1. Instituto Superior Técnico Departamento de Engenharia Mecânica - Secção de Energia e Ambiente Multivariate DEB models Generalization of the standard DEB model for multiple state variables Gonçalo Marques Instituto Superior Técnico, goncalo.marques@ist.utl.pt 4-12 April 2011 6th DEB Course LISBOA, 4-12 April

2. Summary 6 th DEB Course, 4-12 April 2011 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. State variables 6 th DEB Course, 4-12 April 2011 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

4. State variables 6 th DEB Course, 4-12 April 2011 Substrate – compound assimilated by an organism Reserve – assimilation is stocked in the reserve. The output of the reserve (mobilization flux) will be used for every metabolic purpose. Structure – it is linked to size, and therefore it affects assimilation. It needs to be maintained. Maturity – it is a measure of the complexity of the organism. It also needs to be maintained. Product – compound produced by the organism. It could be released into the environment or remain attached to the organism. Either way it doesn’t need maintenance.

5. Multiple state variables 6 th DEB Course, 4-12 April 2011 When we need to add state variables always ask these questions: -Does it comply with the DEB core? -In what situation do I recover the standard DEB model? And does it make sense? -Is this the minimum number of state variables I need to model the feature/behavior/metabolism I want?

6. Multiple substrates 6 th DEB Course, 4-12 April 2011 First let us look at what is happening with one substrate: b p

7. Multiple substrates 6 th DEB Course, 4-12 April 2011

8. Multiple reserves 6 th DEB Course, 4-12 April 2011 There are cases when the organism accumulates different nutrients and there is a need for multiple reserves. But first let us zoom on growth:

9. Multiple reserves 6 th DEB Course, 4-12 April 2011 There are cases when the organism accumulates different nutrients and there is a need for multiple reserves. But first let us zoom on growth:

10. Multiple reserves 6 th DEB Course, 4-12 April 2011 First challenge: Computation of the mobilization fluxes

11. Multiple reserves 6 th DEB Course, 4-12 April 2011 Second challenge: Rejection fluxes

12. Multiple reserves 6 th DEB Course, 4-12 April 2011 Multiple limitation The case of a 3 reserve (C, N, P) model for microalgae. Lorena (2008) N P C

13. Multiple structures 6 th DEB Course, 4-12 April 2011 In cases where it is important to model an organ that doesn’t grow proportional to the rest of the body (changes to morphity), it may be needed to add a new structure.

14. Multiple structures 6 th DEB Course, 4-12 April 2011 ReservesStructuresUptakekappas Static1 setConstant

15. Multiple structures 6 th DEB Course, 4-12 April 2011 ReservesStructuresUptakekappas Static 1 set Constant Dynamic Dependent on uptake

16. Multiple structures 6 th DEB Course, 4-12 April 2011 ReservesStructuresUptakekappas Static 1 set Constant Dynamic Dependent on uptake Plant (Symbiosis) m sets Independent uptakes Constant

17. Multiple modules 6 th DEB Course, 4-12 April 2011

18. Multiple modules Examples of building blocks: December 1-3, 2010

19. Multiple modules 6 th DEB Course, 4-12 April 2011

20. Multiple maturities 6 th DEB Course, 4-12 April 2011 Regrowth of a chestnut tree Does it make sense to talk about multiple maturities? I’m not aware of any simulation made with multiple maturities, but it could make sense.

21. Multiple products 6 th DEB Course, 4-12 April 2011 Does it make sense to use more fluxes for product formation?