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. Multivariate extensions 5a animal heterotroph phototroph plant symbiosis

3. Photosynthesis 5.1.3 2 H2O + 4 h O2 + 4 H+ + 4 e- CO2 + 4 H+ + 4 e- CH2O + H2O CO2 + H2O + light  CH2O + O2

4. Photorespiration 5.1.3a RuP2 ribulose 1,5-biphosphate (C5 + C  2 C3) Transformations are catalized by Rubisco, which evolved in anaerobic environments O2 competes with CO2 which gives an oxidation, rather than a reduction in Calvin (= inverse pentose phosphate cyle) (C5 C3 + C2 ) no synthesis of hydrocarbons at compensation point

5. Calcification 5.1.4

6. Calcification 5.1.4a Original hypothesis: E.huxleyi uses bicarbonate as supplementary DIC source; CO2 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. DEBtool/alga/sgr 5.2.1 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 mE (i,1)-matrix with reserve turnover rate kE (i,1)-matrix with specific maintenance costs from reserve jEM (i,1)-matrix with costs for structure yEV optional (i,1)-matrix with specific maintenance costs from structure jVM; default is jEM/ yEV 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 jEM (i,1)-matrix with structure flux for maintenance jVMM (i,1)-matrix with rejected reserve flux jER scalar with info on failure (0) or success (1) of numerical procedure An example of use is given in mydata_sgr

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 B12 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 Data from Droop 1974 on Pavlova lutheri B12-cont., 10-21.mol.cell-1 P-content, fmol.cell-1 P-conc, μM 106.cells ml-1 B12-conc, pM Spec growth rate, d-1 Spec growth rate, d-1 Spec growth rate, d-1

14. C,N,P-limitation5.2.4 N,P reductions P reductions N reductions Nannochloropsis gaditana (Eugstimatophyta) in sea water Data from Carmen Garrido Perez Reductions by factor 1/3 starting from 24.7 mM NO3, 1.99 mM PO4

15. C,N,P-limitation5.2.4a Nannochloropsis gaditana in sea water DIC For nitrate uptake rate phosphate spec growth rate res. dens. structure spec growth

16. C,N,P-limitation5.2.4b Nannochloropsis gaditana in sea water half-saturation parameters KC = 1.810 mM for uptake of CO2 KN = 3.186 mM for uptake of NO3 KP = 0.905 mM for uptake of PO4 max. specific uptake rate parameters jCm = 0.046 mM/OD.h, spec uptake of CO2 jNm = 0.080 mM/OD.h, spec uptake of NO3 jPm = 0.025 mM/OD.h, spec uptake of PO4 reserve turnover rate kE = 0.034 h-1 yield coefficients yCV = 0.218 mM/OD, from C-res. to structure yNV = 2.261 mM/OD, from N-res. to structure yPV = 0.159 mM/OD, from P-res. to structure carbon species exchange rate (fixed) kBC = 0.729 h-1 from HCO3- to CO2 kCB = 79.5 h-1 from CO2 to HCO3- initial conditions (fixed) HCO3- (0) = 1.89534 mM, initial HCO3- concentration CO2(0) = 0.02038 mM, initial CO2 concentration mC(0) = jCm/ kE mM/OD, initial C-reserve density mN(0) = jNm/ kE mM/OD, initial N-reserve density mP(0) = jPm/ kE mM/OD, initial P-reserve density OD(0) = 0.210 initial biomass (free)

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

18. Organ size & function 5.3.1a Kidney removes N-waste from body At constant food availability JN = aL2 + bL3 Strict isomorphy: kidney size  L3 If kidney function  kidney size: work load reduces with size If kidney function  L2 + cL3 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. defecation feeding food faeces assimilation reserve somatic maintenance maturity maintenance  1- maint maturation reproduction u 1-u growth maturity offspring structure tumour Tumour growth 5.3.2 Dynamic generalization of -rule Allocation to tumour  relative workload Isomorphy: [pMU] = [pM] 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 Van Leeuwen et al., 2003 British J Cancer 89, 2254-2268

21. Tumour Growth: workload allocation 5.3.2a Growth curve of tumour depends on pars no maximum size is assumed a priori If tumour induction occurs late, tumours grows slower Van Leeuwen et al 2003 Brit. J. Cancer89: 2254-2263

22. Tumor growth  DEB theory5.3.2b • 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 fraction of mobilisation flux Allocation to velum vs gut  relative workload Macoma low food Macoma high food Relative organ size is weakly homeostatic

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

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

26. 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