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!
your mixture
data
Process-Based
Model
full data
interpretation
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
total offspring
dose-ratio
dependent
deviation from CA
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?”
total offspring
dose-ratio
dose-ratio
dependent
dependent
deviation
deviationfrom
fromCA
CA
nB
conce
ntratio
nA
nc
co
tio
tra
en
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?”
total offspring
dose-ratio
dose-ratio
dependent
dependent
deviation
deviationfrom
fromCA
CA
nB
conce
ntratio
nA
nc
co
tio
tra
en
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?”
total offspring
dose-ratio
dose-ratio
dependent
dependent
deviation
deviationfrom
fromCA
CA
nB
conce
ntratio
nA
nc
co
tio
tra
en
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?”
total offspring
dose-ratio
dose-ratio
dependent
dependent
deviation
deviationfrom
fromCA
CA
nB
conce
ntratio
nA
nc
co
tio
tra
en
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?”
total offspring
dose-ratio
dose-ratio
dependent
dependent
deviation
deviationfrom
fromCA
CA
nB
conce
ntratio
nA
nc
co
tio
tra
en
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?”
total offspring
dose-ratio
dose-ratio
dependent
dependent
deviation
deviationfrom
fromCA
CA
nB
conce
ntratio
nA
nc
co
tio
tra
en
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?”
total offspring
dose-ratio
dose-ratio
dependent
dependent
deviation
deviationfrom
fromCA
CA
nB
conce
ntratio
nA
nc
co
tio
tra
en
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?”
total offspring
dose-ratio
dose-ratio
dependent
dependent
deviation
deviationfrom
fromCA
CA
nB
conce
ntratio
nA
nc
co
tio
tra
en
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?”
total offspring
dose-ratio
dose-ratio
dependent
dependent
deviation
deviationfrom
fromCA
CA
Relevance for science?
nB
conce
ntratio
nA
nc
co
tio
tra
en
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?”
total offspring
dose-ratio
dose-ratio
dependent
dependent
deviation
deviationfrom
fromCA
CA
Relevance for science?
nB
conce
ntratio
nA
nc
co
tio
tra
en
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?”
total offspring
dose-ratio
dose-ratio
dependent
dependent
deviation
deviationfrom
fromCA
CA
Relevance for risk assessment?
nB
conce
ntratio
nA
nc
co
tio
tra
en
Better questions
do we see:
• time patterns of effects on different endpoints …
EC10 in time
survival
Alda Álvarez et al. (2006)
body length
cumul. reproduction
carbendazim
2.5
pentachlorobenzene
140
Cl
120
Cl
Cl
2
Cl
100
1.5
Cl
80
60
1
40
0.5
20
0
0
5
10
time (days)
15
20
0
0
2
4
6
8
10
time (days)
12
14
16
Cd and Zn in springtails
TU mixture 50% effect, internal concentration
Van Gestel & Hensbergen (1997)
5
Dry weight
Reproduction
TU = 1
4
3
2
1
0
0
1
2
3
4
time (weeks)
5
6
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?
Process-based
external
concentration
A (in time)
external
concentration
B (in time)
Assumption: internal concentration
is linked to the effect
effects
in time
Process-based
external
concentration
A (in time)
external
concentration
B (in time)
Assumption: internal concentration
is linked to the effect
toxicokinetics
toxicokinetics
internal
concentration
A in time
internal
concentration
B in time
“toxicodynamic
animal model”
effects
in time
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 …
toxicokinetics
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
“toxicodynamic
animal model”
All organisms obey conservation
of mass and energy!
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)
Standard DEB animal
food
feces
b
assimilation
reserve
mobilisation
somatic maintenance
growth
structure

1-
maturation
maturity
maturity maintenance
p
reproduction
eggs
Kooijman (2000)
Standard DEB animal
food
feces
b
assimilation
reserve
mobilisation
somatic maintenance
growth
structure

1-
maturation
maturity
maturity maintenance
p
reproduction
eggs
Toxicant effects in DEB
external
concentration
(in time)
toxicokinetics
assimilation
maintenanc
e
maturation
….
internal
over entire life
concentration
in time
repro
DEB
parameters
growth
“toxicodynamic
in time
survival
DEB
animal model”
model
feeding
hatching
…
Kooijman & Bedaux (1996),
Jager et al. (2006, 2010)
cycle
Toxicant effects in DEB
external
concentration
(in time)
Affected DEB parameter has
specific consequences for life cycle
toxicokinetics
internal
concentration
in time
DEB
parameters
in time
repro
growth
DEB
model
survival
feeding
hatching
…
body length
cumulative offspring
Ex.1: maintenance costs
time
Jager et al. (2004)
TPT
time
body length
cumulative offspring
Ex.2: growth costs
time
Alda Álvarez et al. (2006)
Pentachlorobenzene
time
Ex.3: egg costs
body length
cumulative offspring
Chlorpyrifos
time
Jager et al. (2007)
time
Mixture analysis
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
effects on
all endpoints
in time
Mixture analysis
food
external
concentration
A (in time)
feces
b
assimilation
reserve
mobilisation
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 …
somatic maintenance
growth
structure
DEB
model

1-
maturity maintenance
maturation
maturity
p
reproduction
eggs
effects on
all endpoints
in time
Mixture analysis
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
effects on
all endpoints
in time
Mixture analysis
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
effects on
all endpoints
in time
Simple mixture rules
compound
‘target’
DEB parameter
maintenance costs
ingestion rate
growth costs
…
toxicity parameters linked (compare CA)
Simple mixture rules
compound
‘target’
DEB parameter
maintenance costs
ingestion rate
growth costs
…
Simple mixture rules
compound
‘target’
DEB parameter
maintenance costs
ingestion rate
growth costs
…
toxicity parameters independent (compare IA)
Mixture rules
‘same target’ and ‘different target’ are concepually
similar to CA and IA, but:
 CA and IA are prescriptions for combining doseresponse 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
reproduction
compound B
size
compound A
compound A
50% contours in time
reproduction
compound B
size
compound A
compound A
Mixture effects: simulations
• parameters for Daphnia
• ‘other target’ model (ingestion+maint.)
• plots for 21-days exposure
Contours at t=21 days
size
reproduction
50
20
30
50
20
30
5
5
5
compound B
30
50% contours in time
reproduction
t=5
compound B
size
t = 10
t = 15
t = 15
t = 21
compound A
compound A
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
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!
your mixture
data
Process-Based
Model
full data
interpretation
Strategy for data analysis
standard
DEB model
actual
DEB model
experimental
data
fit
fit not satisfactory?
mechanistic
hypothesis
other interactions?
additional
experiments
literature
educated
guesses
Parameter estimates
TK pars
tox pars
DEB pars
external
concentration
A (in time)
internal
concentration
toxico- A in time
DEB
external kinetics
parameters
internal in time
concentration
B (in time) toxico- concentration
kinetics B in time
DEB
model
effects on
all endpoints
in time
Educated extrapolation
TK pars
tox pars
DEB pars
external
concentration
A (in time)
internal
concentration
toxico- A in time
DEB
external kinetics
parameters
internal in time
concentration
B (in time) toxico- concentration
kinetics B in time
populations
DEB
model
effects on
all endpoints
in time
Educated extrapolation
TK pars
tox pars
DEB pars
external
concentration
A (in time)
internal
concentration
toxico- A in time
DEB
external kinetics
parameters
internal in time
concentration
B (in time) toxico- concentration
kinetics B in time
other endpoints
DEB
model
other, e.g.,
feeding
respiration
effects on
all endpoints
in time
Educated extrapolation
TK pars
tox pars
DEB pars
external
concentration
A (in time)
internal
concentration
toxico- A in time
DEB
external kinetics
parameters
internal in time
concentration
B (in time) toxico- concentration
kinetics B in time
DEB
model
time-varying concentrations
effects on
all endpoints
in time
Educated extrapolation
TK pars
tox pars
DEB pars
external
concentration
A (in time)
internal
concentration
toxico- A in time
DEB
external kinetics
parameters
internal in time
concentration
B (in time) toxico- concentration
kinetics B in time
food limitation
DEB
model
effects on
all endpoints
in time
Educated extrapolation
TK pars
tox pars
DEB pars
external
concentration
A (in time)
internal
concentration
toxico- A in time
DEB
external kinetics
parameters
internal in time
concentration
B (in time) toxico- concentration
kinetics B in time
related compounds
DEB
model
effects on
all endpoints
in time
Educated extrapolation
TK pars
tox pars
DEB pars
external
concentration
A (in time)
internal
concentration
toxico- A in time
DEB
external kinetics
parameters
internal in time
concentration
B (in time) toxico- concentration
kinetics B in time
other (related) species
DEB
model
effects on
all endpoints
in time
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
TK pars
tox pars
• depart from defaults (e.g., ‘add_my_pet’ or
standard animal with ‘zoom factor’)
• hopefully vary little between experiments
• depart from QSARs …
• extrapolate between species or toxicants
• at this moment, little help …
• extrapolate between species or toxicants?
Outlook
toxicant
target site
?
DEB
parameters
DEB
model
biochemistry
effect on
life cycle
DEB theory
species specific
 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)
In more detail: survival
fraction surviving
1
0.8
conc. μmol/L
0.6
0
1.33
1.84
3.32
5.81
9.25
0.4
0.2
0
0
20
40
60
time (hours)
80
100
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
Process-based
external
concentration
A (in time)
external
concentration
B (in time)
toxicokinetics
toxicokinetics
internal
concentration
A in time
internal
concentration
B in time
Tolerance distribution
• McCarty et al (1992)
• Lee & Landrum (2006)
Stochastic death
• Ashauer et al. (2007)
• Baas et al. (2007, 2009)
survival as a
chance process
survival
in time
Mortality assumption
thresholds
Tolerance
distribution
1-p
Stochastic death
t
p
x
See Newman and McClosky (2000)
t+Δt
Model Chain
external
concentration
(in time)
Simple models
information content of
standard tests is low
toxicokinetics
internal
concentration
in time
survival as a
chance process
survival
in time
Model Chain
uptake
elimination
scaled concentration
1-comp.
external
concentration
(in time)
toxicokinetics
internal
concentration
in time
external
internal
survival as a
chance process
survival
in time
time
Model Chain
external
concentration
(in time)
toxicokinetics
Assumptions:
death is a chance event for
the individual
the probability to die depends
on the internal concentration.
internal
concentration
in time
survival as a
chance process
survival
in time
Hazard modelling
0 cars/hr
10 cars/hr
20 cars/hr
50 cars/hr
Hazard rate times Δt is
the probability to get hit
by a car in that interval
surviving chickens
12
10
8
6
4
2
0
0
2
4
6
time (days)
8
Model Chain
external
concentration
(in time)
hazard rate
toxicokinetics
internal
concentration
in time
NEC
blank value
internal concentration
survival as a
chance process
survival
in time
Model Chain
external
concentration
(in time)
toxicokinetics
Straightforward statistics …
integrate hazard rate over
time and take exponential …
internal
concentration
in time
survival as a
chance process
survival
in time
Hazard modelling
scaled internal concentration
hazard rate
survival probability
time
time
NEC
time
NEC / killing rate
external concentration
elimination rate
integrate
Minnow, hexachloroethane
concentration (μmol/L)
time (hour)
fathead minnow
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
Survival in time
fraction surviving
1
elimination rate
NEC
killing rate
blank hazard
0.8
conc. μmol/L
0.6
0
1.33
1.84
3.32
5.81
9.25
0.4
0.2
0
0
20
40
60
time (hours)
80
100
0.141 hr-1
5.54 (5.26-5.68) μmol/L
0.0408 L/μmol/hr
0.000124 hr-1
Simple mixture rules
compound
‘target’
hazard rate
2 elimination rates
2 NECs
2 killing rates
hazard rates added
toxicity parameters independent (compare IA)
Simple mixture rules
compound
‘target’
hazard rate
2 elimination rates
1 NEC
1 killing rate
1 “weight factor”
Consequence:
NEC and killing rate
are not independent
weighted scaled
int. conc. added
toxicity parameters linked (compare CA)
Parameter relationships
10
4
narcotics
reactives
killing rate (mM-1h-1)
10
10
10
10
2
0
-2
-4
10
Narcotic: log b† = -1 log c0 – 0.27 (r2=0.61)
Reactive: log b† = -1 log c0 – 1.2 (r2=0.85)
-4
Jager & Kooijman (2009)
10
-2
10
NEC (mM)
0
10
2
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
Advertisement
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