Some recent developments in DEB research Bas Kooijman
Some recent developments in DEB research Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam Bas@bio. vu. nl http: //www. bio. vu. nl/thb/ Marseille, 2005/12/13
Evolution of DEB systems 8. 4
Volume-surface interactions Membrane-mediated transformation rates in isomorphs decrease with length because of transportation distance 2. 2 inactive enzyme in binding phase active enzyme in production phase substrate product Cells can “know” their size from the rate at which concentrations of substrate & product change if transformation is by membrane-bound enzymes
Structural homeostasis 7. 6 possible mechanism for reserve dynamics V E on usu to al ge ny Remaining problem: what if [EG] is not large? Enzymes in membranes that mobilize reserves don’t “observe” vesicle size or substrate conc. No dilution by growth
Reserve dynamics • 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 3. 4
Reserve dynamics 3. 4
Reserve dynamics 3. 4 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
Reserve dynamics 3. 4
Reserve dynamics 3. 4 sd specific use of reserve for assimilation being an alternating Poisson process hazard rates assimilation 1 0 assim = 0 time SU abundance, relative to DEB value assim = 1 50 h-1 10 h-1 2 h-1 10 h-1
Reserve dynamics 3. 4 PHB density, mol/mol in starving active sludge time, h Data from Beun, 2001
Yield vs growth 4. 3. 1 1/yield, mmol glucose/ mg cells Streptococcus bovis, Russell & Baldwin (1979) Marr-Pirt (no reserve) DEB spec growth rate yield 1/spec growth rate, 1/h 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
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 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
: No age, but size: 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 Trichopsis vittatus
Rules for feeding R 1 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. R 2 a food particle disappears at a constant probability rate, or because it is eaten by the individual(s). R 3 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 th = {JXm}-1 L-2. Direction changes if the aimed food particle disappears or a nearer new one appears. Speed changes because of changes in length. 2. 1. 2 R 4 If an individual of length L feeds: scaled reserve density jumps: e e + (LX/ L)3 Change of scaled reserve density e: d/dt e = - e {JXm} LX 3/ L; Change of length L: 3 d/dt L = ({JXm} LX 3 e - L k. M g) (e + g)-1 At time t = 0: length L = Lb, ; reserve density e = f. R 5 a food particle becomes invisible for an individual of length L 1, if an individual of length L 1 is within a distance Ls (L 2/ L 1)2 from the food particle, irrespective of being aimed at.
determin expectation length reserve density Social interaction Feeding time 1 ind 2 ind length reserve density time
Social inhibition of x e parallel Collaboration: Van Voorn, Gross, Feudel, Kooijman biomass conc. x substrate Implications: e reserve stable co-existence of y species 1 competing species z species 2 “survival of the fittest”? absence of paradox of enrichment No socialization substrate conc. sequential dilution rate
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, Kooijman in prep
opossum ferret cat dog 10 log REM sleep, h/d Amount of sleep 3. 1 man elephant 10 log body weight, kg body weight -0. 2 respiration rate body weight No thermo-regulation during REM sleep Dolphins: no REM sleep Links with aging Siegel, J. M. 2001 The REM sleep-memory consolidation hypothesis Science 294: 1058 -1063
Producer/consumer dynamics producer consumer : hazard rate nutr reserve of producer : total nutrient in closed system spec growth of consumer special case: consumer is not nutrient limited Kooijman et al 2004 Ecology, 85, 1230 -1243
Producer/consumer dynamics Consumer nutrient limited tangent Hopf homoclinic bifurcation Consumer not nutrient limited transcritical Hopf bifurcation
Producer/Consumer Dynamics Deterministic model Stochastic model in closed homogeneous system
10 3. 0 Bifurcation diagram Hopf 20 tangent focus 1. 0 consumers Producer/Consumer Dynamics 1. 15 2. 7 0 1. 23 0 1. 53 1. 23 1. 75 2 2. 8 4 6 2. 3 nutrient 8 2. 5 2. 4 isoclines
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
Direction probability around tangent around Hopf 2. 46 0. 12 0. 61 direction probability along isocline 3. 3 3. 165 3. 1 2. 9 1. 23 2. 7 producers P consumers C Tot nut tangent focus Hopf global TS 1. 217 1. 522 3. 165 7. 10 NTS 1. 230 1. 535 2. 801 6. 92
Trophic interactions Transitions between these types frequently occur • 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
Resource dynamics Typical approach
Prey/predator dynamics 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 Kooi et al 1997 J. Biol. Systems, 1: 77 -85
Resource dynamics Nutrient
Resource dynamics Nutrient
Resource dynamics Nutrient
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, Kooijman
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
consumer no preference producer preference for dead and weak predator Producer/consumer/predator total nutrient dynamics 9. 3. 1
Reserve vs structure Kcal/g wet weight cumulative fraction structure time, d carbohydrate lipid reserve protein time of reserve depletion, d Body mass in starving pacific oyster Crassooestrea gigas at 10°C Data from Whyte J. N. C. , Englar J. R. & Carswell (1990). Aquaculture 90: 157 -172.
Reserve E vs structure V
Reserve E vs structure V 100 g wet weight total protein lipid carbohydrate CMC 0, kcal 64. 81 30. 54 16. 80 16. 87 C JCM, kcal/d 0. 1042 0. 0408 0. 0200 0. 0358 401 616 516 0. 319 0. 114 0. 137 JCM, mmol/d 0. 426 0. 136 0. 290 MCE =ME , mol/mol 0. 500 0. 159 0. 341 C, k. J/C-mol MC 0, C-mol 0. 570 MCV =MV , mol/mol t 0 = 200 d 0. 546 0. 191 0. 263 MCV =MV , mol/mol t 0 = 400 d 0. 537 0. 185 0. 278 MCV =MV , mol/mol t 0 = 600 d 0. 531 0. 181 0. 288
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