1. From embryo to senescence with DEB theory for metab org
Bas Kooijman
Dept theoretical biology
Vrije Universiteit Amsterdam
Melbourne, 2012/08/07

2. From embryo to senescence with DEB theory for metab org
Bas Kooijman
Dept theoretical biology
Vrije Universiteit Amsterdam
Contents:
intro
surface/volume
selection
embryo development
ageing
Melbourne, 2012/08/07

3. Energy Budgets Basic processes
Feeding
Digestion
Storing
Growth
Maturation
Maintenance
Reproduction
Product formation
Aging
All processes interact during the life cycle
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
This is the task-list for the qualitative aspects of energy budgets
Quantitative aspects are controlled by consistency requirements:
Assumptions must be internally consistent
Conservation rules should be respected (time, mass, energy, entropy, stoichiometry)
Empirical facts must be captured

4. 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

5. Standard DEB scheme 2b food faeces reserve structure  offspring
1 food type, 1 reserve, 1 structure, isomorph
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
food
faeces
assimilation
reserve
feeding
defecation
structure
somatic
maintenance
growth 
1-
maturity
maintenance
offspring
maturation
reproduction

6. Empirical special cases of DEB 11.1
DEB theory is axiomatic,
based on mechanisms
not meant to glue empirical models
Since many empirical models
turn out to be special cases of DEB theory
the data behind these models support DEB theory
This makes DEB theory very well tested against data
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
temperature dependence of physiological rates
Weibull
survival probability for aging
1891
Huxley
allometric growth of body parts
1955
Best
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
Cooperative binding
Holling
hyperbolic functional response
1920
Pütter
von Bertalanffy growth of individuals
1962
Marr & Pirt
maintenance in yields of biomass
1927
Pearl
logistic population growth
1973
Droop
reserve (cell quota) dynamics
1928
Fisher & Tippitt
Weibull aging
1974
Rahn & Ar
water loss in bird eggs
1932
Kleiber
respiration scales with body weight3/ 4
1975
Hungate
digestion
Mayneord
cube root growth of tumours
1977
Beer & Anderson
development of salmonid embryos
Many existing empirical models turn out to be special cases of DEB models, or very good numerical approximations;
the list continued to grow over the years.
Many of them are quite old and together they concern very different aspects of life;
none of the original authors could be aware of the coherence of these empirical models.
This in itself is for me already a most rewarding side-result of DEB theory.
DEB theory reveals how they all follow from simple physical and chemical phenomena;
this helps to understand under what conditions these models will probably not work that well.
Each of these models was created because it described experimental data well.
Using all this evidence, and the results of some 200 man-year of research by the group working on DEB theory, I dare to state that, at present, DEB theory is the best tested quantitative theory in biology.

7. Growth at constant food
ultimate length, mm
Von Bert growth rate -1, d
length, mm
When animals, here Daphnia magna, are exposed to constant food conditions, length-at-time since birth follows von Bertalanffly curves.
At different food levels, different rates and ultimate lengths result:
The inverse von Bertalanffy rate (the von Bertalanffy time) is linear in the ultimate length.
The slope equals 3 M/v where structural length equals M time physical body length
The intercept equals 3/kM; it cannot be zero, because maintenance would then be infinitely large
time, d
Von Bertalanffy growth curve:

8. Mixtures of V0 & V1 morphs volume, m3 hyphal length, mm
time, min
Bacillus  = 0.2
Collins & Richmond 1962
volume, m3
hyphal length, mm
Fusarium  = 0
Trinci 1990
time, h
volume, m3
time, min
Escherichia  = 0.28
Kubitschek 1990
volume, m3
time, min
Streptococcus  = 0.6
Mitchison 1961
At constant food/substrate the growth curve reveals deviations from isomorphy.
These 4 organisms (1 fungus and 3 eubacteria) only grow in length, not in diameter.
These 4 cases only differ in the aspect ratio at division,
which is zero in the upper-left case with V1-morphy as result
large (such that spheres result after division) in the lower right case with a large role for V0-morphy
Notice the systematic change in shape of the curves, coupled to the values of the aspect ratio
A strong support for the role of surface area in growth

9. Dynamic mixtures of V0- & V1-morphs
Respiration: assim + maint + growth
Assim, maint  mass
Growth in diam  time at constant food
V0-morph
V1-morph
Crusts represent dynamic mixtures between a V0-morph and a V1-morph.
The V0-component becomes dominant for increasing size such that the diameter of the crust increases proportional to time.
Examples of crusts are bryozoans, lichenes, forests (as super-individual)

10. Dynamic mixtures of V0- & V1-morphs
Respiration
mixture  mass1/2
isomorph  mass3/4
Celleporella
15 cm/yr
0.5 cm/yr 2 5 16 33
See next slide
0.5 cm/yr 2 5 16 33
0.5 cm/yr 2 5 16 33
0.5 cm/yr 2 5 16 33
0.5 cm/yr 2 5 16 33
White et al 2011
Am. Nat., 178:

11. Dynamic mixtures of V0- & V1-morphs
Respiration
mixture  mass1/2
isomorph  mass3/4
Celleporella
33, 24 cm/yr
0.5 cm/yr 2 5 16 33
In absence of growth, respiration is proportional to mass (mainly somatic maintenance)
Growth of crusts contributes proportionally to the square root of mass (at constant food) and this contribution dominates at abundant food.
Work by Craig White, Queensland Univ, Melbourne
White et al 2011
Am. Nat., 178:

12. Selection affects par values
Gallus gallus
Red jungle fowl
Indian River Broiler
White leghorn

13. Respiration ontogeny in birds
ml O2 d-1
ml CO2 d-1
altricial
Troglodytes aëdon
Data: Kendeigh 1940
precocial
Gallus domesticus
Data: Romijn & Lokhorst 1951
age, d
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

14. Embryonic development
Zonneveld & Kooijman 1993
Bul. Math. Biol. 55:
Crocodylus johnstoni,
Data: Whitehead 1987
embryo
yolk
O2 consumption, ml/h
weight, g
time, d
time, d

15. Twinning: separation of cells
Kooijman 2012
J. Math. Biol.
subm
Twinning: separation of cells
Twinning: separation of cells
Twinning: separation of cells
Kooijman 2009
J. Math. Biol.
58:
Reserve density tends to increase with max structural length
The minimum amount of initial reserve is when maturation ceases at birth
The maximum amount of initial reserve is at abundant food for the mother at egg formation
The ratio of the max and the min amounts tends to increase with max structural length
When this ratio exceeds 2, twinning is theoretically possible:
The daughter-cells in the 2-cell stage each have enough reserve to complete the embryo stage.
Maternal effect:
reserve density at birth =
reserve density of mother
Parameter estimates from
add_my_pet 2012/06/17,
egg development only

16. Acceleration of development
Embryo: isomorphic
v constant
Early juvenile: V1-morphic
v, {pAm} increase with length
Late juvenile/adult: isomorphic
v, {pAm} constant
Found in:
bivalves, gastropods, copepods, amphipods, decapods, collembolas, echinoderms, lancelets, tunas, flatfish, anchovy, Danio, caecilians, marsupials
length
time since birth

17. Anchovy Engraulis encrasicolus
embryo
0.16 cm
0.22 cm
length, cm
0.4 cm
0.9 cm
time, d
1.2 cm
>4 cm
Pecquerie 2008
PhD thesis VU A’dam

18. Stage transitions at maturity thresholds
Danio rerio
28.5°C
See next slide
Augustine et al 2011
Comp. Biochem. Physiol. A
159 :275–283

19. Stage transitions at maturity thresholds
< birth : isomorph
birth-metamorphosis: V1-morph
> metamorphosis : isomorph
Danio rerio
28.5°C
Data:
Lauwrence et al 2008
While age at stage transitions depends on temperature and food, and length at stage transitions on food,
maturity thresholds do not depend on temperature or food.
Zebra-fish, like in many other fish species, accelerate metabolism between birth and metamorphosis;
specific maximum assimilation and energy conductance are increased
Respiration is proportional to mass in this period, but less than that before birth and after metamorphosis
Both growth and reproduction are retarded in response to caloric restriction in ways that is well captured be DEB theory.
Work by Starrlight Augustine, IRSN, Cadarache
caloric restriction
Data: Augustine
Augustine et al 2011
Comp. Biochem. Physiol. A
159 :275–283

20. Acceleration 10log spec maturity at birth 10log yolkiness
10log acceleration
10log acceleration
coelenterata
lophotrochozoa
ecdysozoa
invert deuterostomata
ectotherm vertebrata
endotherm vertebrata

21. Acceleration of development
yes
Casey Muller
indirect
Pseudophryne bibronii
Crinia georgiana
The DEB definition of direct development: birth coincides with metamorphosis: tadpoles don’t assimilate.
Two species of myobatrachid frogs don’t accelerate and keep  constant.
Two species of myobatrachid frogs accelerate development by lowing  between hatch and birth, resetting  after metamorphosis.
This change increases maturation and respiration and decreases growth.
The direct developers show that  is not changed systematically between hatch and birth among myobatrachid frogs.
Nicky Mitchell
direct
Geocrinia vitellina
Crinia nimbus

22. Acceleration of development
Mueller et al 2012,
Comp. Biochem. Physiol. A
163:
O2 nmol/h
Dry mass, mg
Crinia georgiana
age, d
hatch
birth
max dry weight 500 mg  1
metam
12 °C
age, d
Pseudophryne bibronii
These two myobatrachid frogs are very similar in many respects, but the tadpoles of P. bibronii live in permament pools, while that of C. georgiana in temporary ones that dry up, soon after their metamorphosis. The latter accelerate development by lowering  temporarily, which also reduces growth.
In this way it can leave the pond at the age of 110 days, while P. bibronii needs 200 d. Hatch coincides with birth for P. bibronii.
C. georgiana is 4 mg at metamorphosis, P. bibrionii 35 mg dry, while the maximum weights are 500 and 200 mg, respectively.
Both frogs have a (constant) somatic maintenance rate of some 400 J/d.cm3.
The graphs in the middle just enlarge the graph on the right till birth.
The step-up in respiration at birth is due to the onset of assimilation.
Mueller C., Augustine, S., Kearmey, M., Seymour, R. and Kooijman, S.A.L.M. 2011
Tradeoffs between maturation and growth during accelerated development in frogs
Submitted
Data: Casey Mueller
Model fit: Starrlight Augustine
max dry weight 200 mg
metam
metam 1 
hatch
birth
Dry mass, mg
hatch
birth
O2 nmol/h
age, d
age, d

23. 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

24. Ageing metabolism O2 ROS damage inducing compounds mitochondrional DNA
damage compounds
proteins
effect on hazard
endotherms
continuous
DEB module
Weibull (1951) &
Gompertz (1825) model
are special cases
based on mechanisms
links with energetics

25. Aging: ectotherms & feeding
survival prob
body length, cm
ad libitum
restricted d
time, d
time, d
Poecilia reticulata
Data: Comfort, 1963

26. Aging: endotherms & feeding
level 1
body weight, g
embryo weight, g
0.75
0.44
time, d
time, d
The DEB module for ageing assumes that free radicals originate from O2 consumption and form damage inducing compounds, such as modified mitochondrial DNA.
Damage inducing compounds can induce themselves and form damage compounds (modified proteins), which accumulate in the body and increase the hazard rate.
The three DEB-based post-natal growth curves at the various feeding levels, the embryonic growth curve and the survival functional are all fitted simultaneously to mouse-data.
They illustrate the role of energetics in aging.
This two-step aging mechanism explains why mean life span tends to increase with maximum body length among endotherms, but hardly among ectotherms.
Their difference is in the self-induction of damage inducing compounds, which hardly occurs in ectotherms;
It is part of their evolutionary transition from supply to demand systems.
The role of max body length (between species) and feeding levels (within a species) work out similarly in this case.
Sub-lethal effects of aging can be quantified by linking the concentration of damage compounds to energy parameters, as is done in DEB theory to quantify effects of toxic compounds in general.
This module has applications in ecotoxicology and environmental risk assessment.
0.44
survival probability
Life span
hardly depends on food in ecotherms
decreases for increasing food in endotherms
0.75 1
time, d
Data on Mus musculus:
Weindruch et al 1986, MacDowell et al 1927
Van Leeuwen et al Biogerontology 3:

27. Aging: sex differentiation
survival prob
body length, mm
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

28. Aging in adult insects No growth survival based on
observed reproduction
No growth
Weibull
Model
=3
surviving number
# of eggs/beetle, d-1
initial
random
mort
surviving number
age after eclosion, d
age after eclosion, d
age after eclosion, d
Data: Ernsting & Isaaks, 1991
Data: Rose 1984
High food, 20/10 °C
0.63 a-2
High food, 10 °C
0.547 a-2
Low food, 20/10 °C
0.374 a-2
Notiophilus biguttatus
Drosophila melanogaster

29. 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

30. Ageing among species Conclusion for life span
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

31. DEB tele course 2013 Audience: thank you for your attention
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
Software package DEBtool for Octave/ Matlab
freely downloadable
Slides of this presentation are downloadable from
Cambridge Univ Press 2009
Audience:
thank you for your attention