DEB theory - past and future MPDE 2013 Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Osnabrück, 2013/08/27/09:00-09:45

Energy Budgets Processes feeding digestion storing growth maturation maintenance reproduction product formation aging Life history events zero: start of development birth: start of feeding start of acceleration metamorphosis: end of acceleration puberty: end of maturation start of reproduction Life stages embryo juvenile adult molecule  organ  individual  ecosystem  system earth Fluxes organics food, faeces, biomass minerals CO 2, H 2 O, O 2, NH 3 products wood, shells, moults heat entropy isotopes

Empirical patterns Feeding During starvation, organisms are able to reproduce, grow and survive for some time At abundant food, the feeding rate is at some maximum, independent of food density Growth Many species continue to grow after reproduction has started Growth of isomorphic organisms at abundant food is well described by the von Bertalanffy For different constant food levels the inverse von Bertalanffy growth rate increases linearly with ultimate length The von Bertalanffy growth rate of different species decreases almost linearly with the maximum body length Fetuses increase in weight approximately proportional to cubed time Reproduction Reproduction increases with size intra-specifically, but decreases with size inter-specifically Respiration Animal eggs and plant seeds initially hardly use O 2 The use of O 2 increases with decreasing mass in embryos and increases with mass in juveniles and adults The use of O 2 scales approximately with body weight raised to a power close to 0.75 Animals show a transient increase in metabolic rate after ingesting food (heat increment of feeding) Stoichiometry The chemical composition of organisms depends on the nutritional status (starved vs well-fed) The chemical composition of organisms growing at constant food density becomes constant Energy Dissipating heat is a weighted sum of 3 mass flows: CO 2, O 2 and N-waste

Food chains n=2 time, h glucose Escherichia coli Dictyostelium mg/ml mm 3 /ml cell vol,  m 3 X 0 (0)0.433mg. ml -1 X 1 (0)0.361X 2 (0)0.084mm 3.ml -1 e 1 (0)1e 2 (0)1- X K1 0.40X K g1g1 0.86g2g k M k M2 0.16h -1 k E1 0.67k E2 2.05h -1 j Xm1 0.65j Xm Data from Dent et al 1976 h = h -1, X r = 1mg ml -1, 25 °C Kooijman & Kooi,1996 Nonlin. World 3:

Growth on reserve Optical Density at 540 nm Conc. potassium, mM Potassium limited growth of E. coli at 30 °C Data Mulder 1988; DEB model fitted OD increases by factor 4 during nutrient starvation internal reserve fuels 9 hours of growth time, h

Yield vs growth 1/spec growth rate, 1/h 1/yield, mmol glucose/ mg cells Streptococcus bovis, Russell & Baldwin (1979) Marr-Pirt (no reserve) DEB spec growth rate yield Russell & Cook (1995): this is evidence for down-regulation of maintenance at high growth rates DEB theory: high reserve density gives high growth rates structure requires maintenance, reserves do not

Cell quota Droop 1968 J Mar Biol Assoc UK 48: Vitamin B 12 limited growth of Monochrysis lutheri Droop’s model subsistence quota 540 molecules/cell Droop → DEB quota → structure + reserve static → dynamic include maintenance population → individual V1- → iso-morph

Migration: metabolic memory Some populations of humpback whale Megaptera novaeangliae (36 Mg) migrate 26 Mm anually without feeding, A 15 m mother gets a 6 m calf in tropical waters, gives it 600 l milk/d for 6 months and together return to cold waters to resume feeding in summer

Product Formation throughput rate, h -1 glycerol, ethanol, g/l pyruvate, mg/l glycerol ethanol pyruvate Glucose-limited growth of Saccharomyces Data from Schatzmann, 1975 According to Dynamic Energy Budget theory: Product formation rate = w A. Assimilation rate + w M. Maintenance rate + w G. Growth rate For pyruvate: w G <0

Method of indirect calorimetry Empirical origin (multiple regression): Lavoisier 1780 Heat production = w C CO 2 -production + w O O 2 -consumption + w N N-waste production DEB-explanation: Mass and heat fluxes = w A assimilation + w D dissipation + w G growth Applies to CO 2, O 2, N-waste, heat, food, faeces, … For V1-morphs: dissipation  maintenance

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) Data: Hemmingson 1969; curve fitted from DEB theoryData: Richman 1958; curve fitted from DEB theory

Homeostasis strong constant composition of pools (reserves/structures) generalized compounds, stoichiometric contraints on synthesis weak constant composition of biomass during growth in constant environments determines reserve dynamics (in combination with strong homeostasis) structural constant relative proportions during growth in constant environments isomorphy.work load allocation thermal ectothermy  homeothermy  endothermy acquisition supply  demand systems; development of sensors, behavioural adaptations

Topological alternatives From Lika & Kooijman 2011 J. Sea Res 66:

Test of properties From Lika & Kooijman 2011 J. Sea Res, 66:

Surface area/volume interactions biosphere: thin skin wrapping the earth light from outside, nutrient exchange from inside is across surfaces production (nutrient concentration)  volume of environment food availability for cows: amount of grass per surface area environment food availability for daphnids: amount of algae per volume environment feeding rate  surface area; maintenance rate  volume (Wallace, 1865) many enzymes are only active if linked to membranes (surfaces) substrate and product concentrations linked to volumes change in their concentrations gives local info about cell size ratio of volume and surface area gives a length

Change in body shape Isomorph: surface area  volume 2/3 volumetric length = volume 1/3 V0-morph: surface area  volume 0 V1-morph: surface area  volume 1 Ceratium Mucor Merismopedia

Isomorphic growth diameter,  m Weight 1/3, g 1/3 length, mm time, h time, d Amoeba proteus Prescott 1957 Saccharomyces carlsbergensis Berg & Ljunggren 1922 Pleurobrachia pileus Greve 1971 Toxostoma recurvirostre Ricklefs 1968 Weight 1/3, g 1/3

Mixtures of V0 & V1 morphs 4.2.3a volume,  m 3 hyphal length, mm time, h time, min Fusarium  = 0 Trinci 1990 Bacillus  = 0.2 Collins & Richmond 1962 Escherichia  = 0.28 Kubitschek 1990 Streptococcus  = 0.6 Mitchison 1961

Mixtures of changes in shape Dynamic mixtures between morphs Lichen Rhizocarpon V1- V0-morph V1- iso- V0-morph outer annulus behaves as a V1-morph, inner part as a V0-morph. Result: diameter increases  time

Synthesizing units Are enzymes that follow classic enzyme kinetics E + S  ES  EP  E + P With two modifications: back flux is negligibly small E + S  ES  EP  E + P specification of transformation is on the basis of arrival fluxes of substrates rather than concentrations The concept concentration is problematic in spatially heterogeneous environments, such as inside cells In spatially homogeneous environments, arrival fluxes are proportional to concentrations

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 Kooijman & Troost 2007 Biol Rev, 82, specialization of structure 7 8 animals 6 prokaryotes 9 plants

Add_my_pet 2013/08/28: 303 species 15 phyla all 13 chordate classes survivor function

Allocation to soma pop growth rate, d -1 max reprod rate, #d -1 Frequency distribution of κ among species in the add_my_pet collection: Mean κ = 0.81, but optimum is κ = 0.5 Lika et al 2011, Kooijman & Lika 2013 J. Sea Res, 22: , Biol Rev, subm

Selection for reproduction White Leghorn Red Jungle fowl Indian River broiler Kooijman & Lika 2013 Am Nat subm

Waste to hurry Exploiting blooming resources requires blooming yourself high numerical response short life cycle small body size fast reproduction fast growth high feeding rate resting stages between blooms  -rule explains why [p M ] needs to be high Ecosystem significance: flux through basis food pyramid Kooijman 2013 Oikos 122:

Standard DEB model: growth Rhizoprionodon acutus milk shark

Embryonic development time, d weight, g O 2 consumption, ml/h Crocodylus johnstoni, Data: Whitehead 1987 yolk embryo time, d

Metabolic acceleration Def: long-term increase of respiration relative to standard DEB expectation Types acceleration of maturation (allocation) type X acceleration: food type A acceleration: assimilation type M acceleration: morph type T acceleration: temperature Short-term increase in respiration (no metabolic acceleration) heat increment of feeding boosts of activity migration pregnancy/ lactation

Ctenophora Cnidaria Tunicata Leptocardii Echinodermata Mixini Cephalaspidorphi Chondrichthyes Actinopterygii Amphibia Reptilia Aves Mammalia Chaetognatha Rotifera Gastrotricha Platyhelminthes Annelida Mollusca Tardigrada Nematoda Crustacea Arachnida Enthognatha Insecta Sarcopterygii Deuterostomia Ecdysozoa Lophotrochozoa Platyzoa Radiata Anthocephala Bryozoa Type M acceleration acceleration factor Kooijman 2013 Biol. Rev. subm

Hemimetabolic insect ontogeny Acyrthosiphon pisum pea aphid Locusta migratoria migratory locust Embryo: isomorph Juvenile: V1-morph Adult: no growth °C

Maturity thresholds Radiata Bilateria Platyzoa Lophotrochozoa Ecdyspzoa Invert deuterostomes Ectothermic vert Endothermic vert birth metam puberty Open symbols: acceleration

Growth rates Radiata Bilateria Platyzoa Lophotrochozoa Ecdyspzoa Invert deuterostomes Ectothermic vert Endothermic vert Kooijman & Lika 2013 Proc R Soc B subm birth metam puberty Open symbols: acceleration

Bijection data - parameter space Assumptions abundant food temperature constant water content of E = that of V zero surface linked som maint zero Gompertz stress Known mol-weights of E & V chem potentials of E & V maturity maint rate coeff growth efficiency reproduction efficiency

Supply-demand spectrum controls of energetics: environmental → internal

Supply-demand spectrum

Future DEB research Add_my_pet: taxon-specific patterns application in evolution, ecology, conservation, technology More-reserve/structure systems: nutrition, plants, behavioural ecology Molecular level interaction biochemical modules on basis of mutual syntrophy Ecosystem level canonical community, body size spectra

DEB tele course Free of financial costs; Some 108 or 216 h effort investment Program for 2015: Feb/Mar general theory (5w: 02/19-03/26) April symposium in Marseille (F) (8d +3 d: 04/13-24) 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 2009 Audience : thank you for your attention