Dynamic Energy Budget theory

1 Basic Concepts 2 Standard DEB model 3 Metabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of compounds 7 Extensions of DEB models 8 Co-variation of par values 9 Living together10 Evolution11 Evaluation

Hazard rate 6.1

Definition: instantaneous death rate (dim: time-1)Interpretation of hazard rate times time increment: probability of death, given to be alive

Relationship with survival probability for :

Examples for :

Independent causes of death 6.1a

If causes of death by events 0 are independent of that by events 1 then hazard rate add and survival probabilities multiply

Example of application: death by background mortality and by toxicant in short bioassays: background mortality is accidental which means that the hazard rate is constant

Many factors contribute to hazard 6.1b

• genetic factors (apoptosis)

• starvation (diet deficiencies, type II diabetes)

• environmental factors (physical, chemical, toxicants)

• pathogens (disease)

• accidents (predation)

• aging

Free radicals Aging 6.1c

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 divideTypical 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 agingDamage 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

energetics

growth

maintenance

Free radicals and ageing 6.1d

RespirationRespiration

Oxidative damageOxidative damage

free radicals (internally generated)

survival

feeding

tumour induction

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 6.1e

Amplification mechanisms 6.1f

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 in DEB3 6.1g

Aging: relation to O2-use 6.1h, 7.8.1

time, dtime, d

surv

iva

l pro

b

Re

od

ruct

ion

ra

te,

#/d

Data: Ernsting & Isaaks 1997

0.374

0.547

0.630

high food 10/20°Chigh food 10/10°Clow food 10/20°C

Differences in life span are caused by differences in respiration

Survival in adult Notiophilus biguttatus modified by food and temperature

Aging: sex differentiation 6.1i

time, dtime, d

surv

iva

l pro

b

bo

dy

we

igh

t, g

Data on Daphnia magna: MacArthur & Baillie 1929

Differences in aging between sexes are caused by differences in g

Food intake is constant 6.1j

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

in laboratory rodents

Probably as a result of experimental conditions

Aging: endotherms & feeding 6.1k

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

rate

Aging: endotherms & feeding 6.1l

time, dtime, d

time, d

surv

iva

l pro

ba

bili

tye

mb

ryo

we

igh

t, g

bo

dy

we

igh

t, g

Mus musculus data: Weindruch et al 1986, MacDowell et al 1927

feedinglevel

1

0.75

0.44

0.75

0.44

1

Life span • hardly depends on food in ecotherms• decreases for increasing food in endotherms

Van Leeuwen et al 2002 Biogerontology 3: 373-381

Aging & Energetics 6.1m

Olm Proteus anguinus: a† > 100 aab = 140 d, ap = 14 a, R = 35/12.5 a-1

Can live 10 months without food,so can switch to torpor state

Voituron et al 2010Biol. Lett.

Aging in DEB3 6.1.1

Aging module of DEB theory 6.1.1a

Aging: non-growing ectotherms 6.1.1b

time, dsurv

ival

pro

babi

lity

Data: Rose 1984

Weibullwith shape parameter 3

General Weibull fits DEB 6.1.1c

Data from Elandt-Johnson & Johnson 1980 for white USA males in the period 1969-1971

Both models are fitted to the same dataThey fit equally well and have both 4 parametersContrary to the Weibull model the DEB model- is based on tested assumptions- has links with energetics via hW and hG.

Aging: growing ectotherms 6.1.1d

time, dtime, d

surv

iva

l pro

b

bo

dy

we

igh

t, g

Data: Slob & Janse 1988

Weibull with shape 3 fits ectothermic survival well, even if growth period not small relative to life span

Aging: Function 6.1.3

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

Biology based methods 6.2

Effects based on internal concentrations One compartment accumulation-elimination

Hazard rate or physiological target parameter is linear in internal concentration (small effects only) Dynamic Energy Budget theory is used to identify potential target parameters translate change in parameter to change in endpoint

Interaction of compounds in mixture product of internal concentrations similar to analysis of variance

Kinetics 6.3

Simplest basis: one compartment kinetics

Correct for changes in • body size (growth)• lipid content (starvation)• concentration (transformation)

n,n-compartment models 6.3a

Compound can cross, interface between media with different rates vice versa sub-layers with equal rates for all sublayers

filmmodel

1,1-comparment model

1,1 compartment model 6.3b

Suppose andwhile

Film models 6.3.2

Steady flux approximation

Dilution by growth 6.4.1

Note: • elimination rate decreases with length of isomorph exchange is across surface area• small changes in size already affect kinetics considerably

Dilution by growth 6.4.1a

ke/rB ke/rB

ratio

inte

rnal

/ext

erna

l con

c

trB trB

10 10

2

1

0.5

0.1

2

1

0.5

0.1

scaled body lengthscaled reproduction rate

ke elimination raterB von Bert. growth rate

Q(0) = 0 Q(0) = c

Change in lipid content 6.4.2

Note: • biomass should be decomposed into reserve & structure• applies for slowly changing food densities only

Satiating excretion kinetics 6.4.3

Elimination rate satiates as function of internal concentration

Example:Removal of alcohol from blood by liver

Effects of environmental factors 6.5

• Process-based perspective on disturbances temperature, chemicals, parasites, noise exposure-time explicit methods (response surface)

• Primary target: individuals some effects at sub-organism level can be compensated (NEC) • Effects on populations derived from individuals energy budget basic to population dynamics

• Parameters of budget model individual specific and (partly) under genetic control

Tasks of physiological module 6.5a

in the specification of toxic effects of chemicals

• identify potential target parameters for toxic effects (e.g. max feeding rate, specific maintenance and growth costs) • specify interrelationships between the various physiological processes (e.g. feeding, maintenance, maturation, growth, reproduction)• quantify how endpoints depend on values of target parameters (e.g. how does cumulative number of offspring depend on the specific growth costs?)

Models for toxic effects 6.5b

Three model components:

• kinetics external concentration internal concentration example: one-compartment kinetics

• change in target parameter(s) internal concentration value of target parameter(s) example: linear relationship

• physiology value of parameter endpoint (survival, reproduction) example: DEB model

Effects of parasites 6.5c

Many parasites increase (chemical manipulation) harvest (all) allocation to dev./reprod.

Results larger body size higher food intake reduced reproduction

1- maturitymaintenance

maturityoffspring

maturationreproduction

Modes of action of toxicants 6.5d

food faecesassimilation

reserve

feeding defecation

structurestructure

somaticmaintenance

growth

assimilation

maintenance costs

growth costs

reproduction costs

hazard to embryo

u

tumourtumour

maint tumour induction6

6

endocr. disruption7

7

lethal effects: hazard rateMode of action affectstranslation to pop level

8

Modes of Action of Noise 6.5e

Effects on reproduction• blocking out fouraging time reduction feeding efficiency• disrupting social behaviour short/long term, partner choice

Effects on survival• problems with orientation (migration)• permanent hearing damage• interaction with large-scale fishing

Simplest basis: Change internal conc that exceeds internal NEC

or

with

Change in target parameter 6.5f

Rationale

• approximation for small effects

• effective molecules operate independently

Effect Concentration 6.5g

ECx(t): Concentration that gives x% effect at exposure time t, compared to the blank

LCx(t) = ECx(t) in the case the endpoint is the survival probability (LC = lethal concentration)

Generally: ECx(t) decreases in time the pattern depends on the properties of the chemical and of the test organism

NEC = EC0()

Concentration ranges of chemicals 6.5.1

• too little def: variations in concentration come with variations in effects• enough def: variations in concentration within this range hardly affect physiological behaviour of individuals• too much def: variations in concentration come with variations in effects e.g. water concentration can be too much even for fish

no basic difference between toxic and non-toxic chemicals“too little” and “enough” can have zero range for some chemicalsImplication: lower & upper NEC for each compound

Contr.

NOEC 6.5.1a

NOEC

Res

po

nse

log concentration

LOEC

*

Statistical testing

NOEC No Observed Effect ConcentrationLOEC Lowest Observed Effect Concentration

What’s wrong with NOEC? 6.5.1b

• Power of the test is not known• No statistically significant effect is not no effect;• Effect at NOEC regularly 10-34%, up to >50%• Inefficient use of data

– only last time point, only lowest doses– for non-parametric tests also values discarded

NOECNOECR

es

po

ns

e

log concentration

Contr.Contr.

LOEC

*LOECLOEC

*OECD Braunschweig meeting 1996:NOEC is inappropriate and should be phased out!

OECD Braunschweig meeting 1996:NOEC is inappropriate and should be phased out!

Do No Effect Concentrations exist? 6.5.1c

Essential aspect: compensation at individual levelEach molecule of any compound has an effect at the molecular levelThese effects do not necessarily translate into measurable effects at the individual levelExample: removal of a kidney in a healthy human body does not result in health effects under conditions that are not extremeNEC is specific for• species and chemical compound• endpoint (survival, reproduction) one process (maintenance, reproduction, ..) is most sensitive• experimental/environmental conditions

Assumptions of standard approach 6.5.3

Lethal effects:• Individuals have identical toxico-kinetics• They die for sure if internal conc exceeds threshold• Threshold varies among individuals (log-logistic distribution)

Empirical counter-evidence:• Slope conc-response curve becomes steeper during exposure• LC50 of re-exposed cohort remains the same• Sublethal effects don’t support large differences among individuals

Kooijman (1996) An alternative for NOEC exists, but the standard model has to be replaced first. Oikos 75: 310--316

crossingmust not be

possible

surv

ival

pro

b

log conc

Problems of standard approach 6.5.3a

• Incorporation of exposure time is problematic (translation from acute to chronic effects; links to pharmacology)

• Not applicable in case of varying exposure (peak exposure) • EC-small levels difficult to determine and model-sensitive (links to envir risk assessment)

• Incompatible with NOEC/NEC NEC = EC0(∞)

• Difficult to extrapolate from individual to population from one species to another, one chemical to another

• Problems in quantifying effects of mixtures

log concsurv

ival

pro

b

EC0

too similarrarely significantKooijman 1981Water Res 15:107-119

Fast kinetics 6.5.3c

Effects on survival at instantaneous equilibrium

effect on survival concentration exposure timewell known in pharmacology, desinfection of buildings, green houses

Effect on survival 6.5.3e

Effects of Dieldrin on survival of Poecilia

killing rate 0.038 l g-1 d-1

elimination rate 0.712 d-1

NEC 4.49 g l-1

Effect on assimilation 6.5.4

CuCl2 mg/kgtime, d

wei

ght1

/3,

mg1

/3

Data from Klok & de Roos 1996NEC = 4.45 mg CuCl2 /kg on Lumbricus rubellus

Decrease in assimilation 6.5.4a somatic maint coeff = maturity maint coeff

0 5 10 15 20 25 3015

20

25

30

35

40

45

50

55

60

65

time

bo

dy

le

ng

th

0 5 10 15 20

0

20

40

60

80

100

120

140

160

180

200

time

cu

mu

lati

ve

off

sp

rin

g p

er

fem

ale

Data: Alda Álvarez et al (2006)Fit: Jager

Acrobeloides nanusPentachlorobenzene

Effects on growth 6.5.4b

time, dtime, d

bod

y le

ngth

, m

m

assimilation

maintenance growth

Triphenyltin on Folsomia candida at 20°C

indirect effects

direct effects

3000

1392

646300

0, 0, 64,139

mg kg-1bo

dy

leng

th,

mm

Increase in maintenance costs 6.5.4c

time

cum

ula

tive

off

spri

ng

time

bo

dy

len

gth

TPT

Jager et al. (2004)

Folsomia candidaTri-Phenyl-Tin

Increase cost for structure 6.5.4d

0 5 10 15 20 25 30 3515

20

25

30

35

40

45

50

55

60

65

time

bo

dy

le

ng

th

0 5 10 15 20

0

20

40

60

80

100

120

140

160

180

time

cu

mu

lati

ve

off

sp

rin

g p

er

fem

ale

Acrobeloides nanusCadmium

Data: Alda Álvarez et al (2006)Fit: Jager

0 5 10 15 20 25 30 3515

20

25

30

35

40

45

50

55

60

65

time

bo

dy

le

ng

th

0 5 10 15 20

0

20

40

60

80

100

120

140

160

180

time

cu

mu

lati

ve

off

sp

rin

g p

er

fem

ale

Acrobeloides nanusCadmium

Increase cost for structure 6.5.4e Decrease in maturity maintenance

Data: Alda Álvarez et al (2006)Fit: Jager

0 5 10 15 20 25 30 3515

20

25

30

35

40

45

50

55

60

65

time

bo

dy

le

ng

th

0 5 10 15 20

0

20

40

60

80

100

120

140

160

180

time

cu

mu

lati

ve

off

sp

rin

g p

er

fem

ale

Acrobeloides nanusCadmium

Increase cost for structure 6.5.4f

Decrease in maturity maintenanceIncrease of ageing

Data: Alda Álvarez et al (2006)Fit: Jager

Increase in cost for structure 6.5.4g

time

bo

dy

len

gth

time

cum

ula

tive

off

spri

ng Pentachlorobenzene

Alda Álvarez et al. (2006)

Caenorhabditis elegans

DEB-based effects on body growth 6.5.4h

Indirect effects indicator: effects on ultimate size at constant food• decrease of assimilation rate (food intake, digestion)• increase of specific maintenance costs

Direct effects indicator: no effects on ultimate size at constant food• increase of costs for synthesis of biomass (structural)

Effects on reproduction 6.5.4i

time, dtime, d

cum

# o

ffsp

ring/

♀cu

m #

off

sprin

g/♀

cum

# o

ffsp

ring/

♀

assimilation

maintenance

growth

cost/offspring

hazard

Phenol on Daphnia magna at 20°C

indirect effects

direct effects3200

1800

1000

5600, 320

mg L-1

Direct effect on reproduction 6.5.4j

time, d

cum

. #

youn

g/fe

mal

e

0

0.2

0.4

0.812

g Cd/l

Effect on hazardNEC = 0.023 g Cd/l

DEB-based effects on reproduction 6.5.4k

Indirect effects indicator: effects on onset of reproduction• decrease of assimilation rate (food intake, digestion)• increase of specific maintenance costs• increase of costs for synthesis of biomass (structural)

Direct effects indicator: no effects on onset of reproduction• increase of costs for the synthesis of offspring• decrease of survival probability at birth

Increase in cost for offspring 6.5.4l

time

cum

ula

tive

off

spri

ng

time

bo

dy

len

gth

Chlorpyrifos

Jager et al. (2007)

Folsomia candida

Receptor mediated effects 6.5.5

• Compound knocks out functional receptors• Total amount of receptors is constant• Hazard rate linear in non-functional receptors

: no memory

Free radicals Tumour induction 6.5.6

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

Tumour inducing compounds 6.5.6a

Mode of action: genotoxic compounds: similar to (natural) free radicals enhance aging non-genotoxic compounds: hamper cell-cell communicationTumour growth dynamics similar to growth of body parts -rule for allocation of resources in DEB context growth depends on: physiology via nutrition (feeding conditions) body size (age): fast growth at young age

Leeuwen, I. M. M. van 2003Mathematical models in cancer risk assessmentPhD-thesis, Vrije Universteit Amsterdam

Lung cancer in mice 6.5.6b

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

RNS Aging 6.5.6c

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

Toxicants affect ageing 6.5.6d

0 20 40 60 80 100 1200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

volu

me

tric

bod

y le

ngt

h (m

m)

0 20 40 60 80 100 1200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 20 40 60 80 100 1200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

volu

me

tric

bod

y le

ngt

h (m

m)

Folsomia candidacadmium

Jager et al. (2004)

time (days)0 20 40 60 80 100 120

0

0.2

0.4

0.6

0.8

1

0 20 40 60 80 100 1200

0.2

0.4

0.6

0.8

1

fra

ctio

n s

urv

ivin

g

time (days)

Effect on survival for mixture 6.5.7

Model for survival in time for a binary mixture: 8 parameters in total using data for all observation times control mortality rate, interaction parameter 2 (NEC, killing rate, elimination rate)

Model tested for 6 binary mixtures of metals (Cu, Cd, Pb & Zn) on Folsomia candida (Collembola)

Survival measurements daily for 21 days 6 6 concentrations 22 6 6 = 792 data points for each mixture

Data: Bart van HouteTheory: Bas KooijmanFit: Jan BaasMovie: Jorn Bruggeman

Interaction Cu,Cd, Pb, Zn: Cu & Pb: slightly antagonistic Other combinations: nill

Folsomia candida

Cd & Cu survival of Folsomia 6.5.7a

Log-logistic survival model: c: external concentration; C: LC50, :slope

Independent action:

Concentration addition:

Independent action differs from concentration additionMolecules of one compound have dependent actionNo mechanism behind concentration addition; implicit definition if (these problems don’t apply to biology based methods)

Mixtures in standard approach 6.5.7b

Model comparison for Cd-Cu mixtureResults of spreadsheet 6.5.7c

Conclusion: interaction depends on choice of CA vs IA model exposure time

Time (days)

Interactions with CA as base model

Interactions with IA as base model

2 - 3 No interaction, CA Synergism

4 – 5 Synergism Synergism

6 Synergism Dose level dependent Synergism

7 - 9 Dose level dependent Synergism

Dose level dependent Synergism

10 - 15 No interaction, CA Dose level dependent Synergism

16 Dose Ratio interaction Dose level dependent Synergism

17 No interaction, CA Dose Ratio

18 - 21 low doses S, high doses A* Dose level dependent Synergism

* Change from antagonism to synergism at about 2 * LC50

by Jan Baas

Jonker M.J., Svendsen C., Bedaux, J.J.M., Bongers, M. & Kammenga, J.E.(2005) Significance testing of synergistic/antagonistic, doselevel-dependent, or dose ratio-dependent effects in mixture dose-responseanalysis. Environmental Toxicology and Chemistry, 24: 2701 - 2713.

Process-based vs standard 6.5.7d

Process-based model • free of choice CA vs IA in effects on survival • has one type of interaction for all exposure times• needs 3 toxicity parameters per compound

+ n(n-1)/2 interaction parameters for mix of n compounds= 7 tox parameters per binary mixture

Standard model • needs 2 tox pars per compound per exposure time

+ 1 or 2 exposure-time dependent interaction pars = 5-6 tox parameters per binary mixture per exposure time• interaction complex for mixtures of more than 2 compounds• is inconsistent for mixtures

At constant food density:

At variable food density: individual-based modelling of populations requires modelling of resources

Effects on populations 6.5.8

Population effects can depend on food density 6.5.8a

Population growth of rotifer Brachionus rubens at 20˚Cfor different algal concentrations

3,4-dichloroanilinedirect effect on reproduction

potassium metavanadateeffect on maintenance

Food intake at carrying capacity 6.5.8b

103

cells

/dap

hnid

.d10

3 ce

lls/d

aphn

id.d

log mg V/l log mg Br/l log mg DMQ/l

log mg K2Cr2O7/l log mg AA/l log mg Col/l

9-aminoacridine colchicine

2,6-dimethylquinolinesodium bromidemetavanadate

potassium dichromate

Dynamic Energy Budget theory

1 Basic Concepts 2 Standard DEB model 3 Metabolism 4 Univariate DEB models 5 Multivariate DEB models 6 Effects of compounds 7 Extensions of DEB models 8 Co-variation of par values 9 Living together10 Evolution11 Evaluation