Environmental Engineering Reference
In-Depth Information
k
1
(Ce) (Ci)
CO2
k
2
k
3
CO
2
← Organic C
↑
F
4
k
4
CA
HCO
3
-
→ CO
2
*
Phytoplankton cell
k
4
Fig. 8
Schematic presentation of the active transport of CO
2
. The
δ
13
C of the actively trans-
ported carbon (CO
2
*
) is assumed to be the same as that of the CO
2
in the medium (Ce).
Data
source
Yoshioka (
1997
)
(1)
Active transport of CO
2
. The
δ
13
C value of actively transported inorganic car-
bon is assumed to be the same as that of Ce (Fig.
8
). Extracellular CA may
contribute to the conversion of
HCO
3
−
to CO
2
at the cell surface.
At steady state:
dCi
d
t
=
k
1
Ce
+
F
4
− (
k
2
−
k
3
)
Ci
=
0
(5.16)
where
F
4
is the is the flux of actively transported CO
2
.
The relative contribution of active transport (
f
) can be defined by:
F
4
k
1
Ce
+
F
4
(5.17)
f
=
If 0
≤
f
< 1, (Eq. 5.17) can be rewritten as:
dCi
d
t
1
1
−
f
(5.18)
=
k
1
Ce
− (
k
2
+
k
3
)
Ci = 0
Overall, fractionation becomes:
α =
1
+ ∆
k
1
+ (∆
k
2
− ∆
k
1
)(
1
−
f
)
Ci
Ce
(5.19)
By assuming the same
f
value for
12
CO
2
AND
13
CO
2
,
and
Δ
k
1
=
Δ
k
3
, (Eq.
5.19
)
becomes the same as (Eq.
5.15
) when
k
1
/
k
3
is substituted for (1
−
f
). This supports
the expectation that active transport might be linked with the asymmetric perme-
ability of the cell membrane for CO
2
. Leakiness,
X
(the ratio of efflux to influx of
DIC) (Berry
1988
), can be expressed as follows:
K
3
CI
K
1
CE F
4
(
1
−
F
)
CI
CE
(5.20)
X
=
1
+
When all carbon is transported by active transport (
f
=
1),
k
1
Ce would be zero.
In that case, one cannot substitute
f
=
1 in (Eq.
5.19
), because the denominator in
(Eq.
5.18
) becomes zero. Then,
α
becomes:
X
is not zero, but
α =
1
+
∆
K
2
− ∆
K
1
∆
K
1
+
1
K
3
CI
F
4
=
1
+ (∆
K
2
− ∆
K
1
)
K
3
CI
(5.21)
