Chemical (and other) stress in DEB
5: extrapolations
Tjalling Jager
Dept. Theoretical Biology
Contents
Extrapolations
 Why extrapolation?
 Examples of extrapolation
Why extrapolation
“Protection goal”
Available data
• different exposure time
• different temperature
• different species
• time-varying exposure
• species interactions
• populations
• other stresses
• mixture toxicity
•…
Contents
Example life-cycle dataset
Bindesbøl et al (2007), re-analysed in Jager and Klok (2010)
• copper in Dendrobaena octaedra
• size, survival, cocoons over 20 weeks
• here, only [Cu] > 80 mg/kg
DEB analysis of data
Assumption
• copper leads to a decrease in ingestion rate
8
body length
7
40
80
120
160
200
cumulative offspring per female
9
6
5
4
3
2
1
0
50
100
time (days)
150
35
30
25
80
120
160
200
20
15
10
5
0
0
50
100
time (days)
Jager and Klok, 2010
150
Parameter estimates
TK pars
external
concentration
(in time)
tox pars
DEB pars
internal
concentration
toxico- in time
DEB
kinetics
parameters
in time
DEB
model
to population model …
life-history
traits
Population effects
 Type of information that risk assessors should be
most interested in ...
 Popular endpoints
• intrinsic rate of increase
• toxicant concentration where this rate is zero
• (or multiplication factor lambda, and where it is one)
 Popular (simple) approaches
• matrix models
• Euler-Lotka equation
• ...
Matrix models
1
2
3
4
 In combination with DEB(tox)
• Klok & De Roos (1996), Lopes et al (2005), Klanjscek et al
(2006), Smit et al (2006), Liao et al (2006)
 Discrete time and discrete stages ...
• one state variable (size or age) for the organism …
• DEB generally requires more ...
Euler-Lotka equation
 In constant environment, populations grow exponentially
 In combination with DEB(tox)
• Kooijman & Metz (1984), Jager et al (2004), Alda Álvarez et
al (2005, 2006) ...
 Continuous time and continuous states ...
• straightforward for DEB animals
• only for constant environment ...
Individual-based models
 Follow all individuals seperately …
 Full flexibility for dynamic environments
• but calculation intensive …
• see Martin et al (subm.)
Kooijman (2000)
Population effects
But, this is extinction at:
no-effects
population growth rate (d-1)
0.025
0.02
0.015
•
•
•
•
•
•
abundant food
no predation
no disease
optimal temperature
low competition
…
0.01
0.005
0
60
80
100 120 140 160 180
concentration (mg/kg soil)
200
Jager and Klok, 2010
Extrapolation: food
TK pars
external
concentration
(in time)
tox pars
DEB pars
internal
concentration
toxico- in time
DEB
kinetics
parameters
in time
less food in environment
DEB
model
life-history
traits
Energy budget …
feeding
ad libitum
reproduction
5%
maturation
maintenance
growth
Energy budget …
feeding
limiting
reproduction
50%
maturation
maintenance
growth
Food limitation (90%)
8
body length
7
40
80
120
160
200
cumulative offspring per female
9
6
5
4
3
2
1
0
50
100
time (days)
150
35
30
25
80
120
160
200
20
15
10
5
0
0
50
100
time (days)
150
Food limitation
population growth rate (d-1)
0.025
0.02
food 100%
0.015
0.01
food 90%
0.005
0
60
80
100 120 140 160 180
concentration (mg/kg soil)
200
Jager and Klok, 2010
Extrapolation: chemicals
TK pars
external
concentration
(in time)
tox pars
DEB pars
internal
concentration
toxico- in time
DEB
kinetics
parameters
in time
DEB
model
other compounds (related)
life-history
traits
Process-based QSAR
10
4
killing rate (L/mmol/h)
narcotic
reactive
10
10
10
10
2
0
-2
-4
10
-4
10
-2
0
10
NEC (mmol/L)
10
2
Jager and Kooijman, 2009
Extrapolation: mixtures
TK pars
tox pars
DEB pars
external
concentration
(in time)
internal
concentration
toxico- in time
DEB
kinetics
parameters
external
internal in time
concentration
concentration
toxico- in time
(in time)
DEB
model
kinetics
other compounds (mixtures)
life-history
traits
Mixtures
external
concentration
A (in time)
toxicokinetics
internal
concentration
A in time
DEB
parameters
external
in time
internal
concentration
concentration
B (in time)
toxico- B in time
kinetics
theory implies interactions …
DEB
model
growth
life-history
traits
Mixtures
external
concentration
A (in time)
toxicokinetics
internal
concentration
A in time
DEB
parameters
external
in time
internal
concentration
concentration
B (in time)
toxico- B in time
kinetics
DEB
model
life-history
traits
Simple mixture rules
compound
‘target’
metabolic process
assimilation
maintenance
…
toxicity parameters linked (compare CA)
Simple mixture rules
compound
‘target’
metabolic process
assimilation
maintenance
…
Simple mixture rules
compound
‘target’
metabolic process
assimilation
maintenance
…
toxicity parameters independent (compare IA)
Visual representation
 For binary mixture, model
represents surface that
changes in time …
Baas et al (2007)
PAHs in Daphnia
 Based on standard 21-day OECD test
• 10 animals per treatment
• length, reproduction and survival every 2 days
• no body residues (TK inferred from effects)
fluoranthene
Jager et al (2010)
pyrene
body length (mm)
pyrene
fluoranthene
mixtures
3
2.5
2
1.5
0
0 (solv.)
0.0865
0.173
0.346
1
cumulative offspring per female
0.5
0.0865
0.173
0.260
0.0865
0.260
0.346
0
0 (solv.)
0.213
0.426
0.853
0.213
0.426
0.640
0.640
0.213
0.853
0
90
80
same target
70
60
50
40
30
20
10
0
fraction surviving
1
0.8
0.6
costs reproduction
(and costs growth)
0.4
0.2
0
0
5
10
15
20
0
5
10
15
time (days)
20
0
5
10
15
20
Iso-effect lines
t=
fluoranthene (μM)
0.8
t=
0.7
t=
0.6
t=
14
t=
18
10
50% survival
t=
14
50% reproduction
10
21
t=
t=
0.5
18
t=
21
t=
0.4
t=
14
18
t=
21
0.3
t=
t=
14
t=
18
10
t=
t = 18
21
21
0.2
0.1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
pyrene (μM)
for body length <50% effect
0
0.05
t =t = 10
14
t=
t =18
21
0.1
0.15
t =t = 1
14 0
0.2
pyrene (μM)
0.25
0.3
Extrapolation: species
?
TK pars
external
concentration
(in time)
tox pars
DEB pars
internal
concentration
toxico- in time
DEB
kinetics
parameters
in time
other (related) species
DEB
model
life-history
traits
Experiments nematodes
Species
• Caenorhabditis elegans and Acrobeloides nanus
Chemicals
• cadmium, pentachlorobenzene and carbendazim
Exposure
• in agar
Endpoints
• survival, body size, reproduction over full life cycle
• analysed with extended DEBtox
Studies published as: Alda Álvarez et al.,
2005 (Func. Ecol.), 2006 (ES&T), 2006 (ET&C)
PeCB in A. nanus
450
60
400
55
350
cumulative offspring
65
body length
50
45
40
35
0
20
40
60
80
30
25
20
15
0
5
10
15
20
25
0
20
40
60
80
300
250
200
150
100
50
30
0
0
5
time (days)
Effects on assimilation
A. nanus
10
15
20
25
time (days)
30
35
40
PeCB in C. elegans
140
500
450
0
50
70
90
110
130
cumulative offspring
120
body length
100
80
60
0
50
70
90
110
130
40
20
0
0
2
4
6
time (days)
8
10
400
350
300
250
200
150
100
50
12
0
0
2
4
6
8
10
time (days)
Costs for growth and reproduction
C. elegans
12
14
16
Physiological MoA
C. elegans
PeCB
(narcotic)
Cadmium
(heavy metal)
Carbendazim
(inhibits mitosis)
A. nanus
Physiological MoA
C. elegans
PeCB
(narcotic)
Cadmium
(heavy metal)
Carbendazim
(inhibits mitosis)
A. nanus
costs for growth assimilation
and reproduction
Physiological MoA
C. elegans
PeCB
A. nanus
(narcotic)
costs for growth assimilation
and reproduction
Cadmium
assimilation
(heavy metal)
Carbendazim
(inhibits mitosis)
costs for growth
(+ ageing)
Physiological MoA
C. elegans
PeCB
A. nanus
(narcotic)
costs for growth assimilation
and reproduction
Cadmium
assimilation
costs for growth
(+ ageing)
assimilation
assimilation
(- ageing)
(heavy metal)
Carbendazim
(inhibits mitosis)
Species differences?
Species A
toxicant
Species B
target site
toxicant
target site
maintenance
maintenance
reproduction
reproduction
…
…
Species differences?
toxicant
target site
maintenance
reproduction
…
Extrapolation: exposure
TK pars
external
concentration
(in time)
tox pars
DEB pars
internal
concentration
toxico- in time
metabolic
kinetics
processes
in time
DEB
model
time-varying concentrations
life-history
traits
Time-varying exposure
Specifically relevant for risk assessment
 Such as:
• accidental spills
• plant-protection products
• industrial chemicals; batch production
 Impractical and costly to test each scenario experimentally
Fate modelling
pesticide fate modelling
oil-spill modelling
Time-varying exposure
environ. conc.
time
Time-varying exposure
Assumption
• toxicokinetics follows first-order, one-comp. model
environ. conc.
internal conc.
time
time
Time-varying exposure
Assumption
• effects on energetic processes are reversible
blank value
environ. conc.
assimilation eff.
internal conc.
NEC
time
time
Time-varying exposure
cumul. reproduction
body length
time
time
blank value
assimilation eff.
time
Experimental validation
Daphnia magna and fenvalerate
• modified 21-day reproduction test
• pulse exposure for 24 hours
• two (more or less) constant food levels
Pieters et al (2006)
mode of action:
Pulse exposure
Insights
‘assimilation’
• tox. parameters independent of food
• chemical effects fully reversible
• reproduction rate slows down …
Body length
Cumulative offspring
Fraction surviving
70
1
High food
4
60
0.8
50
3
40
2
0.6
30
0.4
20
1
0.2
10
0
0
70
1
4
Low food
0
60
0.8
50
3
40
2
0.6
30
0.4
20
1
0.2
10
0
0
5
10
15
20
0
0
5
10
15
20
0
0
5
10
15
20
Summary
 Extrapolation is crucial for environmental
management
• extrapolation requires mechanistic theory
• DEB provides a framework for extrapolation
 But, hypotheses for toxicant effects must be ‘correct’
 More work is needed, e.g.,
•
•
•
•
•
•
starvation responses and interaction with toxicants
patterns in DEB parameter values between species
patterns in toxicity parameters (species and chemicals)
reversibility of toxic effects
interactions between chemicals in a mixture
etc. etc. ...
Outlook
toxicant
target site
?
DEB
parameters
biochemistry
DEB
model
effect on
life cycle
DEB theory
species specific
 number of chemicals and species is very large …
 but number of target sites and DEB parameters is limited!
Advertisement
Vacancies
• PhD position at SCK-CEN in Mol (Belgium): radiation effects on
duckweed (Lemna minor) with DEB
More information: http://www.bio.vu.nl/thb
And: http://www.bio.vu.nl/thb/users/tjalling/debtox_papers.htm
Also, check out:
http://cream-itn.eu/