Simplifying biology process-based models for toxicant effects and how to apply them

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

2. 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

3. Organisms are complex …

4. 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 …

5. Reproduction test 50-100 ml of well-defined test medium, 18-22°C

6. Reproduction test Daphnia magna Straus, <24 h old

7. Reproduction test Daphnia magna Straus, <24 h old

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

9. Reproduction test at least 5 test concentrations in geometric series …

10. Response vs. dose Response log concentration

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

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

13. 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 ...

14. 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 …

15. Complexity …

16. Complexity … Environmental chemistry …

17. Complexity … Environmental media as homogeneous boxes …

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

19. Simplifying biology? How much biological detail do we minimally need … • Too much detail …

20. Simplifying biology? How much biological detail do we minimally need … • Too little detail …

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

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

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

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

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

26. 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

27. Models (process and statistical) Models for survival

28. 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)

29. NEC hazard rate blank value (scaled) internal concentration 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 killingrate

30. 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

31. Statistical model Consider a 1-day toxicity test p1 p2 0-1 d >1 d

32. Statistical model Consider a 1-day toxicity test • assume death probabilities are independent binomial distribution p1 p2 0-1 d >1 d

33. Statistical model Consider a 2-day toxicity test p1 p2 p3 0-1 d 1-2 d >2 d

34. Statistical model Consider a 2-day toxicity test • assume death probabilities are independent multinomial distribution p1 p2 p3 0-1 d 1-2 d >2 d

35. Survival analysis Typical data set • number of live animals after fixed exposure period • example: Daphnia exposed to nonylphenol

36. Example nonylphenol 1 0.9 0.8 0.7 0.6 fraction surviving • elimination rate 0.057 (0.026-0.14) 1/hr • no-effect conc. 0.14 (0.093-0.17) mg/L • killing rate 0.66 (0.31-1.7) L/mg/d • blank hazard 0 (not fitted) 1/hr 0.5 0.004 mg/L 0.032 mg/L 0.4 0.056 mg/L 0.3 0.1 mg/L 0.18 mg/L 0.2 0.32 mg/L 0.56 mg/L 0.1 0 0 10 20 30 40 50 time (hr)

37. 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

38. Models (process and statistical) Sub-lethal endpoints

39. 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!

40. Effect on reproduction

41. Effect on reproduction

42. Effect on reproduction

43. Effect on reproduction

44. Effect on reproduction

45. 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

46. Kooijman (2010) 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 …

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

48. Different food densities Jager et al. (2005)

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

50. 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)