DEB course 2013 summary of telepart Bas Kooijman

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

cell vol, m 3 glucose Escherichia coli Dictyostelium time, h X 0(0) 0. 433 mg. ml-1 X 1(0) 0. 361 X 2(0) 0. 084 mm 3. ml-1 e 1(0) 1 e 2(0) 1 - XK 1 0. 40 XK 2 0. 18 g 1 0. 86 g 2 4. 43 - k. M 1 0. 008 k. M 2 0. 16 h-1 k. E 1 0. 67 k. E 2 2. 05 h-1 j. Xm 1 0. 65 j. Xm 2 0. 26 h = 0. 064 h-1, Xr = 1 mg ml-1, 25 °C Data from Dent et al 1976 cell vol, m 3 mm 3/ml mg/ml Food chains n=2 9. 3. 1 b time, h Kooijman & Kooi, 1996 Nonlin. World 3: 77 - 83

Optical Density at 540 nm Conc. potassium, m. M Growth on reserve 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

Yield vs growth 4. 3. 1 h 1/yield, mmol glucose/ mg cells Streptococcus bovis, Russell & Baldwin (1979) Marr-Pirt (no reserve) DEB 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

Cell quota Droop’s model Droop → DEB • quota → structure + reserve • static → dynamic • include maintenance • population → individual • V 1 - → iso-morph subsistence quota 540 molecules/cell Vitamin B 12 limited growth of Monochrysis lutheri Droop 1968 J Mar Biol Assoc UK 48: 689 -733

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

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

Migration: metabolic memory 1. 1. 3 b 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 According to Dynamic Energy Budget theory: For pyruvate: w. G<0 glycerol throughput rate, h-1 Glucose-limited growth of Saccharomyces Data from Schatzmann, 1975 pyruvate, mg/l te va ru py glycerol, ethanol, g/l Product formation rate = w. A. Assimilation rate + w. M. Maintenance rate + w. G. Growth rate ethanol

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, N-waste, heat, food, faeces, … For V 1 -morphs: dissipation maintenance

Macrochemical reaction eq 3. 5

Metabolic rate 8. 2. 2 e slope = 1 0. 0226 L 2 + 0. 0185 L 3 0. 0516 L 2. 44 Log metabolic rate, w O 2 consumption, l/h 2 curves fitted: endotherms ectotherms slope = 2/3 unicellulars Length, cm Intra-species (Daphnia pulex) Data: Richman 1958; curve fitted from DEB theory Log weight, g Inter-species Data: Hemmingson 1969; 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

-rule for allocation Length, mm • 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 Age, d in juveniles? Length, mm Cum # of young Reproduction Ingestion rate, 105 cells/h O 2 consumption, g/h Respiration Ingestion Length, mm Growth: Von Bertalanffy Age, d

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

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 Mucor Ceratium V 0 -morph: surface area volume 0 Merismopedia V 1 -morph: surface area volume 1

Weight 1/3, g 1/3 diameter, m Isomorphic growth 2. 6 c Amoeba proteus Prescott 1957 Saccharomyces carlsbergensis Berg & Ljunggren 1922 time, h Weight 1/3, g 1/3 length, mm time, h Pleurobrachia pileus Greve 1971 Toxostoma recurvirostre Ricklefs 1968 time, d

volume, m 3 4. 2. 3 a Bacillus = 0. 2 Collins & Richmond 1962 time, min Fusarium = 0 Trinci 1990 time, h volume, m 3 hyphal length, mm Mixtures of V 0 & V 1 morphs Escherichia = 0. 28 Kubitschek 1990 time, min Streptococcus = 0. 6 Mitchison 1961 time, min

Mixtures of changes in shape 2 Dynamic mixtures between morphs V 1 - V 0 -morph outer annulus behaves as a V 1 -morph, inner part as a V 0 -morph. Result: diameter increases time Lichen Rhizocarpon V 1 - iso- V 0 -morph

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

Synthesizing units Are enzymes that follow classic enzyme kinetics E + S EP E + P With two modifications: back flux is negligibly small E + S 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

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

Symbiogenesis 2. 7 Ga phagocytosis 2. 1 Ga 1. 27 Ga

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 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) Many species continue to grow after reproduction has started Growth of isomorphic organisms at abundant food is well described by the von Bertalanffy The chemical composition of organisms depends on For different constant food levels the inverse von Bertalanffy growth rate increases linearly with the nutritional status (starved vs well-fed) ultimate length The chemical composition of organisms growing The von Bertalanffy growth rate of different species at constant food density becomes constant decreases almost linearly with the maximum body length Fetuses increase in weight approximately Dissipating heat is a weighted sum of 3 mass flows: proportional to cubed time CO 2, O 2 and N-waste Stoichiometry Energy Reproduction increases with size intra-specifically, but decreases with size inter-specifically

Supply-demand spectrum 1. 2. 5

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