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DEB theory - past and future MPDE 2013

DEB theory - past and future MPDE 2013. Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thb. Osnabr ück , 2013/08/27/09:00-09:45. Energy Budgets. Processes feeding digestion storing growth maturation maintenance

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DEB theory - past and future MPDE 2013

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  1. DEB theory - past and futureMPDE 2013 Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thb Osnabrück, 2013/08/27/09:00-09:45

  2. Energy Budgets • Processes • feeding • digestion • storing • growth • maturation • maintenance • reproduction • product formation • aging Life stages embryo juvenile adult • 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 • Fluxes • organics • food, faeces, biomass • minerals • CO2, H2O, O2, NH3 • products • wood, shells, moults • heat • entropy • isotopes molecule organindividual ecosystemsystem earth

  3. 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 O2 The use of O2 increases with decreasing mass in embryos and increases with mass in juveniles and adults The use of O2 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: CO2, O2 and N-waste

  4. Food chains n=2 glucose mg/ml Escherichia coli mm3/ml cell vol, m3 h = 0.064 h-1, Xr = 1mg ml-1, 25 °C Data from Dent et al 1976 Dictyostelium mm3/ml cell vol, m3 Kooijman & Kooi,1996 Nonlin. World3: 77 - 83 time, h time, h

  5. Growth on reserve Conc. potassium, mM Optical Density at 540 nm time, h 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

  6. Yield vs growth Streptococcus bovis, Russell & Baldwin (1979) Marr-Pirt (no reserve) DEB 1/yield, mmol glucose/ mg cells spec growth rate yield 1/spec growth rate, 1/h 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

  7. Cell quota Droop’s model • Droop → DEB • quota → structure + reserve • static → dynamic • include maintenance • population → individual • V1- → iso-morph subsistence quota 540 molecules/cell Vitamin B12 limited growth of Monochrysis lutheri Droop 1968 J Mar Biol Assoc UK48: 689-733

  8. 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

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

  10. Method of indirect calorimetry Empirical origin (multiple regression): Lavoisier 1780 Heat production = wC CO2-production + wO O2-consumption + wN N-waste production DEB-explanation: Mass and heat fluxes = wA assimilation + wD dissipation + wG growth Applies to CO2, O2, N-waste, heat, food, faeces, … For V1-morphs: dissipation  maintenance

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

  12. 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

  13. Topological alternatives From Lika & Kooijman 2011 J. Sea Res 66: 381-391

  14. Test of properties From Lika & Kooijman 2011 J. Sea Res, 66: 381-391

  15. 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

  16. Change in body shape Isomorph: surface area  volume2/3 volumetric length = volume1/3 Mucor Ceratium Merismopedia V0-morph: surface area  volume0 V1-morph: surface area  volume1

  17. Isomorphic growth diameter, m Weight1/3, g1/3 Amoeba proteus Prescott 1957 Saccharomyces carlsbergensis Berg & Ljunggren 1922 time, h time, h Weight1/3, g1/3 Toxostoma recurvirostre Ricklefs 1968 length, mm Pleurobrachia pileus Greve 1971 time, d time, d

  18. Mixtures of V0 & V1 morphs 4.2.3a volume, m3 hyphal length, mm Bacillus  = 0.2 Collins & Richmond 1962 Fusarium  = 0 Trinci 1990 time, min time, h volume, m3 volume, m3 Escherichia  = 0.28 Kubitschek 1990 Streptococcus  = 0.6 Mitchison 1961 time, min time, min

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

  20. 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

  21. 3 4 5 1 2 prokaryotes 7 plants 9 animals 6 8 Evolution of DEB systems variable structure composition strong homeostasis for structure increase of maintenance costs delay of use of internal substrates inernalization of maintenance installation of maturation program strong homeostasis for reserve Kooijman & Troost 2007 Biol Rev, 82, 1-30 reproduction juvenile  embryo + adult specialization of structure

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

  23. 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: 278-288, Biol Rev, subm

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

  25. Kooijman 2013 Oikos122: 348-357 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 • [pM] needs to be high • Ecosystem significance: • flux through basis food pyramid

  26. Standard DEB model: growth Rhizoprionodon acutus milk shark

  27. Embryonic development Crocodylus johnstoni, Data: Whitehead 1987 embryo yolk O2 consumption, ml/h weight, g time, d time, d

  28. 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

  29. Platyhelminthes Arachnida Nematoda Crustacea Anthocephala Gastrotricha Ecdysozoa Platyzoa Tardigrada Rotifera Enthognatha Bryozoa Insecta Lophotrochozoa Annelida Mollusca Chaetognatha Echinodermata Tunicata Ctenophora Mammalia Amphibia Mixini Deuterostomia Cnidaria Leptocardii Radiata Sarcopterygii Aves Cephalaspidorphi Reptilia Actinopterygii Chondrichthyes 1 2 5 10 Type M acceleration acceleration factor Kooijman 2013 Biol. Rev. subm

  30. Hemimetabolic insect ontogeny °C 30 27 21 24 18 Acyrthosiphon pisum pea aphid Locusta migratoria migratory locust Embryo: isomorph Juvenile: V1-morph Adult: no growth

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

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

  33. 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

  34. Supply-demand spectrum controls of energetics: environmental → internal

  35. Supply-demand spectrum

  36. Supply-demand spectrum

  37. 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

  38. DEB tele course 2015 http://www.bio.vu.nl/thb/deb/ 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 http://www.bio.vu.nl/thb/users/bas/lectures/ Cambridge Univ Press 2009 Audience: thank you for your attention

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