Standard Model

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Transcript Standard Model

Uptake of Chemicals
into Plants
Lectures
by Dr. Stefan Trapp
Stefan Trapp CV
1962 * Germany
1986 dipl geoecology
1992 PhD botany
1998 habil mathematics
1998 DTU applied ecology
Modeling of plant uptake
and phytoremediation
Lecture today
Part 1:
Standard Model
Part 2:
Dynamic Cascade Model
Part 3:
Cell Model
Part 4:
Translaminar Leaf Model
if time: Standard model for ionics
Part 1
Standard Model
for Plant Uptake
of Organic Compounds
I Concepts
II Uptake into Vegetation
III Exercises
How plants function
Roots take up water and solutes
Stems transport water and solutes
Xylem = water pipe
Phloem = sugar pipe
Leaves transpire water
and take up gas
Fruits are sinks for phloem and
xylem
Definition “BCF”
BCF is “bioconcentration factor”
Concentration in plants [mg/kg]
BCF = ――――――――――――――――――
Concentration in soil [mg/kg]
Take care! BCF differs for
- dry weight versus wet weight
- with uptake from air
- for roots, leaves, fruits, wood
Particle
deposition
Exchange with air
Xylem &
Phloem
transport
Direct
soil
contact
Diffusion
Translocation Soil – air
plant
in xylem
Advective uptake with water
Some measured BCF (Organics)
Compound
Properties
mean BCF
PAH, BaP
lipophil
0.001
10-5 to 0.01 roots, leaves
TCE
volatile
< 10-3
< 10-3 fruits, leaves
metabolites
of TCE
polar, nonvolatile
0.01
fruits, leaves
Pesticides
polar, nonvolatile
1
<1 to 10 roots, leaves,
fruits
Explosives
(TNT, RDX)
polar, nonvolatile
3
0.06 to 29 roots, leaves,
fruits
POPs (DDT,
lindane,
PCB)
lipophil
0.01
0.02 to 0.2 roots, leaves
“dioxins”
TCDD/F
lipophil
10-2 to 10-4
10-5 to 10-3 roots, leaves,
fruits
Sulfolane
(detergent)
Polar, nonvolatile
680
Range Plant part
leaves
BCF: Empirical regression by Travis & Arms
Easy to use
Gives good results
Old (ex-RISK)
Problem: only uptake
from soil; no air
Regression with log KOW for C vegetation to C soil (dry wt.)
log BCF  0.578  log K OW  1.588
Principles of plant uptake models
Crop specific models
Root model mass balance
Change of mass in roots =
+uptake with water – transport to shoots
dmR/dt = CWQ – CXyQ
where
m is mass of chemical (mg)
C is concentration [mg/kg, mg/L]
Q is water flow [L/d]
index R is roots, W is water and Xy is xylem
From mass to concentration
m is chemicals’ mass (mg)
M is root mass (kg)
C is concentration (mg/kg)
C=m/M
dmR/dt = d(CR MR)/dt
The root grows – integration for C and M required
(oh no ...!)
Plant mass,
concentration
Dilution by exponential growth
100
75
50
25
0
0
24
48
Time
M (kg)
m/M (mg/kg)
Chemical mass: m = constant
Plant mass: M(t) = M(0) x e+kt
m/M = Concentration in plant: C(t) = C(0) x e-kt
72
Root model concentration
Change of concentration in roots =
+ uptake with water
– transport to shoots
– dilution by growth (rate k)
dCR/dt = CWQ/M – CXyQ/M – kCR
where
k is growth rate [d-1]
CXy is concentration in xylem = CR/KRW
CW is concentration in soil pore water
Partition constant Root to Water KRW
KRW
= equilibrium root to water
Data by Briggs et al.
(1982) for barley
W ca. 0.85
log Kow
KRW = W + L x KOW0.77
Root model solution
Mass balance: change = flux in – flux out
dm
 CW  Q  C Xy  Q
dt
C Soil
CW 
Kd
Concentration: divide by plant mass M
dC CW Q C Xy Q


 kCR
dt
M
M
C Xy
Set to steady-state and solve for CR
0
CW  Q
CR  Q

 k  CR
M
K RW  M
CR 
Q
Q
 kM
K RW
C soil

Kd
CR

K RW
Root Model result for roots to soil
(Csoil = 1 mg/kg)
C root (mg/kg ww)
10
1
0.1
BaP
0.01
TCE
0.001
0.0001
0
2
4
6
8
log Kow
T&A
RCF
root model
For lipophilic compounds: growth dilution.
BCF > factor 100 below equilibrium
Translocation Upwards
Transpiration of plants in Europe
Type
mm/year
mm/d
Broad-leaf trees
500-800
4-5
Needle trees
300-600
2.5-4.5
Corn fields
400-500
Pasture, meadows
300-400
3-6
General rule:
About 2/3rd of precipitation is transpired by plants.
1 mm = 1 L/m2
Translocation upwards in the xylem
A ”standard plant” transpires
500 L water for the production
of 1 kg dry weight biomass!
= approx. 50 L per 1 kg fresh
weight
= approx. 1 L/day for 1 kg
plant mass
Translocation upwards in the Xylem
For translocation upwards, the chemical must cross the root and
come into the xylem.
“TSCF” = transpiration stream concentration factor = CXylem/CWater
Definition TSCF
TSCF = ”Transpiration stream concentration factor”
C_xylem
TSCF 
C_water
[mg/L : mg/L]
If TSCF is high, good translocation upwards.
Two methods:
1) Regression to log KOW (Briggs et al., Dettenmaier et al.)
2) Calculation from root model
Method 1: Regression for TSCF by Briggs (1982)
 - (log K OW - 1.78) 2 
TSCF  0.784  exp 

2.44


Briggs et al. (1982) = optimum curve
Method 2: Regression for TSCF by
Dettenmaier (2009)
11
TSCF 
11  2.6 log K OW
Dettenmaier et al. = sigmoidal curve
Method 2: Calculation of TSCF with Root Model
Model: C Xylem 
C Xy
CW
CR
K RW
CR
Q

/ K RW 
/ K RW
Q
CW
 kM
K RW
Lipophilic chemicals (high log Kow) are
adsorbed in the root and not translocated
Test of TSCF-Methods
Compilation of data from literature
Predicted TSCF
So which TSCF is best?
Uptake of contaminants into leaves
and fruits
Leaves and fruits are highly exposed to air
Additionally high water flux to leaves (xylem)
plus phloem flux (sugar) to fruits
 Contamination possible from soil and air
Model for uptake into leaves
Mass balance: uptake from soil and air
+ - exchange with air
(+ spray application)
- dilution by growth
- metabolism
+ influx with xylem
Outflux from roots
dC R
Q
Q

 KW S  C S 
 CR  k R  CR
dt
MR
M R  K RW
is influx to leaves and fruits
dC L
Q

 CR
dt
M L  K RW
Remember: high for polar compounds (low log Kow)
Leaves – exchange with air
Stomata 
Cuticle
Equilibrium between leaves and air
Leaves are plant material, like roots. But they do not
hang in soil, and not in water. Leaves hang in air.
The concentration ratio between air and water is
C Air
 K AW
CW ater
The concentration ratio between leaves and air is then
C Leaves C Leaves CW ater


 K LW / K AW  K LA
C Air
CW ater C Air
Because KAW < 1 and KLW > 1  KLA >> 1
The model for leafy vegetables
Adapted by the EU in the Technical
Guidance Documents for Risk
Assessment  ”TGD model”
Used also by many soil risk
assessment models
Uptake from soil (via xylem) and from
air (or loss to ...)
+ Exponential growth
Mass balance for the leafy vegetables
The change of mass in leaves =
+ translocation from roots + uptake from air - loss to air
from roots
from air
to air
growth &
degradation
dCL
Q
AL  g
AL  g  1000 L m 3

 CR 
 CA 
 CL  k L  CL
dt M L  K RW
ML
K LA  M L
easy to solve: linear diff. eq. of the type
dC L
 I  kCL
dt
g Conductance leaf - air
cuticle way
stomata way
Estimation of g can be quite complex.
It is convinient to use a default value of 1 mm s-1 = 86.4 m d-1.
Mass Balance of Fruits
essentially identical to the mass balance in leaves
+ influx with xylem
and phloem
+ - exchange with air
( + spray application)
- dilution by growth
- metabolism
Mass balance for Fruits
The change of mass in fruits =
+ flux from xylem and phloem + uptake from air - loss to air
from roots
from air
to air
growth &
degradation
dCF
QF
AF  g
AF  g  1000 L m 3

 CR 
 CA 
 CF  k F  CF
dt
M F  K RW
MF
K FA  M F
easy to solve: linear diff. eq. of the type
dC
 I  kC
dt
Summary: "Standard Model"
A system of coupled linear differential equations
dC R
 CW  Q / M  C R / K RW  Q / M  k  C R
dt
AL  vdep
dCL
Q
AL  g  1000 L m 3

 CR 
 CA 
 CL  k L  CL
dt M L  K RW
ML
K LA  M L
dCF
QF
AF  g
AF  g  1000 L m 3

 CR 
 CA 
 CF  k F  CF
dt
M F  K RW
MF
K FA  M F
where index R is root, W is water, L is soil, F is fruit and A is air.
C is concentration (mg/kg), Q is water flux (L/d), M is plant mass (kg), K is
partition coefficient (L/kg or kg/kg), A is area (m2), g is conductance (m d-1)
and k is rate (d-1).
Standard Model in excel – free for all
Uptake from soil into leaves
1000
100
1
10
C Leaves
-1
1
-3
0.1
-5
0.01
-7
-7
0.001
-3
0.0001
-2
0
log Kow
2
log Kaw
-9
1
4
6
partitioning
air-water
Accumulation in leaves: polar, non-volatile compounds
(such as pesticides, detergents, pharmaceuticals)
Uptake from soil into fruits
10
1
1
-1
0.1
C Fruit
-3
0.01
-5
0.001
-7
-3
0.0001
-2
0
2
-7
log Kaw
1
4
6
log Kow
Accumulation in fruits: less than in leaves, but also
polar and non-volatile compounds
-9
Uptake into fruits from air
10
1
-2
0.1
0
C Fruits
0.01
2
4
0.001
6
2
0.0001
1
-1
-3
log Kaw
-5
6
log Kow
-2
-7
-9
“the usual candidates”: semivolatile lipophilic organic
compounds such as PCB, DDT, PAH, PCDD/F
Bioaccumulation of lipophilic chemicals
We learned at university (did you ???):
”Lipophilic chemical accumulate via the food-chain”
high log KOW  high bioaccumulation
this is only one
out of two
mechanisms
Bioaccumulation of hydrophilic
compounds from soil in plants
A typical plant transpires 500 L water
for the production of 1 kg dry weight
biomass!
= ~ 50 L per 1 kg fresh weight
= ~ 1 L/day for 1 kg plant mass
The chemical comes with the water,
the water evaporates, the chemical
remains.
This can lead to a bioaccumulation
plant to soil of >> factor 100
Transfer to leaves with attached soil
Soil on plant
surfaces (Li et al.
1994)
[g soil/kg plant dw]
Lettuce
Wheat
Cabbage
Default value: 1% attached soil (wet weight)
BCF(leafy vegetables to soil) = BCF model + 0.01
260
4.8
1.1
Direct Soil Uptake
A ”standard” child eats
200 mg soil a day
”Pica child: 10 grams
(acute effects)
How much soil do you eat?
More than you think ...
(1% of 500 g is 5000 mg/d)
Application of the Standard Model
The "Standard Model" is the easiest way to calculate the dynamic
system soil-plant-air in a "correct way". That's why it is rather
popular. It is used by
● EU Chemical risk assessment (TGD, REACH)
● CLEA Contaminated Land Exosure Assessment (UK)
● Csoil (NL)
● RISK (USA)
and also
● Teaching at DTU
● Teaching here and now
☺
Limitations of the Standard Model
The "Standard Model" is only applicable
● for neutral organic compounds
● for exponentially growing plants
● for steady state
Thus it is difficult to simulate real scenarios.
It is more a "generic" model.
More realistic scenarios can be simulated using the "dynamic
cascade model" (see next section).
End of part 1. Any questions?