex (chpX) is embedded in a larger functional unit including the transmembrane proton channel and is associated with the electron transport chain. To confirm the differences in fractionation between these enzyme complexes, however, further work using experimental approaches would be necessary, e.g. by comparing cyanobacterial mutant strains.

Since our MIMS measurements showed that leakage was unaffected by pCO₂ and the slight changes in a _cyt could not explain the observed variation in ε _p, a _carb and/or ε _cyt would need to vary with pCO₂ to explain the observed CO₂-dependence of ε _p. An increase in the activity of the NDH complex could yield an increase in a _carb as well as ε _cyt and therewith ε _p. With an increase in a _carb from 0.7 to 1 and an increase in ε _cyt from 20 to 30‰, the measured increase in ε _p between 380 and 1400 µatm can be explained, almost reproducing MIMS-measured leakage in both scenarios (scenarios 5 and 6, Table 2). A higher activity of NDH at high pCO₂ may seem unexpected in view of its supposed role as part of the CCM. However, in contrast to other components of the CCM such as HCO₃ ^– transporters, the reaction catalysed by the NDH complex contributes to ATP regeneration rather than consuming energy, and thus a downregulation of NDH at high pCO₂ would not provide any energetic benefit to the cell. A positive correlation with pCO₂ might be coupled to the small CO₂ effect on a _cyt (Table 1; Supplementary Figure 1C), increasing the activity of the NDH complex at high pCO₂ levels in the acclimations in response to a higher availability of its substrate CO₂. Note that the change in a _cyt may have been underestimated in our study due to the constant pH in MIMS measurements. Due to its function as a proton pump in the thylakoid membrane, activity of the NDH complex can increase the ratio of ATP to NADPH available in the cell. The production of ATP by high NDH activity at high pCO₂ could, in turn, contribute to the increased ATP requirement to fuel N₂ fixation in Trichodesmium under ocean acidification (e.g. Kranz et al., 2010; Eichner et al., 2014).

Kranz et al. (2010) compared leakage estimates based on MIMS and ¹³C for Trichodesmium grown under different pCO₂ levels as well as light intensities. Applying our model to this data set, MIMS-based leakage estimates could be reproduced with unidirectional fractionation for a low pCO₂ treatment with light intensities similar to our experiment (200 µmol photons m^–2 s^–1; scenario 3, Table 2). In high pCO₂ and low light treatments, the difference between L _MIMS and L _cyt was larger and could consequently only be reconciled with ε _cyt values larger than +30‰. Short-term exposure to high light intensities (300 µmol photons m^–2 s^–1) in our experiment affected CO₂ efflux in cells acclimated to high pCO₂ (ANOVA, P < 0.05; data not shown). Such light sensitivity generally suggests CO₂ efflux to be closely associated to photosynthetic electron transport. As this light effect was only observed under high pCO₂, i.e. conditions associated with higher NDH activity according to our model results, the interrelation of CO₂ efflux and the NDH complex is further corroborated. The observed light effects on CO₂ efflux (this study) and ε _p (Kranz et al., 2010) impose interesting questions with regard to a potential regulation of the NDH complex by the electron transport chain (redox state and/or proton gradient), which should be investigated in future studies. A better understanding of the regulation of the NDH complex is essential to improve confidence in explaining the effects of pCO₂ as well as light on internal C_i fluxes and potential feedbacks on cellular energy budgets of this key N₂ fixer.

Conclusion and outlook

This study demonstrates that internal C_i fluxes via the NDH-1₄ complex need to be considered not only in terms of cellular C_i acquisition, but also with regard to ¹³C fractionation and cellular energy status. The comparison of direct measurements of C_i fluxes with estimates based on isotopic composition revealed that ¹³C fractionation in Trichodesmium cannot be adequately described by only considering external C_i fluxes.

Compatibility with direct leakage measurements was improved by applying a model accounting for internal C_i fluxes around the carboxysome, e.g. via the NDH complex, providing a generalization of the model of Sharkey and Berry (1985) applicable for two compartments. In these model calculations, a large fraction of HCO₃ ^– uptake into the carboxysome (0.7–1, Table 2) and high leakage from the carboxysome (>0.9, Table 2) are assumed, in accordance with the current understanding of carboxysome functioning. A large range of fractionation values for the cytoplasm, representing uncatalysed, unidirectional fractionation as well as enzymatic fractionation by the NDH complex, could significantly improve compatibility of leakage estimates (Table 2), even though the exact interplay of these processes still has to be resolved. While the lack of recent literature data on membrane permeability of cyanobacteria clearly demands future measurements, our model calculations are insensitive to this parameter within a certain range of permeability estimates (<10^–4 m^–2 s^–1). Similarly, the model is independent of other potentially uncertain assumptions such as permeability of the carboxysome and pH values for the different compartments. Once future studies improve confidence in these parameters, a kinetic model can be used to predict internal concentrations and individual C_i fluxes. The agreement of model results with measured values could further be improved by accounting for possible ¹³C enrichment of CO₂ leaking out of the cell as well as a disequilibrium situation in the surroundings of the cell (altering the isotopic signature of HCO₃ ^– taken up).

The model applied here could also be used to improve estimates of leakage based on ¹³C signatures for other species in which several compartments and/or internal C_i fluxes play an important role. For phytoplankton groups that are relevant in terms of paleo-proxies, this could have important implications for the interpretation of C isotope signals.

Supplementary material

Supplementary Figure S1. DIC-saturated rates of C fixa tion (V_max), half saturation DIC concentrations (K_1/2) and HCO₃ ^– : C_i uptake ratios measured at three time points during the day in Trichodesmium grown under two pCO₂ levels and N sources (N₂ and NO₃ ^–).

Supplementary Figure S2. The dependence of intracellular CO₂ concentrations on membrane permeability.

Funding

This work was supported by the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007–2013), ERC grant agreement (205150), and the US National Science Foundation (EF 1040965).

Glossary

Abbreviations:

a_carb

fractional contribution of HCO₃ ^– to total C_i uptake into the carboxysome

acyt

fractional contribution of HCO₃ ^– to total C_i uptake into the cytosol

CA

carbonic anhydrase

CCM

carbon-concentrating mechanism

chl a

chlorophyll a

Ci

inorganic carbon

DIC

dissolved inorganic carbon

K_1/2

half-saturation concentration

L_13C

leakage calculated from ¹³C fractionation

L_carb

modelled leakage from the carboxysome

L_cyt

modelled leakage over the plasma membrane

L_MIMS

leakage estimated by MIMS

MIMS

membrane inlet mass spectrometry

POC

particulate organic carbon

PQ

photosynthetic quotient

V_max

maximal rate

ε_cyt

¹³C fractionation in the cytosol

ε_db

¹³C equilibrium fractionation in the external medium

ε_p

total ¹³C fractionation during POC formation

ε_Rub

13C fractionation by RubisCO.