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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 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
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
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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
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
Inhibition 3.7.4
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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
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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
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nc.
biom
ass
conc
.
No
soci
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atio
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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
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