Links between aging & energetics

Bas KooijmanDept theoretical biology

Vrije Universiteit AmsterdamBas@bio.vu.nl

http://www.bio.vu.nl/thb

Rostock, 2004/10/28

Contents

Rostock, 2004/10/28

• 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

Dynamic Energy Budget theoryfor metabolic organisationUptake of substrates (nutrients, light, food) by organisms and their use (maintenance, growth, development, reproduction)

First principles, quantitative, axiomatic set upAim: Biological equivalent of Theoretical Physics

Primary target: the individual with consequences for• sub-organismal organization• supra-organismal organizationRelationships between levels of organisation

Many popular empirical models are special cases of DEB

molecule

cell

individual

population

ecosystem

system earth

time

spac

e

Space-time scales

When changing the space-time scale, new processes will become important other will become less importantIndividuals are special because of straightforward energy/mass balances

Each process has its characteristic domain of space-time scales

Empirical special cases of DEB year author model year author model1780 Lavoisier multiple regression of heat

against mineral fluxes1950 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

1951 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 1959 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

1932 Mayneord cube root growth of tumours 1977 Beer & Anderson development of salmonid embryos

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

: These gouramis are from the same nest, These gouramis are from the same nest, they have the same age and lived in the same tank they have the same age and lived in the same tankSocial interaction during feeding caused the huge size differenceSocial interaction during feeding caused the huge size differenceAge-based models for growth are bound to fail;Age-based models for growth are bound to fail; growth depends on food intake growth depends on food intake

Not age, but size:Not age, but size:

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 compositionCompounds 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

1- maturitymaintenance

maturityoffspring

maturationreproduction

Basic DEB scheme

food faecesassimilation

reserve

feeding defecation

structurestructure

somaticmaintenance

growth

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

Not constant, depends on size & feeding conditions

Metabolic rate

nconsumptiodioxygen

production dioxidecarbon Quotient n Respiratio

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)

Scaling of metabolic rate

comparison intra-species inter-species

maintenance

growth

weight

nrespiratio3

32

dl

llls

43

32

ldld

lll

EV

h

structure

reserve

32 lll

l0l

0

3lllh

Respiration: contributions from growth and maintenanceWeight: contributions from structure and reserveStructure ; = length; endotherms 3l l

3lllh

0hl

1- maturitymaintenance

maturityoffspring

maturationreproduction

Modes of action of toxicants

food faecesassimilation

reserve

feeding defecation

structurestructure

somaticmaintenance

growth

Lethal effects: hazard rateMode of action affectstranslation to pop level

assimilation

maintenance costs

growth costs

reproduction costs

hazard to embryo

Toxic effect on survivalEffect 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

elephant

mandog

catferret

opossum

10log body weight, kg

10lo

g R

EM

sle

ep, h

/d

Siegel, J. M. 2001 The REM sleep-memory consolidation hypothesisScience 294: 1058-1063

Amount of sleep

No thermo-regulation during REM sleepDolphins: no REM sleep

tbody weigh

raten respiratio

tbody weigh -0.2

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

1-

1-u

Competitive tumour growth

food faecesassimilation

reserve

feeding defecation

structurestructure

somaticmaintenance

growth

maturitymaintenance

maturityoffspring

maturationreproduction

tumourtumour

u

)(][)(][

)(][)(

tVptVp

tVptκ

uMuM

uMuu

Allocation to tumour relative maint workload

Isomorphy: is constantTumour tissue: low spec growth costs low spec maint costs

uκ

Van Leeuwen et al., 2003 The embedded tumour: host physiology is important for the evaluation of tumour growth.British J Cancer 89, 2254-2268

maint

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 divideTypical 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

Hazard rate due to aging damage density: Damage forms damage inducing compounds:Damage inducing compounds form catabolic rate: i.e. dioxygen consumption excluding contributions from assimilationResult for

If mean life span >> growth period: Weibull’s model

Problems:• bad fit with endotherm data, but good fit with ectotherm data• effect of increase in food uptake balanced by dilution by growth

Aging: Damage induction

t s

Ma dsduuVkVsVtV

hth

0 0)()0()(

)()(

}6/exp{})(exp{)(2/)( 3

0

2Ma

t

Ma khtdsshtSkhtth

Vkh

M

a ageing accelerationmaintenance rate coeffstructural volume S

ht time

hazard ratesurvival prob

QDdt

d

CEJQdt

d,

VDh /

VrkκJJJ MGEMECE )(/)( ,,, Vdt

dr lnwith

Aging & Growth

age, dage, d

leng

th, m

m

surv

ival

pro

babi

lity

DEB aging model: kM = 0.073 d-1; ha = 2.53 10-6 d-2

Weibull model: shape par = 3.1Data: Slob & Janse 1988

Von Bertalanffy model: rB = 0.015 d-1

L = 35 mm

Lymnaea stagnalis

Aging in adult insects

age after eclosion, d age after eclosion, d age after eclosion, d

surv

ivin

g nu

mbe

r

surv

ivin

g nu

mbe

r

# of

egg

s/be

etle

, d-1

Drosophila melanogaster Notiophilus biguttatus

Data: Rose 1984Data: Ernsting & Isaaks, 1991

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

:

)(2

)(

30

0 0 12230

21

glκ

eh

dtdttRglκ

ehkh

tth

R

a

t t

R

aMa

survival based onobserved reproductionNo growth

R

glκ

ehkh

tth

R

aMa 3

02

2)(

initialrandom

mort

Weibullmodel

Aging & Sex

age, dage, d

leng

th, m

m

Haz

ard

rate

, d-1

Common aging acceleration 2.587 10-5 d-2

Data: MacArthur & Baillie 1929Conclusion:differences in aging are due todifferences in energetics

Daphnia magna female

male

RNS Aging

age, dage, d

Haz

ard

rate

, d-1

Food levels: 20, 30, 60, 120, 240 paramecia d-1 rotifer-1

Aging acceleration linear in food levelData: Robertson & Salt 1981

Suggestion:Paramecia are rich in NO3

2- & NO22- from lettuce,

which enhances aging

Asplanchna girodi

Ulti

mat

e vo

lum

e 10

-12

m3

Agi

ng a

ccel

erat

ion,

0.0

01 d

-2

One cell from a tetrad

Deinococcus radiodurans(Deinobacteria, Hadobacteria)

Very resistant against -radiationby accumulation of Mn2+

which neutralizes ROS that is formed

-Radiation ROS Aging

Stringent response Aging

kM/rm ha/rm

0.05 0.10

0.10 0.01

0.05 0.01

Fra

ctio

n of

dea

d ce

lls

Scaled throughput rate of chemostat

rm: max spec growth ratekM: maintenance rate coefficientha: aging ratee: scaled reserve densityg: investment ratio

ge

geheh a

1)(

Stringent response occurs in bacteria at low substrate concentration

Substantial change in physiology(e.g. accumulation of ppGpp)

Suggestion:Result of aging in bacteriaLow substrate low growth long division intervals

Aging in humans

age, d

Sur

vivi

ng f

ract

ion

Data from Elandt-Johnson & Johnson 1980

})(exp{)( thhtqtS w

q = 0.988h = 0.0013 a-1

hW = 0.01275 a-1

= 6.8

Aging accelerates in endothermsNot captured by damage induction model

Lung cancer in mice

100 200 300 400 500 600 700

0.2

0.4

0.6

0.8

1Weibull model fitted:High adult incidence rate Following low rate in juveniles

Female mice200ppm butadiene(KM-adjusted data)

Toxicology and carcinogenesis studies of 1,3-butadiene in B6C3F1 miceNational Toxicology Program (USA) 1993

lun

g

can

cer

fre

e p

rob

abil

ity

Amplification mechanisms

Weindruch R 1996 Caloric restriction and aging. Scientific American 231, 46-52.

• 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.

1) Affected mitochondria produce more ROS

2) Affected mitochondria grow and degrade at different rates

Aging: Damage amplification

Hazard rate due to aging damage densityDamage forms catabolic rate + amplification rateSpecific amplification rate is linear in catabolic rateResult for

If mean life span >> growth period: Gompertz’s model

Vdt

drhrrkVhVrkh

dt

dDDDM lnwith)()/()(

Van Leeuwen et al 2002 A mathematical model that accounts for the caloricrestriction on body weight and longivetyBiogerontology 3: 373-381

DMDddDMD

dddDdD

VVkrrrkkhtrtrrhtStrhth

/;/})}exp{1(exp{)(1}exp{)( 1

D

D

D

Vrk

ratemaint volultimate

volumestrucrate hazard

MkVVh

ROS import spec ratedamaged mitoch growth rROS feedback vol

VDh /DrJyD

dt

d DDCEDE ,

CEDVED

DD Jyrr ,

VrkκJJJ MGEMECE )(/)( ,,,

Food intake Surface area

Data from Kluyver 1961 & Grundel 1987

wei

ght1/

3 , g

1/3

age, d age, d

feed

ing

rate

, g/

d

Parusatricapillus

malesfemales

This assumption in DEB theory is usually realistic

20 40 60 80 100time in weeks

100

200

300

400

500

ydobthgie

w

20 40 60 80 100time in weeks

5

10

15

20

25

doofnoitsegni

etar

Carcinogenicity study with B[a]P in ratsKroese et al., (2001) RIVM technical report nr. 658603 010

males

females

females

males

Food intake is constantin laboratory rodents

Probably as a result of experimental conditions

Aging: Damage amplification

Van Leeuwen et al 2002 A mathematical model that accounts for the caloricrestriction on body weight and longivetyBiogerontology 3: 373-381

Data: Weindruch et al, 1986

Feeding level: 1, 0.75, 0.44 times ad libitum Caloric restriction extends life span

time, d

wei

ght,

g

srvi

vors

, %time, d

spec

ific

met

abol

ic r

ate

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: FunctionObservation:

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/

Download slides of Rostock lecture by Bas Kooijmanhttp://www.bio.vu.nl/thb/users/bas/lectures/