Tjalling Jager Dept. Theoretical Biology Simplifying biology process-based models for toxicant effects and how to apply them TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA A AA A

Contents Introduction  Dealing with complexity  Toxicokinetics-toxicodynamic modelling Models (process and statistical)  Dealing with survival  Dealing with sub-lethal effects Wrapping up  (Brief history of things called “DEBtox”)  Concluding remarks

Organisms are complex …

Stressing organisms … … only adds to the complexity  Response to a toxic stress depends on –type of toxicant –organism (species, life stage, etc.) –endpoint (survival, reproduction, etc.) –exposure duration and intensity –environmental conditions  How is this dealt with in ecotoxicology? –standardisation …

Reproduction test ml of well- defined test medium, 18-22°C

Reproduction test Daphnia magna Straus, <24 h old

Reproduction test Daphnia magna Straus, <24 h old

Reproduction test wait for 21 days, and count total offspring …

Reproduction test at least 5 test concentrations in geometric series …

Response vs. dose Response log concentration

Contr. Response vs. dose NOEC Response log concentration LOEC * 1. Statistical testing

Response vs. dose EC50 Response log concentration 1. Statistical testing 2. Curve fitting

If EC50 is the answer … … what was the question? “What is the concentration of chemical X that leads to 50% effect on the total number of offspring of Daphnia magna (Straus) after 21-day constant exposure under standardised laboratory conditions?”  Is this an interesting question? –scientifically: no –for risk assessment...

Practical challenge of RA  Some 100,000 man-made chemicals  For animals, >1 million species described  Exposure conditions are not standardised … –multiple stress is the norm –exposed individuals are different –complex dynamic exposure situations We cannot test all these situations …

Complexity …

Environmental chemistry … Complexity …

Environmental media as homogeneous boxes … Complexity …

Simplifying biology? How much biological detail do we minimally need …

Simplifying biology? How much biological detail do we minimally need …  Too much detail …

Simplifying biology? How much biological detail do we minimally need …  Too little detail …

Simplifying biology? How much biological detail do we minimally need …  Focus on general mechanisms …

external concentration (in time) toxico-kinetic model toxico-kinetic model TKTD modelling internal concentration in time process model for the organism process model for the organism effects on endpoints in time toxicokinetics toxicodynamics

external concentration (in time) toxico-kinetic model toxico-kinetic model TKTD modelling internal concentration in time toxicokinetics

TKTD modelling internal concentration in time process model for the organism process model for the organism effects on endpoints in time toxicodynamics Endpoints of interest:  survival  growth  reproduction ……

independent variable observed variable To apply TKTD models... we also need a model for the deviations  Least-squares is immensely popular...

The statistical model does not receive same amount of attention as process models  Reasons: –many modellers never work with experimental data –modellers don’t like/know statistics –statisticians don’t like/know realistic models

Models (process and statistical) Models for survival

Why do animals die? Observation: –not all animals die at the same time in a treatment Why?  Stochasticity –individuals are random selection from heterogeneous population –death itself should be treated as a stochastic process  Competing hypotheses –although both may play a role –see “GUTS” (Jager et al., 2011)

Survival TKTD A process model can be extremely simple! Assume: –death is a chance process at the level of the individual –there is an internal concentration threshold for effects –above the threshold, probability to die increases linearly (scaled) internal concentration hazard rate blank value NEC killing rate

What about the statistics? Least squares? –independent random errors following a continuous (normal) distribution?  Not a good match: –discrete number of survivors –bounded between zero and 100% –number of survivors are dependent observations

Statistical model Consider a 1-day toxicity test p1p1 p2p2 0-1 d>1 d

Statistical model Consider a 1-day toxicity test –assume death probabilities are independent p1p1 p2p2 0-1 d>1 d binomial distribution

Statistical model Consider a 2-day toxicity test p1p1 p2p2 p3p3 0-1 d1-2 d>2 d

Statistical model Consider a 2-day toxicity test –assume death probabilities are independent p1p1 p2p2 p3p3 0-1 d1-2 d>2 d multinomial distribution

Survival analysis Typical data set –number of live animals after fixed exposure period –example: Daphnia exposed to nonylphenol mg/L0 h24 h48 h

Example nonylphenol time (hr) fraction surviving mg/L mg/L mg/L 0.1 mg/L 0.18 mg/L 0.32 mg/L 0.56 mg/L elimination rate0.057 ( )1/hr no-effect conc.0.14 ( ) mg/L killing rate0.66 ( ) L/mg/d blank hazard0(not fitted)1/hr elimination rate0.057 ( )1/hr no-effect conc.0.14 ( ) mg/L killing rate0.66 ( ) L/mg/d blank hazard0(not fitted)1/hr

Summary survival  Process models can be extremely simple –assume that death is a chance process –starts with 3 parameters  Statistical model provides a good match –multinomial distribution

Models (process and statistical) Sub-lethal endpoints

Simplifying biology How do we deal with growth and reproduction? –these are not outcome of chance processes … –we cannot be species- or stressor-specific Organisms obey mass and energy conservation!

Effect on reproduction

Energy Budget To understand effect on reproduction … –we have to consider how food is turned into offspring Challenge –find the simplest set of rules... –over the entire life cycle... –similar rules for all organisms

Quantitative theory for metabolic organisation from ‘first principles’ –time, energy and mass balance –consistent with thermodynamics Life-cycle of the individual –links levels of organisation –molecule  ecosystems Fundamental, but many practical applications –(bio)production, (eco)toxicity, climate change, evolution … Kooijman (2010) DEB theory

eggs mobilisation Standard DEB animal structure somatic maintenance  growth maturity maintenance 1-  reproduction maturity buffer maturation p foodfeces assimilation reserve b 3-4 states 8-12 parameters system can be scaled to remove dimension ‘energy’ 3-4 states 8-12 parameters system can be scaled to remove dimension ‘energy’

Different food densities Jager et al. (2005)

Toxicant effects in DEB external concentration (in time) toxico- kinetics toxico- kinetics internal concentration in time DEB parameters in time DEB model DEB model repro growth survival feeding hatching … over entire life cycle Affected DEB parameter has specific consequences for life cycle

Toxicant case study  Marine polychaete Capitella (Hansen et al, 1999) –exposed to nonylphenol in sediment –body volume and egg production followed Jager and Selck (2011)

Control growth  Volumetric body length in control time (days) volumetric body length (mm) 0

Control growth Assumption –effective food density depends on body size time (days) volumetric body length (mm) 0

Control growth time (days) volumetric body length (mm) 0 Assumption –initial starvation …

Control reproduction  Ignore reproduction buffer … time (days) cumulative offspring per female 0

NP effects  Compare the control to the first dose

“Hormesis”  Requires a mechanistic explanation … –organism must obey conservation of mass and energy Potential assumptions –decreased investment elsewhere –toxicant relieves a secondary stress –toxicant increases the food availability/quality

NP effects Assumption –NP increases food density/quality

NP effects Assumption –NP affects costs for making structure

Standard DEB animal structure foodfeces maturity maintenancesomatic maintenance assimilation  1-  growth reproduction maturity buffer maturation reserve mobilisation eggs

NP effects Assumption –NP also affects costs for maturation and reproduction

Standard DEB animal structure foodfeces maturity maintenancesomatic maintenance assimilation  1-  growth reproduction maturity buffer maturation reserve mobilisation eggs

Classical strategy data analysis fit satisfactory? descriptive model curve experimental data least squares report EC50 yes

DEB strategy data analysis fit satisfactory? optimise actual DEB model experimental data additional experiments literature educated guesses mechanistic hypothesis affected parameter(s) think summarise conclusions yes DEB theory hypothesis

Strategy for data analysis Are we sure we have the correct explanation? Occam’s razor  Accept the simplest explanation … for now generate predictions actual DEB model test predictions

Statistical model Common assumptions leading to least-squares:  Time is “certain”  Normal errors  Equal variances  Independent errors time observed variable

Body size Individuals are not the same –example: parameters vary between individuals time body length

Body size Behaviour is stochastic –example: food encounter is a chance process time body length

Fitting reproduction Model –energy flux for eggs (J/d) –egg costs (J/egg) –buffer handling... Observations –numbers of eggs in an interval (eggs) –often only mean available … reproduction buffer eggs First … –ignore buffer –repro rate (eggs/d)

Fitting reproduction Cumulative plot... –observations become highly dependent... –what error distribution is appropriate? time cumulative eggs

Fitting reproduction eggs in interval time Per observation interval... –less dependence in observations

Fitting reproduction Is this a bad fit? –not necessarily, when there is a repro buffer... –individuals might spawn at different times... time cumulative eggs

Example Folsomia candida time (d) cubic root wet weight (g 1/3 ) time (d) cumulative offspring  Fit on individuals: –cumulative reproduction per female … –exclude time points with zero reproduction …  Body size and reproduction not independent …

How do we proceed?  Follow individuals over time, in detail –body size over time –timing of spawning events –investment per offspring …  Resolve questions... –between individuals: how variable are parameters? how do parameters co-vary? –within individuals: role of stochastic behaviour? linkage between endpoints?

In the meantime... Don’t throw out the baby with the bath water!  Process models are valuable... How bad is it to assume normal independent errors?  That depends on... –homogeneity of the test population –reproduction buffer size –purpose of the study –...  Confidence intervals suffer most

Wrapping up A short history of DEB in ecotoxicology skip

1984  Chemicals affect the energy budget... –effects on individuals leads to effects on populations

1993  First DEB book... –with a chapter on ecotoxicity  ISO/OECD revision of guidelines in early 90’s

1996  DEBtox software and booklet in 1996 –and 5 papers in open literature –used/adapted by a number of groups

Standard DEB animal structure foodfeces maturity maintenancesomatic maintenance assimilation  1-  growth reproduction maturity buffer maturation reserve mobilisation eggs

mobilisation Simplified DEB animal structure somatic maintenance  growth maturity maintenance 1-  reproduction maturitybuffer maturation p foodfeces assimilation reserve 1-comp. toxicokinetics

Kooijman (2010) 2010  Full DEB model for toxicants –more possible mechanisms of action –more parameters...

2012  Revisiting the simple model... –available data sets do not allow full DEB model –many questions do not need a ful DEB model

Concluding remarks 1  Eco(toxico)logy needs idealisations of biology –TKTD models: survival only: unified in GUTS sub-lethal endpoints: DEB offers platform –much more work is needed!  TKTD requires appropriate statistical models –least-squares is not generally appropriate  For sub-lethal data... –deviations do not represent random error differences between individuals stochastic behaviour (feeding/spawning)

Concluding remarks 2 Current status of TKTD  The use of TKTD models in ecotoxicology is... –rare in scientific settings –absent in risk assessment settings  Ecotoxicology focusses on descriptions...

More information on DEBtox/GUTS: on DEB: Courses –Summercourse TKTD modelling Denmark 2012 –International DEB Tele Course 2013 Symposia –2nd International DEB Symposium 2013 on Texel (NL)