dynamic energy budget theory 1 basic concepts 2 standard deb model 3 metabolismmetabolism 4...

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Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 Metabolism 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

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Page 1: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Dynamic Energy Budget theory

1 Basic Concepts 2 Standard DEB model 3 Metabolism 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 together10 Evolution11 Evaluation

Page 2: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

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 bivariateWe have only indirect access to these quantities

Page 3: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Body composition 3.2a

Page 4: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Ash-Free-Dry/Wet Weight 3.2b

Relevance for energetics:dry mass ↔ wet volume

Page 5: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Growth efficiency 3.2.c

Page 6: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Storage 3.3.2

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

Page 7: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Storage 3.3.2a

Anthochaera paradoxa (yellow wattlebird)fattens up in autumn to the extent that it can’tfly any longer; Biziura lobata (musk duck)must starve before it can fly

Page 8: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Macrochemical reaction eq 3.5

Page 9: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Notation for isotopes 3.6

Page 10: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Reshuffling 3.6a

Page 11: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Fractionation from pools & fluxes 3.6b

Examples• uptake of O2, NH3, CO2 (phototrophs)• evaporation of H2OMechanism• velocity e = ½ m c2

• binding probability to carriers

Examples• anabolic vs catabolic aspects assimilation, dissipation, growthMechanism• binding strength in decomposition

Page 12: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Fractionation from pools & fluxes 3.6c

Page 13: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Oxygenic photosynthesis 3.6d

CO2 + 2 H2O CH2O + H2O + O2

Reshuffling of 18O

Fractionation of 13C

Page 14: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

C4 plants 3.6e

Fractionation• weak in C4 plants• strong in C3 plants

Page 15: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Macrochemical reaction eq 3.6f

Page 16: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

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

reserve structure

Page 17: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Change in isotope fractions 3.6h

For mixed pool j = E, V (reserve, structure)

For non-mixed product j = o (otolith)

Page 18: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Isotopes in biomass & otolith 3.6i

time, d

time, d

time, d time, d

time, d

otolith length otolith length otolith length otolith length

otolith length

bo

dy

len

gth

bo

dy

len

gth

op

aci

ty

tem

pe

ratu

re

f,e

0.00

1

0.00

1

0.00

1

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1

0.00

1

Page 19: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

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

Page 20: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Enzyme kinetics 3.7aUncatalyzed reaction

Enzyme-catalyzedreaction

Page 21: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Synthesizing units 3.7b

Generalized enzymes that process generalized substrates and follow classic enzyme kinetics E + S ES EP E + Pwith 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

Page 22: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Transformation A → B 3.7e

Michealis-Menten (Henri 1902)Holling type II (Holling 1957)

Classification of behavioural modes: free & bound or searching & handling

Page 23: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Simultaneous Substrate Processing 3.7c

Chemical reaction: 1A + 1B 1CPoisson arrival events for molecules A and B

blocked time intervals

• acceptation event¤ rejection event

production

production

Kooijman, 1998Biophys Chem73: 179-188

Page 24: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

SU kinetics: n1X1+n2X2X 3.7d

0 tb tc

time

productrelease

productrelease

binding prod.

cycle

Period between subsequent arrivals is exponentially distributedSum of exponentially distributed vars is gamma distributed

Production flux not very sensitive for details of stoichiometryStoichiometry mainly affects arrival rates

Page 25: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Enzyme kinetics A+BC 3.7.2S

ynth

esiz

ing

Uni

t

Rej

ectio

n U

nit

Page 26: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Isoclines for rate A+BC 3.7.2a

.2 .2.4 .4.6 .6.8

Conc A Conc A

Con

c B

Synthesizing Unit Rejection Unit

almost singlesubstr limitationat low conc’s

.8

Page 27: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Interactions of substrates 3.7.3

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 low high

Page 28: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Interactions of substrates 3.7.3a

Page 29: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Interactions of substrates 3.7.3b

Kooijman, 2001Phil Trans R Soc B356: 331-349

Page 30: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Competition & inhibition 3.7.4d

Page 31: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Inhibition 3.7.4

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Page 32: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Aggressive competition 3.7.4a

V structure; E reserve; M maintenance substrate priority E M; posteriority V MJE flux mobilized from reserve specified by DEB theoryJV flux mobilized from structure amount of structure (part of maint.) excess returns to structurekV dissociation rate SU-V complex kE dissociation rate SU-E complex kV kE depend on such that kM = yMEkE(E. + EV)+yMVkV .V is constant

J EM,

J VM

J EM,

J VM

JE

kV = kE

kV < kE

Page 33: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Social inhibition of x e 3.7.4b

sequential parallel

dilution rate

subs

trat

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nc.

biom

ass

conc

.

No

soci

aliz

atio

n

Implications: stable co-existence of competing species “survival of the fittest”? absence of paradox of enrichment

x substratee reservey species 1z species 2

Page 34: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

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: 5 - 10 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)

Page 35: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Co-metabolism 3.7.5

Consider coupled transformations A C and B DBinding probability of B to free SU differs from that to SU-A complex

Page 36: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Co-metabolism 3.7.5a

binding prob. for substr A

Page 37: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Co-metabolism 3.7.5b

Co-metabolic degradation of 3-chloroaniline by Rhodococcus with glucose as primary substrateData from Schukat et al, 1983

Brandt et al, 2003Water Research37, 4843-4854

Page 38: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Co-metabolism 3.7.5cCo-metabolic anearobic degradation of citrate by E. coli with glucose as primary substrateData from Lütgens and Gottschalk, 1980

Brandt, 2002PhD thesisVU, Amsterdam

Page 39: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

iron bacteriumGallionella

Metabolic modes 3.8.1

4 Fe

8 H+4 Fe(OH)3

4 H2

O2 4 Fe2+

4 H2O

10 H2O

CO2

NH3 H2O

220 g iron 430 g rust + 1 g bact.

Trophy hetero- auto-

energy source chemo photo

carbon source organo litho

Example ofchemolithotrophy

Remember thiswhen you look at your bike/car

Page 40: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

• 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

Modules of central metabolism 3.8.2

Page 41: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Central metabolism 3.8.2a

Adenosine Tri-Phosphate (ATP)• 5 106 molecule in 1 bacterial cell• 2 seconds of synthetic work• mean life span: 0.3 seconds

Page 42: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Central Metabolism 3.8.2b

polymers

monomers

waste/source

source

Page 43: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

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

Page 44: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Compound parameters 3.9a

Page 45: Dynamic Energy Budget theory 1 Basic Concepts 2 Standard DEB model 3 MetabolismMetabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of

Dynamic Energy Budget theory

1 Basic Concepts 2 Standard DEB model 3 Metabolism 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 together10 Evolution11 Evaluation