Multivariate DEB models Generalization of the standard DEB model with multiple state variables

1. 7th DEB Course TEXEL, 15-23 April Multivariate DEB modelsGeneralization of the standard DEB model with multiple state variables Gonçalo Marques Instituto Superior Técnico, goncalo.marques@ist.utl.pt

2. Summary 2 The standard DEB model is built with one reserve, one structure, one maturity and one reproduction buffer for an organism that feeds on one substrate. There are situations when the standard DEB model is not enough to realistically simulate an organism or a specific feature of an organism. However DEB theory gives us the tools to build models beyond the standard DEB model. The construction of the generalized DEB models will be the theme of this presentation. 1. State variables 2. Multiple substrates 3. Multiple reserves 4. Multiple structures 5. Does it make sense to talk about multiple maturities? 6. Multiple products

3. Statevariables 3 Substrate – compoundassimilatedbyanorganism

4. Statevariables 4 Substrate – compoundassimilatedbyanorganism Reserve – assimilationisstocked in the reserve. The output ofthe reserve (mobilization flux) willbeused for everymetabolicpurpose.

5. Statevariables 5 Substrate – compoundassimilatedbyanorganism Reserve – assimilationisstockedinthe reserve. The output ofthe reserve (mobilization flux) willbeused for everymetabolicpurpose.

6. Statevariables 6 Substrate – compoundassimilatedbyanorganism Reserve – assimilationisstockedinthe reserve. The output ofthe reserve (mobilization flux) willbeused for everymetabolicpurpose.

7. Statevariables 7 Substrate – compoundassimilatedbyanorganism Reserve – assimilationisstockedinthe reserve. The output ofthe reserve (mobilization flux) willbeused for everymetabolicpurpose. Structure – itislinked to size, andthereforeit rules assimilation. Itneeds to bemaintained.

8. Statevariables 8 Substrate – compoundassimilatedbyanorganism Reserve – assimilationisstockedinthe reserve. The output ofthe reserve (mobilization flux) willbeused for everymetabolicpurpose. Structure – itislinked to size, andthereforeit rules assimilation. Itneeds to bemaintained.

9. Statevariables 9 Substrate – compoundassimilatedbyanorganism Reserve – assimilationisstockedinthe reserve. The output ofthe reserve (mobilization flux) willbeused for everymetabolicpurpose. Structure – itislinked to size, andthereforeit rules assimilation. Itneeds to bemaintained. Maturity– a measureofthe complexityoftheorganism. Italso needs to bemaintained.

10. Statevariables 10 Substrate – compoundassimilatedbyanorganism Reserve – assimilationisstockedinthe reserve. The output ofthe reserve (mobilization flux) willbeused for everymetabolicpurpose. Structure – itislinked to size, andthereforeit rules assimilation. Itneeds to bemaintained. Maturity– a measureofthe complexityoftheorganism. Italso needs to bemaintained.

11. Statevariables 11 Substrate – compoundassimilatedbyanorganism Reserve – assimilationisstockedinthe reserve. The output ofthe reserve (mobilization flux) willbeused for everymetabolicpurpose. Structure – itislinked to size, andthereforeit rules assimilation. Itneeds to bemaintained. Maturity– a measureofthe complexityoftheorganism. Italso needs to bemaintained. Product– compoundproduced bytheorganism. Itcouldbe releasedintotheenvironmentor remainattached to theorganism. Eitherwayitdoesn’tneed maintenance.

12. State variables 12 State variables define the state of the system. In the standard DEB model the system organism-environment is defined by: Organism – reserve, structure, maturity, reproduction buffer Environment – substrate

13. Statevariables 13 Recall one of the important principles of modelling: Efficiency Balance the effort and level of detail with the insights your data can provide.

14. Modelling criteria • Consistency dimensions, conservation laws, realism (consistency with data) • Coherence consistency with neighbouring fields of interest, levels of organisation • Efficiency comparable level of detail, all vars and pars are effective numerical behaviour • Testability amount of support, hidden variables

15. Multiple state variables 15 • When you need to add state variables remember to ask these questions: • Does it comply with the DEB core? (coherence) • In what situation do I recover the standard DEB model? And does it make sense? (coherence) • Is this the minimum number of state variables I need to model the feature/behavior/metabolism I want? (efficiency and testability)

16. Multiple substrates 16 One substrate: b p

17. Multiple substrates 17 One substrate:

18. Multiple substrates 18 Two substrates: complementary

19. Multiple substrates 19 Two substrates:

20. Multiple substrates 20 Two substrates:

21. Multiple substrates 21 Two substrates:

22. Multiple substrates 22 Two substrates:

23. Multiple substrates 23 Two substrates:

24. Multiple substrates 24 Two substrates:

25. Multiple substrates 25 Two substrates:

26. Multiple substrates 26 Two substrates:

27. Multiple substrates 27 Two substrates:

28. Multiple substrates 28 Two substrates: Sequential complementary

29. Multiple substrates 29 Two substrates: Parallel complementary

30. Multiple substrates 30 • There are several situations that can be seen as a multiple substrate situation: • - Diet • - Nutrients • - Inhibition • … • Note the limiting cases.

31. Multiple reserves 31 There are cases when the organism accumulates different nutrients and there is a need for multiple reserves.

32. Multiple reserves 32

33. Multiple reserves 33

34. Multiple reserves 34 The main scheme is done. Let us now look at some important details.

35. Multiple reserves 35 Growth SU:

36. Multiple reserves 36 Growth SU: Parallel complementary

37. Multiple reserves 37 Computation of the mobilization fluxes:

38. Multiple reserves 38 Computation of the mobilization fluxes: and

39. Multiple reserves 39 Computation of the mobilization fluxes:

40. Multiple reserves 40 Computation of the mobilization fluxes

41. Multiple reserves 41 Computation of the mobilization fluxes We can’t break the cycle and compute analytically.

42. Multiple reserves 42 Rejection fluxes

43. Multiple reserves 43 Rejection fluxes

44. Multiple reserves 44 Rejection fluxes

45. Multiple reserves 45 N Multiple limitation The case of a 3 reserve (C, N, P) model for microalgae. P C Lorena (2008)

46. Multiple structures 46 In cases where it is important to model an organ that doesn’t grow proportional to the rest of the body, it may be needed to add a new structure.

47. Multiple structures 47 In cases where it is important to model an organ that doesn’t grow proportional to the rest of the body, it may be needed to add a new structure.

48. Multiple structures 48 In cases where it is important to model an organ that doesn’t grow proportional to the rest of the body, it may be needed to add a new structure.

49. Multiple structures 49 In cases where it is important to model an organ that doesn’t grow proportional to the rest of the body, it may be needed to add a new structure.

50. Multiple structures 50