Simplifying biology processbased models for toxicant effects and

Simplifying biology process-based models for toxicant effects and how to apply them Tjalling Jager Dept. Theoretical Biology

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

Organisms are complex …

Stressing organisms … … only adds to the complexity Ø 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 Ø How is this dealt with in ecotoxicology? – standardisation …

Reproduction test 50 -100 ml of welldefined test medium, 18 -22°C

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 log concentration

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

Response vs. dose Response 1. Statistical testing 2. Curve fitting EC 50 log concentration

If EC 50 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? ” Ø Is this an interesting question? – scientifically: no – for risk assessment. . .

Practical challenge of RA Ø Some 100, 000 man-made chemicals Ø For animals, >1 million species described Ø 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 …

Complexity … Environmental chemistry …

Complexity … Environmental media as homogeneous boxes …

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

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

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

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

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

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

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

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

The statistical model. . . does not receive same amount of attention as process models Ø 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? Ø Stochasticity – individuals are random selection from heterogeneous population – death itself should be treated as a stochastic process Ø Competing hypotheses – although both may play a role – see “GUTS” (Jager et al. , 2011)

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

What about the statistics? Least squares? – independent random errors following a continuous (normal) distribution? Ø 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 p 1 p 2 0 -1 d >1 d

Statistical model Consider a 1 -day toxicity test – assume death probabilities are independent binomial distribution p 1 p 2 0 -1 d >1 d

Statistical model Consider a 2 -day toxicity test p 1 p 2 p 3 0 -1 d 1 -2 d >2 d

Statistical model Consider a 2 -day toxicity test – assume death probabilities are independent multinomial distribution p 1 p 2 p 3 0 -1 d 1 -2 d >2 d

Survival analysis Typical data set – number of live animals after fixed exposure period – example: Daphnia exposed to nonylphenol mg/L 0 h 24 h 48 h 0. 004 20 20 20 0. 032 20 20 20 0. 056 20 20 20 0. 100 20 20 20 0. 180 20 20 16 0. 320 20 13 2 0. 560 20 2 0

Example nonylphenol 1 0. 004 mg/L 0. 032 mg/L 0. 056 mg/L 0. 18 mg/L 0. 32 mg/L 0. 56 mg/L fraction surviving 0. 9 0. 8 0. 7 0. 6 0. 5 0. 4 0. 3 0. 2 elimination rate no-effect conc. killing rate blank hazard 0. 057 0. 14 0. 66 0 (0. 026 -0. 14) (0. 093 -0. 17) (0. 31 -1. 7) (not fitted) 0. 1 0 0 10 20 30 time (hr) 40 50 1/hr mg/L L/mg/d 1/hr

Summary survival Ø Process models can be extremely simple – assume that death is a chance process – starts with 3 parameters Ø 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

DEB theory 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)

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

Different food densities Jager et al. (2005)

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

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

Control growth Ø Volumetric body length in control volumetric body length (mm) 3 2. 5 2 0 1. 5 1 0. 5 0 0 10 20 30 40 50 time (days) 60 70 80

Control growth Assumption – effective food density depends on body size volumetric body length (mm) 3 2. 5 2 0 1. 5 1 0. 5 0 0 10 20 30 40 50 time (days) 60 70 80

Control growth Assumption – initial starvation … volumetric body length (mm) 3 2. 5 2 0 1. 5 1 0. 5 0 0 10 20 30 40 50 time (days) 60 70 80

Control reproduction Ø Ignore reproduction buffer … cumulative offspring per female 3500 3000 2500 2000 1500 0 1000 500 0 0 10 20 30 40 50 time (days) 60 70 80

NP effects Ø Compare the control to the first dose

“Hormesis” Ø 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 food feces assimilation reserve mobilisation somatic maintenance growth structure 1 - maturation maturity maintenance reproduction buffer eggs

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

Standard DEB animal food feces assimilation reserve mobilisation somatic maintenance growth structure 1 - maturation maturity maintenance reproduction buffer eggs

Classical strategy data analysis descriptive model curve experimental data least squares fit satisfactory? s ye report EC 50

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

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

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

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

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

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 … First … – ignore buffer – repro rate (eggs/d) reproduction buffer eggs

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

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

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

Example Folsomia candida Ø Fit on individuals: – cumulative reproduction per female … – exclude time points with zero reproduction … 0. 07 350 0. 06 300 cumulative offspring cubic root weight (g 1/3) Ø Body size and reproduction not independent … 0. 05 0. 04 0. 03 0. 02 200 150 100 50 0. 01 0 250 0 20 40 60 time (d) 80 0 0 5 10 15 20 25 time (d) 30 35 40

How do we proceed? Ø Follow individuals over time, in detail – body size over time – timing of spawning events – investment per offspring … Ø 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! Ø Process models are valuable. . . How bad is it to assume normal independent errors? Ø That depends on. . . – – homogeneity of the test population reproduction buffer size purpose of the study. . . Ø Confidence intervals suffer most

Wrapping up A short history of DEB in ecotoxicology skip

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

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

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

Standard DEB animal food feces assimilation reserve mobilisation somatic maintenance growth structure 1 - maturation maturity maintenance reproduction buffer eggs

Simplified DEB animal food feces assimilation 1 -comp. toxicokinetics reserve mobilisation somatic maintenance growth structure 1 - maturation maturity maintenance p reproduction buffer eggs

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

2012 Ø 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 Ø 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! Ø TKTD requires appropriate statistical models – least-squares is not generally appropriate Ø For sub-lethal data. . . – deviations do not represent random error • differences between individuals • stochastic behaviour (feeding/spawning)

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

More information on DEBtox/GUTS: http: //www. debtox. info on DEB: http: //www. bio. vu. nl/thb Courses – Summercourse TKTD modelling Denmark 2012 – International DEB Tele Course 2013 Symposia – 2 nd International DEB Symposium 2013 on Texel (NL)