1. Some recent developments in DEB research Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio.vu.nl http://www.bio.vu.nl/thbhttp://www.bio.vu.nl/thb/ Marseille, 2005/12/13

2. Evolution of DEB systems 8.4

3. Volume-surface interactions 2.2 inactive enzyme active enzyme in binding phase active enzyme in production phase product substrate Cells can “know” their size from the rate at which concentrations of substrate & product change if transformation is by membrane-bound enzymes Membrane-mediated transformation rates in isomorphs decrease with length because of transportation distance

4. Structural homeostasis 7.6 usual ontogeny V E Enzymes in membranes that mobilize reserves don’t “observe” vesicle size or substrate conc. No dilution by growth Remaining problem: what if [E G ] is not large? possible mechanism for reserve dynamics

5. Reserve dynamics 3.4 reserve & structure: spatially segregated reserve mobilized at rate  surface area of reserve-structure interface rejected reserve flux returns to reserve SU-reserve complex dissociates to demand-driven maintenance supply-driven growth (synthesis of structure) abundance of SUs such that local homeostasis is achieved

6. Reserve dynamics 3.4

7. avoidance of rejected reserve flux most of reserves are polymers they are used for metabolism as monomers strong homeostasis: amount of monomers  polymers metabolic SUs feed from monomer pool monomerization is self-inhibiting

8. Reserve dynamics 3.4

9. SU abundance, relative to DEB value sd specific use of reserve for assimilation being an alternating Poisson process 10 h -1 50 h -1 2 h -1 assim = 0 assim = 1 0 1 time assimilation 10 h -1 hazard rates

10. Reserve dynamics 3.4 time, h PHB density, mol/mol in starving active sludge Data from Beun, 2001

11. Yield vs growth 4.3.1 1/spec growth rate, 1/h 1/yield, mmol glucose/ mg cells Streptococcus bovis, Russell & Baldwin (1979) Marr-Pirt (no reserve) DEB spec growth rate yield Russell & Cook (1995): this is evidence for down-regulation of maintenance at high growth rates DEB theory: high reserve density gives high growth rates structure requires maintenance, reserves do not

12. Behaviour  Energetics DEB fouraging module: time budgeting Fouraging feeding + food processing, food selection feeding  surface area (intra-species), volume (inter-species) Sleeping repair of damage by free radicals  respiration respiration scales between surface area & volume Social interaction feeding efficiency (schooling) resource partitioning (territory) mate selection (gene quality  energetic parameter values) Migration traveling speed and distance: body size spatial pattern in resource dynamics (seasonal effects) environmental constraints on reproduction

13. These gouramis are from the same nest, they have the same age and lived in the same tank Social interaction during feeding caused the huge size difference Age-based models for growth are bound to fail; growth depends on food intake : These gouramis are from the same nest, they have the same age and lived in the same tank Social interaction during feeding caused the huge size difference Age-based models for growth are bound to fail; growth depends on food intake No age, but size: Trichopsis vittatus

14. Rules for feeding 2.1.2 R1 a new food particle appears at a random site within the cube at the moment one of the resident particles disappears. The particle stays on this site till it disappears; the particle density X remains constant. R2 a food particle disappears at a constant probability rate, or because it is eaten by the individual(s). R3 the individual of length L travels in a straight line to the nearest visible food particle at speed  X 2/3 L 2, eats the particle upon arrival and waits at this site for a time t h = {J Xm } -1 L -2. Direction changes if the aimed food particle disappears or a nearer new one appears. Speed changes because of changes in length. R4 If an individual of length L feeds: scaled reserve density jumps: e  e + (L X / L) 3 Change of scaled reserve density e: d/dt e = - e {J Xm } L X 3 / L; Change of length L: 3 d/dt L = ({J Xm } L X 3 e - L k M g) (e + g) -1 At time t = 0: length L = L b,; reserve density e = f. R5 a food particle becomes invisible for an individual of length L 1, if an individual of length L 1 is within a distance L s (L 2 / L 1 ) 2 from the food particle, irrespective of being aimed at.

15. time reserve density length time 1 ind 2 ind determin expectation Social interaction  Feeding

16. Social inhibition of x  e sequential parallel dilution rate substrate conc. biomass conc. No socialization Implications: stable co-existence of competing species “survival of the fittest”? absence of paradox of enrichment x substrate e reserve y species 1 z species 2 Collaboration: Van Voorn, Gross, Feudel, Kooi, Kooijman

17. Hawk-dove dynamics H hawk (predator) D dove (predator) C consumer (prey) S searching F food handling D social interaction G shared food handling Poggiale, Auger, Kooi, Kooijman in prep

18.  body weight -0.2 respiration rate body weight Amount of sleep 3.1 elephant man dog cat ferret opossum 10 log body weight, kg 10 log REM sleep, h/d Siegel, J. M. 2001 The REM sleep-memory consolidation hypothesis Science 294: 1058-1063  No thermo-regulation during REM sleep Dolphins: no REM sleep Links with aging

19. Producer/consumer dynamics producer consumer nutr reserve of producer : total nutrient in closed system : hazard rate special case: consumer is not nutrient limited spec growth of consumer Kooijman et al 2004 Ecology, 85, 1230-1243

20. Producer/consumer dynamics Consumer nutrient limited Consumer not nutrient limited Hopf bifurcation Hopf bifurcation tangent bifurcation transcritical bifurcation homoclinic bifurcation

21. Producer/Consumer Dynamics Deterministic model Stochastic model in closed homogeneous system

22. Producer/Consumer Dynamics 0 2468 0 10 20 consumers nutrient 1.752.3 2.4 2.5 2.7 3.0 1.23 1.15 1.0 2.8 1.23 1.53 tangentfocus Hopf Bifurcation diagram isoclines

23. Direction probability define directed curve in state space get tangent line in point on directed curve project intensity  step on tangent line add projections normalize prob = 0.5 in neutral point 0  prob  1

24. Direction probability 1.230.610.12 2.46 2.7 2.9 3.1 3.165 3.3 direction probability along isocline consumers C producers P Tot nuttangentfocusHopfglobal TS1.2171.5223.1657.10 NTS1.2301.5352.8016.92 around tangent around Hopf

25. Trophic interactions Competition for same resources size/age-dependent diet choices Syntrophy on products faeces, leaves, dead biomass Parasitism (typically small, relative to host) biotrophy, milking, sometimes lethal (disease) interaction with immune system Predation (typical large, relative to prey) living individuals, preference for dead/weak specialization on particular life stages (eggs, juveniles) inducible defense systems; cannibalism Transitions between these types frequently occur

26. Resource dynamics Typical approach

27. Usual form for densities prey x and predator y: Problems: Not clear how dynamics depends on properties of individuals, which change during life cycle If i(x) depends on x: no conservation of mass; popular: i(x)  x(1-x/K) If yield Y is constant: no maintenance, no realism If feeding function f(cx,cy)  cf(x,y) and/or input function i(cx)  ci(x) and/or output function o(cx)  co(x) for any c>0: no spatial scaling (amount  density) Conclusions: include inert zero-th trophic level (substitutable by mass conservation) need for mechanistic individual-based population models Prey/predator dynamics Kooi et al 1997 J. Biol. Systems, 1: 77-85

28. Nutrient Resource dynamics

29. Nutrient

30. Resource dynamics Nutrient

31. Effects of parasites On individuals : Many parasites increase  (chemical manipulation) harvest (all) allocation to dev./reprod. Results larger body size  higher food intake reduced reproduction On populations : Many small parasites convert healthy (susceptible) individuals to affected ones on contact convert affected individuals into non-susceptible ones Globif project NWO-CLS program Van Voorn, Kooi, Kooijman

32. Effect of grazing 9.3.1 rejuvenation of producers remobilization of nutrients via feces: fast, major flux via dead consumers: slow, minor flux Producers feed on feces and dead biomass: syntrophic aspects

33. Producer/consumer/predator dynamics 9.3.1 producer consumer predator total nutrient no preference  preference for dead and weak 

34. Reserve vs structure Kcal/g wet weight cumulative fraction time, dtime of reserve depletion, d protein lipid carbohydrate Data from Whyte J.N.C., Englar J.R. & Carswell (1990). Aquaculture 90: 157-172. Body mass in starving pacific oyster Crassooestrea gigas at 10°C reserve structure

35. Reserve E vs structure V

36. 100 g wet weighttotalproteinlipidcarbohydrate  C M C0, kcal 64.8130.5416.8016.87  C J CM, kcal/d 0.10420.04080.02000.0358  C, kJ/C-mol 401616516 M C0, C-mol0.5700.3190.1140.137 J CM, mmol/d0.4260.1360.290 M CE =M E, mol/mol0.5000.1590.341 M CV =M V, mol/molt 0 = 200 d0.5460.1910.263 M CV =M V, mol/molt 0 = 400 d0.5370.1850.278 M CV =M V, mol/molt 0 = 600 d0.5310.1810.288