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More-reserves DEB-systems Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam [email protected] http://www.bio.vu.nl/thb/ Marseille, 2007/12/20 More-reserves DEB-systems Contents: • Homeostasis • Evolution of DEB systems Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam [email protected] http://www.bio.vu.nl/thb/ • Central metabolism • Symbiogenesis • Dynamic nutrient limitation Marseille, 2007/12/20 Homeostasis 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 ectothermy homeothermy endothermy supply demand systems development of sensors, behavioural adaptations Evolution of DEB systems 1 strong homeostasis for structure 2 delay of use of internal substrates 3 increase of maintenance costs 4 inernalization of maintenance 5 7 Kooijman & Troost 2007 Biol Rev, 82, 1-30 reproduction juvenile embryo + adult animals 8 strong homeostasis for reserve installation of maturation program prokaryotes variable structure composition 6 plants 9 specialization of structure Central Metabolism 2.5 source polymers monomers waste/source Modules of central metabolism 2.5 • Pentose Phosphate (PP) cycle glucose-6-P ribulose-6-P, NADP NADPH • Glycolysis glucose-6-P pyruvate ADP + P ATP • TriCarboxcyl Acid (TCA) cycle pyruvate CO2 NADP NADPH • Respiratory chain NADPH + O2 NADP + H2O ADP + P ATP Evolution of central metabolism 2.5 in prokaryotes (= bacteria) 3.8 Ga 2.7 Ga i = inverse ACS = acetyl-CoA Synthase pathway RC = Respiratory Chain PP = Pentose Phosphate cycle Gly = Glycolysis TCA = TriCarboxylic Acid cycle Kooijman & Troost 2007 Biol Rev, 82, 1-30 Prokaryotic metabolic evolution 2.5 Heterotrophy: • pentose phosph cycle • glycolysis • respiration chain Phototrophy: • el. transport chain • PS I & PS II • Calvin cycle Chemolithotrophy • acetyl-CoA pathway • inverse TCA cycle • inverse glycolysis Symbiogenesis 2.5 2.7 Ga phagocytosis 2.1 Ga 1.27 Ga Symbiosis 9.1.3 substrate product Symbiosis substrate 9.1.3 substrate Steps in symbiogenesis Free-living, homogeneous Structures merge Free-living, clustering 9.1.3 Internalization Reserves merge biomass density Chemostat Steady States Free living Products substitutable Free living Products complementary Exchange on flux-basis Structures merged throughput rate symbiont host 9.1.3 Endosymbiosis Exchange on conc-basis Reserves merged Host uses 2 substrates Symbiogenesis 9.1.3 • symbioses: fundamental organization of life based on syntrophy ranges from weak to strong interactions; basis of biodiversity • symbiogenesis: evolution of eukaryotes (mitochondria, plastids) • DEB model is closed under symbiogenesis: it is possible to model symbiogenesis of two initially independently living populations that follow the DEB rules by incremental changes of parameter values such that a single population emerges that again follows the DEB rules • essential property for models that apply to all organisms Kooijman, Auger, Poggiale, Kooi 2003 Quantitative steps in symbiogenesis and the evolution of homeostasis Biological Reviews 78: 435 - 463 Maintenance from reserve & structure Tolla et al 2007 J. Theor Biol, 244, 576-587 Multiple reserves imply excretion DEBtool/alga/sgr sgr1, sgr2, sgr3, sgr4 The functions obtain the specific growth rate, the reserve and structure fluxes for maintenance and the rejected reserve fluxes for 1, 2, 3 and 4 reserve systems. All reserves are supplementary for maintenance as well as for growth, while each reserve and structure are substitutable for maintenance. The preference for the use of structure relative to that of reserve for maintenance can be set with a (non-negative) preference parameter. The value zero gives absolute priority to reserve, which gives a switch at specific growth rate 0. All functions sgr have the same structure, and the input/output is presented for sgri where i takes values 1, 2, 3 of 4. Inputs: (i,1)-matrix with reserve density mE (i,1)-matrix with reserve turnover rate kE (i,1)-matrix with specific maintenance costs from reserve jEM (i,1)-matrix with costs for structure yEV optional (i,1)-matrix with specific maintenance costs from structure jVM; default is jEM/ yEV optional scalar or (i,1)-matrix with preference parameter alpha; default is 0 Outputs: scalar with specific growth rate r (i,1)-matrix with reserve flux for maintenance jEM (i,1)-matrix with structure flux for maintenance jVMM (i,1)-matrix with rejected reserve flux jER scalar with info on failure (0) or success (1) of numerical procedure An example of use is given in mydata_sgr Organic carbon pump Wind: weak moderate 9.4 strong producers bind CO2 from atmosphere and transport organic carbon to deep ocean light + CO2 “warm” no nutrients cold nutrients no light readily degradable recovery of nutrients to photo-zone controls pump poorly degradable no growth growth bloom poor growth Reserve Capacity & Growth low turnover rate: large reserve capacity high turnover rate: small reserve capacity 5.2 Simultaneous nutrient limitation 5.2.3 Specific growth rate of Pavlova lutheri as function of intracellular phosphorus and vitamine B12 at 20 ºC Data from Droop 1974 Note the absence of high contents for both compounds due to damming up of reserves, and low contents in structure (at zero growth) P Vitamin B12 kE 1.19 1.22 d-1 yXV 0.39 10- 2.35 mol.cell-1 jEAm 4.91 10- 76.6 10-15 mol.cell-1. d-1 κE 0.69 0.96 kM 0.0079 0.135 d-1 K 0.017 0.12 pM, μM Spec growth rate, d-1 15 21 Spec growth rate, d-1 B12(pM) 68 14.4 6.8 1.44 20.4 1.44 6.8 B12-conc, pM P-conc, μM P-content, fmol.cell-1 Data from Droop 1974 on Pavlova lutheri 5.2.41.44 B12-cont., 10-21.mol.cell-1 Reserve interactions P(μM) Spec growth rate, d-1 C,N,P-limitation N,P reductions 5.2.4 P reductions N reductions Nannochloropsis gaditana (Eugstimatophyta) in sea water Data from Carmen Garrido Perez Reductions by factor 1/3 starting from 24.7 mM NO3, 1.99 mM PO4 C,N,P-limitation 5.2.4 Nannochloropsis gaditana in sea water d C (k E r )mC nCV r jC X J C kC C DIC dt For i C , N , P d N (k E r )mN nNV r j N X nitrate uptake rate dt jim j i d 1 Ki / i P (k E r )mP nPV r jP X phosphate dt spec growth rate d kE r m j k m i i E i res. dens. dt ri i mi yEV d X rX structure dt 1 1 1 1 1 1 1 1 spec growth r rC rN rP rC rN rC rP rN rP rC rN rP C,N,P-limitation 5.2.4 Nannochloropsis gaditana in sea water half-saturation parameters KC = 1.810 mM for uptake of CO2 KN = 3.186 mM for uptake of NO3 KP = 0.905 mM for uptake of PO4 max. specific uptake rate parameters jCm = 0.046 mM/OD.h, spec uptake of CO2 jNm = 0.080 mM/OD.h, spec uptake of NO3 jPm = 0.025 mM/OD.h, spec uptake of PO4 reserve turnover rate kE = 0.034 h-1 yield coefficients yCV = 0.218 mM/OD, from C-res. to structure yNV = 2.261 mM/OD, from N-res. to structure yPV = 0.159 mM/OD, from P-res. to structure carbon species exchange rate (fixed) kBC = 0.729 h-1 from HCO3- to CO2 kCB = 79.5 h-1 from CO2 to HCO3- initial conditions (fixed) HCO3- (0) = 1.89534 mM, initial HCO3- concentration CO2(0) = 0.02038 mM, initial CO2 concentration mC(0) = jCm/ kE mM/OD, initial C-reserve density mN(0) = jNm/ kE mM/OD, initial N-reserve density mP(0) = jPm/ kE mM/OD, initial P-reserve density OD(0) = 0.210 initial biomass (free) Fast/slow substrate uptake DEB-consistent variant of Morel 1987 • uptake depends on substrate concentration and reserve density • reserve mobilization independent of uptake Not yet tested against experimental data DEB tele course 2009 Cambridge Univ Press 2000 http://www.bio.vu.nl/thb/deb/ Free of financial costs; some 250 h effort investment Program for 2009: Feb/Mar general theory April symposium in Brest (2-3 d) Sept/Oct case studies & applications Target audience: PhD students We encourage participation in groups who organize local meetings weekly Software package DEBtool for Octave/ Matlab freely downloadable Slides of this presentation are downloadable from http://www.bio.vu.nl/thb/users/bas/lectures/ Audience: thank you for your attention Organizers: thank you for the invitation