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Biology-based approaches for mixture ecotoxicology. Tjalling Jager. Contents. 14:00-18:00 (coffee at 16:00) Lecture limitations of descriptive approaches framework for a process-based approach Dynamic Energy Budget (DEB) theory sub-lethal effects - PowerPoint PPT Presentation
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Biology-based approaches for mixture ecotoxicology
Tjalling Jager
Contents
14:00-18:00 (coffee at 16:00) Lecture
• limitations of descriptive approaches• framework for a process-based approach
Dynamic Energy Budget (DEB) theory sub-lethal effects
• simplified survival modelling in more detail
Practical exercise• Play with a “toy model” in Excel (survival only)
18:00-18:30 Open discussion
Disclaimer!
Process-BasedModel
Process-BasedModel
your mixturedata full data
interpretationX
Interest in mixtures
Scientific• why are effects of mixtures the way
they are?
Practical• how can we predict the
environmental impact of mixtures?
Practical challenge
Some 100,000 man-made chemicals Large range of natural toxicants For animals alone, >1 million species described Complex exposure situations
Typical approach
A B
Typical approach
Typical approach
Typical approach
wait for 21 days …
Dose-response plot
dose-ratio dependent deviation from CA
dose-ratio dependent deviation from CA
concentration A concentratio
n B
tota
l o
ffsp
rin
g
What question did we answer?
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
dose-ratiodependentdeviation from CA
dose-ratiodependentdeviation from CA
concentration A concentratio
n B
tota
lo
ffsp
rin
g
concentration A concentratio
n B
tota
lo
ffsp
rin
g
What question did we answer?
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
dose-ratiodependentdeviation from CA
dose-ratiodependentdeviation from CA
concentration A concentratio
n B
tota
lo
ffsp
rin
g
concentration A concentratio
n B
tota
lo
ffsp
rin
g
What question did we answer?
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
dose-ratiodependentdeviation from CA
dose-ratiodependentdeviation from CA
concentration A concentratio
n B
tota
lo
ffsp
rin
g
concentration A concentratio
n B
tota
lo
ffsp
rin
g
What question did we answer?
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
dose-ratiodependentdeviation from CA
dose-ratiodependentdeviation from CA
concentration A concentratio
n B
tota
lo
ffsp
rin
g
concentration A concentratio
n B
tota
lo
ffsp
rin
g
What question did we answer?
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
dose-ratiodependentdeviation from CA
dose-ratiodependentdeviation from CA
concentration A concentratio
n B
tota
lo
ffsp
rin
g
concentration A concentratio
n B
tota
lo
ffsp
rin
g
What question did we answer?
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
dose-ratiodependentdeviation from CA
dose-ratiodependentdeviation from CA
concentration A concentratio
n B
tota
lo
ffsp
rin
g
concentration A concentratio
n B
tota
lo
ffsp
rin
g
What question did we answer?
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
dose-ratiodependentdeviation from CA
dose-ratiodependentdeviation from CA
concentration A concentratio
n B
tota
lo
ffsp
rin
g
concentration A concentratio
n B
tota
lo
ffsp
rin
g
What question did we answer?
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
dose-ratiodependentdeviation from CA
dose-ratiodependentdeviation from CA
concentration A concentratio
n B
tota
lo
ffsp
rin
g
concentration A concentratio
n B
tota
lo
ffsp
rin
g
What question did we answer?
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
dose-ratiodependentdeviation from CA
dose-ratiodependentdeviation from CA
concentration A concentratio
n B
tota
lo
ffsp
rin
g
concentration A concentratio
n B
tota
lo
ffsp
rin
g
Relevance for science?
What question did we answer?
“What is effect of constant exposure to this mixture on Daphnia reproduction after 21 days under standard OECD test conditions?”
“What is effect of constant exposure to this mixture on Daphnia reproduction after 21 days under standard OECD test conditions?”
dose-ratiodependentdeviation from CA
dose-ratiodependentdeviation from CA
concentration A concentratio
n B
tota
lo
ffsp
rin
g
concentration A concentratio
n B
tota
lo
ffsp
rin
g
Relevance for science?
What question did we answer?
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
“What is effect of constant exposure to this mixture on total Daphnia reproduction after 21 days under standard OECD test conditions?”
dose-ratiodependentdeviation from CA
dose-ratiodependentdeviation from CA
concentration A concentratio
n B
tota
lo
ffsp
rin
g
concentration A concentratio
n B
tota
lo
ffsp
rin
g
Relevance for risk assessment?
Better questions
do we see:• time patterns of effects on different endpoints …
0.5
1
1.5
2
2.5
0 5 10 15 200
survival
body length
cumul. reproductioncarbendazim
Alda Álvarez et al. (2006)
time (days)0 2 4 6 8 10 12 14 16
0
20
40
60
80
100
120
140
pentachlorobenzene
time (days)
Cl
Cl
Cl Cl
Cl
EC10 in time
Cd and Zn in springtailsVan Gestel & Hensbergen (1997)
0
1
2
3
4
5
0 1 2 3 4 5 6
time (weeks)
TU
mix
ture
50%
eff
ect,
inte
rnal
co
nce
ntr
atio
n
TU = 1ReproductionDry weight
Better questions
do we see:• time patterns of effects on different endpoints …• interactions between compounds and with environment …• differences between species and between compounds …
• can we make useful predictions for risky situations?
externalconcentration
B (in time)
externalconcentration
A (in time)
effectsin time
Process-based
causility
Assumption: internal concentration is linked to the effect
externalconcentration
B (in time)
externalconcentration
A (in time)
toxico-kinetics
toxico-kinetics
toxico-kinetics
toxico-kinetics
Process-based
internalconcentration
A in time
internalconcentration
B in time
“toxicodynamicanimal model”
“toxicodynamicanimal model”
effectsin time
Assumption: internal concentration is linked to the effect
Demands on toxicokinetics model
Complexity should match the level of detail in data
• simplest: scaled one-compartment model one parameter (elimination rate) estimated from effects data only
• most complex: PBPK model … requires detailed measurements …
toxico-kinetics
toxico-kinetics
Demands on animal model
Explain endpoints of interest over entire life cycle• growth, start of reproduction, reproduction rate, survival, …
Explain effects of toxicants on these endpoints Allow to interpret effects of multiple stressors
• combination of chemicals• chemicals and non-chemical stressors
As little chemical- and species-specific as possible• comparison and extrapolation
All organisms obey conservation
of mass and energy!“toxicodynamicanimal model”
“toxicodynamicanimal model”
Look closer at individual
Look closer at individual
Look closer at individual
Look closer at individual
Look closer at individual
Natural role for energetics
Understanding toxic effects on growth and reproduction requires understanding how food is acquired and used to produce traits
Rules for metabolic organisation Start of Dynamic Energy Budget (DEB) theory 30
years ago
What is DEB?Quantitative theory for metabolic
organisation; ‘first principles’• time, energy and mass balance
Life-cycle of the individual• links levels of organisation: molecule
ecosystems
Fundamental; many practical applications• (bio)production, (eco)toxicity, climate change,
evolution …
Kooijman (2000)
Kooijman (2010)
mobilisation
Standard DEB animal
structurestructure
somatic maintenance
growth
maturity maintenance1-
reproduction
maturitymaturity eggseggs
maturation p
food fecesassimilation
reservereserve
b
Kooijman (2000)
mobilisation
Standard DEB animal
food fecesassimilation
structurestructure
somatic maintenance
growth
maturity maintenance1-
reproduction
maturitymaturity eggseggs
maturation
b
p
reservereserve
“toxicodynamicanimal model”
“toxicodynamicanimal model”
Toxicant effects in DEB
externalconcentration
(in time)
toxico-kinetics
toxico-kinetics internal
concentrationin time DEB
parametersin time
DEBmodel
DEBmodel
Kooijman & Bedaux (1996),
Jager et al. (2006, 2010)
repro
growth
survival
feeding
hatching
…
over entire life cycle
assimilationmaintenanc
ematuration
….
Toxicant effects in DEB
externalconcentration
(in time)
toxico-kinetics
toxico-kinetics internal
concentrationin time DEB
parametersin time
DEBmodel
DEBmodel
Affected DEB parameter has specific consequences for life cycle
repro
growth
survival
feeding
hatching
…
Ex.1: maintenance costs
time
cum
ula
tive
off
spri
ng
time
bo
dy
len
gth
TPT
Jager et al. (2004)
Ex.2: growth costs
time
bo
dy
len
gth
time
cum
ula
tive
off
spri
ng Pentachlorobenzene
Alda Álvarez et al. (2006)
Ex.3: egg costs
time
cum
ula
tive
off
spri
ng
time
bo
dy
len
gth
Chlorpyrifos
Jager et al. (2007)
Mixture analysis
externalconcentration
A (in time)
toxico-kinetics
toxico-kinetics internal
concentrationA in time
externalconcentration
B (in time)
toxico-kinetics
toxico-kinetics
internalconcentration
B in time
DEBparameters
in timeDEB
model
DEBmodel effects on
all endpointsin time
theory implies interactions …
Mixture analysis
externalconcentration
A (in time)
externalconcentration
B (in time)
toxico-kinetics
toxico-kinetics
toxico-kinetics
toxico-kinetics
internalconcentration
A in time
internalconcentration
B in time
DEBparameters
in timeDEB
model
DEBmodel effects on
all endpointsin time
theory implies interactions …
mobilisationmobilisation
food fecesassimilation
structurestructure
somatic maintenance
growth
structurestructure
somatic maintenance
growth
maturity maintenance1-
reproduction
maturitymaturity eggseggs
maturation
maturity maintenance1-
reproduction
maturitymaturity eggseggs
maturation
b
p
reservereserve
Mixture analysis
externalconcentration
A (in time)
externalconcentration
B (in time)
toxico-kinetics
toxico-kinetics
toxico-kinetics
toxico-kinetics
internalconcentration
A in time
internalconcentration
B in time
DEBparameters
in timeDEB
model
DEBmodel effects on
all endpointsin time
theory implies interactions …
growth
externalconcentration
A (in time)
toxico-kinetics
toxico-kinetics
externalconcentration
B (in time)
toxico-kinetics
toxico-kinetics
DEBmodel
DEBmodel
internalconcentration
A in time DEBparameters
in timeinternalconcentration
B in time effects onall endpoints
in time
Mixture analysis
Simple mixture rules
compound ‘target’
toxicity parameters linked (compare CA)
maintenance costs
ingestion rate
growth costs
DEB parameter
…
Simple mixture rules
compound ‘target’
maintenance costs
ingestion rate
growth costs
DEB parameter
…
Simple mixture rules
compound ‘target’
toxicity parameters independent (compare IA)
maintenance costs
ingestion rate
growth costs
DEB parameter
…
Mixture rules
‘same target’ and ‘different target’ are concepually similar to CA and IA, but:
CA and IA are prescriptions for combining dose-response curves (at a single time point)
here, applied at target level, yielding mixture effects on all endpoints over entire life cycle
they yield deviations from standard CA and IA (apparent interactions)
Mixture effects: simulations
• parameters for Daphnia• ‘same target’ model (ingestion)• plots for 21-days exposure
Contours at t=21 days
5
20
30
30
50
50
5
20
20
30
30
30
50
50
50
50
com
po
un
d B
size reproduction
compound Acompound A
50% contours in time
t = 5
t = 5
t = 5
t = 10
t = 10
t = 10
t = 15
t = 15
t = 15
t = 21
t = 21
compound At = 5
t = 5
t = 10
t = 10
t = 10
t = 15
t = 15
t = 15
t = 15
t = 21
t = 21
t = 21
t = 21
compound A
com
po
un
d B
t = 5
t = 5
t = 5
t = 10
t = 10
t = 10
t = 15
t = 15
t = 15
t = 21
t = 21
compound At = 5
t = 5
t = 10
t = 10
t = 10
t = 15
t = 15
t = 15
t = 15
t = 21
t = 21
t = 21
t = 21
compound A
com
po
un
d B
size reproduction
Mixture effects: simulations
• parameters for Daphnia• ‘other target’ model (ingestion+maint.)• plots for 21-days exposure
size reproduction
5
5
20
20
30
3030
50
5050
5
5
20
20
20
30
30
30
50
50
50
50
co
mp
ou
nd
B
Contours at t=21 days
50% contours in time
t = 5
t = 10
t = 10
t = 10
t = 15
t = 15
t = 15
t = 1
5
t = 21
t = 21
t = 21
t = 2
1
compound A
co
mp
ou
nd
B
t = 5
t = 5
t =
5
t = 1
0
t = 10t = 10
t = 1
5
t = 15
t = 15
t = 2
1
t = 21
t = 21
compound A
size reproduction
fluoranthene pyrene
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)
Jager et al. (2010)
0 5 10 15 20
0
0.2
0.4
0.6
0.8
1
frac
tio
n s
urv
ivin
g
0 5 10 15 200
0.2
0.4
0.6
0.8
1
frac
tio
n s
urv
ivin
g
0 5 10 15 20
time (days)0 5 10 15 20
time (days)0 5 10 15 200 5 10 15 20
0
10
20
30
40
50
60
70
80
90
cum
ula
tiv
e o
ffsp
rin
g p
er f
ema
le
0
0.5
1
1.5
2
2.5
3b
od
y le
ng
th (
mm
)
00 (solv.)0.08650.1730.346
0
0.5
1
1.5
2
2.5
3b
od
y le
ng
th (
mm
)
00 (solv.)0.08650.1730.346
00 (solv.)0.2130.4260.853
00 (solv.)0.2130.4260.853
0.0865 0.2130.173 0.4260.260 0.6400.0865 0.6400.260 0.2130.346 0.853
0.0865 0.2130.173 0.4260.260 0.6400.0865 0.6400.260 0.2130.346 0.853
pyrene fluoranthene mixtures
costs reproduction(and costs growth)
costs reproduction(and costs growth)
same targetsame target
Iso-effect lines
0 0.05 0.1 0.15 0.2 0.25 0.30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
t = 10
t = 10
t = 14
t = 14
t = 14
t = 14
t = 18
t = 18
t = 18
t = 18
t = 21
t = 21
t = 21
t = 21
pyrene (μM)
flu
ora
nth
ene
(μM
)
50% survival
0 0.05 0.1 0.15 0.2 0.25 0.3
t = 10
t = 14
t = 14
t = 21
t = 21
pyrene (μM)
t = 10
t = 18
t = 18t = 10
50% reproduction
for body length <50% effect
Conclusions PAH mixture
Mixture effect consistent with ‘same target’• as expected for these PAHs• explains all three endpoints, over time
Iso-effect lines are functions of time• which differ between endpoints• in this case: little deviation from CA
Few parameters for all data in time• 14 parameters (+4 Daphnia defaults)
(descriptive would require >100 parameters)
Disclaimer!
Process-BasedModel
Process-BasedModel
your mixturedata full data
interpretationX
fit not satisfactory?
fit
Strategy for data analysis
actualDEB model
experimentaldata
additionalexperiments
literature
educatedguesses
mechanistichypothesis
standardDEB model
other interactions?
Parameter estimates
externalconcentration
A (in time)
externalconcentration
B (in time) toxico-kinetics
toxico-kinetics
toxico-kinetics
toxico-kinetics
internalconcentration
A in time
internalconcentration
B in time
DEBparameters
in timeDEB
model
DEBmodel effects on
all endpointsin time
TK pars tox pars DEB pars
Educated extrapolation
externalconcentration
A (in time)
externalconcentration
B (in time) toxico-kinetics
toxico-kinetics
toxico-kinetics
toxico-kinetics
internalconcentration
A in time
internalconcentration
B in time
DEBparameters
in timeDEB
model
DEBmodel effects on
all endpointsin time
TK pars tox pars DEB pars
populations
Educated extrapolation
externalconcentration
A (in time)
externalconcentration
B (in time) toxico-kinetics
toxico-kinetics
toxico-kinetics
toxico-kinetics
internalconcentration
A in time
internalconcentration
B in time
DEBparameters
in timeDEB
model
DEBmodel effects on
all endpointsin time
TK pars tox pars DEB pars
other endpoints
other, e.g.,feeding
respiration
Educated extrapolation
externalconcentration
A (in time)
externalconcentration
B (in time) toxico-kinetics
toxico-kinetics
toxico-kinetics
toxico-kinetics
internalconcentration
A in time
internalconcentration
B in time
DEBparameters
in timeDEB
model
DEBmodel effects on
all endpointsin time
TK pars tox pars DEB pars
time-varying concentrations
Educated extrapolation
externalconcentration
A (in time)
externalconcentration
B (in time) toxico-kinetics
toxico-kinetics
toxico-kinetics
toxico-kinetics
internalconcentration
A in time
internalconcentration
B in time
DEBparameters
in timeDEB
model
DEBmodel effects on
all endpointsin time
TK pars tox pars DEB pars
food limitation
Educated extrapolation
externalconcentration
A (in time)
externalconcentration
B (in time) toxico-kinetics
toxico-kinetics
toxico-kinetics
toxico-kinetics
internalconcentration
A in time
internalconcentration
B in time
DEBparameters
in timeDEB
model
DEBmodel effects on
all endpointsin time
TK pars tox pars DEB pars
related compounds
Educated extrapolation
externalconcentration
A (in time)
externalconcentration
B (in time) toxico-kinetics
toxico-kinetics
toxico-kinetics
toxico-kinetics
internalconcentration
A in time
internalconcentration
B in time
DEBparameters
in timeDEB
model
DEBmodel effects on
all endpointsin time
TK pars tox pars DEB pars
other (related) species
Final words
A process-based approach is essential …• to progress the science of mixture toxicity• to make useful predictions for RA
Key elements DEB approach• one framework for all endpoints over time• not specific for particular species or compounds• certain interactions are unavoidable …
Of course, more work is needed …• validate predicted interactions and extrapolations• find out if we can explain other interactions
Limitations
A DEB-based analysis cannot be done routinely!• almost every dataset requires additional hypotheses …• DEB offers a framework, not a “foolproof software”
Data requirements are not trivial• basic life history information of the species• body size and repro over a considerable part of the life cycle• preferably survival, feeding rates, egg size, hatching time …
For mixtures, experimental effort may rapidly become excessive
There is help …
DEB pars• depart from defaults (e.g., ‘add_my_pet’ or standard animal with ‘zoom factor’)• hopefully vary little between experiments
TK pars• depart from QSARs …• extrapolate between species or toxicants
tox pars• at this moment, little help …• extrapolate between species or toxicants?
species specific
DEBmodel
Outlook
target sitetoxicant
effect onlife cycle?
number of chemicals and species is very large … but number of target sites and processes is limited!
Once we know the normal biological processes, all external stressors are merely perturbations of these processes (Yang et al., 2004)
Once we know the normal biological processes, all external stressors are merely perturbations of these processes (Yang et al., 2004)
DEBparameters
DEB theorybiochemistry
In more detail: survival
0 20 40 60 80 1000
0.2
0.4
0.6
0.8
1
time (hours)
frac
tio
n s
urv
ivin
g
01.331.843.325.819.25
conc. μmol/L
Introduction
For survival, DEB can be simplified• in most acute tests, animals are not growing• survival can be treated (largely) independent from metabolic
organisation
Simple mixture version in Excel• only survival• only datasets from Baas et al., 2007• no interactions
externalconcentration
B (in time)
externalconcentration
A (in time)
toxico-kinetics
toxico-kinetics
toxico-kinetics
toxico-kinetics
Process-based
internalconcentration
A in time
internalconcentration
B in time
survival as achance process
survival as achance process
survivalin time
Tolerance distribution• McCarty et al (1992)• Lee & Landrum (2006)Stochastic death• Ashauer et al. (2007)• Baas et al. (2007, 2009)
Tolerance distribution• McCarty et al (1992)• Lee & Landrum (2006)Stochastic death• Ashauer et al. (2007)• Baas et al. (2007, 2009)
Mortality assumptionthresholds
See Newman and McClosky (2000)
tx
t+Δtp
1-p
Tolerancedistribution
Stochastic death
survivalin time
survival as achance process
Model Chain
externalconcentration
(in time)
toxico-kinetics
toxico-kinetics
internalconcentration
in time
Simple modelsinformation content of standard tests is low
survivalin time
survival as achance process
Model Chain
externalconcentration
(in time)
toxico-kinetics
toxico-kinetics
internalconcentration
in time
1-comp.uptake elimination
sc
ale
d c
on
ce
ntr
ati
on
external
internal
time
survivalin time
survival as achance process
Model Chain
externalconcentration
(in time)
toxico-kinetics
internalconcentration
in time
Assumptions:
death is a chance event for the individual
the probability to die depends on the internal concentration.
Hazard modelling
0
2
4
6
8
10
12
0 2 4 6 8time (days)
surv
ivin
g c
hic
ken
s
0 cars/hr10 cars/hr20 cars/hr50 cars/hr
Hazard rate times Δt is the probability to get hit by a car in that interval
survivalin time
survival as achance process
Model Chain
externalconcentration
(in time)
toxico-kinetics
internalconcentration
in time
internal concentration
haza
rd r
ate
NEC
blank value
killin
g ra
te
survivalin time
survival as achance process
Model Chain
externalconcentration
(in time)
toxico-kinetics
internalconcentration
in time
Straightforward statistics …
integrate hazard rate over time and take exponential …
Hazard modelling
time
hazard rate
time
scaled internal concentration
NEC
time
survival probability
external concentrationelimination rate
NEC / killing rate integrate
Minnow, hexachloroethane
0 1.33 1.84 3.32 5.81 9.25
0 20 20 20 20 20 20
24 20 20 20 20 20 4
48 20 20 20 20 15 0
72 20 20 19 20 12 0
96 20 20 19 20 10 0
concentration (μmol/L)
time
(h
our
)fathead minnow
Survival in time
0 20 40 60 80 1000
0.2
0.4
0.6
0.8
1
time (hours)
fra
cti
on
su
rviv
ing
01.331.843.325.819.25
conc. μmol/L
elimination rate 0.141 hr-1
NEC 5.54 (5.26-5.68) μmol/Lkilling rate 0.0408 L/μmol/hrblank hazard 0.000124 hr-1
Simple mixture rules
hazard rate
compound ‘target’
toxicity parameters independent (compare IA)
2 elimination rates2 NECs2 killing rates
hazard rates added
2 elimination rates2 NECs2 killing rates
hazard rates added
Simple mixture rules
hazard rate
compound ‘target’
toxicity parameters linked (compare CA)
2 elimination rates1 NEC1 killing rate1 “weight factor”
weighted scaledint. conc. added
2 elimination rates1 NEC1 killing rate1 “weight factor”
weighted scaledint. conc. added
Consequence:NEC and killing rate are not independent
Parameter relationships
Jager & Kooijman (2009)
10-4
10-2
100
102
10-4
10-2
100
102
104
NEC (mM)
killi
ng
rate
(m
M-1
h-1)
narcoticsreactives
Narcotic: log b† = -1 log c0 – 0.27 (r2=0.61)Reactive: log b† = -1 log c0 – 1.2 (r2=0.85)
10-4
10-2
100
102
10-4
10-2
100
102
104
NEC (mM)
killi
ng
rate
(m
M-1
h-1)
narcoticsreactives
Narcotic: log b† = -1 log c0 – 0.27 (r2=0.61)Reactive: log b† = -1 log c0 – 1.2 (r2=0.85)
Visual representation
For binary mixture, model represents surface that changes in time …
Baas et al. (2007)
Data needs
Several observations in time• standard acute test protocols prescribe daily scoring
Note: • body residues are not needed, but can be used• exposure need not be constant• test setup may be non-standard• when animals grow, DEB will be needed …
Improvements• more observations in time is always better• optimal test design depends on chemical and species/size
An Excel exercise
Disclaimer:• Excel is not really suited (unless you have an ODE solver)• you can only use the data from Baas et al., 2007• I only use a part of the data set (you select which part)• I did not include interactions• at this moment, there is no user-friendly software
there is user-unfriendly software though … if you have a nice data set, contact me for collaboration!
Take home message
Realise that …• mixture effects change with exposure time• life-history traits are not independent• descriptive approaches will never explain why
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Vacancies• PhD student in Rennes (France), Marie Curie training
network (CREAM)
Courses• International DEB Tele Course 2011
Symposia• 2nd International DEB Symposium 2011 in Lisbon
More information: http://www.bio.vu.nl/thb