1. DEB course 2013 summary of tele-part Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thb Texel 2013/04/15

2. Food chains n=2 9.3.1b 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 K2 0.18 g1g1 0.86g2g2 4.43- k M1 0.008k M2 0.16h -1 k E1 0.67k E2 2.05h -1 j Xm1 0.65j Xm2 0.26 Data from Dent et al 1976 h = 0.064 h -1, X r = 1mg ml -1, 25 °C Kooijman & Kooi,1996 Nonlin. World 3: 77 - 83

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

4. Yield vs growth 4.3.1h 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

5. Cell quota Droop 1968 J Mar Biol Assoc UK 48: 689-733 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

6. Embryonic development 2.6.2d time, d weight, g O 2 consumption, ml/h Crocodylus johnstoni, Data: Whitehead 1987 yolk embryo time, d

7. Storage Plants store water and carbohydrates, Animals frequently store lipids Many reserve materials are less visible specialized Myrmecocystus serves as adipose tissue for the ant colony

8. Migration: metabolic memory 1.1.3b 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

9. 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

10. Method of indirect calorimetry 4.8.2 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

11. Macrochemical reaction eq 3.5

12. Metabolic rate 8.2.2e 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 0.0226 L 2 + 0.0185 L 3 0.0516 L 2.44 2 curves fitted: (Daphnia pulex) Data: Hemmingson 1969; curve fitted from DEB theoryData: Richman 1958; curve fitted from DEB theory

13. 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

14.  -rule for allocation Age, d Length, mm Cum # of young Length, mm Ingestion rate, 10 5 cells/h O 2 consumption,  g/h large part of adult budget to reproduction in daphnids puberty at 2.5 mm No change in ingest., resp., or growth Where do resources for reprod. come from? Or: What is fate of resources in juveniles? Respiration  Ingestion  Reproduction  Growth: Von Bertalanffy

15. 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  -rule explains why [p M ] needs to be high Ecosystem significance: flux through basis food pyramid Kooijman 2013 Oikos 122: 348-357

16. 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

17. 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

18. Isomorphic growth 2.6c 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

19. 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

20. Mixtures of changes in shape 2 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

21. Flux vs Concentration concept “concentration” implies spatial homogeneity (at least locally) biomass of constant composition for intracellular compounds concept “flux” allows spatial heterogeneity classic enzyme kinetics relate production flux to substrate concentration Synthesizing Unit kinetics relate production flux to substrate flux in homogeneous systems: flux  conc. (diffusion, convection) concept “density” resembles “concentration” but no homogeneous mixing at the molecular level density = ratio between two amounts

22. 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

23. 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, 1-30 543 21 specialization of structure 7 8 animals 6 prokaryotes 9 plants

24. Symbiogenesis 2.7 Ga2.1 Ga 1.27 Ga phagocytosis

25. 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

26. Supply-demand spectrum 1.2.5

27. Energy Budgets Basic processes Feeding Digestion Storing Growth Maturation Maintenance Reproduction Product formation Aging All have ecological implications All interact during the life cycle