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Scaling Relationships Based on Partition Coefficients & Body Size

This article explores the similarities and interactions between scaling relationships based on partition coefficients and body size. It discusses toxicokinetic models, one-compartment models, toxic effects, DEB theory, QSARs, and the implications of body size scaling and interactions.

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Scaling Relationships Based on Partition Coefficients & Body Size

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  1. Scaling relationships based onpartition coefficients & body size have similarities & interactions Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thb/ Lyon, 2006/05/10

  2. Contents • toxicokinetic models • one-compartment, film • toxic effects • DEB theory • QSARs • body size scaling • similarities • interactions Lyon, 2006/05/10

  3. 1-compartment model For a given external concentration as function of time:

  4. 1,1-compartment model medium i interface medium j compound can cross interface between media with different rates vice versa

  5. 1,1 compartment model and Suppose while Conclusion: relationship between par values follows from model structure

  6. n,n-compartment models compound can cross interface between media with different rates vice versa sub-layers with equal rates for all sub-layers

  7. film models Steady flux approximation Kooijman et al 2004 Chemosphere57: 745-753

  8. Elimination rate & partition coeff diffusivities low high 1 film 2 film log 10% saturation time slope = 0.5 slope = 0.5 log P01 log P01 Transition: film  1,1-compartment model Kooijman et al 2004 Chemosphere57: 745-753

  9. Concentration ranges of chemicals • too little • def: variations in concentration come with variations in effects • enough • def: variations in concentration within this range hardly affect • physiological behaviour of individuals • too much • def: variations in concentration come with variations in effects • e.g. water concentration can be too much even for fish • no basic difference between toxic and non-toxic chemicals • “too little” and “enough” can have zero range for some chemicals • Implication: lower & upper NEC for each compound

  10. Effects on organisms • Chemicals, parasites, noise, temperature affect organisms • via changes of parameters values of their dynamic energy budget • these values are functions of internal concentrations • Primary target: individuals • some effects at sub-organism level can be compensated (NEC) • Effects on populations are derived from that on individuals • individuals interact via competition, trophic relationships • Parameters of the energy budget model individual-specific • and (partly) under genetic control

  11. Models for toxic effects • Three model components: • kinetics • external concentration  internal concentration • example: one-compartment kinetics • change in target parameter(s) • internal concentration  value of target parameter(s) • example: linear relationship • physiology • value of parameter  endpoint (survival, reproduction) • example: DEB model

  12. Dynamic Energy Budget theoryfor metabolic organisation • Uptake of substrates (nutrients, light, food) • by organisms and their use (maintenance, growth, • development, reproduction) during life cycle (dynamic) • First principles, quantitative, axiomatic set up • Aim: Biological equivalent of Theoretical Physics • Primary target: the individual with consequences for • sub-organismal organization • supra-organismal organization • Relationships between levels of organisation • Many popular empirical models are special cases of DEB

  13. defecation feeding food faeces assimilation reserve somatic maintenance maturity maintenance  1- maturation reproduction growth maturity offspring structure Standard DEB scheme • Def “standard”: • 1 type of food • 1 type of reserve • 1 type structure • isomorphy

  14. assimilation  maintenance costs defecation feeding food faeces growth costs assimilation reproduction costs reserve  hazard to embryo somatic maintenance  7 maturity maintenance  1-  maint tumour induction 6 maturation reproduction u endocr. disruption growth 7  lethal effects: hazard rate Mode of action affects translation to pop level 8 maturity offspring structure tumour 6 Modes of action of toxicants

  15. Change in target parameter Simplest basis: Change  internal conc that exceeds internal NEC or with • Rationale • effective molecules • operate independently • approximation • for small effects

  16. Effect on survival Effects of Dieldrin on survival of Poecilia killing rate 0.038 l g-1 d-1 elimination rate 0.712 d-1 NEC 4.49 g l-1 • Hazard model for survival: • one compartment kinetics • hazard rate linear in internal concentration

  17. QSARs for tox parameters Slope = -0.5 Slope = 1 Slope = -1 10log elim rate, d-1 10log kill rate, mM-1 d-1 10log NEC, mM 10log Pow 10log Pow 10log Pow Assumption: Each molecule has same effect Alkyl benzenes in Pimephales Data from Geiger et al 1990 • Hazard model for survival: • one compartment kinetics • hazard rate linear in internal concentration

  18. QSARs for tox parameters Slope = -0.5 Slope = 1 Slope = -1 10log elim rate, d-1 10log kill rate, mM-1 d-1 10log NEC, mM 10log Pow 10log Pow 10log Pow Benzenes, alifates, phenols in Pimephales Data from Mackay et al 1992, Hawker & Connell 1985 Assumption: Each molecule has same effect • Hazard model for survival: • one compartment kinetics • hazard rate linear in internal concentration

  19. Covariation of tox parameters Slope = -1 10log NEC, mM 10log killing rate, mM-1 d-1 Pimephales Data from Gerritsen 1997

  20. QSARs for LC50’s 10log LC50.14d, M 10log Pow 10log Pow LC50.14d of chlorinated hydrocarbons for Poecilia. Data: Könemann, 1980

  21. Primary scaling relationships Dependent on max size K saturation constant Lb length at birth Lp length at puberty {pAm} max spec assim rate Independent of max size yEX yield of reserve on food v energy conductance [pM] volume-spec maint. costs {pT} surface-spec maint. costs [EG] spec structure costs ha aging acceleration  partitioning fraction R reproduction efficiency maximum length Lm =  {pAm} / [pM] Kooijman 1986 J. Theor. Biol.121: 269-282

  22. Scaling of metabolic rate Respiration: contributions from growth and maintenance Weight: contributions from structure and reserve Structure ; = length; endotherms

  23. Metabolic rate slope = 1 Log metabolic rate, w O2 consumption, l/h 2 curves fitted: endotherms 0.0226 L2 + 0.0185 L3 0.0516 L2.44 ectotherms slope = 2/3 unicellulars Log weight, g Length, cm Intra-species Inter-species (Daphnia pulex)

  24. Von Bertalanffy growth rate 25 °C TA = 7 kK 10log von Bert growth rate, a-1 10log ultimate length, mm 10log ultimate length, mm At 25 °C : maint rate coeff kM = 400 a-1 energy conductance v = 0.3 m a-1 ↑ ↑ 0

  25. SimilaritiesQSAR  body size scaling 1-compartment model: partition coefficient (= state) is ratio between uptake and elimination rate DEB-model: maximum length (= state) is ratio between assimilation and maintenance rate Parameters are constant for a system, but vary between systems in a way that follows from the model structure

  26. InteractionsQSAR  body size scaling • uptake, elimination fluxes, food uptake  surface area (intra-specifically) • elimination rate  length-1 (exposure time should depend on size) • food uptake  structural volume (inter-specifically) • dilution by growth affects toxicokinetics • max growth  length2 (inter-specifically) • elimination via reproduction: max reprod mass flux  length2 (inter-specifically) • chemical composition: reserve capacity  length4 (inter-specifically) • in some taxa reserve are enriched in lipids • chemical transformation, excretion is coupled to metabolic rate • metabolic rate scales between length2 and length3 • juvenile period  length, abundance  length-3 , pop growth rate  length-1 • links with risk assessment strategies

  27. DEB tele course 2007 Cambridge Univ Press 2000 http://www.bio.vu.nl/thb/deb/ Free of financial costs; some 250 h effort investment Feb-April 2007; target audience: PhD students We encourage participation in groups that organize local meetings weekly French group of participants of the DEB tele course 2005: special issue of J. Sea Res. 2006 on DEB applications to bivalves Software package DEBtool for Octave/ Matlab freely downloadable Slides of this presentation are downloadable from http://www.bio.vu.nl/thb/users/bas/lectures/ Audience: thank you for your attention Organizers: thank you for the invitation

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