Dynamic Energy Budget Theory - I

1. DynamicEnergy Budget Theory - I Tânia Sousa withcontributionsfrom : Bas Kooijman

2. A DEB organism • Metabolism in a DEB individual. • Rectangles are state variables • Arrows are flows of food JXA, reserve JEA, JEC, JES , JEG or structure JVG. • Circles are processes • The full circles is the priority maintenance rule. Feeding ME- Reserve Mobilization Assimilation Growth Maintenance MV - Structure

3. DEB Dynamics • What are thedynamicsofthestate-variables?

4. DEB Dynamics • Thedynamicsofthestate-variables are givenby:

5. DEB Dynamics • Thedynamicsofthestate-variables are givenby: Meaning [EG]? [EG]- specificcostsofgrowth

6. Exercises • Obtainexpressionsthatdependonlyonstatevariablesandparametersfor growth for V-1 morphorganismsusingthefollowingequations

7. Exercises • Theexpressionthatdependsonlyonstatevariablesandparametersfor growth for V1-morph organismsis • Whathappensatconstantfood?

8. Exercises • Theexpressionthatdependsonlyonstatevariablesandparametersfor growth for V1-morph organismsis • Atconstantfoodreserve densityisconstant (weakhomeostasis) - reserve density

9. Exercises • Obtainexpressionsthatdependonlyonstatevariablesandparametersfor growthatconstantfood(weakhomeostasis) for V1-morphs: - reserve density

10. Exercises • Theexpressionthatdependsonlyonstatevariablesandparametersfor growthatconstantfooddensity for V1-morphs (mEisconstant) is: • Is thisexponential growth? Specificgrowth rate isconstant

11. Exercises • Theexpressionthatdependsonlyonstatevariablesandparametersfor growthatconstantfooddensity for V1-morphs (mEisconstant) is: • Is thisexponential growth? Specificgrowth rate isconstant

12. Exercises • Is this exponential growth? • Yes, with

13. Exponential growth in V1-morphs at constant food • Exponential growth • Whatistheslope?

14. Exponential growth in V1-morphs at constant food • Exponential growth • With a slope:

15. Exercises • Exponential growth • With • Whatistherelationshipbetweenthespecificgrowth rate andthedoubling time?

16. Exercises • Exponential growth • With • Therelationshipbetweenthespecificgrowth rate andthedoubling timeis:

17. Exercises • Exponential growth • With • How does thespecificgrowth rate dependson reserve density?

18. Exponential growth in V1-morphs at constant food • Exponential growth in DEB theory • DEB theorypredicts: • increaseswiththe reserve density (foodlevel)

19. Exponential growth in V1-morphs at constant food • Exponential growth in DEB theory • DEB theorypredicts: • increaseswiththe reserve density (foodlevel) • How does thespecificgrowth rate dependsonthespecificenergyconductance, maintenanceneedsandonyVE?

20. Exponential growth in V1-morphs at constant food • Exponential growth in DEB theory • DEB theorypredicts: • increaseswiththe reserve density (foodlevel) • decreaseswithspecificmaintenanceneedsandincreaseswith and

21. Doubling time in V1-morphs at constant food • Doubling time:

22. A DEB organismAssimilation, dissipationandgrowth • Metabolism in a DEB individual. • Rectangles are state variables • Arrows are flows of food JXA, reserve JEA, JEC, JES , JEG or structure JVG. • Circles are processes • The full circles is the priority maintenance rule. Feeding ME- Reserve Mobilization Assimilation Growth Maintenance MV - Structure

23. 3 types of aggregated chemical transformations • Assimilation: X(substrate)+M  E(reserve) + M + P • linked to surface area • Dissipation: E(reserve) +M  M • somatic maintenance: linked to surface area & structural volume • Growth: E(reserve)+M  V(structure) + M • Compounds: • Organic compounds: V, E, X and P • Mineral compounds: CO2, H2O, O2 and Nwaste

24. yXE=1.345 Reserve Turnover Rate: X – Glycerol C3H8O3 E=2.11h-1 Assimilation: CH1.66O0.422N0.312 Biomass: E+ V E - Reserve Catabolism: Energy Investment Ratio: O2, NH3 g=1 =1 Maintenance Rate Coefficient: yVE=0.904 Maintenance: Growth: M=0.021h-1 CH1.64O0.379N0.198 CO2, H2O, and sensible heat V - Structure Dissipation: Klebsiella Aerogenes in DEB Theory • Characteristics: Gram-negative bacteria and a facultatively anaerobic rod (V1-morph). T=35ºCpH: 6.8

25. Exercises • Obtaintheaggregatedchemicalreactions for assimilation, dissipationandgrowth for klebsiellaaerogenes in a chemostat (seenext slide) • Identifyin theseequationsyXE, yPEandyVE. • Constraintsonthe yield coeficients • Degreesoffreedom

26. Exercises • What istherelationshipbetweentheseequationsand, ,,,, , and ?

27. Exercises • What istherelationshipbetweentheseequationsand, , ,, , and ? • Howwouldyouobtaintheaggregatechemicaltransformation?

28. Exercises • What istherelationshipbetweentheseequationsand, , ,, , and ? • Howwouldyouobtaintheaggregatechemicaltransformation? • Compute the total consumptionof O2. • Writeit as a functionof, and .

29. Exercises • What istherelationshipbetweentheseequationsand, , ,, , and ? • Howwouldyouobtaintheaggregatechemicaltransformation? • Compute the total consumptionof O2. • Writeit as a functionof, and . • Thestoichiometryoftheaggregatechemicaltransformationthatdescribestheorganismhas 3 degreesoffreedom: anyflowproducedorconsumed in theorganismis a weightedaverageofanythreeotherflows

30. Exercises • Write theenergy balance for eachchemical reactor (assimilation, dissipationandgrowth)

31. Exercises • Write theenergy balance for eachchemical reactor (assimilation, dissipationandgrowth) • Compute the total metabolicheatproductionas a function of , and .

32. Exercises • Write theenergy balance for eachchemical reactor (assimilation, dissipationandgrowth) • Compute the total metabolicheatproductionas a function of , and . • Indirectcalorimetry (estimatingheatproductionwithoutmeasuringit): Dissipatingheatisweighted sum ofthreemassflows: CO2, O2andnitrogeneouswaste (Lavoisier in the XVIII century).

33. Dissipating heat Steam from a heap of moist Prunus serotina litter illustrates metabolic heat production by aerobic bacteria, Actinomycetes, fungiandotherorganisms

34. yXE=1.345 Reserve Turnover Rate: X – Glycerol C3H8O3 E=2.11h-1 Assimilation: CH1.66O0.422N0.312 Biomass: E+ V E - Reserve Catabolism: Energy Investment Ratio: O2, NH3 g=1 =1 Maintenance Rate Coefficient: yVE=0.904 Maintenance: Growth: M=0.021h-1 CH1.64O0.379N0.198 CO2, H2O, and sensible heat V - Structure Dissipation: Klebsiella Aerogenes in DEB Theory • Characteristics: Gram-negative bacteria and a facultatively anaerobic rod (V1-morph). T=35ºCpH: 6.8

35. Comparison with experimental data I Esener et al. (1982, 1983) yield (C-molWoutput.C-molX-1) O2 (molO2.C-molWoutput-1.h-1) CO2 (molCO2.C-molWoutput-1.h-1) D(h-1) Measurements (points) and DEB model results (lines).

36. Comparison with experimental data II Esener et al. (1982, 1983) nHW (molH.C-molW-1) nOW (molO.C-molW-1) nNW (molN.C-molW-1) D(h-1) Measurements (points) and DEB model results (lines).

37. Heat Production vs. Dilution rates • Irreversibilities are equal to the amount of heat released • Production of biomass becomes more efficient kJ per C-mol biomass inside the chemostat per hour kJ per C-mol biomass formed kJ per mol O2 consumed Thornton’s coefficient D(h-1)