Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam DEB theory & ecotox applications Lyon, 2008/09/19

Contents : What is DEB theory? Evolution & body size scaling Unexpected links & reconstructions Applications of DEB theory Effects of chemical compounds Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Lyon, 2008/09/19 DEB theory & ecotox applications

Dynamic Energy Budget theory consists of a set of consistent and coherent assumptions uses framework of general systems theory links levels of organization scales in space and time: scale separation quantitative; first principles only equivalent of theoretical physics interplay between biology, mathematics, physics, chemistry, earth system sciences fundamental to biology; many practical applications for metabolic organization

Research strategy 1) use general physical-chemical principles to develop an educated quantitative expectation for the eco-physiological behaviour of a generalized species 2) estimate parameters for any specific case compare the values with expectations from scaling relationships deviations reveal specific evolutionary adaptations 3) study deviations from model expectations learn about the physical-chemical details that matter in this case but had to be ignored because they not always apply Deviations from a detailed generalized expectation provide access to species-specific (or case-specific) modifications

Empirical special cases of DEB yearauthormodelyearauthormodel 1780Lavoisier multiple regression of heat against mineral fluxes 1950Emerson cube root growth of bacterial colonies 1825Gompertz Survival probability for aging 1951Huggett & Widdas foetal growth 1889Arrhenius temperature dependence of physiological rates 1951Weibull survival probability for aging 1891Huxley allometric growth of body parts 1955Best diffusion limitation of uptake 1902Henri Michaelis--Menten kinetics 1957Smith embryonic respiration 1905Blackman bilinear functional response 1959Leudeking & Piret microbial product formation 1910Hill Cooperative binding 1959Holling hyperbolic functional response 1920Pütter von Bertalanffy growth of individuals 1962Marr & Pirt maintenance in yields of biomass 1927Pearl logistic population growth 1973Droop reserve (cell quota) dynamics 1928Fisher & Tippitt Weibull aging 1974Rahn & Ar water loss in bird eggs 1932Kleiber respiration scales with body weight 3/ Hungate digestion 1932Mayneord cube root growth of tumours 1977Beer & Anderson development of salmonid embryos DEB theory is axiomatic, based on mechanisms not meant to glue empirical models Since many empirical models turn out to be special cases of DEB theory the data behind these models support DEB theory This makes DEB theory very well tested against data DEB theory reveals when to expect deviations from these empirical models

Individual  Ecosystem population dynamics is derived from properties of individuals + interactions between them evolution according to Darwin: variation between individuals + selection material and energy balances: most easy for individuals individuals are the survival machines of life

Evolution of DEB systems variable structure composition strong homeostasis for structure delay of use of internal substrates increase of maintenance costs inernalization of maintenance installation of maturation program strong homeostasis for reserve reproduction juvenile  embryo + adult 8 Kooijman & Troost 2007 Biol Rev, 82, 1-30

Standard DEB model Isomorph with 1 reserve & 1 structure feeds on 1 type of food has 3 life stages (embryo, juvenile, adult) Extensions : more types of food and food qualities more types of reserve (autotrophs) more types of structure (organs, plants) changes in morphology different number of life stages

Primary scaling relationships assimilation {J EAm } max surface-specific assim rate  L m feeding {b} surface- specific searching rate digestion y EX yield of reserve on food growth y VE yield of structure on reserve mobilization venergy conductance heating,osmosis {J ET } surface-specific somatic maint. costs turnover,activity [J EM ] volume-specific somatic maint. costs regulation,defencek J maturity maintenance rate coefficient allocation  partitioning fraction egg formation  R reproduction efficiency life cycle[M H b ] volume-specific maturity at birth life cycle [M H p ] volume-specific maturity at puberty aging h a aging acceleration maximum length L m =  {J EAm } / [J EM ] Kooijman 1986 J. Theor. Biol. 121:

Metabolic rate Log weight, g Log metabolic rate, w endotherms ectotherms unicellulars slope = 1 slope = 2/3 Length, cm O 2 consumption,  l/h Inter-species Intra-species L L L curves fitted: (Daphnia pulex)

DEB theory reveals unexpected links Length, mm O 2 consumption, μl/h 1/yield, mmol glucose/ mg cells 1/spec growth rate, 1/h Daphnia Streptococcus respiration  length in individual animals & yield  growth in pop of prokaryotes have a lot in common, as revealed by DEB theory Reserve plays an important role in both relationships, but you need DEB theory to see why and how

Otolith growth & opacity standard DEB model: otolith is a product otolith growth has contributions from growth & dissipation (= maintenance + maturation + reprod overheads) opacity  relative contribution from growth DEB theory allows reconstruction of functional response from opacity data as long as reserve supports growth Reconstruction is robust for deviations from correct temperature trajectory Laure Pecquerie 2007: reading the otolith

Otolith opacity  Functional response time, d otolith length,  m opacity temp correction reserve density functional response Laure Pecquerie 2007: reading the otolith body length, cm

Applications of DEB theory bioproduction: agronomy, aquaculture, fisheries pest control biotechnology, sewage treatment, biodegradation (eco)toxicology, pharmacology medicine: cancer biology, obesity, nutrition biology global change: biogeochemical climate modeling conservation biology; biodiversity economy; sustainable development Fundamental knowledge of metabolic organisation has many practical applications

Biology based methods Effects based on internal concentrations One compartment accumulation-elimination Hazard rate or physiological target parameter is linear in internal concentration (small effects only) Dynamic Energy Budget theory is used to identify potential target parameters translate change in parameter to change in endpoint Interaction of compounds in mixture  product of internal concentrations similar to analysis of variance

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

Effects on growth time, d body length, mm assimilation maintenance growth Triphenyltin on Folsomia candida at 20°C indirect effects direct effects , 0, 64,139 mg kg -1 body length, mm

Effects on reproduction time, d cum # offspring/♀ assimilation maintenance growth cost/offspring hazard Phenol on Daphnia magna at 20°C indirect effects direct effects , 320 mg L -1

Population effects can depend on food density Population growth of rotifer Brachionus rubens at 20˚C for different algal concentrations 3,4-dichloroaniline direct effect on reproduction potassium metavanadate effect on maintenance

Suppose that the elimination rate is large  internal conc is fast at equilibrium, hazard rate is constant Conclusion : effect on survival  concentration  exposure time well known in pharmacology desinfection of buildings, green houses Hazard model

Effect on survival for single compound Effects of Dieldrin on survival of Poecilia NEC 4.49  g l -1 killing rate l  g -1 d -1 elimination rate d -1

Effect on survival for mixture Model for survival in time for a binary mixture: 8 parameters in total using data for all observation times control mortality rate, interaction parameter 2  (NEC, killing rate, elimination rate) Model tested for 6 binary mixtures of metals (Cu, Cd, Pb & Zn) on Folsomia candida (Collembola) Survival measurements daily for 21 days 6  6 concentrations 22  6  6 = 792 data points for each mixture

Data: Bart van Houte Theory: Bas Kooijman Fit: Jan Baas Movie: Jorn Bruggeman Interaction Cu,Cd, Pb, Zn: Cu & Pb: slightly antagonistic Other combinations: nill Folsomia candida Cd & Cu  survival of Folsomia

DEB tele course Free of financial costs; some 250 h effort investment Program for 2009: Feb/Mar general theory April symposium in Brest (2-3 d) Sept/Oct case studies & applications Target audience: PhD students We encourage participation in groups that organize local meetings weekly Software package DEBtool for Octave/ Matlab freely downloadable Slides of this presentation are downloadable from Cambridge Univ Press 2000 Audience : thank you for your attention Organizers : thank you for the invitation