2. The bioaccumulation model
Fig. 1 shows the chemical two-compartment bioaccumulation model. Three main processes are
accounted for: uptake of TcO
4 −
, release of TcO
4 −
, and reduction of Tc. As a start we assume first-or-
der rate processes, although this is not a priori correct, since many biological processes are regu-
lated by Michaelis – Menten kinetics. By defining two phases in the uptake curve we are able to
treat the uptake with pseudo first-order rate constants. Furthermore, dilution of the tech-
netium concentration in duckweed as a result of increasing biomass : 6 growth and decrease
of the TcO
4 −
concentration in the medium B 0.1 for the duration of the experiment 5 h are
neglected. Another important point in the model is that it only accounts for chemical species; spa-
tial distribution of the Tc-species such as a distri- bution over the vacuole, cytoplasm, etc. is not
incorporated. This is discussed in more detail in Section 5. The overall rates of TcO
4 −
transport into duckweed and formation of reduced com-
plexes respectively, are: d[TcO
4 −
]
duckweed
dt =
k
1
[TcO
4 −
]
solution
− k
2
+ k
3
[TcO
4 −
]
duckweed
1 d[TcX]
duckweed
dt =
k
3
[TcO
4 −
]
duckweed
2 where k
1
is the influx rate constant l kg
− 1
h
− 1
, k
2
the efflux rate constant h
− 1
, and k
3
the reduction rate constant h
− 1
, t the time h, [TcO
4 −
]
duckweed
the TcO
4 −
concentration in duck- weed mol kg
− 1
fresh wt., [TcX]
duckweed
the con- centration of reduced Tc compounds in duckweed
mol kg
− 1
fresh wt, and [TcO
4 −
]
solution
the TcO
4 −
concentration in the nutrient solution mol l
− 1
. More details on the derivation of these differential
equations can be found in the article by Krijger et al. 1999a. Solving the Laplace transformations
of Eqs. 1 and 2, and summing both equations, the
total Tc
concentration in
duckweed [Tc]
duckweed
as a function of time is: [Tc]
duckweed
t = k
1
k
2
[TcO
4 −
]
solution
k
2
+ k
3 2
1 − e
− k
2
+ k
3
t
+ k
1
k
3
[TcO
4 −
]
solution
k
2
+ k
3
t 3
The first right-hand part denotes the balance between uptake and release of TcO
4 −
, the second part the reduction of TcO
4 −
and accumulation. The efflux and reduction pseudo first-order rate
constants might be strongly influenced by possible Michaelis – Menten kinetics, since the TcO
4 −
con- centration in duckweed rises from zero to a cer-
tain steady
state level.
Comparing Michaelis – Menten kinetics with first-order rate
processes:
6 =
V
max
K
m
+ [TcO
4 −
] [TcO
4 −
] k[TcO
4 −
] 4
in which 6 is the reaction rate mol kg
− 1
h
− 1
, V
max
the maximum reaction rate mol kg
− 1
h
− 1
, K
m
the Michaelis constant mol l
− 1
and [TcO
4 −
] the TcO
4 −
concentration mol kg
− 1
, k the rate equation h
− 1
analogue of the pseudo first-or- der rate constants applied in Eqs. 1 – 3. This
rate equation is roughly inversely proportional to the TcO
4 −
concentration: k =
V
max
K
m
+ [TcO
4 −
] 5
If the TcO
4 −
concentration is constant, the rate equation can be treated as first-order rate con-
stant, and in turn, the accumulation can be de- scribed in terms of pseudo first-order rate
constants. Therefore, two phases in the accumula- tion curve Eq. 3 can be considered. The first
phase represents the uptake rate at the beginning, where efflux and reduction are negligible, while
the TcO
4 −
concentration in the nutrient solution remains practically constant:
6
uptake
= k
1
t[TcO
4 −
]
solution
6 The efflux and reduction might be treated as
first-order, when the TcO
4 −
concentration in duck- weed reaches a steady state, i.e. the second phase
Eqs. 4 and 5:
pdf text line
d[TcO
4 −
]
duckweed
dt =
[ [TcO
4 −
]
duckweed
t = k
1
k
2
+ k
3
[TcO
4 −
]
solution
7 From here, the accumulation of [Tc]
total
in duckweed follows a linear function of time:
[Tc]
duckweed
t = k
1
k
2
k
2
+ k
3 2
[TcO
4 −
]
solution
+ k
1
k
3
[TcO
4 −
]
solution
k
2
+ k
3
t 8
Eqs. 6 and 8 were used to fit the accumula- tion curves see Section 3.
3. Material and methods
Kategori