Damage-related protein turnover explains inter-specific patterns of
maintenance rate in the DEB theory.
Olivier Maury, Olivier Aumont, Jean-Christophe Poggiale
Empirical patterns of
maintenance
Protein turnover &
aerobic metabolism
Intra- and inter-specific
scaling of maintenance
Impacts on the DEB
theory?
Conclusion
What is somatic maintenance
➥ Somatic maintenance = energy used to maintain the structure in a viable state.
➥ Costs not associated to the production of biomass (growth & reprod.) or to development (maturation):
•
•
•
•
•
•
removing and replacing damaged proteins (turnover = 70-90% of maintenance costs),
maintaining chemical & electrical gradients through cellular membranes,
forming products (scales, hair, nails, etc),
maintaining muscular tonicity,
circulating body fluids (blood, lymph, etc), moving,
etc…
➥ Somatic maintenance rate can either be proportional
•
to structural volume
pM = [ pM ] V
•
to structural surface
pT = { pT }V 2 3
Empirical patterns of
maintenance
Protein turnover &
aerobic metabolism
Intra- and inter-specific
scaling of maintenance
Impacts on the DEB
theory?
Conclusion
Interspecific body-size scaling relationships
➥ Somatic maintenance = similar metabolic processes between species  intensive parameter
➙
➙
➙ Inter-specific body-size scaling relationships (Kooijman, 2010)
Respiration rate
Gestation time
(eutherian mammals)
Incubation time
(birds)
Growth rate
Length at puberty
(fish)
Empirical patterns of
maintenance
Protein turnover &
aerobic metabolism
Intra- and inter-specific
scaling of maintenance
Impacts on the DEB
theory?
Conclusion
Trait-based approaches
➥ An infinite number of species can be represented using the same DEB parameters
6
5
4
3
2
1
0
0
20
40
60
80
100
120
140
160
180
200
Body Length (cm)
0.12
Ageing Mortality (d-1)
0.1
Biomass (J.J-1.m-3.m-3)
Structural Growth Rate (cm3.d-1)
7
0.08
0.06
0.04
0.1
0.02
1
10
100
1000
Body Length (cm)
0
0
20
40
60
80
100
120
140
160
180
200
Body Length (cm)
Maury & Poggiale, 2013
Empirical patterns of
maintenance
Protein turnover &
aerobic metabolism
Intra- and inter-specific
scaling of maintenance
Impacts on the DEB
theory?
Conclusion
“Waste to hurry” paper (Kooijman, 2013)
➥ Are inter-specific scaling rules verified in the add-my-pet collection (2013, 165 species)?
Kooijman, 2013
➥
varies over more than 3 orders of magnitude from 3 to 8000 J.d-1.cm-3 at 20°C.
➥ It exhibits both a trend and huge variability around this trend.
➥
varies logically in the inverse proportion
Empirical patterns of
maintenance
Protein turnover &
aerobic metabolism
Intra- and inter-specific
scaling of maintenance
Impacts on the DEB
theory?
Conclusion
“Waste to hurry” paper (Kooijman, 2013)
➥ More recent addmypet estimates confirm the trends of somatic maintenance
3.E+03
[p_M], J/d.cm^3
3.E+02
3.E+01
3.E+00
3.E-01
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
1.E+06
1.E+08
Maximum structural volume Vm (cmx^3)
303 species
685 species
http://www.bio.vu.nl/thb/deb/deblab/add_my_pet/patterns.html
➥ Small species have a high and large species have a low somatic maintenance rate:
➥ Species waste resources for remaining small, growing fast, and speed-up the life-cycle
➥ Respond rapidly to environmental variability = evolutionary argument
➥ Phenomenological, no clear mechanism for explaining the generality of the pattern observed
➥ Can we find a mechanistic process that would explain dispersion & trend of estimated maintenance?
Empirical patterns of
maintenance
Protein turnover &
aerobic metabolism
Intra- and inter-specific
scaling of maintenance
Impacts on the DEB
theory?
Conclusion
A simple physiological mechanism to explain the patterns of maintenance
➥ protein turnover rate & cell repair constitute the most important component of maintenance,
Damaged
protein removal
Heating
costs
FOOD
pM
ingestion
pX
k
p A
GUT
E
FECES
V
pD
D
pC
1-k
egestion
pG+pD
Structural
maintenance
pR
EH/ER
pJ
Maturity
maintenance
Embryo
Empirical patterns of
maintenance
Protein turnover &
aerobic metabolism
Intra- and inter-specific
scaling of maintenance
Impacts on the DEB
theory?
Mass balance
Damaged
protein removal
Heating
costs
Structural
maintenance
V
E
D
Conclusion
Empirical patterns of
maintenance
Protein turnover &
aerobic metabolism
Intra- and inter-specific
scaling of maintenance
Impacts on the DEB
theory?
Conclusion
Protein turnover is linked to aerobic metabolism
➥ Mass balance equation:
➥
Aerobic organisms oxidize organic molecules to produce ATP  reactive oxygen species (ROS)
➥
ROS oxidize amino acids in proteins  protein damage rate proportional to aerobic metabolism
(cf. ageing).
O (cm3.J-1) volume of structural proteins damaged by one joule spent in aerobic metabolism.
➥ Degrading damaged structural proteins has a cost
(J.cm-3) cost of removing a fixed volume of damaged structure
➥
➥ With
The fraction of aerobic metabolism allocated to protein turnover.
Empirical patterns of
maintenance
Protein turnover &
aerobic metabolism
Intra- and inter-specific
scaling of maintenance
Impacts on the DEB
theory?
The maintenance rate varies with both L and Lm
➥
The total volume-specific maintenance rate varies at the intraspecific level with V
➥
The total volume-specific maintenance rate varies at the interspecific level with Vm
Total volume-specificm
a i ntenance rate (J.d-1)
10000
1000
100
10
Lm=0.02cm Lm=0.2cmL =2cm
m
Lm=20cm
1
0.00001
0.0001
0.001
0.01
0.1
1
10
Lm=200cm
100
1000
Structural length L (cm)
➥
If you want to waste and hurry: be small, have a small Vb, and die long before reaching Vm
Conclusion
Empirical patterns of
maintenance
Protein turnover &
aerobic metabolism
Intra- and inter-specific
scaling of maintenance
Impacts on the DEB
theory?
Conclusion
Addmypet maintenance estimates distribute in the expected interval
➥
We can plot expected highest (at Vb) and lowest (at Vm) maintenance curves
➥ Lb fixed arbitrarily at
4.10-3 Lm
3.E+04
3.E+03
3.E+02
Vb
3.E+01
Vm
3.E+00
3.E-01
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
1.E+06
Total volume-specificm
a i ntenance rate
(J.cm-3.d-1)
Total volume-specificm
a i ntenance rate
(J.cm-3.d-1)
3.E+04
3.E+03
3.E+02
3.E+01
3.E+00
3.E-01
1.E-08
Maximum structural volume Vm (cm3)
➥
1.E-06
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
Maximum structural volume Vm (cm3)
Addmypet estimate fall somewhere in between min and max values
➥ They would correspond to an average value for the range of sizes used for estimation
1.E+06
Empirical patterns of
maintenance
Protein turnover &
aerobic metabolism
Intra- and inter-specific
scaling of maintenance
Impacts on the DEB
theory?
Conclusion
1000000
100000
3.E+04
10000
Total volume-specificm
a i ntenance rate
(J.cm-3.d-1)
Maximum reserve energy density [Em]
Influence of the scaling of the maximum reserve energy density [Em]
y = 3612.5x0.3819
1000
100
10
1
0.001
0.01
0.1
1
10
100
3.E+03
3.E+02
3.E+01
3.E+00
3.E-01
1.E-08
1000
1.E-06
Maximum structural length Lm (cm)
3.E+03
3.E+02
3.E+01
3.E+00
3.E-01
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
Maximum structural volume Vm (cm3)
1.E+06
3.E+03
3.E+02
3.E+01
3.E+00
3.E-01
1.E-08
1.E-02
1.E+00
1.E+02
1.E+04
1.E+06
3.E+04
Total volume-specificm
a i ntenance rate
(J.cm-3.d-1)
3.E+04
Total volume-specificm
a i ntenance rate
(J.cm-3.d-1)
Total volume-specificm
a i ntenance rate
(J.cm-3.d-1)
3.E+04
1.E-04
Maximum structural volume Vm (cm3)
1.E-06
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
Maximum structural volume Vm (cm3)
1.E+06
3.E+03
3.E+02
3.E+01
3.E+00
3.E-01
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
Maximum structural volume Vm (cm3)
1.E+06
Empirical patterns of
maintenance
Protein turnover &
aerobic metabolism
Intra- and inter-specific
scaling of maintenance
Impacts on the DEB
theory?
Conclusion
Does it change the DEB theory?
➥
Growth at constant food keeps Von Bertalanffy
100
r=0
r = 0.1
r = 0.2
r = 0.3
r = 0.4
r = 0.5
r = 0.6
r = 0.7
90
Structural Length L (cm)
80
70
60
50
40
30
20
10
0
0
10000
20000
30000
40000
50000
60000
70000
80000
Age (d)
➥
Reproductive flux keeps the same as well
r=0
r = 0.1
r = 0.2
r = 0.3
r = 0.7
Empirical patterns of
maintenance
Protein turnover &
aerobic metabolism
Intra- and inter-specific
scaling of maintenance
Impacts on the DEB
theory?
Conclusion
Conclusion
➥ Empirical patterns of maintenance in addmypet
invalidate DEB interspecific scaling rules.
➥ We propose a simple mechanism to explain empirical inter-specific scaling of maintenance.
•
Making protein turnover explicit in maintenance.
•
Linking protein damage rate to aerobic metabolism.
➥ It would restore inter-specific scaling rules in the DEB theory.
➥ It would explain a (large?) part of the inter-specific variability of estimated maintenance.
➥ It provides a simple mechanism to the “waste to hurry” evolutionary hypotheses.
➥ Inter-specific patterns in addmypet suggest modifications of the standard DEB equations at the
individual level  strengthening the consistency of the theory.
➥ Adding one extra mechanistic parameter is more parsimonious than re-estimating it for every species.
➥ Parameter estimation for selected species should be conducted with modified DEB equations to test our
proposition.