1. Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 Metabolism 4 Univariate DEB models 5 Multivariate DEB modelsMultivariate 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. Multivariate extensions 5a animal heterotroph phototroph symbiosis plant

3. Photosynthesis 5.1.3 2 H 2 O + 4 h  O 2 + 4 H + + 4 e - CO 2 + 4 H + + 4 e -  CH 2 O + H 2 O CO 2 + H 2 O + light  CH 2 O + O 2

4. no synthesis of hydrocarbons at compensation point Photorespiration 5.1.3a RuP 2 ribulose 1,5-biphosphate (C 5 + C  2 C 3 ) (C 5  C 3 + C 2 ) Transformations are catalized by Rubisco, which evolved in anaerobic environments O 2 competes with CO 2 which gives an oxidation, rather than a reduction in Calvin (= inverse pentose phosphate cyle)

5. Calcification 5.1.4

6. Calcification 5.1.4a Original hypothesis: E.huxleyi uses bicarbonate as supplementary DIC source; CO 2 might be growth limiting However: non-calcifying strains have similar max growth rate New hypothesis: carbonate is used for protection against grazing Emiliania huxleyi

7. sgr1, sgr2, sgr3, sgr4 The functions obtain the specific growth rate, the reserve and structure fluxes for maintenance and the rejected reserve fluxes for 1, 2, 3 and 4 reserve systems. All reserves are supplementary for maintenance as well as for growth, while each reserve and structure are substitutable for maintenance. The preference for the use of structure relative to that of reserve for maintenance can be set with a (non-negative) preference parameter. The value zero gives absolute priority to reserve, which gives a switch at specific growth rate 0. All functions sgr have the same structure, and the input/output is presented for sgri where i takes values 1, 2, 3 of 4. Inputs: (i,1)-matrix with reserve density m E (i,1)-matrix with reserve turnover rate k E (i,1)-matrix with specific maintenance costs from reserve j EM (i,1)-matrix with costs for structure y EV optional (i,1)-matrix with specific maintenance costs from structure j VM ; default is j EM / y EV optional scalar or (i,1)-matrix with preference parameter alpha; default is 0 Outputs: scalar with specific growth rate r (i,1)-matrix with reserve flux for maintenance j EM (i,1)-matrix with structure flux for maintenance j VM M (i,1)-matrix with rejected reserve flux j ER scalar with info on failure (0) or success (1) of numerical procedure An example of use is given in mydata_sgr DEBtool/alga/sgr 5.2.1

8. 1 Reserve – 1 Structure 5.2

9. 2 Reserves – 1 Structure 5.2a

10. Reserve Capacity & Growth 5.2b low turnover rate: large reserve capacity high turnover rate: small reserve capacity

11. Multiple reserves imply excretion 5.2.2 Excreted reserve(s) might be modified to toxicants

12. Simultaneous nutrient limitation 5.2.3 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)

13. Reserve interactions 5.2.3a Spec growth rate, d -1 P-content, fmol.cell -1 P-conc, μM B 12 -conc, pM B 12 -cont., 10 -21.mol.cell -1 PVitamin B 12 kEkE 1.191.22 d -1 y XV 0.39 10 - 15 2.35 mol.cell -1 j EAm 4.91 10 - 21 76.6 10 -15 mol.cell -1. d -1 κEκE 0.690.96 kMkM 0.00790.135 d -1 K0.0170.12 pM, μM Data from Droop 1974 on Pavlova lutheri P(μM)B 12 (pM) 1.4468 14.46.8 1.4420.4 1.446.8 10 6.cells ml -1

14. C,N,P-limitation 5.2.4 Nannochloropsis gaditana (Eugstimatophyta) in sea water Data from Carmen Garrido Perez Reductions by factor 1/3 starting from 24.7 mM NO 3, 1.99 mM PO 4 N,P reductions N reductions P reductions

15. C,N,P-limitation 5.2.4a Nannochloropsis gaditana in sea water For DIC nitrate phosphate res. dens. structure uptake rate spec growth rate spec growth

16. C,N,P-limitation 5.2.4b half-saturation parameters K C = 1.810 mM for uptake of CO 2 K N = 3.186 mM for uptake of NO 3 K P = 0.905 mM for uptake of PO 4 max. specific uptake rate parameters j Cm = 0.046 mM/OD.h, spec uptake of CO 2 j Nm = 0.080 mM/OD.h, spec uptake of NO 3 j Pm = 0.025 mM/OD.h, spec uptake of PO 4 reserve turnover rate k E = 0.034 h -1 yield coefficients y CV = 0.218 mM/OD, from C-res. to structure y NV = 2.261 mM/OD, from N-res. to structure y PV = 0.159 mM/OD, from P-res. to structure carbon species exchange rate (fixed) k BC = 0.729 h -1 from HCO 3 - to CO 2 k CB = 79.5 h -1 from CO 2 to HCO 3 - initial conditions (fixed) HCO 3 - (0) = 1.89534 mM, initial HCO 3 - concentration CO 2 (0) = 0.02038 mM, initial CO 2 concentration m C (0) = j Cm / k E mM/OD, initial C-reserve density m N (0) = j Nm / k E mM/OD, initial N-reserve density m P (0) = j Pm / k E mM/OD, initial P-reserve density OD(0) = 0.210 initial biomass (free) Nannochloropsis gaditana in sea water

17. Static generalisation of κ-rule 5.3.1 time, d Data: Gille & Salomon 1994 Modelling: Ingeborg van Leeuwen Muscovy duck & mallard whole body heart

18. Organ size & function 5.3.1a Kidney removes N-waste from body At constant food availability J N = aL 2 + bL 3 Strict isomorphy: kidney size  L 3 If kidney function  kidney size: work load reduces with size If kidney function  L 2 + cL 3 for length L of kidney or body work load can be constant for appropriate weight coefficients This translates into a morphological design constraint for kidneys

19. Human kidney 5.3.1b From : Mader, S. S. 1993 Biology, WCB; Wolpert, L. 1998 Principles of development, Oxford

20. Tumour growth 5.3.2 Allocation to tumour  relative workload Van Leeuwen et al., 2003 British J Cancer 89, 2254-2268 1-   u foodfaeces assimilation reserve feeding defecation structure somatic maintenance growth maturity maintenance maturity offspring maturation reproduction tumour  1-  u maint Dynamic generalization of  -rule Isomorphy: [p MU ] = [p M ] Tumour tissue: low spec growth & maint costs Growth curve of tumour depends on pars no maximum size is assumed a priori Model explains dramatic tumour-mediated weight loss If tumour induction occurs late, tumours grow slower Caloric restriction reduces tumour growth but the effect fades

21. Tumour Growth: workload allocation 5.3.2a If tumour induction occurs late, tumours grows slower Growth curve of tumour depends on pars no maximum size is assumed a priori Van Leeuwen et al 2003 Brit. J. Cancer 89: 2254-2263

22. Tumor growth  DEB theory 5.3.2b The shape of the tumor growth curve is not assumed a priori, and is very flexible, depending on parameter values The model predicts that, in general, tumors develop faster in young than in old hosts According to the model, tumors grow slower in calorically restricted hosts than in ad libitum fed hosts. The effect of CR on tumor growth fades away during long-term CR The model explains why tumor-mediated body-weight loss is often more dramatic than expected

23. Organ growth 5.3.2c Allocation to velum vs gut  relative workload Macoma high food Macoma low food fraction of mobilisation flux Relative organ size is weakly homeostatic

24. From: Mader, s. S. 1993 Biology, WCB, Dubuque Development poaceae (angiospermae) 5.3.3

25. Development dicotyledonae (angiospermae) 5.3.3a From: Mader, s. S. 1993 Biology, WCB, Dubuque

26. 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