Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Population consequences of toxic effects on individuals Bremen, 2007/12/12

Contents : What is DEB theory? Individuals  populations Populations  ecosystems Toxic effects on individuals Scaling relationships Toxic effects on populations Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bremen, 2007/12/12 Population consequences of toxic effects on individuals

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

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

Isomorph with 1 reserve & 1 structure feeds on 1 type of food has 3 life stages (embryo, juvenile, adult) Processes: Balances: mass, energy, entropy, time Standard DEB model 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 feeding digestion maintenance storage product formation maturation growth reproduction aging

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

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

Individuals  Populations Populations: collections of individuals individuals follow trajectories in i-states during life cycle individual interact (e.g. competition for food) Physiologically-structured population dynamics Individuality: more important if ratio between weights of adults and neonates increases. Less important for unicellulars that divide into two daughters Population dynamics requires modelling of resources (nutrient recycling, syntrophy)

Individuals  Populations Steady state: Euler-Lotka equation specified by model specific growth rate

1-species mixotroph community 9.4 Mixotrophs are producers, which live off light and nutrients as well as decomposers, which live off organic compounds which they produce by aging Simplest community with full material cycling

1-species mixotroph community 9.4 Cumulative amounts in a closed community as function of total C, N, light E: reserve V: structure D E : reserve-detritus D V : structure-detritus rest: DIC or DIN Note: absolute amount of detritus is constant

Canonical community 9.4 Short time scale: Mass recycling in a community closed for mass open for energy Long time scale: Nutrients leaks and influxes Memory is controlled by life span (links to body size) Spatial coherence is controlled by transport (links to body size)

1-spec. vs canon. community 9.4 Total nitrogen Total carbon Total nitrogen 1-species: mixotroph community 3-species: canonical community biomass nutrient detritus biomass detritus nutrient consumer producer decomposer producer consumer Total carbon

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

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

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

Effect on assimilation CuCl 2 mg/kgtime, d weight 1/3, mg 1/3 Data from Klok & de Roos 1996 NEC = 4.45 mg CuCl2 /kg on Lumbricus rubellus

Effects on growth time, d body length, mm assimilation maintenancegrowth 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

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)

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

QSARs for tox parameters 10 log NEC, mM 10 log elim rate, d log kill rate, mM -1 d log P ow Slope = -1 Slope = 1Slope = -0.5 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

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

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

Similarities QSAR  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

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  length 2 (inter-specifically) elimination via reproduction: max reprod mass flux  length 2 (inter-specifically) chemical composition: reserve capacity  length 4 (inter-specifically) in some taxa reserve is enriched in lipids chemical transformation, excretion is coupled to metabolic rate metabolic rate scales between length 2 and length 3 juvenile period  length, abundance  length -3, pop growth rate  length -1 links with risk assessment strategies Interactions QSAR  body size scaling

0 number of daphnids Maintenance first cells.day max number of daphnids time, d 30  10 6 cells.day -1 Chlorella-fed batch cultures of Daphnia magna, 20°C neonates at 0 d: 10 winter eggs at 37 d: 0, 0, 1, 3, 1, 38 Kooijman, 1985 Toxicity at population level. In: Cairns, J. (ed) Multispecies toxicity testing. Pergamon Press, New York, pp Maitenance requirements: 6 cells.sec -1.daphnid -1

Food intake at carrying capacity cells/daphnid.d log mg V/l log mg Br/llog mg DMQ/l log mg K 2 Cr 2 O 7 /l log mg AA/llog mg Col/l 9-aminoacridine colchicine 2,6-dimethylquinoline sodium bromidemetavanadate potassium dichromate

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

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 who 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