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DEB theory - past and future MPDE 2013. Bas Kooijman Dept theoretical biology Vrije Universiteit Amsterdam [email protected] http://www.bio.vu.nl/thb. Osnabr ück , 2013/08/27/09:00-09:45. Energy Budgets. Processes feeding digestion storing growth maturation maintenance - PowerPoint PPT Presentation
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DEB theory - past and futureMPDE 2013
Bas KooijmanDept theoretical biology
Vrije Universiteit [email protected]
http://www.bio.vu.nl/thb
Osnabrück, 2013/08/27/09:00-09:45
Energy Budgets
Processes
• feeding• digestion• storing• growth• maturation• maintenance• reproduction• product formation• aging
Life history events
• zero: start of development• birth: start of feeding start of acceleration• metamorphosis: end of acceleration• puberty: end of maturation start of reproduction
Life stages
embryo
juvenile
adult
molecule organ individual ecosystem system earth
Fluxes
• organics food, faeces, biomass
• minerals CO2, H2O, O2, NH3
• products wood, shells, moults
• heat• entropy• isotopes
Empirical patternsFeeding During starvation, organisms are able to reproduce, grow and survive for some time At abundant food, the feeding rate is at some maximum, independent of food density
Growth Many species continue to grow after reproduction has started Growth of isomorphic organisms at abundant food is well described by the von Bertalanffy For different constant food levels the inverse von Bertalanffy growth rate increases linearly with ultimate length The von Bertalanffy growth rate of different species decreases almost linearly with the maximum body length Fetuses increase in weight approximately proportional to cubed time
Reproduction Reproduction increases with size intra-specifically, but decreases with size inter-specifically
Respiration Animal eggs and plant seeds initially hardly use O2
The use of O2 increases with decreasing mass in embryos and increases with mass in juveniles and adults The use of O2 scales approximately with body weight raised to a power close to 0.75 Animals show a transient increase in metabolic rate after ingesting food (heat increment of feeding)
Stoichiometry The chemical composition of organisms depends on the nutritional status (starved vs well-fed) The chemical composition of organisms growing at constant food density becomes constant
Energy Dissipating heat is a weighted sum of 3 mass flows: CO2, O2 and N-waste
Food chains n=2
time, h time, h
glucose
Escherichia coli
Dictyostelium
mg/
ml
mm
3 /m
lm
m3 /
ml
cell
vol,
m3
cell
vol,
m3
X0(0) 0.433 mg. ml-1
X1(0) 0.361 X2(0) 0.084 mm3.ml-1
e1(0) 1 e2(0) 1 -
XK1 0.40 XK2 0.18
g1 0.86 g2 4.43 -
kM1 0.008 kM2 0.16 h-1
kE1 0.67 kE2 2.05 h-1
jXm1 0.65 jXm2 0.26
ml
mm,
ml
g 3μ
13
h,hmm
mg
Data from Dent et al 1976h = 0.064 h-1, Xr = 1mg ml-1, 25 °C
Kooijman & Kooi,1996 Nonlin. World 3: 77 - 83
Growth on reserve
Opt
ical
Den
sity
at 5
40 n
m
Con
c. p
otas
sium
, mM
Potassium limited growth of E. coli at 30 °CData Mulder 1988; DEB model fitted
OD increases by factor 4 during nutrient starvationinternal reserve fuels 9 hours of growth
time, h
Yield vs growth
1/spec growth rate, 1/h
1/yi
eld,
mm
ol g
luco
se/
mg
cells
Streptococcus bovis, Russell & Baldwin (1979)
Marr-Pirt (no reserve)DEB
spec growth rate
yield
Russell & Cook (1995): this is evidence for down-regulation of maintenance at high growth ratesDEB theory: high reserve density gives high growth rates structure requires maintenance, reserves do not
Cell quota
Droop 1968J Mar Biol Assoc UK 48: 689-733
Vitamin B12 limited growth of Monochrysis lutheri
Droop’s model
subsistence quota540 molecules/cell
Droop → DEB• quota → structure + reserve• static → dynamic• include maintenance• population → individual• V1- → iso-morph
Migration: metabolic memory
Some populations of humpback whale Megaptera novaeangliae (36 Mg) migrate 26 Mm anually without feeding, A 15 m mother gets a 6 m calf in tropical waters, gives it 600 l milk/d for 6 months and together return to cold waters to resume feeding in summer
Product Formation
throughput rate, h-1
glyc
erol
, eth
anol
, g/l
pyru
vate
, mg/
l
glycerol
ethanol
pyru
vate
Glucose-limited growth of SaccharomycesData from Schatzmann, 1975
According to Dynamic Energy Budget theory:
Product formation rate = wA . Assimilation rate + wM . Maintenance rate + wG . Growth rate
For pyruvate: wG<0
Method of indirect calorimetry
Empirical origin (multiple regression): Lavoisier 1780
Heat production = wC CO2-production + wO O2-consumption + wN N-waste production
DEB-explanation:Mass and heat fluxes = wA assimilation + wD dissipation + wG growthApplies to CO2, O2, N-waste, heat, food, faeces, …
For V1-morphs: dissipation maintenance
Metabolic rate
Log weight, g
Log metabolic rate,
w
endotherms
ectotherms
unicellulars
slope = 1
slope = 2/3
Length, cm
O2 consum
ption,
l/h
Inter-speciesIntra-species
0.0226 L2 + 0.0185 L3
0.0516 L2.44
2 curves fitted:
(Daphnia pulex)
Data: Hemmingson 1969; curve fitted from DEB theoryData: Richman 1958; curve fitted from DEB theory
Homeostasisstrong constant composition of pools (reserves/structures) generalized compounds, stoichiometric contraints on synthesis
weak constant composition of biomass during growth in constant environments determines reserve dynamics (in combination with strong homeostasis)
structural
constant relative proportions during growth in constant environments isomorphy .work load allocation
thermal ectothermy homeothermy endothermy
acquisition supply demand systems; development of sensors, behavioural adaptations
Surface area/volume interactions• biosphere: thin skin wrapping the earth light from outside, nutrient exchange from inside is across surfaces production (nutrient concentration) volume of environment
• food availability for cows: amount of grass per surface area environment food availability for daphnids: amount of algae per volume environment
• feeding rate surface area; maintenance rate volume (Wallace, 1865)
• many enzymes are only active if linked to membranes (surfaces) substrate and product concentrations linked to volumes change in their concentrations gives local info about cell size ratio of volume and surface area gives a length
Change in body shapeIsomorph: surface area volume2/3
volumetric length = volume1/3
V0-morph: surface area volume0
V1-morph: surface area volume1
Ceratium
Mucor
Merismopedia
Isomorphic growth
diam
eter
, m
Wei
ght1/
3 , g
1/3
leng
th, m
m
time, h time, h
time, dtime, d
Amoeba proteusPrescott 1957
Saccharomyces carlsbergensisBerg & Ljunggren 1922
Pleurobrachia pileusGreve 1971
Toxostoma recurvirostreRicklefs 1968
Wei
ght1/
3 , g
1/3
Mixtures of V0 & V1 morphs 4.2.3a
volu
me,
m
3vo
lum
e,
m3
volu
me,
m
3
hyph
al le
ngth
, mm
time, h time, min
time, mintime, min
Fusarium = 0Trinci 1990
Bacillus = 0.2Collins & Richmond 1962
Escherichia = 0.28Kubitschek 1990
Streptococcus = 0.6Mitchison 1961
Mixtures of changes in shape
Dynamic mixtures between morphs
Lichen Rhizocarpon
V1- V0-morph
V1- iso- V0-morph
outer annulus behaves as a V1-morph, inner part as a V0-morph. Result: diameter increases time
Synthesizing units
Are enzymes that 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
The concept concentration is problematic in spatially heterogeneous environments, such as inside cellsIn spatially homogeneous environments, arrival fluxes are proportional to concentrations
Evolution of DEB systemsvariable structure
composition
strong homeostasisfor structure
delay of use ofinternal substrates
increase ofmaintenance costs
inernalization of maintenance
installation ofmaturation program
strong homeostasisfor reserve
reproductionjuvenile embryo + adult
Kooijman & Troost 2007 Biol Rev, 82, 1-30
54321
specialization of structure
7
8
an
ima
ls
6
pro
ka
ryo
tes
9plants
Add_my_pet
2013/08/28:
303 species
15 phyla
all 13 chordate classes
surv
ivor
fun
ctio
n
surv
ivor
fun
ctio
n
Allocation to somapo
p gr
owth
rat
e, d
-1
max
rep
rod
rate
, #d-1
Frequency distribution of κ among species in the add_my_pet collection:
Mean κ = 0.81, but optimum is κ = 0.5
Lika et al 2011 , Kooijman & Lika 2013J. Sea Res, 22: 278-288, Biol Rev, subm
Selection for reproduction
White Leghorn
Red Jungle fowl
Indian River broiler
Kooijman & Lika 2013Am Nat subm
Waste to hurryExploiting blooming resources requires blooming yourself
• high numerical response• short life cycle• small body size• fast reproduction• fast growth• high feeding rate• resting stages between blooms
-rule explains why [pM] needs to be high
Ecosystem significance:flux through basis food pyramid
Kooijman 2013Oikos 122: 348-357
Embryonic development
time, d
wei
ght,
g
O2 c
onsu
mpt
ion,
ml/h
Crocodylus johnstoni,Data: Whitehead 1987
yolk
embryo
time, d
Metabolic accelerationDef: long-term increase of respiration relative to standard DEB expectation
Types• acceleration of maturation (allocation)• type X acceleration: food• type A acceleration: assimilation• type M acceleration: morph• type T acceleration: temperature
Short-term increase in respiration (no metabolic acceleration)• heat increment of feeding• boosts of activity• migration• pregnancy/ lactation
Ctenophora
Cnidaria
Tunicata
Leptocardii
Echinodermata
Mixini
Cephalaspidorphi
Chondrichthyes Actinopterygii
Amphibia
ReptiliaAves
Mammalia
Chaetognatha
Rotifera
Gastrotricha
Platyhelminthes
AnnelidaMollusca
Tardigrada
NematodaCrustacea
Arachnida
Enthognatha
Insecta
1 2 5 10
Sarcopterygii
Deuterostomia
Ecdysozoa
Lophotrochozoa
Platy
zoa
Radiata
Anthocephala
Bryozoa
Type M acceleration
acceleration factor Kooijman 2013Biol. Rev. subm
Hemimetabolic insect ontogeny
Acyrthosiphon pisumpea aphid
Locusta migratoriamigratory locust
Embryo: isomorphJuvenile: V1-morphAdult: no growth
30 27 24 21 18 °C
Maturity thresholds
RadiataBilateriaPlatyzoaLophotrochozoaEcdyspzoaInvert deuterostomesEctothermic vertEndothermic vert
birth metam
puberty
Open symbols:acceleration
Growth ratesRadiataBilateriaPlatyzoaLophotrochozoaEcdyspzoaInvert deuterostomesEctothermic vertEndothermic vert
Kooijman & Lika 2013Proc R Soc B subm
birth metam
puberty
Open symbols:acceleration
Bijection data - parameter space
Assumptions• abundant food• temperature constant• water content of E = that of V• zero surface linked som maint• zero Gompertz stress
Known• mol-weights of E & V• chem potentials of E & V• maturity maint rate coeff • growth efficiency • reproduction efficiency
Future DEB research
• Add_my_pet: taxon-specific patterns application in evolution, ecology, conservation, technology
• More-reserve/structure systems: nutrition, plants, behavioural ecology
• Molecular level interaction biochemical modules on basis of mutual syntrophy
• Ecosystem level canonical community, body size spectra
DEB tele course 2015
http://www.bio.vu.nl/thb/deb/
Free of financial costs; Some 108 or 216 h effort investment
Program for 2015: Feb/Mar general theory (5w: 02/19-03/26) April symposium in Marseille (F) (8d +3 d: 04/13-24) 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/
Cambridge Univ Press 2009
Audience: thank you for your attention