Standard DEB model summary of telepart of DEB

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

Interactions of substrates 3. 7. 3 b Kooijman, 2001 Phil Trans R Soc B 356: 331 -349

Change in body shape 4. 2. 2 Isomorph: surface area volume 2/3 volumetric length = volume 1/3 Mucor Ceratium V 0 -morph: surface area volume 0 Merismopedia V 1 -morph: surface area volume 1

Weight 1/3, g 1/3 diameter, m Isomorphic growth 2. 6 c Amoeba proteus Prescott 1957 Saccharomyces carlsbergensis Berg & Ljunggren 1922 time, h Weight 1/3, g 1/3 length, mm time, h Pleurobrachia pileus Greve 1971 Toxostoma recurvirostre Ricklefs 1968 time, d

volume, m 3 4. 2. 3 a Bacillus = 0. 2 Collins & Richmond 1962 time, min Fusarium = 0 Trinci 1990 time, h volume, m 3 hyphal length, mm Mixtures of V 0 & V 1 morphs Escherichia = 0. 28 Kubitschek 1990 time, min Streptococcus = 0. 6 Mitchison 1961 time, min

Mixtures of changes in shape 4. 2. 4 a Dynamic mixtures between morphs V 1 - V 0 -morph outer annulus behaves as a V 1 -morph, inner part as a V 0 -morph. Result: diameter increases time Lichen Rhizocarpon V 1 - iso- V 0 -morph

input, output Digestive system 7. 3 a completely stirred reactor stomach model input, output time plugflow reactor gut model time both reactors in series 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. 1 b

Standard DEB model 2 a Isomorph with 1 reserve & 1 structure feeds on 1 type of food has 3 life stages (embryo, juvenile, adult) Processes: feeding digestion maintenance storage product formation maturation 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 growth reproduction aging

Standard DEB scheme 2 b 1 food type, 1 reserve, 1 structure, isomorph food feeding defecation faeces assimilation somatic maintenance growth structure reserve 1 - maturity maintenance maturation reproduction maturity offspring 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 E, 1 V isomorph 2. 9 c all quantities scaled dimensionless

1 E, 1 V isomorph 2. 9 C, continued

time, cum. feeding, 10 reprod. hazards, h, h. H acceleration, q maturity, v. H length l, survival S reserve density, e 1 E, 1 V isomorph 2. 9 d time,

scaled flux of NH 3 scaled flux of O 2 scaled flux of H 2 O scaled flux of CO 2 1 E, 1 V isomorph 2. 9 D, continued time,