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Standard DEB model summary of tele-part of DEB course 2011

Standard DEB model summary of tele-part of DEB course 2011. Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thb /. Lisbon, 2011/04/04. Homeostasis 1.2. strong homeostasis constant composition of pools (reserves/structures)

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Standard DEB model summary of tele-part of DEB course 2011

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  1. Standard DEB modelsummary of tele-part of DEB course 2011 Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thb/ Lisbon, 2011/04/04

  2. Homeostasis 1.2 strong homeostasis constant composition of pools (reserves/structures) generalized compounds, stoichiometric contraints on synthesis weak homeostasis constant composition of biomass during growth in constant environments determines reserve dynamics (in combination with strong homeostasis) structural homeostasis constant relative proportions during growth in constant environments isomorphy .work load allocation thermal homeostasis ectothermy  homeothermy  endothermy acquisition homeostasis supply  demand systems development of sensors, behavioural adaptations

  3. Supply-demand spectrum 1.2.5

  4. Maturation 2.5.2

  5. Maturity & its maintenance 2.5.3a DEB implementation is motivated by 4 observations 1 Contrary to age, volume at birth or puberty hardly depends on food density. So stage transitions cannot be linked to age. 2 Some species continue growing after puberty. Other species, such as birds, only reproduce well after the growth period. So stage transitions cannot be linked to size. 3 Total cumulative energy investment in development at any given size of the individual depends on food density; this can be removed by allowing for maturity maintenance. 4 Ultimate reproduction rate is a continuous function of food density This demonstrates the existence of maturity maintenance.

  6. Macrochemical reaction eq 3.5

  7. Simultaneous Substrate Processing 3.7c production production Chemical reaction: 1A + 1B 1C Poisson arrival events for molecules A and B blocked time intervals • acceptation event ¤ rejection event Kooijman, 1998 Biophys Chem 73: 179-188

  8. Interactions of substrates 3.7.3b Kooijman, 2001 Phil Trans R Soc B 356: 331-349

  9. Change in body shape 4.2.2 Isomorph: surface area  volume2/3 volumetric length = volume1/3 Mucor Ceratium Merismopedia V0-morph: surface area  volume0 V1-morph: surface area  volume1

  10. Isomorphic growth 2.6c diameter, m Weight1/3, g1/3 Amoeba proteus Prescott 1957 Saccharomyces carlsbergensis Berg & Ljunggren 1922 time, h time, h Weight1/3, g1/3 Toxostoma recurvirostre Ricklefs 1968 length, mm Pleurobrachia pileus Greve 1971 time, d time, d

  11. Mixtures of V0 & V1 morphs 4.2.3a volume, m3 hyphal length, mm Bacillus  = 0.2 Collins & Richmond 1962 Fusarium  = 0 Trinci 1990 time, min time, h volume, m3 volume, m3 Escherichia  = 0.28 Kubitschek 1990 Streptococcus  = 0.6 Mitchison 1961 time, min time, min

  12. Mixtures of changes in shape 4.2.4a Dynamic mixtures between morphs V1- V0-morph outer annulus behaves as a V1-morph, inner part as a V0-morph. Result: diameter increases  time Lichen Rhizocarpon V1- iso- V0-morph

  13. input, output input, output input, output time time time Digestive system 7.3a completely stirred reactor • Stomach • good in buffering • residence times • exponentially distributed • many short times, few large ones • Gut • bad in buffering • residence time • constant • digestion requires some time stomach model plugflow reactor gut model both reactors in series

  14. Reserve residence time 2.3.1b

  15. storage product formation maturation growth reproduction aging feeding digestion maintenance Standard DEB model 2a Isomorph with 1 reserve & 1 structure feeds on 1 type of food has 3 life stages (embryo, juvenile, adult) Processes: Balances: mass, energy , entropy, time • Extensions: • more types of food and food qualities • more types of reserve (autotrophs) • more types of structure (organs, plants) • changes in morphology • different number of life stages

  16. defecation feeding food faeces assimilation reserve somatic maintenance maturity maintenance  1- maturation reproduction growth maturity offspring structure Standard DEB scheme 2b 1 food type, 1 reserve, 1 structure, isomorph time: searching & handling feeding  surface area weak & strong homeostasis κ-rule for allocation to soma maintenance has priority somatic maint  structure maturity maint  maturity stage transition: maturation embryo: no feeding, reprod juvenile: no reproduction adult: no maturation maternal effect: reserve density at birth equals that of mother initially: zero structure, maturity

  17. 1E,1V isomorph 2.9c all quantities scaled dimensionless

  18. 1E,1V isomorph 2.9C, continued

  19. 1E,1V isomorph 2.9d length l, survival S reserve density, e maturity, vH time,  time,  time,  cum. feeding,10  reprod. acceleration, q hazards, h, hH time,  time,  time, 

  20. 1E,1V isomorph 2.9D, continued scaled flux of CO2 scaled flux of H2O time,  time,  scaled flux of NH3 scaled flux of O2 time,  time, 

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