Note
A model of carbon isotopic fractionation and active
carbon uptake in phytoplankton
Klaus Keller
Department of Civil Engineering and Operations Research, Princeton University, Princeton, NJ
08540, [email protected]
Franc
ois M.M. Morel
Department of Geosciences, Princeton University
Abstract
The carbon isotopic fractionation of phytoplankton photosynthesis (p) has been interpreted
by previous authors as inconsistent with active bicarbonate uptake. This interpretation
contradicts the results of numerous physiological studies demonstrating signicant active
bicarbonate uptake in phytoplankton. Using a simple model of cellular regulation of carbon
acquisition we show that an upward curvature of p as a function of the ratio of growth rate
to carbon dioxide concentration does not exclude active bicarbonate uptake. Our model
describes adequately published carbon isotope data for cyanobacteria, diatoms and coccolithophores consistent with active bicarbonate uptake.
KEY WORDS: phytoplankton carbon isotopic fractionation model active carbon uptake
bicarbonate carbon dioxide
The carbon isotopic fractionation of phytoplankton photosynthesis (p) is an important
biogeochemical signal used, for example, to estimate ancient carbon dioxide concentrations
(e.g., Jasper and Hayes [1990]). Unfortunately, many observations contradict the existing
p models. Most p models consider only diusive carbon dioxide (CO2) transport into
the cell (e.g., Laws et al. [1995]) which is inconsistent with laboratory and eld data that
demonstrate active uptake of CO2 and/or bicarbonate (HCO3,) (e.g., Sikes et al. [1980],
Tortell et al. [1997], for a review see Raven [1997]). Further, these models predict a linear
relationship between [CO 2] (the ratio of growth rate () and carbon dioxide concentration
([CO2])) and p [Francois et al., 1993, Laws et al., 1995] which is contradicted by some
observations (e.g., Laws et al. [1997]). Models that incorporate a cellular regulation of
active carbon uptake neglect the eects of either growth rate or active HCO3, uptake on p
[Laws et al., 1997, Popp et al., 1998, Yoshioka, 1997].
Based on a model interpretation, Laws et al. [1997] and Popp et al. [1998] concluded that
the upward curvature of p with increasing [CO 2] (i.e., an increasing positive deviation from
a linear relationship) which they observed is inconsistent with HCO3, uptake. However,
independent experiments demonstrate HCO3, uptake for several of the very species they
investigated (e.g., Sikes et al. [1980], Colman and Rotatore [1995]). It is important to resolve
this discrepancy since phytoplankton unable to take up HCO3, may be CO2-limited, even
if they actively transport CO2 [Riebesell et al., 1993]. Here we present a simple model of
phytoplankton carbon uptake and isotopic fractionation and show that existing isotope data
are consistent with active HCO3, uptake.
To model p we use an approximated carbon isotope balance of a phytoplankton cell
[Francois et al., 1993], resulting in:
p = up + (fix , diff ):
(1)
In this equation up, fix, and diff represent the fractionation eects of the carbon uptake
processes, carbon xation, and diusive carbon loss from the cell, respectively, and is the
ratio of cellular carbon loss to carbon inux. p is well approximated by 13 CCO2 - 13COM ,
the dierence between the isotopic compositions of the external CO2 and the organic matter
1
pools [Goericke et al., 1994]. Note that this stylized model neglects a host of potentially
important cellular characteristics such as respiration or cellular compartments.
The ratio of carbon loss to carbon inux () is a function of the diusive CO2 inux
(equal to [CO2] P A, where P denotes the membrane permeability and A the membrane
surface area), the cellular carbon demand (equal to Qc, where Qc represents the cellular
carbon content), as well as the active carbon uptake uxes. To model the regulation of
carbon uptake in the simplest way possible, we assume that the cells adjust their active
carbon uptake in a constant ratio ( ) to their carbon xation rate. We neglect the diusive
ux of the charged HCO3, molecule across the lipid cell membrane as well as the eects of
the diusive boundary layer. The ratio of carbon loss to carbon inux is then:
1 + ( , 1) [CO2Q] PC A
:
(2)
=
1 + [CO2Q] PC A
The fractionation eect of the carbon uptake processes (up) is calculated by an isotopic
mass balance of the carbon uxes into the internal CO2 pool. We assume the fractionation of the carbon uptake mechanism (t) to be equal to the fractionation by diusion
(t = diff = 0.7 o =oo [O'Leary, 1984]). Because we assume zero HCO3, eux, all the
HCO3, actively taken up has to be completely converted into CO2. In this situation,
the intracellular dehydration shows no isotopic fractionation. Finally, in the case of active
HCO3, uptake, the substrate for the carbon uptake mechanism has an isotopic composition
(13 Csource) which is around 9 o=oo higher than 13 CCO2 [Mook et al., 1974]. up is then:
up = t +
and p becomes:
[CO2 ]
PA
Qc
+
(13 CCO2 , 13Csource);
(3)
1 + ( , 1) [CO2Q] PC A
p = t + [CO2] P A ( CCO2 , Csource) +
(fix , diff ):(4)
QC
1
+
+
[CO2 ] P A
Qc
For pure diusive CO2 uptake (i.e., = 0) this reduces to the model proposed by Francois
et al. [1993] (and to a simplied version of the model of Rau et al. [1996]), which both predict
p to be a linear function of the variable [CO 2] . The variable [CO 2] , which is proportional to
the ratio of carbon demand to maximum diusive CO2 inux, eectively quanties the
extent of deciency of diusive CO2 supply for the photosynthetic carbon demand.
13
13
2
We use this model to analyze published data for the microalgae Phaeodactylum tricornutum, Porosira glacialis, Emiliania huxleyi, and the cyanobacterium Synechococcus sp.. Our
model is capable of tting other isotope data as well (e.g., Fielding et al. [1998], results not
shown) and the discussed data sets are chosen to represent a wide variety of phytoplankton
species. To estimate the model parameters, we vary them within reasonable ranges to minimize the mean square model error of 13 COM (Table 1). For this study, we assume HCO3,
as substrate for the carbon uptake mechanism (although the model can of course account
for active CO2 uptake). To simplify the discussion, we express the observations and the
model results as 13 COM , normalized to a 13CCO2 of -7.5 o=oo and a 13 CHCO3, of +1.5 o=oo
(representative of seawater at 15 oC [Mook et al., 1974, Goericke et al., 1994]).
The model ts (Figure 1) demonstrate that the model is able to represent the main features of the data rather well. The membrane permeabilities of the microalgae are relatively
high (varying between 1.1 to 3.310,5 ms,1) while the ratios of active HCO3, uptake to carbon xation are relatively low (between 0 and 2.3). The P. glacialis data are best described
in our model with no active HCO3, uptake (e.g., = 0). This may be reasonable, given
the low growth rates of P. glacialis which range between 0.09 and 0.32 day,1 . Alternative
explanations cannot be excluded, however, such as a dierent regulation of active carbon
uptake than assumed in our model.
For the microalgae (i.e., all the species except Synechococcus sp.), 13COM increases
signicantly with [CO 2] . At very low [CO 2] values, the diusive CO2 exchange uxes across
the membrane are large compared to the carbon xation and active carbon uptake uxes.
In this situation, the preference for 12 CO2 by carbon xation does not signicantly aect
the isotopic composition of the internal CO2 pool, because the gross CO2 uxes keep the
internal and external CO2 pools close to isotopic equilibrium. The resulting fractionation
eect of photosynthesis is close to the large fractionation by carbon xation, and 13COM
is low. As [CO 2] increases, the diusive CO2 exchange uxes across the membrane decrease
relative to the carbon xation and active carbon uptake uxes. As a result, the preference for
12
CO2 by carbon xation increasingly enriches the internal carbon pool with 13 CO2, carbon
xation uses more 13 CO2, and 13COM increases.
3
Table. 1
Fig. 1
For low to intermediate [CO 2] values, the 13COM data for the microalgae may be approximated by a straight line as would be predicted from a pure CO2 diusion model, although
the net CO2 diusion ux may in fact be outwards. For example, for the species E. huxleyi at [CO2 ] = 10,2 mol m,3 and = 0.5 day,1 (resulting in [CO 2] = 50 day,1 mol,1 m3 )
the modeled active HCO3, uptake ux is 8.910,18 mol C cell,1s,1 while the net diusion
loss is 4.810,18 mol C cell,1s,1 . The large diusive CO2 exchange uxes (in our example
1.610,17 mol C cell,1s,1 inwards and 2.010,17 mol C cell,1s,1 outwards) dominate the
other uxes and largely determine the isotopic disequilibrium across the membrane. This
situation is caused by the relatively high CO2 membrane permeability and low ratio of active carbon uptake to carbon xation. Note that the approximately linear range of 13COM
may sometimes be exceeded by oceanic [CO 2] values (e.g., [CO 2] = 260 day,1 mol,1m3 for
[CO2] = 810,3 mol m,3 and = 2.1 day,1 [Codispoti et al., 1982, Eppley, 1972]).
For the cyanobacterium Synechococcus sp., the estimated CO2 membrane permeability
is low (310,8 ms,1, equal to the experimental estimate of Salon et al. [1996]), while the
ratio of active HCO3, uptake to carbon xation is high (7.5, equal to the maximum value for
Synechococcus sp. observed by Tchernov et al. [1997] at high light levels). The fractionation
eect of carbon xation is estimated as 30 o=oo. A perhaps more realistic fractionation of
21.5 o=oo (observed for the freshwater cyanobacteria Anacystis nidulans [Guy et al., 1993])
would be obtained if the fractionation by the carbon uptake mechanism were around 8 o=oo ,
or if the cells were taking up predominantly CO2. However, as long as important model
parameters like the fractionation eects of the carbon uptake mechanism and carbon xation
for Synechococcus sp. are unknown, the isotope data seems consistent with active HCO3,
uptake. Note that the model parameters for Synechococcus sp. are at the extremes of the
imposed ranges (Table 1). Allowing, for example, a lower cell membrane permeability would
slightly reduce the model error, but violate the experimental estimate of Salon et al. [1996].
13 COM for Synechococcus sp. is approximately constant over the range of [CO 2] of
interest. This is explained in our model by the small CO2 exchange uxes relative to the
other uxes, caused by the relatively low CO2 membrane permeability and relatively high
ratio of active carbon uptake to carbon xation. This results in an approximately constant
4
ratio of cellular carbon loss to carbon inux, and 13COM .
Laws et al. [1997] and Popp et al. [1998] concluded that a downward curvature of 13 COM
with increasing [CO 2] excludes active HCO3, uptake. In contrast, our analysis shows that the
downward curvature of 13 COM is consistent with active HCO3, uptake. To analyze whether
HCO3, or CO2 is actively taken up, Laws et al. [1997] compared the 13 COM predicted
from a linear extrapolation at low [CO 2] values with the actual measurements. A downward
curvature at higher [CO 2] values indicates a decrease in 13 COM at higher ratios of active
carbon uptake to carbon inux. Laws et al. [1997] reasoned that active HCO3, uptake
would introduce a positive shift in 13COM and is hence inconsistent with the observed
downward shift. This reasoning neglects that an increased ratio of active carbon uptake to
carbon inux additionally increases the ratio of CO2 eux to carbon inux (equation 2),
relative to the linear extrapolation. This higher ratio of CO2 eux to carbon inux acts
to decrease 13COM and explains the observed downward curvature | even in the case of
active HCO3, uptake. In fact, assuming CO2 instead of HCO3, as substrate for the carbon
uptake mechanism (i.e., 13 Csource = -7.5 o=oo) results in dierent calibration parameters, but
indistinguishable model ts. Experimental data indicate that both HCO3, and CO2 are
possible substrates for the carbon uptake mechanism (e.g., Salon et al. [1996], Tchernov
et al. [1997]). Our results illustrate that the shape of the discussed 13 COM data as a
function of [CO 2] is a poor indicator of the carbon species entering the cell.
In conclusion, the discussed isotope data can be described adequately by a simple and
plausible model that represents the regulation of active carbon uptake with a single parameter. Neither an approximately linear relationship between [CO 2] and p nor an upward
curvature of p with [CO 2] can exclude active HCO3, or CO2 uptake. Whether HCO3, or
CO2 is actively taken up by a particular microalgae cannot presently be decided on the basis
of isotope data (except for the case when 13 COM is higher than 13 CCO2 , indicating that
HCO3, is a signicant carbon source). Available models of carbon isotopic fractionation
are insuciently constrained to distinguish between these possibilities.
Acknowledgments We are grateful to G. H. Rau and P. D. Tortell for helpful discussions.
5
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7
Figure caption
Fig. 1: Comparison of experimental data for Phaeodactylum tricornutum (squares, Laws
et al. [1997]), Synechococcus sp. (circles, Popp et al. [1998]), Emiliania huxleyi (stars,
Bidigare et al. [1997]), and Porosira glacialis (crosses, Popp et al. [1998]), with the model
ts (lines). Shown are 13COM data for [CO 2] values less than 350 day,1 mol,1m3 . Model
parameters and the root mean square errors of the model ts are given in Table 1.
8
Table 1:
Model parameters, their allowed ranges,
and the root mean square error (rmse) for the model ts.
We use the cell surface areas and cellular carbon contents given by
Popp et al. [1998].
parameter
unit
allowed range
E. huxleyi
P. tricornutum
P. glacialis
Synechococcus sp.
fix
o =oo
20-30 a
25.3
26.6
23.0
30.0
P
ms,1
310,8-410,3
1.810,5
3.310,5
1.110,5
3.010,8
a
Adopting the range for ribulose 1,5-bisphosphate
carboxylase-oxygenase [Goericke et al., 1994]
and assuming negligible -carboxylation.
b Gutknecht et al. [1977], Salon et al. [1996]
c Range between pure diusive uptake (i.e., = 0)
and the maximum value in Synechococcus sp.
observed by Tchernov et al. [1997].
9
b
|
0-7.5
2.2
2.3
0.0
7.5
rmse
c
o =oo
{
0.63
1.2
3.1
1.2
−10
P. glacialis
δ13COM [o/oo]
−15
−20
P. tricornutum
E. huxleyi
Synechococcus sp.
−25
−30
−35
0
50
100
150
200
µ
______
[d−1 mol−1 m3 ]
[CO2]
Fig. 1
10
250
300
350