1. Metabolic organisation of cells as basis for ecological phenomena Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thbhttp://www.bio.vu.nl/thb/ München, 2006/10/24

2. Contents introduction surface-volume interactions homeostasis & reserve heat & metabolism single reserve systems multiple reserve systems body size scaling producer-consumer dynamics München, 2006/04/25

3. Dynamic Energy Budget theory for metabolic organisation Uptake of substrates (nutrients, light, food) by organisms and the use of these substrates (maintenance, growth, development, reproduction) First principles, quantitative, axiomatic set up Aim: Biological equivalent of Theoretical Physics Primary target: the individual with consequences for sub-organismal organization supra-organismal organization Relationships between levels of organisation Many popular empirical models are special cases of DEB

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. Empirical special cases of DEB yearauthormodelyearauthormodel 1780Lavoisier multiple regression of heat against mineral fluxes 1950Emerson cube root growth of bacterial colonies 1825Gompertz Survival probability for aging 1951Huggett & Widdas foetal growth 1889Arrhenius temperature dependence of physiological rates 1951Weibull survival probability for aging 1891Huxley allometric growth of body parts 1955Best diffusion limitation of uptake 1902Henri Michaelis--Menten kinetics 1957Smith embryonic respiration 1905Blackman bilinear functional response 1959Leudeking & Piret microbial product formation 1910Hill Cooperative binding 1959Holling hyperbolic functional response 1920Pütter von Bertalanffy growth of individuals 1962Marr & Pirt maintenance in yields of biomass 1927Pearl logistic population growth 1973Droop reserve (cell quota) dynamics 1928Fisher & Tippitt Weibull aging 1974Rahn & Ar water loss in bird eggs 1932Kleiber respiration scales with body weight 3/ 4 1975Hungate digestion 1932Mayneord cube root growth of tumours 1977Beer & Anderson development of salmonid embryos DEB theory is axiomatic, based on mechanisms not meant to glue empirical models Since many empirical models turn out to be special cases of DEB theory the data behind these models support DEB theory This makes DEB theory very well tested against data

6. Some DEB pillars life cycle perspective of individual as primary target embryo, juvenile, adult (levels in metabolic organization) life as coupled chemical transformations (reserve & structure) time, energy, entropy & mass balances surface area/ volume relationships (spatial structure & transport) homeostasis (stoichiometric constraints via Synthesizing Units) syntrophy (basis for symbioses, evolutionary perspective) intensive/extensive parameters: body size scaling

7. 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

8. 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 growing in length only

9. 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

10. 1-  maturity maintenance maturity offspring maturation reproduction Standard DEB scheme foodfaeces assimilation reserve feeding defecation structure somatic maintenance growth 

11. measured quantities  primary pars Standard DEB model (isomorph, 1 reserve, 1 structure) reserve & maturity: hidden variables measured for 2 food levels primary parameters

12. Homeostasis Homeostasis: constant body composition in varying environments Strong homeostasis  generalized compounds applies to reserve(s) and structure(s) separately Weak homeostasis: ratio reserve/structure becomes and remains constant if food or substrate is constant (while the individual is growing) applies to juvenile and adult stages, not to embryos Structural homeostasis: suborganismal structures have a constant relative size

13. Biomass: reserve(s) + structure(s) Reserve(s), structure(s): generalized compounds, mixtures of proteins, lipids, carbohydrates: fixed composition Compounds in reserve(s): equal turnover times, no maintenance costs structure: unequal turnover times, maintenance costs Reasons to delineate reserve, distinct from structure metabolic memory explanation of respiration patterns (freshly laid eggs don’t respire) biomass composition depends on growth rate fluxes are linear sums of assimilation, dissipation and growth basis of method of indirect calorimetry explanation of inter-species body size scaling relationships

14. Reserve dynamics Follows from weak homeostasis partitionability requirement [p C ] is first degree homogeneous in [E] Mechanism structural homeostasis reserve mobilization  reserve-structure interface mobilized reserve arrives at SU’s for somatic maintenance & growth maintenance is a demand process, growth a supply process rejected mobilized reserve returns to reserve  -rule follows from competing SU’s for maturity maint. & maturation dilution by growth

15. 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

16. Indirect calorimetry Empirical finding (Lavoisier, 1780): heat dissipation = weighted sum of O 2, CO 2, N-waste fluxes Explanation by DEB theory : Mass & energy balances show that dissipating heat, and all mineral and organic fluxes are weighted sums of 3 basic energy fluxes (assimilation, maintenance, growth) Empirical finding for many micro-organisms : heat dissipation  O 2 flux DEB theory : offers constraints on elemental composition of reserve relative to structure involving chemical potentials of minerals and organic (generalized) compounds gives expression for proportionality factor

17. Biomass composition Data Esener et al 1982, 1983; Kleibsiella on glycerol at 35°C n HW n OW n NW O2O2 CO 2 Spec growth rate, h -1 Spec growth rate Spec growth rate, h -1 Relative abundance Spec prod, mol.mol -1.h -1 Weight yield, mol.mol -1 n HE 1.66 n OE 0.422 n NE 0.312 n HV 1.64 n OV 0.379 n NV 0.189 k E 2.11 h -1 k M 0.021 h -1 y EV 1.135 y XE 1.490 r m 1.05 h -1 g = 1 μ E -1 pApA pMpM pGpG JCJC 0.14 1.00-0.49 JHJH 1.15 0.36-0.42 JOJO -0.35-0.97 0.63 JNJN -0.31 0.31 0.02 Entropy J/C-mol.K Glycerol69.7 Reserve74.9 Structure 52.0 Sousa et al 2004 Interface, subm

18. Product Formation throughput rate, h -1 glycerol, ethanol, g/l pyruvate, mg/l glycerol ethanol pyruvate Glucose-limited growth of Saccharomyces Data from Schatzmann, 1975 DEB theory: Product formation rate = w A. Assimilation rate + w M. Maintenance rate + w G. Growth rate For pyruvate: w G <0 Leudeking & Piret (1959): Product formation rate = w M. Maintenance rate + w G. Growth rate Cannot explain observed pattern

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

20. Interactions of substrates 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 low high

21. Interactions of substrates 5.1 Kooijman, 2001 Phil Trans R Soc B 356: 331-349

22. 1 Reserve – 1 Structure

23. 2 Reserves – 1 Structure

24. Reserve Capacity & Growth low turnover rate: large reserve capacity high turnover rate: small reserve capacity

25. Simultaneous nutrient limitation Specific growth rate of Pavlova lutheri as function of intracellular phosphorus and vitamine B 12 at 20 ºC Data from Droop 1974 Note the absence of high contents for both compounds due to damming up of reserves, and low contents in structure (at zero growth) Kooijman, 1996 Biophys. Chem. 73: 179-188

26. Steps in metabolic evolution Variable biomass composition Strong homeostasis Reserves: first order  partitionability Maintenance: carrier, regulation, turnover, defense Increase of reserve capacity Control of morphology  -rule  cell cycle Syntrophy & compartmentalization: mitochondria, plastids, genome organisation Reduction of number of reserves Emergence of life stages Further increase of maintenance costs Supply  demand systems

27. Evolution of DEB systems Kooijman & Troost 2007 Biol.Rev,to appear

28. primary parameter values tend to co-vary across species primary parameters can be expressed such that only the specific assimilation rate depends on max size specific assimilation rate must be  structural length application: write physiological property as function of parameters (including maximum body weight) evaluate this property as function of max body weight Inter-species body size scaling Kooijman 1986 J. Theor. Biol. 121: 269-282

29. 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 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 h a aging acceleration maximum length L m =  {J EAm } / [J EM ] Kooijman 1986 J. Theor. Biol. 121: 269-282

30. Scaling of metabolic rate intra-speciesinter-species maintenance growth Respiration: contributions from growth and maintenance Weight: contributions from structure and reserve Structure ; = length; endotherms Kooijman et al 2007 SAR & QSAR to appear

31. 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)

32. Feeding rate slope = 1 poikilothermic tetrapods Data: Farlow 1976 Inter-species: J Xm  V Intra-species: J Xm  V 2/3 Mytilus edulis Data: Winter 1973 Length, cm Filtration rate, l/h

33. Von Bertalanffy growth rate 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

34. 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

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

36. Producer/consumer dynamics Deterministic model Stochastic model in closed homogeneous system

37. 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

38. 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

39. DEB tele course 2007 http://www.bio.vu.nl/thb/deb/ Free of financial costs; some 250 h effort investment Feb-April 2007; target audience: PhD students We encourage participation in groups that organize local meetings weekly French group of participants of the DEB tele course 2005: special issue of J. Sea Res. 2006 on DEB applications to bivalves 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 2000 Audience : thank you for your attention Sebastian Diehl : thank you for the invitation