Dynamic Energy Budget theory

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 models 8 Co-variation of par values 9 Living together 10 Evolution 11 Evaluation

2. Body size 3.2 • length: depends on shape and choice (shape coefficient) • volumetric length: cubic root of volume; does not depend on shape • contribution of reserve in lengths is usually small • use of lengths unavoidable because of role of surfaces and volumes • weight: wet, dry, ash-free dry • contribution of reserve in weights can be substantial • easy to measure, but difficult to interpret • C-moles (number of C-atoms as multiple of number of Avogadro) • 1 mol glucose = 6 C-mol glucose • useful for mass balances, but destructive measurement • Problem: with reserve and structure, body size becomes bivariate • We have only indirect access to these quantities

3. Body composition 3.2a

4. Ash-Free-Dry/Wet Weight 3.2b Relevance for energetics: dry mass ↔ wet volume

5. Growth efficiency 3.2.c

6. Storage 3.3.2 Plants store water and carbohydrates, Animals frequently store lipids Many reserve materials are less visible specialized Myrmecocystus serve as adipose tissue of the ant colony

7. Storage 3.3.2a Anthochaera paradoxa (yellow wattlebird) fattens up in autumn to the extent that it can’t fly any longer; Biziura lobata (musk duck) must starve before it can fly

8. Macrochemical reaction eq 3.5

9. Notation for isotopes 3.6

10. Reshuffling 3.6a

11. Fractionation from pools & fluxes 3.6b • Examples • uptake of O2, NH3, CO2(phototrophs) • evaporation of H2O • Mechanism • velocity e = ½ m c2 • binding probability to carriers • Examples • anabolic vs catabolic aspects • assimilation, dissipation, growth • Mechanism • binding strength in decomposition

12. Fractionation from pools & fluxes 3.6c

13. Oxygenic photosynthesis 3.6d CO2 + 2 H2O CH2O + H2O + O2 Reshuffling of 18O Fractionation of 13C

14. C4 plants 3.6e • Fractionation • weak in C4 plants • strong in C3 plants

15. Macrochemical reaction eq 3.6f

16. Isotopes in products 3.6g • Product flux: fixed fractions of assimilation, dissipation, growth • Assumptions: • no fractionation at separation from source flux • separation is from anabolic sub-flux catabolic flux product flux anabolic flux reserve structure

17. Change in isotope fractions 3.6h For mixed pool j = E, V (reserve, structure) For non-mixed product j = o (otolith)

18. Isotopes in biomass & otolith 3.6i body length temperature f,e time, d time, d time, d 0.001 0.001 body length time, d otolith length time, d 0.001 0.001 0.001 opacity otolith length otolith length otolith length otolith length

19. Flux vs Concentration 3.7 • 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

20. Enzyme kinetics 3.7a Uncatalyzed reaction Enzyme-catalyzed reaction

21. Synthesizing units 3.7b • Generalized enzymes that process generalized substrates • and 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 • In spatially homogeneous environments: • arrival fluxes  concentrations

22. Transformation A → B 3.7e Classification of behavioural modes: free & bound or searching & handling Michealis-Menten (Henri 1902) Holling type II (Holling 1957)

23. Simultaneous Substrate Processing 3.7c production production Chemical reaction: 1A + 1B 1C Poisson arrival events for molecules A and B blocked time intervals • acceptation event ¤ rejection event Kooijman, 1998 Biophys Chem 73: 179-188

24. SU kinetics: n1X1+n2X2X3.7d product release product release time 0 tb tc binding prod. cycle Period between subsequent arrivals is exponentially distributed Sum of exponentially distributed vars is gamma distributed Production flux not very sensitive for details of stoichiometry Stoichiometry mainly affects arrival rates

25. Enzyme kinetics A+BC 3.7.2 Synthesizing Unit Rejection Unit

26. almost single substr limitation at low conc’s Isoclines for rate A+BC 3.7.2a .2 .6 .8 .2 .4 .6 .8 .4 Conc B Conc A Conc A Rejection Unit Synthesizing Unit

27. Interactions of substrates 3.7.3 • Substrate interactions in DEB theory are based on Synthesizing Units (SUs): • generalized enzymes that follow the rules of classic enzyme kinetics but • working depends in fluxes of substrates, rather than concentrations • “concentration” only has meaning in homogeneous environments • backward fluxes are small in S + E  SE  EP  E + P • Basic classification • substrates: substitutable vs complementary • processing: sequential vs parellel • Mixture between substitutable & complementary substrates: • grass  cow; sheep brains  cow; grass + sheep brains  cow • Dynamics of SU on the basis of time budgetting • offers framework for foraging theory • example: feeding in Sparus larvae (Lika, Can J Fish & Aquat Sci, 2005): • food searching sequential to mechanic food handling • food processing (digestion) parellel to searching & handling • gives deviations from Holling type II high low low

28. Interactions of substrates 3.7.3a

29. Interactions of substrates 3.7.3b Kooijman, 2001 Phil Trans R Soc B 356: 331-349

30. Competition & inhibition 3.7.4d

31. Inhibition 3.7.4 A does not affect B in yACAC; B inhibits binding of A A inhibits binding of B in yACAC; B inhibits binding of A unbounded fraction binding prob of A arrival rate of A dissociation rate of A yield of C on A

32. Aggressive competition 3.7.4a V structure;E reserve; M maintenance substrate priority E  M; posteriority V  M JE flux mobilized from reserve specified by DEB theory JV flux mobilized from structure  amount of structure (part of maint.) excess returns to structure kV dissociation rate SU-V complex kE dissociation rate SU-E complex kV kE depend on  such that kM = yMEkE(E. + EV)+yMVkV .V is constant JEM, JVM kV = kE JEM, JVM kV < kE JE

33. Social inhibition of x  e 3.7.4b sequential parallel substrate conc. No socialization x substrate e reserve y species 1 z species 2 Implications: stable co-existence of competing species “survival of the fittest”? absence of paradox of enrichment biomass conc. dilution rate

34. Evolution & Co-existence 3.7.4c • Main driving force behind evolution: • Darwin: Survival of the fittest (internal forces) • involves out-competition argument • Wallace: Selection by environment (external forces) • consistent with observed biodiversity • Mean life span of typical species: 5 - 10 Ma • Sub-optimal rare species: • not going extinct soon (“sleeping pool of potential response”) • environmental changes can turn rare into abundant species • Conservation of bio-diversity: • temporal and spatial environmental variation • mutual syntrophic interactions • feeding rates not only depends on food availability (social interaction)

35. Co-metabolism 3.7.5 Consider coupled transformations A  C and B  D Binding probability of B to free SU differs from that to SU-A complex

36. Co-metabolism 3.7.5a binding prob. for substr A

37. Co-metabolism 3.7.5b Co-metabolic degradation of 3-chloroaniline by Rhodococcus with glucose as primary substrate Data from Schukat et al, 1983 Brandt et al, 2003 Water Research 37, 4843-4854

38. Co-metabolism 3.7.5c Co-metabolic anearobic degradation of citrate by E. coli with glucose as primary substrate Data from Lütgens and Gottschalk, 1980 Brandt, 2002 PhD thesis VU, Amsterdam

39. Metabolic modes 3.8.1 CO2 NH3 H2O iron bacterium Gallionella Example of chemolithotrophy 10 H2O O2 4 Fe2+ 4 Fe(OH)3 8 H+ Remember this when you look at your bike/car 4 H2O 4 H2 220 g iron  430 g rust + 1 g bact. 4 Fe

40. Modules of central metabolism 3.8.2 • Pentose Phosphate (PP) cycle • glucose-6-P ribulose-6-P, • NADP NADPH • Glycolysis • glucose-6-P pyruvate • ADP + P ATP • TriCarboxcyl Acid (TCA) cycle • pyruvate CO2 • NADP NADPH • Respiratory chain • NADPH + O2 NADP + H2O • ADP + P ATP

41. Central metabolism 3.8.2a • Adenosine Tri-Phosphate (ATP) • 5 106 molecule in 1 bacterial cell • 2 seconds of synthetic work • mean life span: 0.3 seconds

42. Central Metabolism 3.8.2b source polymers monomers waste/source

43. Assumptions of auxiliary theory 3.9 • A well-chosen physical length  (volumetric) structural length for isomorphs • Volume, wet/dry weight have contributions from structure, reserve, reproduction buffer • Constant specific mass & volume of structure, reserve, reproduction buffer • Constant chemical composition of juvenile growing at constant food

44. Compound parameters 3.9a

45. 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 models 8 Co-variation of par values 9 Living together 10 Evolution 11 Evaluation