1. Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 Metabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of compounds 7 Extensions of DEB modelsExtensions of DEB models 8 Co-variation of par values 9 Living together 10 Evolution 11 Evaluation

2. Linear pathway 7.1.1 SU i SU i+1 : Product i : Intermediary metabolite i = If all metabolites would follow the full pathway:

3. Chain of length 1 7.1.1a Change in Unbounded fraction Steady state Unbounded fraction Production flux

4. Closed handshaking at all nodes 7.1.1b Change in Unbounded fractions Steady state Unbounded fractions Production fluxes

5. Open handshaking at all nodes 7.1.1c Change in Unbounded fractions Steady state Unbounded fractions Production fluxes

6. General handshaking 7.1.1d Change in Unbounded fractions Steady state Unbounded fractions Production fluxes Rejection fluxes

7. Trans-stage feeding strategies 7.2 Juvenile mayflies (Emphemeroptera) cover all adult needs for food; Adult’s digestive system is filled with air Adult Anoplius viaticus collects all food (here Trochosa terricola) for the juvenile stage of the next generation; the adult feeds on nectar

8. Food deposits 7.2.1 Melanerpes formicivorus (acorn woodpecker) stores acorns & beech-mast in crevices (upto 60000) from hundreds of km around its residence

9. Farming: external storage 7.2.1a Ambrosia beetles garden fungi under tree bark, and some have special structures in their head, mycangia, to transport the fungus The gardener-nurse caste of leafcutter ants garden fungi under ground, transplanting them onto fresh substrate and weeding out wrong species of fungus The social amoeba Dictyostelium carries bacteria in their multi-cellular slug-stage and inoculate fresh stubstrate with them

10. Fast/slow substrate uptake 7.2.2 DEB-consistent variant of Morel 1987 uptake depends on substrate concentration and reserve density reserve mobilization independent of uptake Not yet tested against experimental data

11. Short vs long-term nutrient uptake 7.2.2a Morel 1987 on nutrient uptake in algae Variant that is consistent with DEB/Droop

12. Satiation-driven feeding 7.2.3 Suppose that satiation s is a system variable which increases instantaneously with an amount s X upon feeding on a food particle decays exponentially at rate k S during starvation Feeding occurs when a food particle arrives, while satiation s(t) < 1 The resulting feeding rate is numerically well described by Doucet, 2003 The H-response: A satiation-driven functional response (not published) Extendable to more food types, preferences are set by type-specific satiation thresholds

13. Functional surface area 7.2.5 Heliozoans and foraminiferans have threat- like extensions of protoplasm on which they take up food particles functional surface area depends on feeding rate relative to ratio of moving rate and thickness of stagnant water mantle

14. Diffusion limitation 7.2.5b distance from membrane substrate concentration Uptake rate: saturation constants substrate conc., - at membr max uptake rate 0 generally: mantle thickness

15. External digestion 7.2.6 Yield metab on enzyme time, h conc enzyme, metab distance from cell, mm solitary feeding social feeding social feeding strategy solitary intracellular metab profile t = ∞

16. Moving gut 7.3 From: Mader, S. S. 1993 Biology, WCB Sleigh, M. 1989 Protozoa, E. Arnold, London Feeding vacuoles of ciliates travel from the cell mouth to the cell anus, where the feaces is excreted. These vacuoles can be considered as a moving gut. Paramecium, Tetrahymena (Ciliophora)

17. Digestive system 7.3a time input, output time input, output time input, output completely stirred reactor plugflow reactor both reactors in series stomach model gut model Stomach good in buffering residence times exponentially distributed many short times, few large ones Gut bad in buffering residence time constant digestion requires some time

18. Social inhibition of X  E 3.7.4b sequential parallel dilution rate substrate conc. biomass conc. No socialization Implications: stable co-existence of competing species “survival of the fittest”? absence of paradox of enrichment X substrate E reserve Y species 1 Z species 2

19. Mitochondria 7.6 Transformations: 1 Oxaloacetate + Acetyl CoA + H 2 O = Citrate + HSCoA 2 Citrate = cis-Aconitrate + H 2 O 3 cis-Aconitrate + H 2 O = Isocitrate 4 Isocitrate + NAD + = α-Ketoglutarate + CO 2 + NADH + H + 5 α-Ketoglutarate + NAD + + HSCoA = Succinyl CoA + CO 2 + NADH + H + 6 Succinyl CoA + GDP 3- + P i 2- + H + = Succinate + GTP 4- + HSCoA 7 Succinate + FAD = Fumarate + FADH 2 8 Fumarate + H 2 O = Malate 9 Malate + NAD + = Oxaloacetate + NADH + H + TriCarboxylic Acid cycle Enzymes pass metabolites directly to other enzymes Enzymes catalizing transformations 5 and 7 are linked to the inner membrane (and FAD/FADH 2 ) All enzymes are linked into a metabolon Net transformation: Acetyl CoA + 3 NAD + + FAD + GDP 3- + P i 2- + 2 H 2 O = 2 CO 2 + 3 NADH + FADH 2 + GTP 4- + 2 H + + HSCoA

20. Dilemma of pathway enzymes 7.6b Many metabolites have a dual function: building block for synthesis of functional units substrate to generation of energy (ATP) or reducing power (NADH, NADPH) Cell’s need for building blocks depends on variable growth rate Problem: How is cell’s need “known” by enzyme molecules of pathway? Example of competing needs: growth versus maintenance Kooijman & Segel 2005 How growth affects the fate of cellular substrates. Bull Math Biol 67: 57-77

21. Pathway  whole cell 7.6c Fixed stoichiometries for maintenance and growth Variable overall stoichiometry Can a model for pathway kinetics give this result?

22. Constraints on pathway dynamics 7.6d Amount of SU i per mol of structure: Supply flux to pathway: metabolite i enzyme i rejection, production flux spec maintenance flux spec growth rate yield coefficients (fixed) reserve density M E /M V abundance of X 0 in E abundance of S i in E, V Requirements by cell for maintenance and growth:

23. Pathways & allocation 7.6e reserve maintenance structure Mixture of products & intermediary metabolites that is allocated to maintenance (or growth) has constant composition Kooijman & Segel 2005

24. Diauxic growth 7.9.4a time, h biomass conc., OD 433 acetate oxalate Substrate conc., mM Growth of acetate-adapted Pseudomonas oxalaticus OX1 data from Dijkhuizen et al 1980 SU-based DEB curves fitted by Bernd Brandt Adaptation to different substrates is controlled by: enzyme turnover 0.15 h -1 preference ratio 0.5 cells Brandt, 2002 PhD thesis VU, Amsterdam

25. Numerical matching for n=4 7.6f Product flux Rejected flux Unbound fraction  = 0.73, 0.67, 0.001, 0.27 handshaking  = 0.67, 0.91, 0.96, 0.97 binding prob k = 0.12, 0.19, 0.54, 0.19 dissociation n SE = 0.032,0.032,0.032,0.032 # in reserve n SV = 0.045,0.045,0.045,0.045 # in structure y EV = 1.2 res/struct k E = 0.4 res turnover j EM = 0.02 maint flux n 0E = 0.05 sub in res 0 0 1 1 1 2 2 2 3 3 3 4 4 Spec growth rate

26. Matching pathway  whole cell 7.6g No exact match possible between production of products and intermediary metabolites by pathway and requirements by the cell But very close approximation is possible by tuning abundance parameters and/or binding and handshaking parameters Good approximation requires all four tuning parameters per node growth-dependent reserve abundance plays a key role in tuning Kooijman and Segel 2005

27. Aging in adult insects 7.8.1 age after eclosion, d surviving number # of eggs/beetle, d -1 Drosophila melanogaster Notiophilus biguttatus Data: Rose 1984 Data: Ernsting & Isaaks, 1991 High food, 20/10 °C 0.63 a -2 High food, 10 °C 0.547 a -2 Low food, 20/10 °C 0.374 a -2 survival based on observed reproduction No growth initial random mort Weibull Model  =3

28. Metabolic acceleration 7.8.2 Def: long-term increase of respiration relative to standard DEB expectation Types of acceleration R: maturation X: food A: assimilation M: morph T: temperature Short-term increase in respiration (no metabolic acceleration) heat increment of feeding boosts of activity migration pregnancy/ lactation

29. Type R acceleration 7.8.2a Change in allocation to boost maturation Increase in respiration Decrease in growth Hit maturity threshold earlier at smaller size Mueller et al 2012, Comp. Biochem. Physiol. A 163: 103-110

30. Type R acceleration 7.8.2b indirect direct acceleration development no yes Pseudophryne bibronii Geocrinia vitellina Crinia georgiana Crinia nimbus

31. Type R acceleration 7.8.2c Mueller et al 2012, Comp. Physiol. Biochem. A, 163:103-110 Crinia georgiana Pseudophryne bibronii age, d hatch birth max dry weight 500 mg max dry weight 200 mg 12 °C metam

32. Type X acceleration 7.8.2d Def: increase of food intake during ontogeny, but no change in potential food intake Known examples concern change in food type

33. Type X acceleration 7.8.2e Caenorhabditis elegans Byerly et al 1976 Developmental Biol. 51: 23-33. Perca fluviatilis Persson et al 2004 Ecol. Mon. 74: 135–157 organic compounds → bacteria zooplankton → fish

34. Type A acceleration 7.8.2f Def: increase of potential food intake during ontogeny, but no change in mobilisation Known examples concern sex dimorphy Increase in reserve capacity

35. Type A acceleration 7.8.2g Doryteuthis pealei longfin inshore squid Mirounga leonina southern elephant seal

36. Type M acceleration 7.8.2h Def: increase of potential food intake during ontogeny, combined with increase in potential mobilisation Increase of specific assimilation {p Am } and energy conductance v with length from birth to metamorphosis No change in reserve capacity One-parameter extension of standard DEB model: maturity level at metamorphosis Applies to all species with morphological metamorphosis, but also to some taxa without

37. 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 12510 Sarcopterygii Deuterostomia Ecdysozoa Lophotrochozoa Platyzoa Radiata Anthocephala Bryozoa

38. Anchovy Engraulis encrasicolus 7.8.2i time, d length, cm 0.16 cm 0.22 cm 0.4 cm 0.9 cm 1.2 cm >4 cm embryo Pecquerie 2008 PhD thesis VU A’dam

39. Stage transitions at maturity thresholds Danio rerio 28.5°C Augustine et al 2011 Comp. Biochem. Physiol. A 159 :275–283 7.8.2j

40. Stage transitions at maturity thresholds Augustine et al 2011 Comp. Biochem. Physiol. A 159 :275–283 Danio rerio 28.5°C Data: Lauwrence et al 2008 caloric restriction Data: Augustine < birth : isomorph birth-metamorphosis: V1-morph > metamorphosis : isomorph 7.8.2k

41. Hemimetabolic insect ontogeny 7.8.2l Acyrthosiphon pisum pea aphid Locusta migratoria migratory locust Embryo: isomorph Juvenile: V1-morph Adult: no growth 3027 24 21 18 °C

42. Maturity thresholds 7.8.2m Radiata Bilateria Platyzoa Lophotrochozoa Ecdyspzoa Invert deuterostomes Ectothermic vert Endothermic vert birth metam puberty Open symbols: acceleration

43. Growth rates 7.8.2n 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

44. Type T acceleration 7.8.2o Def: increase of all rates due to ontogenetic increase in body temperature of endotherms Mostly confined to birds. Embryos are ectothermic Neonate heating capacity not sufficient to maintain target temperature

45. Type T acceleration 7.8.2p t-T and t-L curves fitted simultaneously t-T inferred from t-L curve

46. Stagnation of development 7.8.2q The axolotl, Ambystoma mexicanum, does not loose its gills due to lack of jodium and so to synthesize a particular hormone it can reproduce, however, despite its larval appearence

47. Adaptation 7.9.3 glucose, mg/l specific growth rate, h -1 “wild type” Schulze & Lipe, 1964 glucose-adapted Senn, 1989 Glucose-limited growth of Escherichia coli 70 mg/l 0.06 mg/l max.5 max many types of carriers only carriers for glucose

48. Adaptation 7.9.4 Batch culture, Monod special case Model elements: uptake of substrate by specific carriers carrier densities n A and n B metabolic signals from uptake  f i n i relative signal s A = p A f A n A /  i p i f i n i carrier production by SUs that are fed by relative signals that inhibit reciprocally carriers have a common turnover rate Result: Expression fraction  0 asymptotically in absence of substrate biomass density substrate i conc scaled func response saturation coeff for i yield of biom on substr spec growth rate max spec growth rate on i expression fraction for i carrier turnover rate preference ratio Brandt et al, 2004 Water Research, 38, 1003 - 1013

49. Diauxic growth 7.9.4b biomass conc., OD 590 Growth of succinate-adapted Azospirillum brasilense intracellular amounts followed with radio labels data from Mukherjee & Ghosh 1987 Adaptation to different substrates is controlled by: enzyme turnover 0.7 h -1 preference ratio 0.8 time, h fructose conc, mM succinate conc, mM succinate fructose cells suc in cells fruc in cells Brandt, 2002 PhD thesis VU, Amsterdam

50. Adaptation in degradation 7.9.4.c time, h Kooijman & Troost 2007 Biol Rev 82: 1-30 concentration, g/l -- E. coli -- fumarate -- pyruvate -- E. coli -- fumarate -- glucose Active pyruvate carriers suppress expression of fumarate carriers Active glucose carriers don’t suppress expression of fumarate carriers

51. Dynamic Energy Budget theory 1 Basic ConceptsBasic Concepts 2 Standard DEB modelStandard DEB model 3 MetabolismMetabolism 4 Univariate DEB modelsUnivariate DEB models 5 Multivariate DEB modelsMultivariate DEB models 6 Effects of compoundsEffects of compounds 7 Extensions of DEB modelsExtensions of DEB models 8 Co-variation of par valuesCo-variation of par values 9 Living togetherLiving together 10 EvolutionEvolution 11 EvaluationEvaluation