From embryo to senescence
with DEB theory for metab org
Bas Kooijman
Dept theoretical biology
Vrije Universiteit Amsterdam
Bas@bio.vu.nl
http://www.bio.vu.nl/thb/
Melbourne, 2012/08/07
From embryo to senescence
with DEB theory for metab org
Bas Kooijman
Dept theoretical biology
Vrije Universiteit Amsterdam
Bas@bio.vu.nl
http://www.bio.vu.nl/thb/
Contents:
• intro
• surface/volume
• selection
• embryo development
• ageing
Melbourne, 2012/08/07
Energy Budgets
Basic processes
Life history events
• Feeding
• Digestion
• Storing
• Growth
• Maturation
• Maintenance
• Reproduction
• Product formation
• Aging
• zero:
start of development
• birth:
start of feeding
start of acceleration
• metamorphosis:
end of acceleration
• puberty:
end of maturation
start of reproduction
All processes interact during the life cycle
Life stages
embryo
juvenile
adult
Some DEB pillars
• life as coupled chemical transformations
• life cycle perspective of individual as primary target
• energy & mass & time balances
• stoichiometric constraints via Synthesizing Units
• surface area/ volume relationships
• spatial structure & transport
• syntrophy (basis for symbioses)
• homeostasis
• intensive/extensive parameters: scaling
• evolutionary perspective
Standard DEB scheme 2b
1 food type, 1 reserve, 1 structure, isomorph
food
feeding
defecation
faeces
assimilation
reserve
somatic
maintenance
growth
structure

1-
maturity
maintenance
maturation
reproduction
maturity
offspring
time: searching & handling
feeding  surface area
weak & strong homeostasis
κ-rule for allocation to soma
maintenance has priority
somatic maint  structure
maturity maint  maturity
stage transition: maturation
embryo: no feeding, reprod
juvenile: no reproduction
adult: no maturation
maternal effect: reserve density
at birth equals that of mother
initially: zero structure, maturity
Empirical special cases of DEB
11.1
year author
model
year
author
model
1780
Lavoisier
multiple regression of heat
against mineral fluxes
1950
Emerson
cube root growth of bacterial
colonies
1825
Gompertz
Survival probability for aging
1951
Huggett & Widdas
foetal growth
1889
Arrhenius
1891
DEB theory
is axiomatic,
temperature dependence of
1951
Weibull
rates
basedphysiological
on mechanisms
allometric growth of body parts
Huxley
1955
Best
not meant
to glue empirical
models
survival probability for aging
diffusion limitation of uptake
1902
Henri
Michaelis--Menten kinetics
1957
Smith
embryonic respiration
1905
Blackman
bilinear functional response
1959
Leudeking & Piret
microbial product formation
1910
Hill
1973
Droop
1920
1927
Since many
empirical models
Cooperative binding
hyperbolic functional response
1959
Holling
to begrowth
special
cases
of &DEB
theory
von Bertalanffy
of
maintenance in yields of biomass
Pütterturn out
1962
Marr
Pirt
individuals
the data
behind these models support DEB
theory
logistic population growth
reserve (cell quota) dynamics
Pearl
1928
Fisher &
Tippitt
Weibull aging
1974
Rahn & Ar
water loss in bird eggs
1932
Kleiber
respiration scales with body
weight3/ 4
1975
Hungate
digestion
1932
Mayneord
cube root growth of tumours
1977
Beer & Anderson
development of salmonid embryos
This makes DEB theory very well tested against data
length, mm
Von Bert growth rate -1, d
Growth at constant food
time, d
Von Bertalanffy growth curve:
ultimate length, mm
volume, m3
Bacillus  = 0.2
Collins & Richmond 1962
time, min
Fusarium  = 0
Trinci 1990
time, h
volume, m3
volume, m3
hyphal length, mm
Mixtures of V0 & V1 morphs
Escherichia  = 0.28
Kubitschek 1990
time, min
Streptococcus  = 0.6
Mitchison 1961
time, min
Dynamic mixtures of
V0- & V1-morphs
Respiration: assim + maint + growth
Assim, maint  mass
Growth in diam  time at constant food
V0-morph
V1-morph
Dynamic mixtures of
V0- & V1-morphs
Celleporella
15 cm/yr
Respiration
mixture  mass1/2
isomorph  mass3/4
33
33
16
16
5
5
2
2
0.5 cm/yr
0.5 cm/yr
White et al 2011
Am. Nat., 178: 746-754
Dynamic mixtures of
V0- & V1-morphs
Celleporella
33, 24 cm/yr
Respiration
mixture  mass1/2
isomorph  mass3/4
33
16
5
2
0.5 cm/yr
White et al 2011
Am. Nat., 178: 746-754
Selection affects par values
Gallus gallus
Red jungle fowl
Indian River Broiler
White leghorn
ml O2 d-1
ml CO2 d-1
Respiration ontogeny in birds
altricial
Troglodytes aëdon
Data: Kendeigh 1940
age, d
precocial
Gallus domesticus
Data: Romijn & Lokhorst 1951
age, d
Observations: just prior to hatching
• respiration shows a plateau in precocial, not in altricial birds
• pore size and frequency in egg shell is such that O2 flux has constant resistance
Conclusion: ontogeny is constrained by diffusion limitation in precocial birds (Rahn et al 1990)
DEB theory: reserve dynamics controls ontogeny (same pattern in species without shells)
Minimization of water loss causes observed constant flux resistance
Embryonic development
weight, g
embryo
yolk
time, d
O2 consumption, ml/h
Zonneveld & Kooijman 1993
Bul. Math. Biol. 55: 609-635
Crocodylus johnstoni,
Data: Whitehead 1987
time, d
Twinning: separation of cells
Kooijman 2009
J. Math. Biol.
58: 377--394
Maternal effect:
reserve density at birth =
reserve density of mother
Kooijman 2012
J. Math. Biol.
subm
Parameter estimates from
add_my_pet 2012/06/17,
egg development only
Embryo: isomorphic
v constant
length
Acceleration of development
Early juvenile: V1-morphic
v, {pAm} increase with length
Late juvenile/adult: isomorphic
time since birth
v, {pAm} constant
Found in:
bivalves, gastropods, copepods, amphipods, decapods,
collembolas, echinoderms, lancelets, tunas, flatfish, anchovy,
Danio, caecilians, marsupials
Anchovy Engraulis encrasicolus
length, cm
embryo
0.16 cm
0.4 cm
time, d
1.2 cm
>4 cm
Pecquerie 2008
PhD thesis VU A’dam
0.9 cm
0.22 cm
Stage transitions
at maturity thresholds
Danio rerio
28.5°C
Augustine et al 2011
Comp. Biochem. Physiol. A
159 :275–283
Stage transitions
< birth
: isomorph
birth-metamorphosis: V1-morph
> metamorphosis : isomorph
at maturity thresholds
Danio rerio
28.5°C
Data:
Lauwrence et al 2008
caloric restriction
Data: Augustine
Augustine et al 2011
Comp. Biochem. Physiol. A
159 :275–283
10log
10log
yolkiness
spec maturity
at
birth
Acceleration
10log
coelenterata
lophotrochozoa
ecdysozoa
invert deuterostomata
ectotherm vertebrata
endotherm vertebrata
acceleration
10log
acceleration
Acceleration of development
acceleration
no
yes
development
Casey Muller
indirect
Crinia georgiana
Geocrinia vitellina
Crinia nimbus
Nicky Mitchell
Pseudophryne bibronii
direct
Acceleration of development
birth
metam
birth
max dry weight 500 mg
Dry mass, mg
hatch
Crinia georgiana
1
metam
Mueller et al 2012,
Comp. Biochem. Physiol. A
163: 103-110
¼
age, d
0
12 °C
O2 nmol/h

½
hatch
¾
hatch
birth
1
¾
¼
age, d
0
hatch
birth

½
O2 nmol/h
Dry mass, mg
max dry weight 200 mg
metam
Pseudophryne bibronii
metam
age, d
age, d
Free radicals  Aging
Aging results from damage by Reactive Oxygen Species (ROS) Gerschman 1954
link with DEB model via dioxygen consumption & metabolic activity
Aging is binary in unicellulars, and gradual in multicellulars
age-affected cells no longer divide
Typical aging only occurs in multicellulars with irreversible cell differentiation
that have post-mitotic tissues
Induction of damage inducing compounds  dioxygen consumption
contribution from assimilation is not included
because of more local occurrence in organism
Empirical evidence points to acceleration of aging
Damage inducing compounds generate
• damage inducing compounds
• damage compounds; hazard rate  density of damage compounds
Some chemical compounds (e.g. RNS) and -radiation can stimulate aging
Ageing
metabolism
O2
ROS
damage inducing compounds
continuous
endotherms
mitochondrional DNA
damage compounds
proteins
effect on hazard
DEB module
• Weibull (1951) &
Gompertz (1825) model
are special cases
• based on mechanisms
• links with energetics
body length, cm
survival prob
Aging: ectotherms & feeding
- ad libitum
- restricted 100-600 d
time, d
Poecilia reticulata
Data: Comfort, 1963
time, d
Aging: endotherms & feeding
embryo weight, g
body weight, g
feeding
level
1
0.75
0.44
survival probability
time, d
time, d
0.44
0.75
time, d
1
Van Leeuwen et al 2002 Biogerontology 3: 373-381
Life span
• hardly depends on food in ecotherms
• decreases for increasing food in endotherms
Data on Mus musculus:
Weindruch et al 1986, MacDowell et al 1927
body length, mm
survival prob
Aging: sex differentiation
time, d
time, d
Differences in aging between sexes are caused by
differences in energy investment ratio g
Data on Daphnia magna: MacArthur & Baillie 1929
age after eclosion, d
h(t ) 

he
t2 
 ha k M  a 0 3 R 
2
κ R gl 
Data: Rose 1984
Drosophila melanogaster
No growth
surviving number
surviving number
Weibull
Model
=3
# of eggs/beetle, d-1
Aging in adult insects
age after eclosion, d
Data: Ernsting & Isaaks, 1991
Notiophilus biguttatus
survival based on
observed reproduction
initial
random
mort
age after eclosion, d
h e t t1
t2
h(t )  ha k M  a 0 3   R(t 2 ) dt 2 dt1
2
κ R gl 0 0
ha e0
: High food, 20/10 °C
κ R gl 3
-2
0.63 a
High food, 10 °C
0.547 a-2
Low food, 20/10 °C
0.374 a-2
General Weibull fits DEB
Both models are fitted to the same data
They fit equally well and have both 4 parameters
Contrary to the Weibull model the DEB model
- is based on tested assumptions
- has links with energetics via hW and hG.
Data from Elandt-Johnson & Johnson 1980 for white USA males in the period 1969-1971
Ageing among species
Right whale
slope 1/3, 1/5
Conclusion for life span
• hardly depends on max body size of ectotherms
• increases with length in endotherms
Ricklefs & Finch 1995
DEB tele course 2013
http://www.bio.vu.nl/thb/deb/
Free of financial costs;
Some 108 or 216 h effort investment
Program for 2013:
Feb/Mar general theory (5w)
April symposium at NIOZ-Texel (NL) (8 + 3 d)
Target audience: PhD students
We encourage participation in groups
who organize local meetings weekly
Cambridge Univ Press 2009
Software package DEBtool for Octave/ Matlab
freely downloadable
Slides of this presentation are downloadable from
http://www.bio.vu.nl/thb/users/bas/lectures/
Audience:
thank you for your attention