604
K. M. G. Mostofa et al.
(2) Active transport of HCO 3
− : The transported carbon has the same δ 13 C value
as HCO 3
− , as depicted in the scheme shown in (Fig. 9). The overall fractionation equation is substantially different from Eq. (5.19), although the steadystate for Ci is denoted by a similar term as Eq. (5.16), which can be written
as:
where Δk 4 denotes the fractionation in the CO 2 —HCO 3
− dissociation process.
Note that f and X are the same as those in the active transport of CO 2 .
Considering that the second- and third-order terms of Δk i are negligible, and
Δk 1 = Δk 3 , then α can be approximated as follows:
When f = 1, α becomes:
which implies that the overall fractionation decreases by (Δk 1 + Δk 4 ) when
all carbon derives from the active transport of HCO 3
− ( f = 1) , compared to
the passive diffusion model (Eq. 5.15). It can be deduced from (Eq. 5.24) that
all fractionation steps, including overall fractionation would be affected by f.
The difference between (Eqs. 5.19 and 5.24) or (Δk 1 + Δk 4 ) corresponds to the
difference in δ 13 C values between CO 2 and HCO 3
− . These equations indicate that
the overall fractionation from [CO 2 ] aq to organic carbon may be less than unity
under some conditions (Yoshioka 1997).
From a reanalysis of Hinga’s data (Hinga et al. 1994) one gets that the active transport of CO 2 for S. costatum can contribute ~ 30–40 % of the total carbon influx. The
relative contribution of active transport can reach 25–35 %, without any change in
CO 2 demand for an uptake of 10 % of the total carbon mediated by β-carboxylation
(5.25)
X =
k 3 Ci
F 4
(5.23)
α =
(∆k 1 + 1)(∆k 3 + 1)(1 − X) + (∆k 1 + 1)(∆k 2 + 1)X
(∆k 3 + 1)(1 − f ) + (∆k 1 + 1)(∆k 3 + 1)(∆k 4 + 1) f
(5.24)
α = 1 + ∆k 1 (1 − f ) + (∆k 2 − ∆k 1 )(1 − f )
Ci
Ce
− ∆k 4 f
(5.25)
α = 1 + (∆k 2 − ∆k 1 )
k 3 Ci
F 4
− ∆k 4
(Ce)
(Ci)
CO 2
CO 2 → Organic C
HCO 3
- →HCO 3
- *
Phytoplankton cell
→
←
k 3
k 1
←
→
k 4
↑F 4
k 2
CA
Fig. 9 Schematic presentation of the active transport of HCO 3
− . The δ 13 C of the actively transported carbon (HCO 3
−* ) is assumed to be the same as that of HCO 3
− in the medium. Data
source Yoshioka (1997)
K. M. G. Mostofa et al.
(2) Active transport of HCO 3
− : The transported carbon has the same δ 13 C value
as HCO 3
− , as depicted in the scheme shown in (Fig. 9). The overall fractionation equation is substantially different from Eq. (5.19), although the steadystate for Ci is denoted by a similar term as Eq. (5.16), which can be written
as:
where Δk 4 denotes the fractionation in the CO 2 —HCO 3
− dissociation process.
Note that f and X are the same as those in the active transport of CO 2 .
Considering that the second- and third-order terms of Δk i are negligible, and
Δk 1 = Δk 3 , then α can be approximated as follows:
When f = 1, α becomes:
which implies that the overall fractionation decreases by (Δk 1 + Δk 4 ) when
all carbon derives from the active transport of HCO 3
− ( f = 1) , compared to
the passive diffusion model (Eq. 5.15). It can be deduced from (Eq. 5.24) that
all fractionation steps, including overall fractionation would be affected by f.
The difference between (Eqs. 5.19 and 5.24) or (Δk 1 + Δk 4 ) corresponds to the
difference in δ 13 C values between CO 2 and HCO 3
− . These equations indicate that
the overall fractionation from [CO 2 ] aq to organic carbon may be less than unity
under some conditions (Yoshioka 1997).
From a reanalysis of Hinga’s data (Hinga et al. 1994) one gets that the active transport of CO 2 for S. costatum can contribute ~ 30–40 % of the total carbon influx. The
relative contribution of active transport can reach 25–35 %, without any change in
CO 2 demand for an uptake of 10 % of the total carbon mediated by β-carboxylation
(5.25)
X =
k 3 Ci
F 4
(5.23)
α =
(∆k 1 + 1)(∆k 3 + 1)(1 − X) + (∆k 1 + 1)(∆k 2 + 1)X
(∆k 3 + 1)(1 − f ) + (∆k 1 + 1)(∆k 3 + 1)(∆k 4 + 1) f
(5.24)
α = 1 + ∆k 1 (1 − f ) + (∆k 2 − ∆k 1 )(1 − f )
Ci
Ce
− ∆k 4 f
(5.25)
α = 1 + (∆k 2 − ∆k 1 )
k 3 Ci
F 4
− ∆k 4
(Ce)
(Ci)
CO 2
CO 2 → Organic C
HCO 3
- →HCO 3
- *
Phytoplankton cell
→
←
k 3
k 1
←
→
k 4
↑F 4
k 2
CA
Fig. 9 Schematic presentation of the active transport of HCO 3
− . The δ 13 C of the actively transported carbon (HCO 3
−* ) is assumed to be the same as that of HCO 3
− in the medium. Data
source Yoshioka (1997)