Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of compounds 7 Extensions of DEB models 8 Co-variation of par values 9 Living together 10 Evolution 11 Evaluation

Body size 3.2 length: depends on shape and choice (shape coefficient) volumetric length: cubic root of volume; does not depend on shape contribution of reserve in lengths is usually small use of lengths unavoidable because of role of surfaces and volumes weight: wet, dry, ash-free dry contribution of reserve in weights can be substantial easy to measure, but difficult to interpret C-moles (number of C-atoms as multiple of number of Avogadro) 1 mol glucose = 6 C-mol glucose useful for mass balances, but destructive measurement Problem: with reserve and structure, body size becomes bivariate We have only indirect access to these quantities

Body composition 3.2a

Ash-Free-Dry/Wet Weight 3.2b Relevance for energetics: dry mass ↔ wet volume

Growth efficiency 3.2.c

Storage Plants store water and carbohydrates, Animals frequently store lipids Many reserve materials are less visible specialized Myrmecocystus serve as adipose tissue of the ant colony

Storage 3.3.2a Anthochaera paradoxa (yellow wattlebird) fattens up in autumn to the extent that it can’t fly any longer; Biziura lobata (musk duck) must starve before it can fly

Macrochemical reaction eq 3.5

Notation for isotopes 3.6

Reshuffling 3.6a

Fractionation from pools & fluxes 3.6b Examples uptake of O 2, NH 3, CO 2 (phototrophs) evaporation of H 2 O Mechanism velocity e = ½ m c 2 binding probability to carriers Examples anabolic vs catabolic aspects assimilation, dissipation, growth Mechanism binding strength in decomposition

Fractionation from pools & fluxes 3.6c

Oxygenic photosynthesis 3.6d CO H 2 O  CH 2 O + H 2 O + O 2 Reshuffling of 18 O Fractionation of 13 C

C 4 plants 3.6e Fractionation weak in C 4 plants strong in C 3 plants

Macrochemical reaction eq 3.6f

Isotopes in products 3.6g Product flux: fixed fractions of assimilation, dissipation, growth Assumptions: no fractionation at separation from source flux separation is from anabolic sub-flux catabolic flux anabolic flux product flux reservestructure

Change in isotope fractions 3.6h For mixed pool j = E, V (reserve, structure) For non-mixed product j = o (otolith)

Isotopes in biomass & otolith 3.6i time, d otolith length body length opacity temperature f,ef,e 

Flux vs Concentration 3.7 concept “concentration” implies spatial homogeneity (at least locally) biomass of constant composition for intracellular compounds concept “flux” allows spatial heterogeneity classic enzyme kinetics relate production flux to substrate concentration Synthesizing Unit kinetics relate production flux to substrate flux in homogeneous systems: flux  conc. (diffusion, convection) concept “density” resembles “concentration” but no homogeneous mixing at the molecular level density = ratio between two amounts

Enzyme kinetics 3.7a Uncatalyzed reaction Enzyme-catalyzed reaction

Synthesizing units 3.7b Generalized enzymes that process generalized substrates and follow classic enzyme kinetics E + S  ES  EP  E + P with two modifications: back flux is negligibly small E + S  ES  EP  E + P specification of transformation is on the basis of arrival fluxes of substrates rather than concentrations In spatially homogeneous environments: arrival fluxes  concentrations

Transformation A → B 3.7e Michealis-Menten (Henri 1902) Holling type II (Holling 1957) Classification of behavioural modes: free & bound or searching & handling

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:

SU kinetics: n 1 X 1 +n 2 X 2  X 3.7d 0tbtb tctc time product release product release binding prod. cycle Period between subsequent arrivals is exponentially distributed Sum of exponentially distributed vars is gamma distributed Production flux not very sensitive for details of stoichiometry Stoichiometry mainly affects arrival rates

Enzyme kinetics A+B  C Synthesizing Unit Rejection Unit

Isoclines for rate A+B  C 3.7.2a Conc A Conc B Synthesizing Unit Rejection Unit almost single substr limitation at low conc’s.8

Interactions of substrates Substrate interactions in DEB theory are based on Synthesizing Units (SUs): generalized enzymes that follow the rules of classic enzyme kinetics but working depends in fluxes of substrates, rather than concentrations “concentration” only has meaning in homogeneous environments backward fluxes are small in S + E  SE  EP  E + P Basic classification substrates: substitutable vs complementary processing: sequential vs parellel Mixture between substitutable & complementary substrates: grass  cow; sheep brains  cow; grass + sheep brains  cow Dynamics of SU on the basis of time budgetting offers framework for foraging theory example: feeding in Sparus larvae (Lika, Can J Fish & Aquat Sci, 2005): food searching sequential to mechanic food handling food processing (digestion) parellel to searching & handling gives deviations from Holling type II low high

Interactions of substrates 3.7.3a

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

Competition & inhibition 3.7.4d

Inhibition A does not affect B in y AC A  C; B inhibits binding of A unbounded fraction binding prob of A arrival rate of A dissociation rate of A yield of C on A A inhibits binding of B in y AC A  C; B inhibits binding of A

Aggressive competition 3.7.4a V structure; E reserve; M maintenance substrate priority E  M; posteriority V  M J E flux mobilized from reserve specified by DEB theory J V flux mobilized from structure  amount of structure (part of maint.) excess returns to structure k V dissociation rate SU-V complex k E dissociation rate SU-E complex k V k E depend on  such that k M = y ME k E (  E. +  EV )+y MV k V .V is constant J E M, J V M JEJE k V = k E k V < k E

Social inhibition of x  e 3.7.4b 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

Evolution & Co-existence 3.7.4c Main driving force behind evolution: Darwin: Survival of the fittest (internal forces) involves out-competition argument Wallace: Selection by environment (external forces) consistent with observed biodiversity Mean life span of typical species: Ma Sub-optimal rare species: not going extinct soon (“sleeping pool of potential response”) environmental changes can turn rare into abundant species Conservation of bio-diversity: temporal and spatial environmental variation mutual syntrophic interactions feeding rates not only depends on food availability (social interaction)

Co-metabolism Consider coupled transformations A  C and B  D Binding probability of B to free SU differs from that to SU-A complex

Co-metabolism 3.7.5a binding prob. for substr A

Co-metabolism 3.7.5b Co-metabolic degradation of 3-chloroaniline by Rhodococcus with glucose as primary substrate Data from Schukat et al, 1983 Brandt et al, 2003 Water Research 37,

Co-metabolism 3.7.5c Co-metabolic anearobic degradation of citrate by E. coli with glucose as primary substrate Data from Lütgens and Gottschalk, 1980 Brandt, 2002 PhD thesis VU, Amsterdam

iron bacterium Gallionella Metabolic modes Fe 8 H + 4 Fe(OH) 3 4 H 2 O2O2 4 Fe 2+ 4 H 2 O 10 H 2 O CO 2 NH 3 H 2 O 220 g iron  430 g rust + 1 g bact. Trophyhetero-auto- energy sourcechemophoto carbon sourceorganolitho Example of chemolithotrophy Remember this when you look at your bike/car

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 CO 2 NADP NADPH Respiratory chain NADPH + O 2 NADP + H 2 O ADP + P ATP Modules of central metabolism 3.8.2

Central metabolism 3.8.2a Adenosine Tri-Phosphate (ATP) molecule in 1 bacterial cell 2 seconds of synthetic work mean life span: 0.3 seconds

Central Metabolism 3.8.2b polymers monomers waste/source source

Assumptions of auxiliary theory 3.9 A well-chosen physical length  (volumetric) structural length for isomorphs Volume, wet/dry weight have contributions from structure, reserve, reproduction buffer Constant specific mass & volume of structure, reserve, reproduction buffer Constant chemical composition of juvenile growing at constant food

Compound parameters 3.9a

Dynamic Energy Budget theory 1 Basic ConceptsBasic Concepts 2 Standard DEB modelStandard DEB model 3 MetabolismMetabolism 4 Univariate DEB modelsUnivariate DEB models 5 Multivariate DEB modelsMultivariate DEB models 6 Effects of compoundsEffects of compounds 7 Extensions of DEB modelsExtensions of DEB models 8 Co-variation of par valuesCo-variation of par values 9 Living togetherLiving together 10 EvolutionEvolution 11 EvaluationEvaluation