Transcript Slide 1

Links between
aging & energetics
Bas Kooijman
Dept theoretical biology
Vrije Universiteit Amsterdam
[email protected]
http://www.bio.vu.nl/thb
Rostock, 2004/10/28
Contents
• DEB theory
introduction
metabolic rate
• Effects of toxicants
sublethal effects
lethal effects
• Effects of free radicals
sleep
tumour induction & growth
• Aging
dilution by growth
damage amplification
effects of caloric restriction
Rostock, 2004/10/28
Dynamic Energy Budget theory
for metabolic organisation
Uptake of substrates (nutrients, light, food)
by organisms and their use (maintenance, growth,
development, reproduction)
First principles, quantitative, axiomatic set up
Aim: Biological equivalent of Theoretical Physics
Primary target: the individual with consequences for
• sub-organismal organization
• supra-organismal organization
Relationships between levels of organisation
Many popular empirical models are special cases of DEB
Space-time scales
space
Each process has its characteristic domain of space-time scales
system earth
ecosystem
population
individual
cell
molecule
When changing the space-time scale,
new processes will become important
other will become less important
Individuals are special because of
straightforward energy/mass balances
time
Empirical special cases of DEB
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, 1951 Weibull
temperature dependence of
physiological rates
based
on mechanisms
allometric growth of body parts
Huxley
1955
Best
not meant to glue empirical models
survival probability for aging
diffusion limitation of uptake
Henri
Michaelis--Menten kinetics
1957
Smith
embryonic respiration
1905
Blackman
bilinear functional response
1959
Leudeking & Piret
microbial product formation
1910
Hill
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
1902
1920
1927
1928
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
Pütter turn out
1962
Marr
Pirt
individuals
the
data
behind these 1973
models
support DEB
theory
logistic population growth
reserve (cell quota) dynamics
Pearl
Droop
This makes DEB theory very well tested against data
Not: age, but size: These gouramis are from the same nest,
they have the same age and lived in the same tank
Social interaction during feeding caused the huge size difference
Age-based models for growth are bound to fail;
growth depends on food intake
Trichopsis vittatus
Some DEB pillars
• life cycle perspective of individual as primary target
embryo, juvenile, adult (levels in metabolic organization)
• life as coupled chemical transformations (reserve & structure)
• time, energy & mass balances
• surface area/ volume relationships (spatial structure & transport)
• homeostasis (stoichiometric constraints via Synthesizing Units)
• syntrophy (basis for symbioses, evolutionary perspective)
• intensive/extensive parameters: body size scaling
Biomass: reserve(s) + structure(s)
Reserve(s), structure(s): generalized compounds,
mixtures of proteins, lipids, carbohydrates: fixed composition
Compounds in
reserve(s): equal turnover times, no maintenance costs
structure: unequal turnover times, maintenance costs
Reasons to delineate reserve, distinct from structure
• metabolic memory
• explanation of respiration patterns (freshly laid eggs don’t respire)
• biomass composition depends on growth rate
• fluxes are linear sums of assimilation, dissipation and growth
basis of method of indirect calorimetry
• explanation of inter-species body size scaling relationships
Basic DEB scheme
food
feeding
defecation
faeces
assimilation
reserve
somatic
maintenance
growth
structure

1-
maturity
maintenance
maturation
reproduction
maturity
offspring
Metabolic rate
Usually quantified in three different ways
• consumption of dioxygen
• production of carbon dioxide
• dissipation of heat
DEB theory: These fluxes are weighted sums of
• assimilation
• maintenance
• growth
Weight coefficients might differ
Respiration Quotient
carbon dioxide production
dioxygenconsumption
Not constant, depends on size & feeding conditions
Metabolic rate
slope = 1
0.0226 L2 + 0.0185 L3
0.0516 L2.44
Log metabolic rate, w
O2 consumption, l/h
2 curves fitted:
endotherms
ectotherms
slope = 2/3
unicellulars
Length, cm
Intra-species
(Daphnia pulex)
Log weight, g
Inter-species
Scaling of metabolic rate
Respiration: contributions from growth and maintenance
Weight: contributions from structure and reserve
3
Structure  l ; l = length; endotherms lh  0
comparison
intra-species inter-species
maintenance
 lh l   l 3
 lh l   l 3
growth
 l l 2  l 3
0
 l0
l
ls l 2  l 3

dl3
lh l 2  l 3

dV l 3  d E l 4
reserve
structure
respiration
weight
Modes of action of toxicants
 assimilation
food
 maintenance costs
defecation
feeding
faeces

 growth costs
assimilation
 reproduction costs
reserve
somatic
maintenance

1-

growth

structure
 hazard to embryo
maturity
maintenance

maturation
reproduction
Lethal effects:
hazard rate
maturity
offspring

Mode of action affects
translation to pop level
Toxic effect on survival
Effect of Dieldrin on
survival of Poecilia
One-compartment kinetics
Hazard rate is linear in
internal concentration
killing rate 0.038 l g-1 d-1
elimination rate 0.712 d-1
NEC 4.49 g l-1
Many factors contribute to hazard
• genetic factors (apoptosis)
• starvation (diet deficiencies, type II diabetes)
• environmental factors (physical, chemical, toxicants)
• pathogens (disease)
• accidents (predation)
• aging
Free radicals  Sleep
opossum
ferret
cat
dog
man
10log
REM sleep, h/d
Amount of sleep
elephant
10log
body weight, kg
Siegel, J. M. 2001
The REM sleep-memory consolidation hypothesis
Science 294: 1058-1063
 body weight -0.2
respirat ion rate

body weight
No thermo-regulation
during REM sleep
Dolphins: no REM sleep
Free radicals  Tumour induction
Tumour induction is
linear in conc free radicals
& other tumour inducing compounds
It can occur via
genotoxic effect (damage of genome)
non-genotic effects
(effects on cell-to-cell signalling)
No Effect Concentration might be positive
Competitive tumour growth
food
defecation
feeding
faeces
assimilation
reserve
somatic
maintenance
growth
structure

maint
1-
u 1-u
tumour
maturity
maintenance
Allocation to tumour
 relative maint workload
[ pMu ] Vu (t )
κu (t ) 
[ pM ] V (t )  [ pMu ] Vu (t )
Isomorphy:
κu is constant
Tumour tissue:
low spec growth costs
low spec maint costs
maturation
reproduction
maturity
offspring
Van Leeuwen et al., 2003
The embedded tumour: host physiology
is important for the evaluation of
tumour growth.
British J Cancer 89, 2254-2268
Tumor growth  DEB theory
• The shape of the tumor growth curve is not assumed a priori,
and is very flexible, depending on parameter values
• The model predicts that, in general,
tumors develop faster in young than in old hosts
• According to the model, tumors grow slower in
calorically restricted animals than in ad libitum fed animals.
• The effect of CR on tumor growth fades away during long-term CR
• The model explains why tumor-mediated body-weight loss
is often more dramatic than expected
Free radicals  Aging
Aging results from damage by Reactive Oxygen Species (ROS) Gerschman 1954
link with DEB model via dioxygen consumption & metabolic activity
Dioxygen use in association with assimilation is not included
because of more local occurrence in organism
Its affects are 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
Empirical evidence points to an acceleration mechanism
• damage inducing compounds
• amplification of existing damage
Some chemical compounds (e.g. RNS) and -radiation can stimulate aging
Aging: Damage induction
Hazard rate due to aging  damage density: h  D / V
Damage forms  damage inducing compounds: dtd D  Q
Damage inducing compounds form  catabolic rate: dtd Q  J
i.e. dioxygen consumption excluding contributions from assimilation
d
Result for J E,C  ( J E,M  J E,G ) / κ  (kM  r) V with r  ln V
dt
s
ha t 

h(t ) 
V ( s)  V (0)  k M 0 V (u ) du  ds

0

V (t ) 
If mean life span >> growth period: Weibull’s model
E ,C
t
h(t )  t ha kM / 2  S (t )  exp{ h(s) ds}  exp{t 3ha kM / 6}
2
0
Problems:
• bad fit with endotherm data, but good fit with ectotherm data
• effect of increase in food uptake balanced by dilution by growth
ha ageing acceleration
k M maintenance rate coeff
V structural volume
t time
h hazard rate
S survival prob
length, mm
survival probability
Aging & Growth
Lymnaea stagnalis
age, d
DEB aging model:
kM = 0.073 d-1; ha = 2.53 10-6 d-2
Weibull model: shape par = 3.1
Data: Slob & Janse 1988
age, d
Von Bertalanffy model:
rB = 0.015 d-1
L = 35 mm
age after eclosion, d
h(t ) 

he
t2 
 ha k M  a 0 3 R 
2
κ R gl 
Weibull
model
Data: Rose 1984
Drosophila melanogaster
No growth
surviving number
surviving number
# 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 ) dt2 dt1
2
κ R gl 0 0
ha e0
: High food, 20/10 °C
κ R gl3
-2
0.63 a
High food, 10 °C
0.547 a-2
Low food, 20/10 °C
0.374 a-2
Aging & Sex
female
length, mm
Hazard rate, d-1
Daphnia magna
male
age, d
Common aging acceleration 2.587 10-5 d-2
Data: MacArthur & Baillie 1929
age, d
Conclusion:
differences in aging are due to
differences in energetics
RNS  Aging
Food levels:
20, 30, 60, 120, 240 paramecia d-1 rotifer-1
Aging acceleration linear in food level
Data: Robertson & Salt 1981
age, d
Aging acceleration, 0.001 d-2
age, d
Ultimate volume 10-12 m3
Hazard rate, d-1
Asplanchna girodi
Suggestion:
Paramecia are rich in
NO32- & NO22- from lettuce,
which enhances aging
-Radiation  ROS  Aging
Deinococcus radiodurans
(Deinobacteria, Hadobacteria)
Very resistant against -radiation
by accumulation of Mn2+
which neutralizes ROS that is formed
One cell from a tetrad
Fraction of dead cells
Stringent response  Aging
kM/rm ha/rm
0.05
0.10
0.10
0.01
0.05
0.01
rm: max spec growth rate
kM: maintenance rate coefficient
ha: aging rate
e: scaled reserve density
g: investment ratio
h(e)  ha e
1 g
e g
Stringent response occurs in bacteria
at low substrate concentration
Substantial change in physiology
(e.g. accumulation of ppGpp)
Scaled throughput rate of chemostat
Suggestion:
Result of aging in bacteria
Low substrate  low growth 
long division intervals
Aging in humans
Surviving fraction
S (t )  q exp{ht  (hwt )  }
q = 0.988
h = 0.0013 a-1
hW = 0.01275 a-1
 = 6.8
Aging accelerates in endotherms
Not captured by damage induction model
age, d
Data from Elandt-Johnson & Johnson 1980
Lung cancer in mice
lung cancer free probability
1
Weibull model fitted:
High adult incidence rate
Following low rate in juveniles
0.8
Female mice
200ppm butadiene
(KM-adjusted data)
0.6
0.4
0.2
100
200
300
400
500
600
700
Toxicology and carcinogenesis studies of 1,3-butadiene in B6C3F1 mice
National Toxicology Program (USA) 1993
Amplification mechanisms
1) Affected mitochondria produce more ROS
Weindruch R 1996 Caloric restriction and aging. Scientific American 231, 46-52.
2) Affected mitochondria grow and degrade at different rates
• Kowald
A 2001 The mitochondrial theory of aging, Biological Signals & Receptors 10, 162-175.
• Kowald A & Kirkwood TBL 2000 Accumulation of defective mitochondria through delayed degradation of damaged
organelles and its possible role in the aging of post-mitotic cells. Journal of Theoretical Biology 202, 145-160.
Aging: Damage amplification
Hazard rate due to aging  damage density h  D / V
d
Damage forms  catabolic rate + amplification rate dt D  y J  r D
Specific amplification rate is linear in catabolic rate rDD  rD  yVED J E,C
Result for J E,C  ( J E,M  J E,G ) / κ  (kM  r) V
d
d
h  (k M  r ) (hV / VD  k D )  (rD  r ) h with r  ln V
dt
dt
If mean life span >> growth period: Gompertz’s model
DE
E ,C
D
D
h(t )  hD exp{rd t}  1  S (t )  exp{hD rd1 (1  rd t  exp{rd t})}
hD  k M k D / rd ; rd  rD  kM V / VD
Van Leeuwen et al 2002 A mathematical
model that accounts for the caloric
restriction on body weight and longivety
Biogerontology 3: 373-381
h
k D ROS import spec rate
V
rD damaged mitoch growth r V
kM
VD ROS feedback vol
hazardrate
struc volume
ultimatevol
maint rate
Food intake  Surface area
weight1/3, g1/3
feeding rate, g/d
This assumption in DEB theory is usually realistic
males
females
age, d
Parus
atricapillus
Data from Kluyver 1961 & Grundel 1987
age, d
Food intake is constant
in laboratory rodents
500
males
Probably as a result of
experimental conditions
300
females
200
100
25
20
40
60
time in weeks
80
Carcinogenicity study with B[a]P in rats
Kroese et al., (2001)
RIVM technical report nr. 658603 010
100
food ingestion rate
body weight
400
males
20
15
females
10
5
20
40
60
time in weeks
80
100
Aging: Damage amplification
Caloric restriction extends life span
srvivors, %
weight, g
Feeding level: 1, 0.75, 0.44 times ad libitum
Data: Weindruch et al, 1986
Van Leeuwen et al 2002 A mathematical
model that accounts for the caloric
restriction on body weight and longivety
Biogerontology 3: 373-381
specific metabolic rate
time, d
time, d
Aging  DEB theory
• The aging process can be modelled within the DEB framework
as a result of internally produced ROS that affects the hazard rate
no max life span exists; consistency with lethal effects of toxicants
• The model is able to predict differences in life expectancy
on the basis of differences in food intake
• The model predicts CR-induced decrease in
mass-adjusted energy expenditure to disappear with long-term CR
• The model provides a physiologically-based interpretation
of the Gompertz parameters
• The model suggests that two essential feed-back processes take place
Aging: Function
Observation:
Aging related hazard rate
• remains low during embryonic and juvenile stages
• becomes high at start of reproduction
Suggestion:
Organisms
• decrease protection level in adult stage
• use ROS to create genetic diversity among gametes
• use genetic diversity for adaptation to changing environment
• efficient defence (peroxidase dismutase) or repair systems
or reduced ROS production can increase life span,
but reduce genome diversity
Aging: Open questions
• Damage Induction (DI)  Damage Amplification (DA) model
Should 1-par DI-model always be replaced by 3-par DA model?
Can DI-model approximate DA-model under certain conditions?
How important is dilution by growth?
• Is it possible to improve the models,
while preserving simplicity & generality
workload model for synthesis of mitochondria
• Is dioxygen consumption that is linked to assimilation of importance?
• Should/can cause of death by aging be specified more explicitly?
tumours, weakening of defense systems (immune system)
DEB tele-course 2005
Feb – April 2005, 10 weeks, 200 h
no financial costs
http://www.bio.vu.nl/thb/deb/course/
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