Chemical (and other) stress in DEB
2: toxicokinetics
Tjalling Jager
Dept. Theoretical Biology
Contents
Toxicokinetics
 The one-compartment model and diffusion
 Effects of composition and reproduction
 Complications: toxicants in soil and feeding
“Biology-based” modelling
toxicodynamics
external
concentration
(in time)
toxico-kinetic
model
internal
concentration
in time
process model
for the organism
toxicokinetics
effects on
endpoints
in time
“Biology-based” modelling
external
concentration
(in time)
toxico-kinetic
model
internal
concentration
in time
toxicokinetics
Toxicokinetic modelling
 Quite popular in
(eco)toxicology and
pharmacology
 Models differ in
complexity
Start from diffusion
Let’s assume …
• well-mixed homogeneous cube with water, in a solution
• cube has a semi-permeable membrane
• exchange proportional to area and concentration difference
Start from diffusion
Let’s change the cube …
• the same cube, now filled with oil ...
• correct one concentration with partition coefficient between
oil and water
Start from diffusion
Let the cube grow …
• without changing the shape
• leads to dilution and change in surface:volume ratio
Diffusion in organisms
Let’s move to an organism …
•
•
•
•
can we talk about internal ‘concentration’?
can we assume it is ‘well-mixed’?
what is the surface area for exchange?
when size and composition is constant …
One-compartment model
 Model is a classic, and often fits well …
Scaled concentration
Problem
• often, internal concentrations are not measured …
• or not relevant for effects
 Effects data contain information ...
• effects over time provides info on build up of body residue
• but, no information about absolute levels
concentration
external
scaled internal
time
Adding some realism
Organisms may grow ...
• dilution of concentration
• change of surface:volume ratio
“Biology-based” modelling
external
concentration
(in time)
body size
growth
toxico-kinetic
model
internal
concentration
in time
process model
for the organism
effects on
endpoints
in time
Active uptake
 Uptake/elimination of chemicals may be active
• ions such as metals, nutrients
• chemicals may be metabolised, or bound
 No difference as long as:
• uptake flux  external concentration
• elimination flux  internal concentration
 But ...
• active processes can saturate
• possible link to metabolic processes
More realism
Body composition may change
• reserve density changes with food level and toxicants
• females build up a reproduction buffer
Females may reproduce
• chemicals can be transferred to eggs
reserve
water
structure
buffer
eggs
More realism
Assumptions
•
•
•
•
distribution chemical over internal compartments is fast
reserve, buffer and egg have same composition
only structure exchanges with environment
chemicals from buffer are transferred to egg
reserve
water
structure
buffer
eggs
More realism
reserve
water
structure
buffer
eggs
Reproduction buffer
Assumptions
• chemical follows reserves associated with eggs
• rest remains in buffer
overhead
buffer
eggs
remainder
reserve
chemical
Simulations
structural length
physical length
0.2
0.2
0.15
0.15
cumul. reproduction
5000
4000
3000
0.1
0.1
2000
0.05
0
0.05
0
20
40
time
60
0
1000
0
concentration structure
20
40
time
60
0
concentration reserves
4
4
3
3
3
2
2
2
1
1
1
0
20
40
time
60
0
0
20
40
time
60
20
40
time
60
concentration total
4
0
0
0
0
20
40
time
60
Simulations
structural length
physical length
0.2
0.2
0.15
0.15
cumul. reproduction
5000
4000
3000
0.1
0.1
2000
0.05
0
0.05
0
20
40
time
60
0
1000
0
concentration structure
20
40
time
60
0
concentration reserves
15
15
10
10
10
5
5
5
0
20
40
time
60
0
0
20
40
time
60
20
40
time
60
concentration total
15
0
0
0
0
20
40
time
60
Simulations
structural length
physical length
cumul. reproduction
0.2
0.2
0.15
0.15
3000
0.1
0.1
2000
0.05
0.05
1000
0
0
20
40
time
60
0
4000
0
concentration structure
20
40
time
60
0
concentration reserves
15
15
10
10
10
5
5
5
0
20
40
time
60
0
0
20
40
time
60
20
40
time
60
concentration total
15
0
0
0
0
20
40
time
60
Simulations
structural length
physical length
cumul. reproduction
0.2
0.2
0.15
0.15
3000
0.1
0.1
2000
0.05
0.05
1000
0
0
20
40
time
60
0
4000
0
concentration structure
20
40
time
60
0
concentration reserves
30
30
25
25
25
20
20
20
15
15
15
10
10
10
5
5
5
0
20
40
time
60
0
0
20
40
time
60
20
40
time
60
concentration total
30
0
0
0
0
20
40
time
60
Reproduction buffer
Assumptions
• chemical follows reserves associated with eggs
• rest remains in buffer
overhead
buffer
remainder
eggs
Simulations
structural length
physical length
cumul. reproduction
0.2
0.2
0.15
0.15
3000
0.1
0.1
2000
0.05
0.05
1000
0
0
20
40
time
60
0
4000
0
concentration structure
20
40
time
60
0
concentration reserves
15
15
10
10
10
5
5
5
0
20
40
time
60
0
0
20
40
time
60
20
40
time
60
concentration total
15
0
0
0
0
20
40
time
60
Simulations
structural length
physical length
cumul. reproduction
0.2
0.2
0.15
0.15
3000
0.1
0.1
2000
0.05
0.05
1000
0
0
20
40
time
60
0
4000
0
concentration structure
20
40
time
60
0
concentration reserves
50
50
40
40
40
30
30
30
20
20
20
10
10
10
0
20
40
time
60
0
0
20
40
time
60
20
40
time
60
concentration total
50
0
0
0
0
20
40
time
60
Simulations
structural length
physical length
cumul. reproduction
0.2
0.2
0.15
0.15
3000
0.1
0.1
2000
0.05
0.05
1000
0
0
20
40
time
60
0
4000
0
concentration structure
20
40
time
60
0
concentration reserves
20
20
15
15
15
10
10
10
5
5
5
0
20
40
time
60
0
0
20
40
time
60
20
40
time
60
concentration total
20
0
0
0
0
20
40
time
60
What happens in an egg?
During the embryonic phase …
• mass is lost so concentration increases
• if PEV > 1, conversion reserve to structure increases
concentration structure even more
• how does egg exchange toxicants with surroundings?
water
overheads
maintenance
??
reserve
reserve
structure
structure
Assumptions realistic?
Difficult to say ...
 Most test setups avoid growth, reproduction and
changes in feeding status ...
 Some support:
• Russell et al 1999: lipid-normalised concentrations in fish
and eggs are similar
• Daley et al 2009: fish eggs increase in fugacity of PCBs over
incubation
 This extension takes the DEB assumptions to their
logical consequences
• with a minimum of additional parameters
“Biology-based” modelling
external
concentration
(in time)
body size
growth
reserves
reproduction rate
buffer handling
toxico-kinetic
model
internal
concentration
in time
process model
for the organism
(and toxicant
effects on them)
effects on
endpoints
in time
“Biology-based” modelling
internal
concentration
in time
external
concentration
(in time)
toxico-kinetic
process model
model
for the organism
effects on
endpoints
in time
More extensions?
Plenty of options to make it more complex …
•
•
•
•
•
uptake from food/inhalation
saturating uptake or elimination
biotransformation
more compartments (as in PBPK)
...
Summarising
 TK models range from simple to complex
• simplest is scaled one-compartment model with constant
composition (1 parameter: ke)
 DEB offers logical links to include effects of growth,
reserve and reproduction
• one-compartment model with varying parameters
• TK becomes closely integrated with the DEB organism
• toxicants can affect their own TK …