dynamic energy budget theory
DESCRIPTION
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 together 10 Evolution 11 Evaluation. - PowerPoint PPT PresentationTRANSCRIPT
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