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

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

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

Body composition 3.2a

Ash-Free-Dry/Wet Weight 3.2b

Relevance for energetics:dry mass ↔ wet volume

Growth efficiency 3.2.c

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

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

Macrochemical reaction eq 3.5

Notation for isotopes 3.6

Reshuffling 3.6a

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

Fractionation from pools & fluxes 3.6c

Oxygenic photosynthesis 3.6d

CO2 + 2 H2O CH2O + H2O + O2

Reshuffling of 18O

Fractionation of 13C

C4 plants 3.6e

Fractionation• weak in C4 plants• strong in C3 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

reserve structure

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

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

0.00

1

0.00

1

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 3.7aUncatalyzed reaction

Enzyme-catalyzedreaction

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

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 1CPoisson arrival events for molecules A and B

blocked time intervals

• acceptation event¤ rejection event

production

production

Kooijman, 1998Biophys Chem73: 179-188

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

Enzyme kinetics A+BC 3.7.2S

ynth

esiz

ing

Uni

t

Rej

ectio

n U

nit

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

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

Interactions of substrates 3.7.3a

Interactions of substrates 3.7.3b

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

Competition & inhibition 3.7.4d

Inhibition 3.7.4

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BAABB

BAACAC

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ABBA

BBABABB

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BABBAA

A does not affect B in yACAC; B inhibits binding of A

CA

A

A

A

ykjρθ..

BA

AAA

kkkjρj

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unbounded fractionbinding prob of Aarrival rate of Adissociation rate of Ayield of C on A

A inhibits binding of B in yACAC; B inhibits binding of A

BAABBA

BAACAC

AACAC

ABBA

BAABABB

ABABBAA

BABBAA

kkkjkj

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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

Social inhibition of x e 3.7.4b

sequential parallel

dilution rate

subs

trat

e co

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

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)

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

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 substrateData from Schukat et al, 1983

Brandt et al, 2003Water Research37, 4843-4854

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

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

• 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

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

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 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