Stable carbon isotope signals in particulate organic and inorganic carbon of coccolithophores – A numerical model study for Emiliania huxleyi

Journal of Theoretical Biology 420 (2017) 117–127

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Stable carbon isotope signals in particulate organic and inorganic carbon of coccolithophores – A numerical model study for Emiliania huxleyi

MARK

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Lena-Maria Holtz , Dieter Wolf-Gladrow, Silke Thoms Alfred-Wegener-Institut, Helmholtz-Zentrum für Polar- und Meeresforschung, Am Handelshafen 12, 27570 Bremerhaven, Germany

A R T I C L E I N F O

A BS T RAC T

Keywords: Numerical model Isotope fractionation δ13C Proxy Vital effect

A recent numerical cell model, which explains observed light and carbonate system effects on particulate organic and inorganic carbon (POC and PIC) production rates under the assumption of internal pH homeostasis, is extended for stable carbon isotopes (12C, 13C). Aim of the present study is to mechanistically understand the stable carbon isotopic fractionation signal (ε) in POC and PIC and furthermore the vital effect(s) included in measured εPIC values. The virtual cell is divided into four compartments, for each of which the 12C as well as the 13 C carbonate system kinetics are implemented. The compartments are connected to each other via transmembrane fluxes. In contrast to existing carbon fractionation models, the presented model calculates the disequilibrium state for both carbonate systems and for each compartment. It furthermore calculates POC and PIC production rates as well as εPOC and εPIC as a function of given light conditions and the compositions of the external carbonate system. Measured POC and PIC production rates as well as εPIC values are reproduced well by the model (comparison with literature data). The observed light effect on εPOC (increase of εPOC with increasing light intensities), however, is not reproduced by the basic model set-up, which is solely based on RubisCO fractionation. When extending the latter set-up by assuming that biological fractionation includes further carbon fractionation steps besides the one of RubisCO, the observed light effect on εPOC is also reproduced. By means of the extended model version, four different vital effects that superimpose each other in a real cell can be detected. Finally, we discuss potential limitations of the εPIC proxy.

1. Introduction Marine phytoplankton is an important regulator of atmospheric pCO2 via photosynthetic CO2 fixation. Additionally, some phytoplankters precipitate calcium carbonate (CaCO3). In contrast to photosynthesis, the latter process shifts the carbonate system of seawater towards higher CO2 concentrations. Amongst the most important pelagic calcifiers are coccolithophores, most of which precipitate CaCO3 intracellularly (Paasche, 2002). The CaCO3 platelets built by coccolithophores (coccoliths) can be found in marine sediment layers and their carbon isotopic composition is believed to contain valuable information on past seawater carbonate system compositions (Ziveri et al., 2011). However, due to the metabolic activity of coccolithophores, isotopic signals in particulate inorganic carbon (PIC) (and particulate organic carbon, POC) cannot be translated directly into the corresponding signals in seawater. This metabolically induced offset is termed ‘vital effect’. In order to reconstruct past seawater carbonate systems from the carbon isotopic composition of coccoliths, the vital effect has to be understood first. Aiming to understand the isotopic

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signals in PIC and POC mechanistically, we analyse the vital effect by means of a numerical carbon isotope model. Emiliania huxleyi was chosen as model organism, because it is one of the most abundant and best studied coccolithophores in today's ocean. Net rates of photosynthetic CO2 fixation as well as of CaCO3 precipitation vary with environmental variables such as light, temperature, and carbonate system compositions (Zondervan et al., 2002; Raven and Crawfurd, 2012; Sett et al., 2014). In the present work, focus is set to light intensities and carbonate system compositions. A superior mechanistic concept of how these abiotic factors regulate cellular carbon fluxes and therewith the production rates of POC and PIC has long been missing. While intracellular carbon fluxes cannot be measured directly, a couple of indirect methods are available. Besides POC and PIC production rates, which give evidence about the net fluxes into POC and PIC, respectively, external carbon sources of POC and PIC can be determined by different methods (e.g. Paasche, 2002). By means of the 14C disequilibrium method, for instance, an increase in relative CO2 usage for POC production was determined with increasing external CO2 concentrations (Kottmeier et al., 2014, carbonate system

Corresponding author. E-mail address: [email protected] (L.-M. Holtz).

http://dx.doi.org/10.1016/j.jtbi.2017.01.030 Received 6 June 2016; Received in revised form 15 January 2017; Accepted 19 January 2017 Available online 24 January 2017 0022-5193/ © 2017 Elsevier Ltd. All rights reserved.

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Stoll (2013) studying the incorporation of 12C and 13C into calcite. This model divides the cell into three compartments [cytosol, chloroplast, and coccolith vesicle (CV)] and describes CO2 and HCO−3 fluxes through them. The numerical model presented here follows the approach of Zeebe et al. (1999, carbon flux model for foraminifera), who implemented the kinetics of both carbonate systems (12C and 13C). The separation between 12C and 13C fluxes as well as the implementation of the carbonate system kinetics is essential when aiming to understand the isotopic signals in POC and PIC mechanistically. The two carbonate systems are coupled to each other only via their reactions with H+ , OH−, and H2O. In contrast to Zeebe et al. (1999), who restrict their calculations to the growth medium of the foraminifera cell (carbonate system variations are calculated as a function of distance r from the centre of the cell), we calculate the intracompartmental carbonate systems of E. huxleyi by separating the cell into four compartments (cytosol, chloroplast stroma, thylakoid/pyrenoid complex, and CV), in each of which both carbonate systems are resolved kinetically. The implementation of cellular compartmentation is necessary, because cells regulate the internal fluid of each compartment to another pH value. Furthermore, some specialised compartments contain carbonic anhydrases (CA), enzymes that catalyse the otherwise very slow interconversion between CO2 and HCO−3 . The kinetic fractionation differs between CA-catalysed and non-catalysed reactions, which we account for in the model. In a cell, transport systems that facilitate the flux of carbon molecules across membranes can add one further coupling mechanism: Some transporter systems may carry 12C and 13C isotopes (e.g. H12CO−3 and H13CO−3 ) across a membrane in the ratio present in the compartment from where they are transported, while others may fractionate against one of the two carbon isotopes (most likely against 13C, Zeebe and Wolf-Gladrow, 2001). Diffusive net fluxes of gas molecules are driven by their concentrational gradients (here: [12 CO 2 ] or [13CO 2 ] gradient) across the compartment-confining membranes. As RubisCO discriminates against 13CO2, 13CO2 accumulates within the cell. It follows that CO2 diffusing into the cell should be enriched in 12CO2 (in comparison to external CO2). Carbon dioxide diffusing out of the cell, in contrast, should be enriched in 13CO2 (Holtz et al., 2015a). Due to the small cell size of our model organism (cell diameter of ca. 5 μm), carbonate system dynamics within the boundary layer adjacent to the cell are neglected here (Wolf-Gladrow and Riebesell, 1997; Flynn et al., 2012). To sum up, in contrast to the above-mentioned mass balance models, we decouple 12C and 13C fluxes, calculate carbonate system kinetics for each isotopic species, and include cellular compartmentation. With this approach, we aim to gain a mechanistic understanding of cellular carbon fluxes in E. huxleyi, and therewith an explanation for the stable carbon isotopic fractionation values in POC and PIC (εPOC and εPIC ). In order to do so, we extend the previously developed numerical cell model (Holtz et al., 2015b) for the carbon isotopes 12C and 13C and herewith related flux modifications. The new model is used to simulate POC and PIC production rates as well as εPOC and εPIC values at different light and carbonate system conditions. The simulations are then compared to observations and the underlying cellular carbon fluxes are analysed.

manipulation via pCO2). The remaining fraction originates from external HCO−3 . The carbon isotopic compositions of POC and PIC can also give evidence about external carbon sources, because CO2 contains less 13C (∼9‰) than HCO−3 in bulk seawater (Zeebe and WolfGladrow, 2001). Since the isotopic label of PIC is very similar to the one of external HCO−3 , the isotopic carbon composition of PIC gives strong evidence for HCO−3 being the prime external carbon source of PIC (Rost et al., 2002). In two previous studies (Holtz et al., 2015a,b), a numerical cell model was set up, which divides the virtual cell into four compartments. Cellular carbon fluxes through E. huxleyi are calculated by applying the full kinetics of the carbonate system for all cellular compartments. The latter model (Holtz et al., 2015b) provides a mechanistic explanation for the trends observed in POC and PIC production rates with changing light and carbonate system conditions under the assumption of internal pH homeostasis (for external pH values >7.6 ). The model outputs in Holtz et al. (2015b) are compared to data that were conducted on the basis of different carbonate system manipulation methods (constant or varying pH) and with different strains. Some of the observed trends were previously explained by proton effects, because correlations between external proton concentrations and measured POC and PIC production rates were observed. The model (Holtz et al., 2015b) is able to reproduce the observed correlations. The mechanism leading to the calculated correlations, however, is more complex: the maximum HCO−3 uptake rate (which we assume to vary with the abiotic conditions the cells are acclimated to via increase or reduction of membrane proteins that can transport HCO−3 ), for instance, is varied as a function of the CO2 saturation state of Ribulose-1.5-bisphosphate Carboxylase/Oxygenase (RubisCO). At low external CO2 concentrations, the model (Holtz et al., 2015b) calculates higher POC and PIC production rates for cells grown at high pH values (high external [HCO−3 ]) than for those grown at low pH values (low external [HCO−3 ]), which is well in line with observations (Fig. 12 in Holtz et al., 2015b). Thus, the model explains the observed pattern in POC and PIC production rates by changes in external HCO−3 concentrations. In our model (Holtz et al., 2015b), POC is built from external CO2 and HCO−3 with an increase of CO2 usage at high CO2 concentrations. This is in accordance with experimental evidence (Rost et al., 2003; Kottmeier et al., 2014). Particulate inorganic carbon is mainly built from external HCO−3 , which also is in line with experimental findings (Rost et al., 2002). In these previous model studies (Holtz et al., 2015a,b), however, carbon fluxes were not divided into 12 C and 13C fluxes. First isotope fractionation models for photosynthetic carbon fixation date back to the 80s (Farquhar, 1983; Sharkey and Berry, 1985). These simplistic analytical models consider the cell as one compartment and presume that HCO−3 was the exclusive external carbon source of POC. Sharkey and Berry (1985) assume, for example, that external HCO−3 is taken up with the 13C:12C ratio as it occurs outside the cell. Subsequently, HCO−3 is quantitatively converted to CO2 inside the cell which then exhibits the same 13C:12C ratio as external HCO−3 . The net discrimination of RubisCO (against 13C, Farquhar et al., 1989), which is added to the described effect, is additionally dependent on the fraction of CO2 that escapes from the cell. Strongly simplifying this additional effect, the fraction of CO2 that escapes from the cell is presumed to be proportional to the ratio between CO2 efflux and HCO−3 uptake. Later models allow for an additional uptake of external CO2 (Schulz et al., 2007) which is assumed to exhibit the same 13C:12C ratio as external CO2. Low 13C:12C ratios in POC are explained by high ratios between CO2 efflux and carbon uptake rates (the so-called ‘leakage’ or ‘leakiness’) in these models. Based on assumptions similar to the ones of Farquhar (1983) and Sharkey and Berry (1985), yet dividing the cell into cytosol and chloroplast, Schulz et al. (2007) provide an extended mass balance model to describe carbon isotopic fractionation for E. huxleyi. Recently, one further analytical mass balance-based isotope fractionation model for coccolithophores was published by Bolton and

2. Calculation of production rates and fractionation values Model outputs will be compared to various datasets (Riebesell et al., 2000; Rost et al., 2002; Langer et al.; Hoppe et al., 2011; Bach et al., 2013; Sett et al., 2014; Hermoso et al., 2016), which are based on different carbonate system manipulation methods (cf. Appendix A for further information). The conventional approach to determine cellular POC and PIC production rates is to multiply the cellular content of POC or PIC, respectively, with the specific growth rate μ (d−1). The latter value gives 118

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the number of cell divisions into e cells per day. Instead of μ, we introduce an alternative parameter value for cell division here, namely the ‘daughter cell formation rate’ R dc (d−1):

R dc = e μ·1 d − 1

et al., 2015b). Accordingly, in silico pH values of CS, CP, and TP are regulated via H+ fluxes across the compartment-enclosing membranes. Carbon dioxide fixation via RubisCO occurs inside the TP and is assumed to be light- and CO2-dependent. In case the CO2 concentration around RubisCO falls below a predefined threshold, the plasma membrane's potential for HCO−3 uptake is upregulated in the model. The substrates Ca2+ and HCO−3 for PIC production are actively imported from the CS into the CV ((5) in Fig. 1). In contrast to our previous model (Holtz et al., 2015b), where transporter (5) was made dependent on POC production rates, it is made dependent on respiration rates here. Respiration was not taken into account in our previous model, but since respirational CO2 release may impact εPOC and εPIC , it is considered here. Further differences to the set-up in Holtz et al. (2015b) are:

(1) −1

Since the exponent to e has to be dimensionless, μ (unit: d ) is multiplied by 1 d. e μ·1 d gives the total number of cells (daughter cells and mother cell) evolving from one mother cell during one day. Hence, R dc gives the number of daughter cells (mother cell excluded) built by each mother cell per day. Production of POC and PIC takes place primarily during the illumination phase. Thus, production rates of POC and PIC (POC rate and PIC rate, respectively; unit: mol C cell−1 h−1) are referred to hour of illumination:

POC rate = cell.POC·

PIC rate = cell.PIC·

R dc hi

•

(2)

R dc hi

(3)

•

where ‘hi’ gives the duration of the illumination phase in hours per day (h d−1). ‘cell. POC’ and ‘cell. PIC’ stand for the (minimum) cellular POC or PIC content (unit: mol C cell−1) that is assumed to be reached directly after cell division, i.e. after the dark phase, during which cell division takes place (Müller et al., 2008). It should be noted, however, that in most studies, samples for cell. POC and cell. PIC are taken a couple of hours after the onset of illumination. Furthermore, in terms of continuously illuminated cells (L:D=24:0 h), cell division is not synchronised, i.e. measured ‘cell. POC’ and ‘cell. PIC’ values may rather give a daily mean value than the daily minimum value. It follows that the presented observations may overestimate production rates. Additional information on the applied equations is provided in Appendix A.1. The isotopic composition (δ) of a sample is determined by:

⎡ ([13C]/[12 C]) ⎤ sample δ13Csample = ⎢ 13 − 1⎥ ·1000 12 ⎢⎣ ([ C]/[ C])standard ⎦⎥

x Rub x

x Rub

f

δ13C product

(4)

• •

(5)

1000

13

For the calculation of εPOC , ‘δ Csource ’ denotes the isotopic composition of CO2 in bulk seawater:

εPOC =

δ13CCO2 − δ13CPOC 1+

δ13CPOC 1000

(6)

For the calculation of εPIC , the isotopic composition of DIC (dissolved inorganic carbon; sum of CO2, HCO−3 , and CO32−) in bulk seawater is used for δ13Csource :

εPIC =

δ13CDIC − δ13CPIC 1+

δ13CPIC 1000

f

x ·R Rub max·[ CO 2]TP

K Rub m

+ [CO2]TP

(8)

(7)

Rub ⎧ ⎪1 + ε for x = 12 C =⎨ 1000 ⎪ ⎩1 for x = 13C

(9)

‘[ CO 2]TP ’ denotes the CO2 or CO2 concentration around RubisCO (i.e. inside the TP) and ‘[CO2]TP ’ the total CO2 concentration. ‘K Rub m ’ and ‘ε Rub ’ give the half saturation constant and isotopic fractionation of RubisCO determined by Boller et al. (2011) for E. huxleyi (72 mol m−3 and 11‰). A value of 11‰ for ε Rub is very low in comparison to those measured for other species (commonly in the range from 20‰ to 30‰, Boller et al., 2011). McNevin et al. (2007), however, measured a similar value for a mutant of tobacco RubisCO. ‘R Rub max ’ denotes the maximum CO2 fixation rate of RubisCO that is calculated as a function of prevailing light conditions. A detailed description of the mathematical implementation is given in Appendix B.2. HCO−3 cannot leak out of the cell in the basic model set-up (but see Appendices C.4 and C.7). As in Holtz et al. (2015b), two HCO−3 uptake systems ((2a) and (2b)) are assumed for the plasma membrane, where the constitutive system (2a) exhibits a lower HCO−3 uptake capacity (i.e. HCO−3 is transported more slowly by uptake system (2a)) than the inducible system (2b). For both systems, uptake rates are dependent on the external HCO−3 concentrations. In contrast to Holtz et al. (2015b), HCO−3 concentrations that exceed 4 mmol m−3 and 1.6 mmol m−3, respectively, do not increase the uptake rates by (2a) and (2b) any further (Appendix B.2, description to (2a) and (2b)). This extension enables the model to reproduce the data of Bach et al. (2013) by means of the same parameter set as the remaining datasets. x

δ13Csource − δ13C product 1+

R Rub =

where

where ‘([13C]/[12C])standard’ denotes a standard value ([13C]/[12 C])PDB. Isotopic fractionation (ε) is generally calculated as follows:

ε=

All model equations that contain carbon are doubled (C → 12C and 13 C). Applied reaction rate constants of the carbonate systems are given in the Appendix (Table B.1). Fixation of 12CO2 and 13CO2 by RubisCO is calculated as follows (cf. Appendix B.2, description to (13) and (16)):

12

13

Parameter values for the basic model set-up are given in Appendix B. Model forcings are the irradiance levels and carbonate system compositions, at which the experiments were conducted. In contrast to Holtz et al. (2015b), only one parameter set is applied for all model runs in the present study (Tables B.1–B.4 in Appendix B).

For more information refer to Appendix A.2. 3. Model The general set-up of the model follows the one of Holtz et al. (2015b), where the cell is divided into four compartments (cytosol, CS; chloroplast stroma, CP; thylakoid/pyrenoid complex, TP; coccolith vesicle, CV; cf. Fig. 1), in each of which the carbonate system dynamics are calculated. We assume that above external pH values of 7.6, the cell is able to strictly regulate internal pH values (pH homeostasis) (Holtz

4. Outputs from the basic model set-up 4.1. Particulate organic and inorganic carbon production rates Measured and calculated POC and PIC production rates are given in 119

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Fig. 1. Model set-up. Arrows with solid lines indicate substrate fluxes. Arrows with dotted lines indicate regulation mechanisms. External (in seawater or culture medium) carbonate system (especially [CO2 ] and [HCO− 3 ]) and light intensities constitute the model forcings. CA – carbonic anhydrase, CPs – chloroplast stroma, CS – cytosol, TP – thylakoid/pyrenoid complex, CV – coccolith vesicle. Inside the CS, the CPs, and the TP, pH values are regulated: pH CS = 7 , pH CPs (during illumination) = 8, pH TP (during illumination) = 5, pH CPs (during darkness) = 7, pH TP (during darkness) = 7.

absolute values of the HCO−3 influx do not deviate strongly from those calculated for the CO2 efflux. The sum of HCO−3 and CO2 fluxes hence yields very small numbers in the denominator of the expression for the relative CO2 usage of the cells (equation given in description to Fig. 3), which explains the very high relative CO2 efflux calculated by the model. Overall, the data are reproduced surprisingly well, especially when having in mind that different datasets from different laboratories and different strains are used (cf. Appendix A.1), while only one parameter set is applied.

Fig. 2 for each dataset separately, except for the one of Hermoso et al. (2016), which neither includes POC nor PIC production rates. In line with the datasets, calculated POC and PIC production rates are low at limiting external CO2 concentrations. Furthermore, a decrease in PIC production rates at high CO2 concentrations is calculated for some of the data, which is in line with the data of Rost et al. (2002), Langer et al., Hoppe et al. (2011), and Sett et al. (2014). The model explains this pattern as follows: at high CO2 concentrations, RubisCO is substrate (CO2)-saturated. Thus, a low uptake capacity for HCO−3 is calculated. In contrast to POC production, which can either use external CO2 or HCO−3 as substrate, PIC production is dependent on external HCO−3 as substrate (cf. Holtz et al., 2015b). In line with the dataset of Bach et al. (2013), the calculated initial slopes of POC and PIC production rates versus external CO2 concentrations (Fig. 2) are higher for the high pH condition (red lines) than for the low pH condition (black lines). The model explains the effect observed by Bach et al. (2013) primarily by higher HCO−3 uptake rates at high pH values (high external [HCO−3 ]) than at low pH values (low external [HCO−3 ]). The uptake rates of HCO−3 depend on the external HCO−3 concentration and the uptake capacity for HCO−3 (regulation mechanism (15) in Fig. 1) in the model. The measured dependency of the PIC production rates on the external HCO−3 concentrations is only weekly altered by the applied pH value (Fig. A.2 in Appendix or Fig. 12 in Holtz et al., 2015b). Maximal POC and PIC production rates at 150 μmol photons m−2 s−1 are often overestimated by the model (cf. outputs to the data of Riebesell et al., 2000; Rost et al., 2002; Bach et al., 2013; Fig. 2). Under all tested abiotic conditions, external HCO−3 constitutes the prime carbon source for PIC production in the model (i.e. due to the model extensions in the present model, HCO−3 for PIC production is not provided by means of the CO2 to HCO−3 conversion inside the chloroplast under very high CO2 concentrations as in our previous model, Holtz et al., 2015b). Relative CO2 uptake of the cell increases with increasing external CO2 concentrations (Fig. 3), which is well in line with the data of Kottmeier et al. (2014), where relative CO2 usage for POC production increases with increasing external CO2 concentrations. Carbon dioxide that leaks out of the virtual cell originates from HCO−3 , which is taken up and converted to CO2 inside the chloroplast (Holtz et al., 2015b). At very low irradiance levels (15 μmol photons m−2 s−1), the model calculates a high relative CO2 efflux (Fig. 3). This is because the

4.2. Light effect on εPOC and εPIC The dataset of Rost et al. (2002) shows a decrease in εPIC with increasing irradiance levels, which is reproduced by the model (Fig. 4, right panel). This decrease results from the strong 13CO2 accumulation around RubisCO at high carbon fixation rates, i.e. at high irradiance levels: the isotopic signature of CO2 that is accumulated around RubisCO ‘spreads’ through the whole cell via CO2–HCO−3 interconversions (Table 1). The calculated light effect on εPIC is hence strongly related to the so-called ‘RubisCO effect’ (e.g. Spero and DeNiro, 1987), which for instance explains why shells of symbiont-bearing foraminifera exhibit lower εPIC values than foraminifera that do not host photosynthetic symbionts. In the following, we will hence refer to this effect as RubisCO effect. The dataset of Rost et al. (2002) further shows that εPOC values of cells grown at 16:8 h light:dark cycles (red, Fig. 4, left panel) are lower than the corresponding values of cells that grew under continuous illumination (turquois, Fig. 4). This pattern is reproduced by the model and stems from higher HCO−3 usage at 16:8 h conditions as measured by Rost et al. (2007). Higher HCO−3 usage was calculated at these conditions, because instantaneous POC production rates (per hour, during illumination phase) exceed those at continuous illumination (Rost et al., 2002). The same dataset further shows an increase in εPOC with increasing irradiance levels (Fig. 4, left panel). The model calculates the opposite trend due to the RubisCO effect. Furthermore, calculated εPOC values are significantly lower than the measured values (note: applied fractionation factor of RubisCO is comparatively low; ε Rub = 11‰ (Boller et al., 2011) in Eq. (8)). Aiming at decreasing the model-data offset, the impact of various model variants was tested, some of which are presented in Appendix C. 120

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Fig. 2. Comparison of measured and calculated rates for particulate organic and inorganic carbon (POC and PIC) over the range of CO2 concentrations used in experiments. Filled symbols or data connected by solid lines represent observations, empty symbols or dotted lines represent the model outputs. For the datasets of Rost et al. (2002) and Bach et al. (2013), lines (solid – data, dotted – model) indicate different experimental set-ups: Rost et al. (2002) applied different light intensities (I = 15, 30, 80, 150 μmol photons m−2 s−1) and two different light:dark cycles (c – 24:0 h, v – 16:8 h). Symbols used in the graphic for the data of Rost et al. (2002) are composed of I and the applied light:dark cycle. 15c, for instance, stands for 15 μmol photons m−2 s−1 and a light:dark cycle of 24:0 h. Bach et al. (2013) used decoupled carbonate systems and conducted their experiments either at a pH value of ∼7.7, a pH value of ∼8.3, or at constant CO2 concentrations. (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.).

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• • • •

• •

• Fig. 3. Calculated, relative CO2 uptake of the cells [ = CO2 flux across the plasma membrane/(CO2 + HCO− 3 fluxes across the plasma membrane)]. An influx of CO2 into the cell is given in case CO2 uptake (y-axis) is positive. An efflux of CO2 out of the cell is given in case CO2 uptake is negative (negative CO2 uptake or ‘leakage’, grey shaded areas). In the model, HCO− 3 cannot leak out of the cell. A CO2 usage of 100% implies that the cell covers its carbon demand completely via diffusive CO2 uptake and no HCO− 3 is taken up.

None of the scenarios based on realistic parameter values however, reproduce the observed increase of εPOC with increasing light intensities over the complete range of applied light intensities.

A CO2 usage of 50% implies that the cell covers its carbon demand by 50% via diffusive CO2 uptake and 50% via HCO− 3 uptake. A value of −100% implies that the cell takes up twice as much carbon as it requires in the form of HCO− 3 , half of which is lost via CO2 efflux from the cell. Rost et al. (2002) applied different light intensities (I = 15– 150 μmol photons m−2 s−1) and two different light:dark cycles (c – 24:0 h, v – 16:8 h). Bach et al. (2013) used decoupled carbonate systems and exhibited their experiments either at a pH value of ∼7.7 (l pH), a pH value of ∼8.3 (h pH), or at constant CO2 concentrations (c CO2).

5. An alternative explanation for observed light effect on εPOC As in other fractionation models, biological carbon isotopic fractionation is exclusive due to RubisCO in our model. Any subsequent biologically induced fractionation steps are hence not taken into account. It is, however, known that during the oxidating step of pyruvate to acetyl coenzyme A one further fractionation step takes place (De Niro and Epstein, 1977) which explains why lipids are generally more strongly depleted in 13C than carbohydrates (Kennicutt II et al., 1992; Riebesell et al., 2000; Benthien et al., 2007). It might be expected that all enzyme-catalysed reactions assimilating or releasing CO2 or HCO−3 fractionate (Hayes, 2001). From the findings of De Niro and Epstein (1977), we conclude that εPOC should increase with rising relative lipid synthesis rates. Fernandez et al. (1996) show that E. huxleyi produces and stores large amounts of lipids during the illumination phase, a high percentage of which is metabolically

Our findings from these test scenarios are:

•

•

order to get rid of the H13CO−3 , which accumulates inside the cytoplasm as a consequence of the fractionating HCO−3 transporter, HCO−3 can diffuse across the plasma membrane. In this scenario, the Ca2+/HCO−3 /H+ transporter inside the CV membrane fractionates also (ε = 5‰) in order to keep εPIC high. However, the calculated RubisCO effect still determines the trends of εPOC and εPIC with increasing light intensities. Higher respiration rates (Appendix C.10) lead to slightly lower εPOC values, because the increasing carbon demand (due to higher gross photosynthesis rates, i.e. net photosynthesis rate plus respiration rate) is covered by an additional uptake of HCO−3 , which further leads to slightly higher PIC production rates. Implementing a higher εRub value (24‰, Appendix C.9) leads to higher εPOC values (Table 1) that are better in line with the data. Implementing a fractionation value of 5‰ for HCO−3 uptake at the plasma membrane (Appendix C.5), the chloroplast envelope (Appendix C.6), or the coccolith vesicle membrane (Appendix C.8) does not lead to lower model-data offsets. No significant difference to the basic model set-up occurs, when H12CO−3 and H13CO−3 pass the membrane independently of each other and bidirectionally (Appendix C.4). In the basic model set-up, H12CO−3 and H13CO−3 are taken up into the cell (one direction only) in the same ratio as they are present in the growth medium (description to fluxes (2a) and (2b) in Appendix B.2). Increasing relative respiration rates towards low irradiance levels may contribute to the observed light effect on εPOC (Appendix C.11). It is, however, not possible to reproduce the observed variation over the whole irradiance range (from 15 μmol photons m−2 s−1 to 150 μmol photons m−2 s−1). TP Too low PCO (CO2 permeability of thylakoid/pyrenoid complex) 2 values (0.005 m h−1 in Appendix C.3, 0.01 m h−1 in basic model setup) lead to light effects in εPOC and εPIC that contradict the observations (Rost et al., 2002): εPOC decreases and εPIC increases TP with increasing irradiance levels. Low PCO values prevent 13CO2 2 from diffusing away from RubisCO, which then leads to a high accumulation of 13CO2 around RubisCO and hence higher 13CO2 fixation rates into POC. Implementing negative fractionation as measured by Romanek et al. (1992) during CaCO3 precipitation (εCaCO3 = − 1‰, Appendix C.1) does not lead to significant effects on εPOC and εPIC , respectively. Thus, in steady state, the model calculates that the isotopic composition of HCO−3 that is imported into the coccolith vesicle (same composition as HCO−3 in cytosol) exhibits a stronger effect on the isotopic composition of PIC than the fractionation during the precipitation process.

An increase of εPOC with increasing light intensities throughout the applied range of light intensities is only calculated for a model scenario (Appendix C.6), where an unrealistically high ε value (80‰) is assumed for the transport of HCO−3 into the chloroplast (no efflux here), while the calculated εPOC values become much too low (ε ∼ − 20‰). In a similar scenario (Appendix C.7), the HCO−3 transporter in the chloroplast envelope is activated only in case RubisCO becomes substrate-limited and fractionates with a (high) ε value of 40‰. In 122

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Fig. 4. Measured (filled symbols, connected by solid lines; mean over the applied range of carbonate systems) and calculated (open symbols, connected by dotted lines; mean over the applied range of carbonate systems) εPOC and εPIC values for the data of Rost et al. (2002). At 15 μmol photons m−2 s−1, no calcite was precipitated in the model (i.e. no εPIC value). Red – light:dark cycle of 16:8 h, turquois – light:dark cycle of 24:0 h (For interpretation of the references to colour in this figure caption, the reader is referred to the web version of this paper.).

carbon compounds, Kennicutt II et al., 1992) are accumulated during the illumination phase. We are aware, however, that our implementation is too simplistic to fully account for in vivo processes since (i) the subsequent fractionation steps do not take place within the pyrenoid as it is implemented in the model and (ii) the regulation of εeff may certainly be much more complex than implemented in the model code. To account for the described hypothesis, we modify our basic model set-up as follows: εeff increases linearly from 11‰ at 0 μmol photons m−2 s−1 to 30‰ at 150 μmol photons m−2 s−1. The applied range in εeff is large and is not thought to represent in vivo conditions. It is, however, essential for our work-around solution, because carbon fractionation takes place exclusively during carbon assimilation inside the thylakoid/pyrenoid complex in the model, whereby 13C around RubisCO is significantly accumulated (cf. point (i) above). Thus, in order to compensate for the strong RubisCO effect at high light intensities, εeff has to be high (probably overestimated) at high light TP , the permeability of the thylakoid/ intensities. Furthermore, PCO 2 pyrenoid complex towards CO2, has to be increased by a factor of five (from 0.01 m h−1 to 0.05 m h−1) to facilitate the 13CO2 flux away from the virtual RubisCO. Calculated εPOC values now increase with light intensity, while εPIC TP values decrease (Fig. 6). Associated with the (too) high PCO value, 2 RubisCO becomes more CO2 limited leading to higher HCO−3 uptake rates and hence an increase in PIC production rates (Fig. 6). The higher (relative) HCO−3 uptake rates add one further reason, why the implemented εeff values have to be comparatively high.

Table 1 Calculated ε values for internal CO2 (internal δ CO2 relative to external δ CO2 ) and HCO− 3 (internal δ HCO− relative to external δ HCO−) within the cytosol (CS), the chloroplast stroma 3 3 (CPs), the thylakoid/pyrenoid complex (TP), and the coccolith vesicle (CV). For each of the two light levels (I=30 μmol photons m−2 s−1 and 150 μmol photons m−2 s−1; both: 24:0 h light:dark cycle, dataset of Rost et al., 2002), the mean ε values (over different carbonate systems) are determined. The values are calculated once for the basic model set-up (εRub =11‰) and once for one of the test scenarios (εRub =24‰, Appendix C.8). I (μmol photons m−2 s−1)

εRub

Site

11‰

CS CPs TP CV

24‰

CS CPs TP CV

30

εCO2

150

εHCO−

εCO2

−0.76 −3.55 −6.50 −0.78

1.09 3.11 −5.27 1.09

−0.85 −4.56 −11.63 −0.84

0.29 1.80 −9.63 0.29

−1.13 −5.37 −10.03 −1.13

0.51 1.32 −8.52 0.51

−1.31 −7.57 −19.84 −1.31

−0.08 −0.78 −16.55 −0.08

3

εHCO− 3

transferred into proteins during the following dark phase, when cellular biomass is prepared for daughter cell formation. Simultaneously, a high percentage of carbohydrates (εcarbohydrates<εlipids ) produced during the illumination phase is lost to respiration during the dark phase. Assuming that cells grown at high light intensities store relatively more carbon in the form of lipids during the illumination phase, high amounts of which are converted into proteins during the following dark phase, their εPOC values at the end of the illumination phase should exceed those of cells grown at low light intensities (Fig. 5). Furthermore assuming that cells grown at high light intensities exhibit higher losses in carbohydrates during the dark phase (higher daughter cell formation rates, hence higher energy demand), the isotopic effect should be increased during the following dark phase. Leaving aside the respiration effect, εPOC values of newly built daughter cells should be very similar to the corresponding value of their mother cell just before the dark phase, even though their biomass compositions (lipids, carbohydrates, proteins) may vary significantly. In the following, we try to reproduce the observed light effect in εPOC by using an effective fractionation value εeff which involves all carbon fractionating steps including the initial assimilation step by RubisCO (εRub ). εeff increases with increasing carbon fixation rates (which are – at nutrient replete conditions – primarily determined by light intensities). The idea behind this (heuristic) formulation is that at high carbon fixation rates, more lipids (and maybe other isotopically light

5.1. CO2 effect on εPOC and εPIC Some of the available data suggest an increase of εPOC and εPIC values with increasing CO2 concentrations at high irradiance levels (Fig. A.3 in Appendix). However, this CO2 effect does not constitute a general pattern that can be observed in the published observations. Some of the data do not show a trend at all, while others even show the opposite trend (Fig. A.3 in Appendix). In the following, we will focus on the data and model outputs at 150 μmol photons m−2 s−1 (Fig. 7). For the complete data and model output refer to the Appendix (Fig. C.38). The basic model set-up yields an increase for εPOC and εPIC values with increasing CO2 concentrations (Fig. 7, top). Calculated εPIC values are in a similar range as the data. The slope in εPIC determined by Hermoso et al. (2016) is lower than the corresponding slope determined by Rost et al. (2002). The model also yields a lower slope for the data of Hermoso et al. (2016) than for the data of Rost et al. (2002). This pattern is explained as follows: Rost et al. (2002) adjusted their carbonate systems via pH changes, while keeping DIC more or less constant. The HCO−3 concentrations in this study varied only between 2.1 mol m−3 and 2.6 mol m−3. Hermoso et al. (2016), in contrast, 123

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Fig. 5. Hypothesis why cells grown at high light intensities (top) exhibit higher εPOC values than cells grown at low irradiance levels.

in the εPIC data of Hermoso et al. (2016). However, the model does not explain why the εPIC data of Rost et al. (2002) that were collected at a light:dark cycle of 16:8 h are higher than the data that were collected at a light:dark cycle of 24:0 h (Rost et al., 2002) and the data of Hermoso et al. (2016) (light:dark=14:10 h). Rost et al. (2006) determined higher HCO−3 usage for cells grown at a light:dark cycle of 16:8 h than for those grown at continuous illumination. It follows that if the observed pattern resulted from a carbon source effect, the εPIC values at 14:10 h would be the lowest values and 24:0 h the highest ones. The observations, however, show a different pattern.

adjusted their carbonate systems via DIC changes, while keeping the pH constant. The HCO−3 concentrations in their experiments varied between <2 mol m −3 and >10 mol m −3. Due to the high HCO−3 concentrations in the growth medium of the latter study, the model calculates higher relative HCO−3 usage, i.e. lower relative CO2 usage, at CO2 concentrations that exceed 30 mmol m−3 than for the experiment of Rost et al. (2002) (Fig. 3). The isotopic signal around RubisCO, which spreads through the whole cell (RubisCO effect) and therewith also into the coccolith vesicle, where PIC is precipitated, is impacted by the isotopic signal of the assimilated carbon. This explains the lower slope

Fig. 6. Measured (filled symbols, solid lines) and calculated (open symbols and dotted lines) εPOC and εPIC values as well as measured and calculated particulate organic and inorganic carbon (POC and PIC) production rates for the data of Rost et al. (2002). In contrast to the basic model set-up, εeff is introduced (Section 5). Red – light:dark cycle of 16:8 h, turquois – light:dark cycle of 24:0 h. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

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Fig. 7. Variation of εPOC and εPIC with external [CO2] at 150 μmol photons m−2 s−1. Light:dark cycles vary between 14:10 and 24:0 h. Data – filled symbols, model outputs – open symbols. Top: model outputs of the base run configuration, bottom: model outputs of the extended model version. The dataset of Rost et al. (2002) comprises data for particulate organic and inorganic carbon (POC and PIC), the ones of Riebesell et al. (2000) and Hermoso et al. (2016) comprise only POC and PIC data, respectively.

yield satisfactory results in terms of εPOC and εPIC , the main drivers for the observed light and carbonate system effects on POC and PIC production remain the concentrations of CO2 and HCO−3 in seawater and the applied light intensities. The (extended) model yields four different vital effects on εPOC and εPIC . Since the four effects superimpose each other, it is difficult to clearly attribute observed effects to one of the four calculated effects. (1) Carbon source (CO2 or HCO−3 ) effect on εPOC and εPIC : Higher HCO−3 usage leads to lower εPOC values, because HCO−3 is isotopically heavier than CO2 in chemical equilibrium (seawater). This effect is observed by Rost et al., (2002, 2006), where cells that were exposed to a dark phase during growth (i.e. higher instantaneous growth rates, Rost et al., 2002) take up more HCO−3 (Rost et al., 2006) and exhibit lower εPOC values (Rost et al., 2002) than those grown at continuous illumination (Fig. 7). Furthermore, the described effect may well play a role in the observed decrease of εPOC and εPIC values with decreasing CO2 concentrations, where at low CO2 concentrations, the relative contribution of external HCO−3 to POC production is high. Therewith, the isotopic signal (ε) around RubisCO, which spreads through the whole cell (RubisCO effect) and also into the coccolith vesicle, where CaCO3 is precipitated, shifts towards higher 13C concentrations and lower εPIC values at low external CO2 concentrations. The virtual cells simulating the experiment of Hermoso et al. (2016) take up relatively more HCO−3 at high CO2 concentrations than the virtual cells simulating the experiment of Rost et al. (2002) (16:8 h, 150 μmol photons m−2 s−1). The higher HCO−3 uptake leads to a lower slope of εPIC with increasing external CO2 concentrations in the Hermoso et al. (2016) experiment than in the experiment of Rost et al. (2002). We further find that increasing respiration rates (i.e. higher gross – but same net POC production rates) generally lead to (slightly) lower ε values due to a shift towards higher photosynthetic HCO−3 usage (higher respiration rates imply higher cellular carbon demands here). (2) CO2 effect on εPOC and εPIC : 12CO2 and 13CO2 molecules diffuse across all biomembranes and hence impact the isotopic carbon signal in all cellular compartments and of all carbon species, where the latter effect arises from carbon species interconversions. In contrast to the carbon source effect (1), which impacts εPIC via the RubisCO effect (Section 4.2), the CO2 effect impacts εPIC via the diffusive exchange of 12 CO2 and 13CO2 between the external medium and the cell. Both effects (1 and 2) superimpose each other and lead to increasing ε values with increasing CO2 concentrations. The described

With respect to the CO2 effect, our test scenarios on the basic model set-up (Appendix C) lead to the following findings:

•

• •

εPOC and εPIC values increase with external CO2 concentrations, when diffusive fluxes of 12CO2 and 13CO2 across all compartment-enclosing membranes are high. Changing the CO2 permeabilities of cellular membranes with applied abiotic conditions (i.e. assumed acclimation effects to different light and carbonate system conditions, Appendix C.12) can lead to decreasing ε values with increasing external CO2 concentrations. In model scenario C.7 (Appendix), the calculated εPOC values decrease with increasing CO2 concentrations at all tested light intensities, because the impact of the strongly fractionating HCO−3 transporter in the chloroplast envelope decreases with increasing CO2 concentrations. A decrease of εPIC with increasing external CO2 concentrations was observed by Rost et al. (2002) under continuous illumination (24:0 h) at 15 μmol photons m−2 s−1 and 30 μmol photons m−2 s−1. TP When assuming low PCO (Appendix C.3) values, the effect of 2 external CO2 concentrations on εPOC and εPIC is weakened, particularly at high irradiance levels. Calculated εPIC values even decrease TP slightly with increasing CO2 concentrations, when PCO is low. 2 In the dataset of Sett et al. (2014), a slight increase in POC and PIC production rates occurs at circa 35–40 mmol CO2 m−3, when applying Eqs. (A.1) and (A.2) (Appendix A.1) to calculate production rates. This pattern is also calculated in some model versions (e.g. Appendix C.11). In the model, cells shift from predominant HCO−3 (at low [CO2]) to CO2 (at high [CO2]) usage here, which could explain the observed pattern.

In comparison to the basic model set-up, the extended model version yields reduced model-data offsets for εPOC and εPIC . In particular, the model-data offset in εPOC is reduced significantly. The slopes calculated by means of the extended model version for εPIC , however, TP are lower than the measured ones (Fig. 7, bottom) due to the high PCO 2 value that is not thought to represent in vivo values (cf. point (i) in Section 5) though. 6. Discussion In the present study, a recent carbon flux model (Holtz et al., 2015b) was extended for the two stable carbon isotopes 12C and 13C. While some modifications had to be applied on the model in order to 125

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light spectra) fluctuate over time. Under fluctuating light intensities, cells exhibit phases with low as well as high light intensities. As described above, the applied light intensity impacts the CO2 dependency of εPIC , partly leading to contradicting trends. Thus, further investigation is required to resolve the impact of varying light intensities on the correlation between εPIC and CO2. The absolute εPIC values determined by Rost et al. (2002) and Hermoso et al. (2016) for cells grown at 150 μmol photons m−2 s−1 (with applied dark phases of 8 h and 10 h, respectively) are not well in line (Fig. 7, Section 5.1). Reasons for this discrepancy may be the utilisation of different strains, the procedure of experiments in different laboratories, or the deviating lengths of the applied dark phase.

pattern is observed in some of the available εPOC and εPIC data for E. huxleyi, particularly at high irradiance levels (Fig. 7). However, a generic pattern for all experimental conditions is not observed in the available datasets (Fig. A.3 in Appendix). At low irradiance levels, for instance, the opposite trend is observed: εPIC decreases with increasing CO2 concentrations. The model reproduces this opposite trend for instance when the membrane permeability towards CO2 of the thylakoid/pyrenoid complex is diminished (Appendix C.3). Our interpretation of the observed, light-dependent variability is that algae exhibit a physiological plasticity that is not implemented fully in our model: parameter values that are set to a constant value in the virtual cell may depend on the acclimation state and could hence be variable in the real one. Cells that are acclimated to low light intensities, for instance, have to economise more smartly with the available energy than cells acclimated to saturating light intensities. In order to reduce the efflux of CO2 from the chloroplast (cf. 15 µmol m−2 s−1 scenario in Fig. 2) at low light intensities, permeabilities towards CO2 supporting the accumulation of CO2 around RubisCO may be downregulated. In case external CO2 concentrations were high in this hypothetic low light scenario, the permeability of the plasma membrane towards CO2 may be upregulated simultaneously to increase the cellular potential for diffusive CO2 uptake. In case external CO2 concentrations were low, in contrast, the permeability of the plasma membrane (and/or the thylakoid/pyrenoid complex) towards CO2 may be downregulated as well to decrease the rates of diffusive CO2 efflux. (3) Light effect on εPIC : Calculated εPIC values decrease with increasing irradiance levels, because high photosynthetic CO2 fixation rates lead to larger 13C accumulation around RubisCO, the isotopic signal of which spreads through the whole cell via carbon species interconversions (RubisCO effect). This effect was observed by Rost et al. (2002) (Fig. 6) and is often amplified by the carbon source effect (1), because the relative contribution of HCO−3 to the external carbon source of POC increases with rising light intensities (RubisCO effect). (4) Light effect on εPOC : Measured εPOC values increase with increasing irradiance levels (Rost et al., 2002). This trend can be reproduced via the introduction of εeff in the extended model version. By means of this model extension, we try to account for the shift in metabolic pathways exhibiting different fractionation pattern onto POC. At low carbon fixation rates (here via light limitation), we assume that photosynthetic CO2 fixation by RubisCO was the prime fractionating pathway, while at high carbon fixation rates, additional pathways such as lipid synthesis had to be added. However, further effects may contribute to the observed pattern. In Appendix C.11, for instance, we reproduced an increase in εPOC with increasing light intensities (only between 80 μmol photons m−2 s−1 and 150 μmol photons m−2 s−1 though) by increasing relative respiration rates with decreasing light intensities (q.v. Appendix C.6).

7. Conclusion Prime aim of the present study was to understand εPOC and εPIC values measured for E. huxleyi mechanistically. By means of our modelling study, we are able to distinguish between four different effects, namely the carbon source effect (1), the CO2 effect (2), the light effect on εPIC (3), and the light effect on εPOC (4). While the first three effects are reproduced easily and thus explained by the basic model setup, the fourth one is not. Reasons for this discrepancy may be the low complexity of the model to describe carbon isotopic fractionation processes, their individual fractionation factors and sites. Assuming that the activity of different metabolic pathways depends on carbon assimilation rates and that different metabolic pathways exhibit different fractionation factors, we introduce an effective parameter value for isotope fractionation, εeff , which increases with increasing carbon assimilation rates. By means of this amended model set-up, the fourth effect is reproduced as well. Another aim of the presented study was to understand the vital effect on εPIC , which is of particular importance for the reconstruction of ancient seawater conditions from εPIC values. The present study delivers a mechanistic explanation for three different vital effects ((1)– (3) in Section 6), two of which are induced by the external carbonate system. The third effect, in contrast, is traced back to the applied light intensity. Under natural conditions, the depth of the surface layer varies and therewith the prevailing, integrated light intensity. Furthermore, εPIC values measured in laboratories stem from cells that were illuminated with one constant light intensity and light spectrum during the applied illumination phase, which does not reflect natural conditions though. Thus, we conclude that the impact of natural light conditions on εPIC values remains to be investigated before εPIC can be applied as a robust proxy for ancient seawater conditions. Acknowledgements We thank Björn Rost and Dorothee Kottmeier for helpful comments on an earlier manuscript version. Furthermore, we thank Dörte Rosenbaum for proofreading the manuscript and two anonymous reviewers who helped us to improve the manuscript. L.-M.H. was funded by the Federal Ministry of Education and Research (BMBF, project ZeBiCa2).

6.1. εPIC of coccolithophores as paleoproxy? Even though a general pattern in εPIC with external parameter values is not observed in the available data sets, some trends were found. The εPIC values determined by Rost et al. (2002) (mean over a range of different carbonate systems), for instance, decrease with increasing light intensities, particularly in case the cells were illuminated continuously (L:D = 24:0 h, Fig. A.3 in Appendix). Depending on the applied irradiance level, additional correlations occur between εPIC and external CO2 concentrations (Fig. A.3 in Appendix): At saturating irradiance levels and a light:dark cycle of 16:8 h, εPIC values increase with increasing CO2 concentrations. At limiting light intensities and continuous illumination (L:D = 24:0 h), in contrast, εPIC values decrease with increasing CO2 concentrations (Fig. A.3 in Appendix). It follows that knowledge on the light conditions coccolithophores were exposed to during growth is essential in order to reconstruct past carbonate system conditions from coccoliths isolated from sediments. However, none of the light conditions applied so far in laboratory experiments reflect natural conditions, where light intensities (and

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