Journal of Plankton Research Vol.19 no.10 pp.1455-1476, 1997
Phytoplanktonic carbon isotope fractionation: equations
accounting for CO2-concentrating mechanisms
Takahito Yoshioka
Institute for Hydrospheric-Atmospheric Sciences, Nagoya University, Furo-cho,
Chikusa-ku, Nagoya 464-01, Japan
Abstract A model of carbon isotope discrimination by phytoplankton was developed which took into
account the occurrence of a carbon-concentrating mechanism (CCM). A simple equation was
obtained for the model involving CO2 active transport. In the case of HCO3~ active transport, another
equation was developed based on a series of approximations. The former equation was used to
analyse reported and newly obtained data from culture experiments and field observations in both
freshwater and marine environments. In most cases, a linear relationship between a combined parameter, (1 -/)Ci, which was made up of the relative contribution of active CO2 uptake to total carbon
uptake (/) and the intracellular CO2 concentration (Ci), and CO2 concentration in bulk solution (Ce)
was obtained as (1 -/)Ci = aCe - b, with a high correlation coefficient (r2 > 0.9). The slope a is suggested as a measure of the ratio of diffusive to total (diffusive + active) CO2 transport, while b/a represents CO2 demand.
Introduction
In studies on the global carbon cycle, the stable carbon isotope natural abundance
(813C value) has been proved to be a powerful tool for estimating processes (e.g.
Quay et al, 1992). The inverse relationship between [CO2]aq and the 813C of
organic matter produced by phytoplankton has been widely recognized, with
various equations proposed for expressing such a relationship (e.g. Freeman and
Hayes, 1992; Rau et al, 1992). For geochemical purposes, [CO2]aq was estimated
using the regression equations between [CO 2 ] aq or log [CO2]aq and the isotope
fractionation factor (ep) (Hollander and McKenzie, 1991; Freeman and Hayes,
1992; Goericke and Fry, 1994). Equations based on the fractionation model
during plant photosynthesis have also been developed (Berry, 1988; Rau et al.,
1992; Raven et al., 1993). From the ecophysiological point of view, carbon isotope
fractionation by phytoplankton has been used for assessments of growth rate
(Takahashi et al, 1991) and CO 2 availability (Fogel et al, 1992).
Mechanisms directly associated with the carbon uptake process in phytoplankton should be considered in developing the fractionation equation. It is
recognized that phytoplankton actively transport CO 2 by a carbon-concentrating
mechanism (CCM) (Sharkey and Berry, 1985; Burns and Beardall, 1987; Thielmann et al., 1990), which affects the 813C value of phytoplankton. Some equations
take the CCM into account (Sharkey and Berry, 1985; Fogel et al, 1992).
However, it has been assumed that when the CCM is considered in the equation,
it must be in response to the total CO 2 uptake. When active transport occurs,
the equation using flux (F) is adopted (Berry, 1988; Fogel et al, 1992). In these
cases, only active transport is used in CO 2 influx, and its efficiency in respect to
carbon assimilation is represented by 'leakiness'. (3-Carboxylation catalysed by
© Oxford University Press
1455
T.Yojbiokfl
phosphoenolpyruvate carboxylase and phosphoenolpyruvate carboxykinase also
affects the 813C of phytoplankton (Descolas-Gros and Fontugne, 1985; Falkowski,
1991). However, culture experiments of marine phytoplankton showed no
relationship between p-carboxylation and the 813C value of particulate organic
carbon (POC) (Leboulanger et al, 1995).
Seasonal changes in the 813C value of phytoplankton have been found in freshwater lakes (Yoshioka et al, 1989; Zohary et al, 1994). A remarkable increase in
the 813C value in the bloom season suggests that phytoplankton photosynthesis
may be limited by CO2 depletion (Takahashi et al., 1990). However, since no fractionation model seems to be generally agreed, as mentioned above, application
of the fractionation equation to the field data seems to present difficulties. In this
paper, we briefly review the fractionation equations reported for phytoplankton
photosynthesis on a physiological basis, and propose a new equation in which
active transport of inorganic carbon by the CCM is considered. Furthermore, the
proposed equation is applied to the analyses of culture experiments and field data
from marine and freshwater environments.
Method
Lake Kizaki (36°33'N, 137°50'E) is a mesotrophic lake in Honshu Island, Japan.
Its surface area is 1.4 km2 with a maximum depth of -29 m. Field observations
were carried out at the centre of Lake Kizaki during April-July 1992. Water temperature and photon flux density (PFD) were measured by a thermistor thermometer (ET-5, Toho-Dentan, Co., Ltd) and photometer (Model LI-189,
LI-COR, Co., Ltd) lowered to the sampling depth (2 m). Samples were taken with
a Van Dorn water sampler. The pH value of each sample was measured on board
with a pH meter (HPH-110, Denki-Kagaku Keisoku, Co., Ltd). Samples for the
measurement of dissolved inorganic carbon (DIC) concentrations were introduced into a glass-stoppered bottle and preserved with formalin solution. DIC
concentration was measured by an infrared analyser (VIA-300, Horiba, Co., Ltd).
A glass cylinder (-200 ml in volume) was used for the 813C measurement of DIC.
Sample water was introduced through the Teflon screw stop valve at one end of
the cylinder. After overfilling water to twice or more than the cylinder volume,
saturated CuSO4 solution (2 ml) was added as a preservative, and a syringe
septum of silicone rubber was placed at the other end. The entire sample in the
cylinder was introduced into a stripping apparatus (Kroopnick, 1974) by pure N2
gas through a rubber septum. DIC was extracted by acidification and purified
cryogenically within 12 h after sampling.
Samples for isotope and photosynthetic activity measurements were put into
polyethylene bottles, stored in an insulated box, and brought back to the laboratory. After samples were filtered through a 334 urn mesh net to eliminate zooplankton, suspended particles were collected on a pre-combusted glassfibrefilter
(Whatman GF type C). Chlorophyll content was measured by the methanol
extraction procedure (Marker et al, 1980). For isotope measurement, filters were
rinsed with a small amount of dilute HC1 solution (-0.005 N) and distilled water,
and dried at 60°C overnight. POC was converted to CO2 gas according to the
1456
Pbytoplanktonk carbon isotope fractionation
method of Minagawa et al. (1984). In the preparation of CO2 gas, the carbon
content of the POC was manometrically determined.
The carbon isotope ratio was measured with an isotope ratio mass spectrometer (delta S or MAT 251, Finnigan MAT Instruments Inc.). The isotope ratio is
expressed as a per mil deviation (813C value) from the PDB standard as follows:
8
13C
( ^Miiiple
=
_
\ "• standard
where R denotes 13C/12C.
Concentrations and 813C values of [CO2]aq were calculated using the dissociation constants of carbonate (Stumm and Morgan, 1981) and equilibrium isotope
fractionation factors (Deines et al., 1974).
Photosynthetic activity was measured by O 2 production in the oxygen bottles
which were placed under various PFDs. During 4-5 h of incubation, the bottles
were kept in a water bath at in situ temperature. After incubation, the dissolved
O2 concentration was measured by the Winkler method. In situ photosynthetic
activity was calculated from the resultant O2 production rate-PFD curve and
the assumption of stoichiometric conversion of CO2 carbon to carbohydrate
carbon.
Model description
Basic equation for expressing photosynthetic carbon isotope fractionation
The theoretical basis of photosynthetic carbon isotope fractionation was derived
from land C3 plants (e.g. O'Leary, 1981; Farquhar et al., 1989). The notations are
designated as follows.
The photosynthetic carbon uptake process is:
i
2
CO 2out <— CO2in—> organic carbon
where kt is the rate constant for process /. Processes 1 and 3 are the diffusive influx
and efflux of CO2, respectively. Process 2 is the carboxylation step by ribulose bisphosphate carboxylase-oxygenase (RUBISCO).
At steady state, or
as follows:
— = 0, the overall fractionation factor (a) is equated
&
A*,)i|
(1)
where Ce and Ci are the CO2 concentrations in air and at the carboxylation site,
respectively, and A/c, = a, - 1. In the equation of O'Leary (1981), subscripts for
efflux and carboxylation steps were 2 and 3, respectively, and £, = 1 + AJfc,:
1457
T.Yoshioka
When a = AAcb b = Afc2 and C0 2 concentrations in air and intercellular leaf spaces
are expressed in partial pressure pt and piy respectively, equation (1) is equated
to Farquhar's equation:
A-
-\ - a + (b - a\
(3)
Re-examination of fractionation equation
When only passive diffusion contributes to the inward and outwardfluxesof CO2,
the fractionation equation for phytoplankton photosynthesis is substantially the
same as that for land C3 plants (Table I), although Ce denotes the CO2
Table L Fractionation equations for land plant and phytoplankton photosynthesis
Literature
Fractionation equation
Land plant
£12
O'Leary (1981)
-^5- (overall) = £,-
Farquhar er al. (1989)
A = a + (b - a) —
Phytoplankton
Passive diffusion model
Rau er al. (1992)
—- = (613CpUnl - 813Cco2 + d)Kd + f)
Fogel er al. (1992)
A = a + (ft-a)-^-
Francois er aL (1993)
ep = e,
Jasper er al. (1994)
ep = A
Laws era/. (1995)
Active transport
Berry (1988)
Fogel era/. (1992)
Francois er al. (1993)
A and B in Jasper er al. (1994) are -27%o and -130%<i uM, respectively.
|j in Laws et al. (1995) means growth rate, u = K,Ce - A^Ci.
Subscripts represent each process in CO2 uptake kinetics and are adjusted as follows: 1, influx of CO2;
2, CO2 assimilation by RUBISCO; 3, efflux of CO2. Note that subscripts were changed from the original ones in O'Leary (1981), Francois er al. (1993) and Laws er al. (1995).
1 -v-jT
1458
TP*-)(£2-
£3)-
Phytoplanktonic carbon isotope fractionation
Table IL List of fractionation factors relating to the photosynthetic carbon assimilation (after Berry,
1988)
Symbol
a (land plant)
a (phytoplankton) d and EI
a,
b and/
e,
Fractionation
Process
CO2 diffusion, air
CO2 diffusion, aqueous phase
Active transport of HCO3"
RUBISCO and 10% PEPCase
RUBISCO
Dissolution of CO2
Hydration of CO2 (kinetic)
Hydration of CO2 (equilibrium)
4.4
0.7
Negligible
27.0
29.4
1.1
2.0
-9.0
concentration in bulk solution, or [CO2]aq, and CO2 diffusion must be considered
in the aqueous phase. Fractionation factors involved in these equations are presented in Table II.
The fractionation equation for passive diffusion-phytoplankton photosynthesis is basically the same as equation (1). Rau et al. (1992) introduced the term
'CO2 demand = Ce - Ci' into their model (Table I). Francois et al. (1993) analysed
the relationship between the 813C value of paniculate organic matter (POM) and
[CO2]aq in the southwestern Indian Ocean using the fractionation equation
including the (Ce - Ci) term:
e p = e, + 1 \
(e2 - Ej)
t-e
(4)
/
Data from the SW Indian Ocean fit the model in which (Ce - Ci) was 7-9 uM.
Assuming a constant (Ce - Ci) value, Jasper et al. (1994) found a significant correlation between ep and Ce in the Pigmy Basin with a = 29.2%o and b = -109%o
uM (Table I). When (Ce - Ci) is constant, equation (1) at the infinite Ce is:
a = 1 + Ak2
(5)
This means that overall fractionation reaches the maximum value which
corresponds to that of RUBISCO (a = 1.029, or Ak2 = 0.029; Roeske and O'Leary,
1984) at a high Ce condition. Many authors have used Ak2 = 0.027, taking a 10%
contribution of PEPCase to total carbon assimilation into consideration (Farquhar and Richards, 1984). The fractionation factor must approach 1.027-1.029
at high Ce. However, culture experiments conducted by Hinga et al. (1994)
showed that fractionation by Skeletonema costatum and Emiliania huxley became
maximal before reaching these levels. (Ce - Ci) seemed to increase with the
increase in Ce. The authors suggested the possibility of (3-carboxylation at high
Ce. Indeed, it was found that the activity of the PEPCKase of S.costatum
increased to >50% of RUBISCO activity at the end of growth (Descolas-Gros
and Fontugne, 1985, 1990). However, the contention that low fractionation at
high Ce is due to the p-carboxylation has been controversial (Goericke et al.,
1994), especially in the case of PEPCKase-mediating (J-carboxylation, which
shows similar discrimination against 13CO2 to that of RUBISCO (Arnelle and
1459
T.Yoshiota
O'Leary, 1992). Active transport by a CCM may contribute to a fractionation at
high Ce lower than that given by the fractionation equation.
Laws et al. (1995) concluded that passive CO2 diffusion was sufficient to sustain
maximum growth of Phaeodactylum tricornutum and this alga would not need
active transport of inorganic carbon at a [CO2]aq of 10 uM. In their analysis, the
maximum growth rate was expected when the CO2 influx was equal to growth
rate. However, this situation means Ci = 0, then, growth rate (photosynthetic
activity) = 0, or is even negative, because of oxygenase activity of RUBISCO. The
contradiction may occur because growth rate is not independent of Ce and Ci.
Since CCM requires an energy expenditure (Berry, 1988), one may suppose that
diffusive transport of CO2, if possible, is operative together with active transport.
From the reported equations shown in Table I, it is difficult to identify the relative contribution of active transport to total CO2 influx.
In the derivation of equation (1), it is assumed that the resistance to CO2 diffusion is similar in either direction across the cell membrane, or k\ = k3 (Francois
etai, 1993). This assumption originally came from the expectation that resistance
to CO2 diffusion through the stoma of a plant leaf would be the same in both
directions (O'Leary, 1981). In the case of phytoplankton which may have a CCM,
one may expect different values for this resistance (k^ * k3), probably (kt > k3).
If that is so, the fractionation equation
M
1
) ^ -
(6)
may provide some measure of the contribution of active transport. Equation (6)
is the equation just before assumingfcj= k3 in deriving equation (1). Ifwe assume,
as many authors have, that the resistances to CO2 diffusion in both directions
across the cell membrane are the same (symmetric permeability), a fractionation
equation is required to express the decrease in fractionation with the increase in
the relative contribution of active transport (/) as some function off. Practically,
/and kx * k3 may have the same meaning for CO2 acquisition by phytoplankton,
although their physiological connotations must be determined by further study.
Thus, we may expect that the active transport of inorganic carbon by CCM may
be dealt with as a homologue of the asymmetric permeability of the cell membrane for CO2.
Deviation of fractionation equations involving active transport
In this section, we develop fractionation equations expressing the active transport of inorganic carbon. A wide range of phytoplankton can actively transport
CO2 and HCO3" (Burns and Beardall, 1987). However, the presence of internal
and external carbonic anhydrase (CA), which catalyses the equilibrium between
CO2 and HC0 3 ", complicates the determination of the inorganic carbon species
crossing the cell membrane. Concerning the isotope ratio of the substrate for
photosynthesis, the difference in inorganic carbon species makes for a considerable variation in the fractionation factor, because fractionation between dissolved
1460
Phytoplanktonic carbon isotope fractionatfon
CO2 ([CO2]aq) and HCO3~ is as hifih a s 10%° m b ° t n equilibrium and CAcatalysed reactions (Deines et ai, 1974; Paneth and O'Leary, 1985). Fractionation
equations will be developed below for two cases, in which transported carbon has
the 813C value of either bulk [CO2]aq or HCO3~. Isotope fractionation in the active
transport step is not considered.
(i) Active transport of CO2. The 813C value of actively transported inorganic
carbon is assumed to be the same as that of Ce (Figure 1). Extracellular CA may
contribute to the conversion of HCO 3 " t o CO2 a t t n e ce^ surface.
At steady state:
^
=fcjCe+ F4 - (k2 + A:3)Ci = 0
(7)
The relative contribution of active transport (/) is denned by:
<8)
'=WTTK
If 0 <>f< 1, equation (7) can be rewritten as:
^
- ^-f fcjCe - (k2 + A:3)Ci = 0
(9)
Overall fractionation is:
a = 1 +A*! + (A/c2 - A/:,)(l - / § -
(10)
assuming the same/value for 12CO2 and 13CO2, and Afcj = A/:3 (see Appendix 1).
Equation (10) is the same as equation (6) when —-?is substituted for (1 - / ) . This
supports the expectation that active transport might be dealt with as a homologue
of the asymmetric permeability of the cell membrane for CO2. Leakiness, X (the
ratio of efflux to influx of DIC; Berry, 1988), is expressed as follows:
(Ce)
CO,
k, f
«
I'
(Ci)
CO,
k,
1
•
Org. C
I
t
C 1
°*
Phytoplanktoncell /
Fig. L Scheme of active transport of CO?. The 813C of actively transported carbon (CO2*) is assumed
to be the same as that of CO2 in medium (Ce).
1461
T.Yoshioka
When all carbon is transported by active transport (/= 1), kxCt would be zero.
In this case, one cannot substitute / = 1 in equation (10), because the denominator in equation (9) becomes zero. Then, a becomes:
fair- _ Mr.
a= 1 + -
+1
lr-O\
F4
- A*i)^-
(12)
X is not zero, but
X
^
(13)
(ii) Active transport of HCOf. In the scheme shown in Figure 2, transported
carbon has the same 813C value as HCO3~. Although the steady state for Ci is
expressed by the same equation as equation (7), the overall fractionation equation is quite different from equation (10):
- X) + (Afr + 1)(M2 + 1)X
where Afc4 denotes the fractionation in the CO2-HCO3" dissociation process (see
Appendix 2). Definitions of /and X are the same as those in the active transport
of CO2.
Assuming that the second- and third-order terms of A/c, are negligible, and that
once again AAj = AJt3, then a is approximated as follows:
a = 1 + A*,(l-/) + (A*2- A*!)(l - / ^
M4/
(15)
Org. C
Phytoplankton cell /
Fig. 2. Scheme of active transport of HCO3-. The B13C of actively transported carbon (HCO3-*) is
assumed to be the same as that of HCO3" in medium.
1462
Phytoplanktonk carbon isotope tractionatktn
W h e n / = 1, a becomes:
a = 1 + (AA:2 - A f c O ^ - - AA:4
(16)
PA
From equation (15), it was deduced that all fractionation steps including overall
fractionation would be affected by /. The difference between equations (10) and
(15), or (A&i + A&4)/, corresponds to the difference in 813C values between CO2
and HCO3~. Equation (16) implies that overall fractionation decreases by (A£j +
A/c4), in comparison with the passive diffusion model, equation (6), when all
carbon derives from the active transport of HCO3~ (/= 1). Therefore, it was suggested that the approximations in this model did not invalidate the scheme of
carbon assimilation in Figure 2. These equations indicate that overall fractionation from [CO2]aq to organic carbon may be less than unity under some conditions.
Results
Field observations
POC at a 2 m depth in Lake Kizaki increased during April-May 1992, then
decreased (Table III). Peridinium bipes predominated in the biomass throughout
the observation period. The in situ gross production rate (Pg) and chlorophyll
(Chi) a content changed with POC, although Pg was mainly affected by light
intensity. Pg per unit of Chi a ranged from 0.03 to 0.19 mol C g"1 Chi a tr 1 .
The DIC concentration gradually decreased from 300 to 160 uM. Because of
an increase in pH of the lake water, the fraction of [CO2]aq in DIC decreased
markedly by early May (Table III). On June 3, 10 and 23, and July 6, pH values
measured by a pH meter were unavailable. However, the measurements by
colour indicator showed little change in the pH value (9.0-9.4) on those days.
Furthermore, pH meter measurements made on May 25, June 15 and July 21 also
showed little change during June-July (Table III). Judging from these observations, it was estimated that the pH value remained constant at 9.4 from June 3
to July 6. The [CO2]aq concentration was extremely low (<0.2 uM) after May 25.
The 813C value of POC increased to -18.5%o during April-June, although the
maximum levels of 813C were l-2%o lower than those found in previous years
(Yoshioka et at., 1989; T.Yoshioka, unpublished data). After June, the 813C of
POC maintained a constant level as high as -18.5%o. Since Pg varied with PFD on
sampling dates, the temporal change in the 813C of POC did not follow that in Pg.
The 813C of POC seemed to change with DIC and [CO2]*, (Table III).
A clear hyperbolic relationship was found between [CO2]aq concentration (Ce)
and the 813C of POC (Figure 3). It seemed that carbon isotope fractionation might
be controlled by [CO2]aq during the observation period. The fractionation factor
(a), calculated from 813C values of [CO2]aq and POC, ranged from 1.013 to 1.002
(Table III). In general, a was calculated from the carbon isotope ratio of POM
and [CO2]aq on the sampling data. It should be noted, however, that the fractionation equation assumes a steady state, while the environmental conditions for
1463
Table i n . Summary of field observation in Lake Kizaki in 1992
Date
WT(°C)
pH
Chlo
(MgH)
PFD
(uE nr 2 s-')
Pg
DIC
COz*,
POC
DIC
April 9
8.40
9.18
10.12
10.46
12.04
1430
14.59
16.61
18.04
18.38
18.22
20.32
21.49
7.68
8.45
8.98
9.28
9.19
9.55
9.4>
9.4"
9.44
9.4'
9.4*
9.39
17.4
26.0
183
19.5
23.1
52.6
82.1
74.9
20.1
24.2
36.1
145
234
6.1
165
183
390
1.5
1.1
2.1
2.0
1.5
5.4
6.3
3.8
334
47.7
60.0
153
65.7
150
162
1.5
2.0
1.9
Blank, not determined.
•Estimated pH values from the measurements by colour indicator.
POC
a
-28.7
-24.3
-23.5
-22.1
-20.6
-20.0
-19.2
-18.6
-18.6
1.01259
1.00884
[8 1 3 C
(MM)
April 24
Mayl
May 6
May 12
May 16
May 25
June 3
June 10
June 15
June 23
July 6
July 21
co^
(MM h- 1 )
300
19.9
3.11
298
268
270
252
213
191
202
194
178
157
171
0.78
0.37
0.41
0.14
0.18
0.18
0.16
0.16
0.14
0.15
no
178
108
128
144
297
467
408
125
268
197
89
-7.1
-5.8
-6.0
-6.1
-45
-16.5
-15.6
-5.8
-5.1
-6.3
-15.1
-14.3
-15.3
-6.4
-7.4
-15.4
-16.2
-15.9
-14.1
-18.3
-18.5
-193
1.00635
1.00660
1.00420
1.00442
1.00334
1.00295
1.00233
Phytoplanfctonic caibon isotope fractionation
-15.0
-20.0
-2S.0
-30.0
0
5
10
15
[COJ.,(nM)
Fig. 3. Relationship between 813C of POC and [COJ,, concentration in Lake Kizaki.
phytoplankton are not always at a steady state in nature. The variation in such
conditions during the growing season may lead to an overestimation of a. Nevertheless, calculated a values in Lake Kizaki were quite low, particularly in June
and July, which suggested that photosynthetic carbon uptake would be limited by
the CO2 supply.
Application of the fractionation equation
When a and Ce are known, kt Ci and (1 -/)Ci are analytically estimated as combined parameters, from equation (6) and equation (10), respectively. However,
algebraic analysis using equation (15) is difficult, because Ci and/appear in some
terms in the equation. Other independent data on Ci or/are required to use equation (15), although such data are usually difficult to obtain from the natural ecosystem. When HCO3" is actively transported, overall fractionation apparently
decreases, compared with CO2 active transport. If HCO3" transport occurs, the
contribution of CCM may be smaller than that estimated by equation (10).
However, it is difficult to estimate the carbon acquisition mechanism of natural
phytoplankton over relatively long periods, such as a week and a month.
The physiological implications of carbon isotope fractionation by phytoplankton calculated with equation (10) are discussed, using data from culture
experiments by Hinga et al. (1994) and from the field observations. We used the
following values for fractionation factors of diffusion, Akx = 0.0007, and carboxylation, Mc2 = 0.029.
(i) Culture experiments (Hinga et al, 1994). Hinga et al. (1994) have presented a
systematic data set on carbon isotope fractionation by phytoplankton culture.
Each plot in Hinga's Figure 4, which showed the relationship between ep and Ce
1465
T.Yoshioka
in the culture experiments, was read using digital slide calipers. Before analysis,
the value of ep was transformed to a value for a.
From equation (10), we obtained the following relationship between (1 -/)Ci
andCe:
(17)
The data analysis showed that there were intercepts (/ 0) for linear regression for
(1 -/)Ci and Ce, as follows:
At 9°C, (1 -/)Ci - 0.69Ce - 2.6, r2 = 1.000
At 15°C, (1 - /)Ci = 0.60Ce - 2.1, r2 = 0.992
At 25°C, (1 - /)Ci = 0.69Ce - 3.8, r2 = 0.999
(18)
(19)
(20)
Fractionation factors for each temperature were obtained as follows:
At 9°C, a = 1.00O7 + 0.0283 X 0.69 X
At 15°C, a = 1.0007 + 0.0283 X 0.60 X
At 25°C, a = 1.0007 + 0.0283 X 0.69 X
Ce-3.8
Ce
Ce-3.6
(21)
(22)
Ci
Ce-5.6
(23)
Hinga's data fairly matched with these fractionation equations (Figure 4).
These equations suggested that the isotope fractionation due to carboxylation by
120
^
Relationship between fractionation factor (a) and [CC^],,, concentration vi the culture experiments of S.costatum (Hinga el aL, 1994). Symbols indicate culture temperatuie: open circle, 9°C;
closed triangle, 15°C; closed circle, 25°C. lines denote the fractionation equations for each temperature; 9°C, dotted line equation (21); 15°C, dashed line equation (22); 25°C, solid line equation (23),
see the text
1466
Pbytoplanktonic carbon botope fractionation
1.015
1.010
1.005
1.000
5
10
15
20
[CO.Ml'M)
Fig. 5. Relationship between the fractionation factor (a) and [CC^]^ in Lake Kizaki. The solid line
denotes equation (24). The broken line denotes equation (25).
RUBISCO might not occur below a certain low Ce level, such as 3.8 uM at 9°C,
3.6 uM at 15°C and 5.6 uM at 25°C.
(ii) Field observation (Lake Kizaki). Equation (10) was also applied to the data
set from Lake Kizaki, and the following equation was obtained:
Ce - 0.26
a = 1.0007 + 0.0283 X 0.42 X
Ce
(24)
The estimate of a from equation (24) does not agree with the a at low Ce concentrations (Figure 5). Based on the data from April 24 to July 6, we obtained the
next equation:
a = 1.0007 + 0.0283 X 0.29 X
Ce-0.13
Ce
(25)
In both cases, it suggested that the fractionation in carboxylation step did not
occur under a low Ce concentration of <0.3 uM.
Discussion
Implication of combined parameter, (1 -f)Ci
Hinga et al. (1994) analysed their data using Rau's model (Rau et ai, 1992), and
found that fractionation data distributed across the contour of CO2 demand
(Ce - Ci). They suggested that p-carboxylation was expected at a high Ce condition, because there was no reason why CO2 demand should increase with an
increase in Ce. According to Rau's model, a linear relationship with the slope of
unity will be expected between Ce and Ci, assuming constant CO2 demand
1467
T.Yoshioka
constant CO, demand
variable CO, demand
m
CO, demand
t
Ce
Fig. 6. Schematic diagram showing the relationship between Ce and Ci. Solid lines show the constant
CO2 demands. The broken line shows the variable CO2 demand with Ce.
(Figure 6). In our analysis using Hinga's data, even if / = 0, the slopes of Ce-Ci
relationships do not change from equations (18), (19) and (20), and are less than
unity. One may conclude that CO2 demand changes with Ce in a linear fashion.
However, the mechanism is not suggested by the diffusion model.
The CO2 demand, according to the definition by Rau et al. (1992), corresponds
to the Ce level below which the isotope fractionation derived from carboxylation
by RUBISCO does not occur. Therefore, it is suggested that the subtrahends (3.8,
3.6, 5.6, 0.26 and 0.13) in the numerators in equations (21)-(25) represent CO2
demand. The coefficients of numerics (0.69, 0.60, 0.69, 0.42 and 0.29), except for
0.0283, may indicate the relative contribution of diffusive transport of CO2, or
(1 - / ) . Thus, the apparently variable CO2 demand with changing Ce (Figure 6)
can be expressed by (1 -f) < 1 for some CO2 demand. Although the physiological judgements of these considerations may be very difficult, characterization of
photosynthesis by culture and natural phytoplankton population may be
achieved by the combined parameter, or CO2 demand and /.
Characterization of phytoplanktonic photosynthesis using CO2 demand and f
value
From equations (21)-(23), it was suggested that carbon assimilation by S.costatum might operate under almost constant CO2 demand (-4-6 uM), and that the
active transport of CO2 contributed -30-40% of the total carbon influx. If 10%
of the total carbon uptake were mediated by p-carboxylation (A&2 = 0.027), the
relative contribution of active transport would reach 25-35% without any change
in CO2 demand.
In Lake Kizaki, since P.bipes predominated during the observation period
(data not shown), equation (25) may reflect the physiology of this alga. The CO2
demand is considerably lower than that of S.costatum. The relative contribution
of CCM (J) was estimated to be 60-70% of total carbon uptake. Berman-Frank
1468
Phytopfauiktonic carbon isotope fractionation
et al. (1994,1995) reported that the CA activity of Peridinium gatunense in Lake
Kinneret was stimulated by low [CO2]aq concentrations (1-10 uM). Although the
species of Peridinium and the level of alkalinity (or DIC concentration) are different from those in Lake Kinneret, the CA activity of P.bipes in Lake Kizaki may
also increase under low [CO2]aq concentrations. The high value of / in Lake
Kizaki might reflect an intense CA activity of P.bipes.
The CO2 demand and/were calculated using the published data (Table IV).
While /values in freshwater lakes were significantly higher than those in marine
environments (r-test, P < 0.05), CO2 demands were significantly lower (P < 0.01).
Negative CO2 demand estimated for Mohonk Lake may indicate the predominance of CCM, or may be caused by species succession and physiological changes
in phytoplankton attributable to a significant increase in water temperature
(11.1-25.6°C) and pH values (6.92-9.50). In a similar context to the latter case,
the organic matter of diatom and other algae on April 9 in Lake Kizaki might
have caused a discordance in the ot-Ce relationship, as shown in Figure 5.
Alternatively, CA activity (or CCM) of the algal community might have changed
during April 9 and April 24.
Carbon isotope fractionation of phytoplankton is thought to be affected by
various factors other than [CO2]aq. The relationship between carbon isotope discrimination and the growth rate of phytoplankton was found in both culture and
enclosure experiments (Fry and Wainwright, 1991; Takahashi et al, 1991; Laws et
al, 1995). Since the growth rate of phytoplankton depends, in general, on temperature, nutrient concentration and light intensity, discrimination also depends
on these physicochemical parameters. The difference in the 813C values both
within and between species of phytoplankton may indicate the metabolic performance among phytoplankton (Fry, 19%). Therefore, it has been recognized
that the 813C value of organic matter derived from phytoplankton may not be
controlled solely by [CO2]aq concentration (Thompson and Calvert, 1994; Laws
et al, 1995; Johnston, 1996).
The fractionation equation itself, based on a physiological model, does not
imply that [COJaq controls the fractionation factor, but rather that it is determined either by the relative ratio of CO2 concentration at the carboxylation site
to ambient CO2 concentration, or by the efflux-influx ratio of CO2. Factors such
as growth rate, temperature and light intensity can be considered to modify these
ratios. Since there are interspecies differences in such factors as growth rate,
photosynthetic activity and CA activity, the discrimination between [COJ aq and
POC may vary from season to season and from place to place, independently of
[COJaq concentration. The [COJaq may not be estimated by the POC and sediment carbon isotope analysis (Francois et al, 1993). However, when a high correlation between the combined parameter (1 -/)Ci and [CO2]aq concentration is
observed, these factors seem to remain constant or have little effect on carbon
isotope fractionation in comparison with [COJaq concentration. If such situations
are to be expected at specific times and places in aquatic environments, the combined parameter (1 -/)Ci, proposed in this paper, would prove its usefulness in
characterizing phytoplankton photosynthesis and in estimating [COJaq.When the
correlation is low, species succession among phytoplankton with distinct
1469
TaMe IV. Comparison of calculated /and CO2 demand using equation (10)
[COJ^ (uM)
Marine
Skeletoncma costatumb
Delaware Bay
Southwest Indian Ocean
9°C
15°C
25°C
Spring
Summer
f
CO2 demand (uM)
1.000
0.992
0.999
0.332
0.941
0.962
Average ± 1 cr
0.31
0.40
0.31
0.65
0.28
0.24
037 ± 0.14
0.5-35
0.981
0.42
-0.54"
0.13-2.2
0.15-3.6
0.990
0.941
0.86
0.85
032
0.14-20
0.14-3.1
0.998
0.997
Average ± 1 a
0.58
0.71
0.67 ± 0.19
0.26
0.13
0.29 ± 0.21
-5-50
-5-110
-10-120
14.2-19.4
11.8-22.7
9.8-21.6
3.8
3.6
5.6
3.4
4.0
5.2
Remarks
Hinga etal, 1994
Fogel etai, 1992
Francois etal., 1993
4.4 ± 0.90
Freshwater
Mohonk Lake
Lake Suwac
July 6-September 12,1986
June 19-August 18,1987
Lake Kizaki
April 9-July 21,1992
April 24-July 21,1992
0.64
Herczeg and Fairbanks, 1987
Takahashiefa/.,1990
Microcyslis spp.
Microcystis spp.
This study
Diatom and P.bipes
P.bipes dominate
"Correlation coefficient between Ce and (1 -/)Ci.
b
Data were estimated from Figure 4 in Hinga et al. (1994).
c
[CO2]»q was recalculated from original data because the [CO?]*, concentration was not shown in Takahashi etal. (1990). Mass balance consideration was not
applied for the calculation of the parameters.
d
Data were not used for calculating the average.
Phytoplanktonic carbon isotope fractionation
photosynthetic characters, and input of organic carbon with different 813C value,
may have occurred. Therefore, the isotopic analyses of individual species and
specific biomarkers for phytoplankton would be important.
Analysis using the new fractionation equation should improve our understanding of phytoplankton ecophysiology and the biogeochemical carbon cycle in
aquatic environments, although the physiological meanings of the combined
parameter must be rigorously checked in future studies.
Acknowledgements
I am grateful to Prof. H.Hayashi and Prof. E.Wada for their encouragement. I wish
to thank the many students of the Faculty of Science of Shinshu University, especially Mr K.Matsushima, for their assistance in the field survey. I am also grateful to
Prof. Y.Saijo for allowing the use of his facilities in Lake Kizaki. This study was
supported by a Grant-in-Aid for Encouragement of Young Scientists, nos 01740378
and 02854079, from the Ministry of Education, Science, Sports and Culture, Japan.
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Received on April 1,1997; accepted on June 3, 1997
1472
PhytopUnktonic carbon isotope fractionation
Appendix 1: Derivation of equation (10)
From equation (9):
ratio of Ci is:
Ce'
k2 + k3 ' ( 1 - / 0
Ce
k\
(ii)
(I"/)
where a prime (') means the term for 13C.
Assuming f = f, then:
kV Ce'
13
C/12C ratio of Ce is
Ce
k2 + k3
, k3'
k3
k\' \ k2
where A/c; = —-^ - 1 or AA:, = a, - 1.
^C/iZC of organic product is R- =
k2' Ci'
1
_,. = —r
RQ
(V)
From equations (iv) and (v), the overall fractionation factor a is as follows:
(vi)
1473
T.Yosfaioka
Assuming A/CJ = Ak3, then:
Since (k2 + k3)Ci = ^ C e + F4,
(vii)
/* 4
Leakiness,
— - 2 — _ = (1 _ / ) - £ _ _
K]Ce + r 4
(vm)
«! Ce
From equations (vii) and (viii):
. ,,.
- k* Ci
(ix)
If the resistances to CO2 diffusion are the same in both directions across the cell
membrane (k\ = k3), equation (ix) becomes as follows [equation (10) in the text]:
Ak1)(l-f)^
(x)
Appendix 2: Derivation of equation (15)
At steady state:
^ - = klCe + F4-(k2
~ Jt2' + k3'
1474
+
k3)Ci = 0
(i)
Ptaytopbuiktoiiic carbon isotope fractionatkm
k2'
k2
k2 k2 + k3
k£ k3 yfaCe
k£_
A^Ce
F±
k3 k2 + k3) {k^Ce k^Ce + F4
Equation (iii) is substituted by leakiness X =
k3 Ci
k2d
+ K3Q
,,
.
F4 k}Ce + F
kand Ak, = —^ - 1.
Ac,-
Then:
3
(v)
"4
From equations (iv) and (v):
-X) + (Ak1 + 1)(M2 + 1)X
(M 3 + 1)(1 - / ) + (M, + 1)(M 3 + 1)(M4 + 1)/
(vi)
Equation (vi) is the same as equation (14) in the text.
Assuming Ak^kj = 0 and AkjAkjAkk » 0:
_ 1 + Mj + Ak3 + (Ak2 - Ak3)X
Ak3 + (A*, + Ak4)f
Aki 4- (Ak2 - MC3)*- (Akt + Ak.,)/
1
M
(M, + Ak4)f
(AJt 2 -AJt 3 );r(Akl + Ak4)f
1475
XYoshioka
I
I
1
a « 1 + AA:j + (Ak2 - Ak3)X - (Akx + Ak4)f
From Akx = Ak3:
a * 1 + Mj + (A£2 - A^^Z - (AA:j + Ak^f
Since X =
^t3 Ci
(1 - / ) , then equation (vii) becomes as follows:
+(AJt2 - M j ) ^- (l-f)Q—(Aki
^ ^
If kx = k3, then:
Equation (ix) is equation (15) in the text.
1476
(vii)
+ Ak4)f
(viii)