1. DEB theory for metabolic organisation Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thb Helsinki, 2010/03/24

2. Contents Preliminary concepts methodology Outline of basic theory for a 1-reserve, 1-structure isomorph Implications of theory body size scaling relationships Evolutionary aspects syntrophy, symbiogenesis Population consequences interactions between individuals >

3. Dynamic Energy Budget theory links levels of organization molecules, cells, individuals, populations, ecosystems scales in space and time: scale separation interplay between biology, mathematics, physics, chemistry, earth system sciences framework of general systems theory quantitative; first principles only equivalent of theoretical physics fundamental to biology; many practical applications (bio)production, medicine, (eco)toxicity, climate change for metabolic organization

4. molecule cell individual population ecosystem system earth time space Space-time scales When changing the space-time scale, new processes will become important other will become less important Individuals are special because of straightforward energy/mass balances Each process has its characteristic domain of space-time scales

5. Some DEB principles life as coupled chemical transformations life cycle perspective of individual as primary target energy & mass & time balances homeostasis stoichiometric constraints via Synthesizing Units surface area/ volume relationships spatial structure & transport synthrophy (basis for symbioses) intensive/extensive parameters: scaling evolutionary perspective

6. These gouramis are from the same nest, they have the same age and lived in the same tank Social interaction during feeding caused the huge size difference Age-based models for growth are bound to fail; growth depends on food intake : These gouramis are from the same nest, they have the same age and lived in the same tank Social interaction during feeding caused the huge size difference Age-based models for growth are bound to fail; growth depends on food intake Not age, but size: Trichopsis vittatus

7. 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 the ability to run metabolism independent of the (fluctuating) environment

8. 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

9. 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

10. Interactions of substrates

11. 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 environ food availability for daphnids: amount of algae per volume environ 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

12. 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

13. Shape correction function at volume V actual surface area at volume V isomorphic surface area at volume V = for V0-morph V1-morph isomorph Static mixtures between V0- and V1-morphs for aspect ratio V1-morphs are special because surfaces do not play an explicit role their population dynamics reduce to an unstructured dynamics; reserve densities of all individuals converge to the same value in homogeneous environments

14. Mixtures of V0 & V1 morphs 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

15. Biofilms Mixtures of iso- & V0-morphs Isomorph: V 1 = 0 V0-morph: V 1 =  mixture between iso- & V0-morph biomass grows, but surface area that is involved in nutrient exchange does not solid substrate biomass

16. Mixtures of changes in shape 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

17. Biomass: reserve(s) + structure(s) Reserve(s), structure(s): generalized compounds, mixtures of proteins, lipids, carbohydrates: fixed composition Reasons to delineate reserve, distinct from structure metabolic memory biomass composition depends on growth rate explanation of respiration patterns (freshly laid eggs don’t respire) method of indirect calorimetry fluxes are linear sums of assimilation, dissipation and growth fate of metabolites (e.g. conversion into energy vs buiding blocks) inter-species body size scaling relationships

18. Reserve vs structure Reserve does not mean: “set apart for later use” compounds in reserve can have active functions Life span of compounds in reserve: limited due to turnover of reserve all reserve compounds have the same mean life span structure: controlled by somatic maintenance structure compounds can differ in mean life span Important difference between reserve and structure: no maintenance costs for reserve Empirical evidence: freshly laid eggs consist of reserve and do not respire

19. Body size 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 Cmol 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

20. Storage 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

21. Arrhenius relationship ln rate 10 4 T -1, K -1 reproduction young/d ingestion 10 6 cells/h growth, d -1 aging, d -1 Daphnia magna

22. Arrhenius relationship 10 3 /T, K -1 ln pop growth rate, h -1 10 3 /T H 10 3 /T L r 1 = 1.94 h -1 T 1 = 310 K T H = 318 K T L = 293 K T A = 4370 K T AL = 20110 K T AH = 69490 K

23. Life stages embryojuvenileadult fertilizationbirth puberty death weaning babyinfant Essential: switch points, not periods birth: start of feeding puberty: start of allocation to reproduction Switch points sometimes in reversed order (aphids)

24. Isomorph with 1 reserve & 1 structure feeds on 1 type of food has 3 life stages (embryo, juvenile, adult) Processes: Balances: mass, energy, entropy, time Standard DEB model Extensions: more types of food and food qualities more types of reserve (autotrophs) more types of structure (organs, plants) changes in morphology different number of life stages feeding digestion maintenance storage product formation maturation growth reproduction aging

25. 1-  maturity maintenance maturity offspring maturation reproduction Standard DEB model foodfaeces assimilation reserve feeding defecation structure somatic maintenance growth 

26.  -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

27. Embryonic development time, d weight, g O 2 consumption, ml/h ;  : scaled time l : scaled length e: scaled reserve density g: energy investment ratio Crocodylus johnstoni, Data from Whitehead 1987 yolk embryo

28. Growth at constant food time, d ultimate length, mm length, mm Von Bert growth rate -1, d Von Bertalanffy growth curve:

29. Reproduction at constant food length, mm 10 3 eggs Gobius paganellus Data Miller, 1961 Rana esculenta Data Günther, 1990

30. Concept overview DEB principles not age, but size 5 types of homeostasis flux vs concentration Synthesizing Units surface area/volume iso-, V0-, V1-morphs shape correction function reserve & structure body size: weight, Cmol,.. effects of temperature life stages standard DEB model

31. Scales of life Life span 10 log a Volume 10 log m 3 earth whale bacterium water molecule life on earth whale bacterium ATP

32. Inter-species body size scaling parameter values tend to co-vary across species parameters are either intensive or extensive ratios of extensive parameters are intensive maximum body length is allocation fraction to growth + maint. (intensive) volume-specific maintenance power (intensive) surface area-specific assimilation power (extensive) conclusion : (so are all extensive parameters) write physiological property as function of parameters (including maximum body weight) evaluate this property as function of max body weight Kooijman 1986 Energy budgets can explain body size scaling relations J. Theor. Biol. 121: 269-282

33. Primary scaling relationships assimilation {J EAm } max surface-specific assim rate  L m feeding {b} surface-specific searching rate digestion y EX yield of reserve on food growth y VE yield of structure on reserve mobilization venergy conductance heating,osmosis {J ET } surface-specific somatic maint. costs turnover,activity [J EM ] volume-specific somatic maint. costs regulation,defencek J maturity maintenance rate coefficient allocation  partitioning fraction to soma egg formation  R reproduction efficiency life cycle[M H b ] volume-specific maturity at birth life cycle [M H p ] volume-specific maturity at puberty aging agingh a Weibull aging acceleration  L m agings G Gompertz stress coefficient maximum length L m =  {J EAm } / [J EM ] Kooijman 1986 J. Theor. Biol. 121: 269-282

34. Scaling of metabolic rate intra-speciesinter-species maintenance growth Respiration: contributions from growth and maintenance Weight: contributions from structure and reserve Structure ; = length; endotherms

35. Metabolic rate 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)

36. At 25 °C : maint rate coeff k M = 400 a -1 energy conductance v = 0.3 m a -1 25 °C T A = 7 kK 10 log ultimate length, mm 10 log von Bert growth rate, a -1 ↑ ↑ 0 Von Bertalanffy growth rate

37. 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

38. Evolution of central metabolism i = inverse ACS = acetyl-CoA Synthase pathway PP = Pentose Phosphate cycle TCA = TriCarboxylic Acid cycle RC = Respiratory Chain Gly = Glycolysis Kooijman & Hengeveld 2005 In: Reydon & Hemerik (eds): Current Themes in theor. biol.. Springer in prokaryotes (= bacteria) 3.8 Ga2.7 Ga

39. Prokaryotic metabolic evolution Chemolithotrophy acetyl-CoA pathway inverse TCA cycle inverse glycolysis Phototrophy: el. transport chain PS I & PS II Calvin cycle Heterotrophy: pentose phosph cycle glycolysis respiration chain

40. Symbiogenesis 2.7 Ga2.1 Ga 1.27 Ga phagocytosis

41. Resource dynamics Typical approach

42. Resource dynamics Nutrient

43. Resource dynamics Nutrient

44. Producer/consumer dynamics producer consumer nutr reserve of producer : total nutrient in closed system : hazard rate special case: consumer is not nutrient limited spec growth of consumer Kooijman et al 2004 Ecology, 85, 1230-1243

45. Producer/consumer dynamics Consumer nutrient limited Consumer not nutrient limited Hopf bifurcation Hopf bifurcation tangent bifurcation transcritical bifurcation homoclinic bifurcation

46. Producer/Consumer Dynamics Deterministic model Stochastic model in closed homogeneous system

47. Producer/Consumer Dynamics 0 2468 0 10 20 consumers nutrient 1.752.3 2.4 2.5 2.7 3.0 1.23 1.15 1.0 2.8 1.23 1.53 tangentfocus Hopf Bifurcation diagram isoclines

48. Food chains n=2 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

49. Canonical community Short time scale: Mass recycling in a community closed for mass open for energy Long time scale: Nutrients leaks and influxes Memory is controlled by life span (links to body size) Spatial coherence is controlled by transport (links to body size)

50. DEB tele course 2011 http://www.bio.vu.nl/thb/deb/ Free of financial costs; some 250 h effort investment Program for 2011: Feb/Mar general theory (5w) April course + symposium in Lisbon (2w + 3 d) 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/ 2010/03/30: 10 h DEB video-course by Roger Nisbet Cambridge Univ Press 2009 Audience : thank you for your attention