Standard DEB model summary of tele-part of DEB course 2011 Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Lisbon, 2011/04/04

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

Supply-demand spectrum 1.2.5

Maturation 2.5.2

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.

Macrochemical reaction eq 3.5

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

Interactions of substrates 3.7.3b Kooijman, 2001 Phil Trans R Soc B 356:

Change in body shape Isomorph: surface area  volume 2/3 volumetric length = volume 1/3 V0-morph: surface area  volume 0 V1-morph: surface area  volume 1 Ceratium Mucor Merismopedia

Isomorphic growth 2.6c diameter,  m Weight 1/3, g 1/3 length, mm time, h time, d Amoeba proteus Prescott 1957 Saccharomyces carlsbergensis Berg & Ljunggren 1922 Pleurobrachia pileus Greve 1971 Toxostoma recurvirostre Ricklefs 1968 Weight 1/3, g 1/3

Mixtures of V0 & V1 morphs 4.2.3a volume,  m 3 hyphal length, mm time, h time, min Fusarium  = 0 Trinci 1990 Bacillus  = 0.2 Collins & Richmond 1962 Escherichia  = 0.28 Kubitschek 1990 Streptococcus  = 0.6 Mitchison 1961

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

Digestive system 7.3a time input, output time input, output time input, output completely stirred reactor plugflow reactor both reactors in series stomach model gut model 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

Reserve residence time 2.3.1b

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 Standard DEB model 2a 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 feeding digestion maintenance storage product formation maturation growth reproduction aging

1-  maturity maintenance maturity offspring maturation reproduction Standard DEB scheme 2b foodfaeces assimilation reserve feeding defecation structure somatic maintenance growth  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 1 food type, 1 reserve, 1 structure, isomorph

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

1E,1V isomorph 2.9C, continued

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

1E,1V isomorph 2.9D, continued time,  scaled flux of CO 2 scaled flux of H 2 O scaled flux of O 2 scaled flux of NH 3