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![Page 1: Scaling relationships based on partition coefficients & body size have similarities & interactions Bas Kooijman Dept theoretical biology Vrije Universiteit.](https://reader038.fdocuments.in/reader038/viewer/2022103123/56649d385503460f94a11de5/html5/thumbnails/1.jpg)
Scaling relationships based onpartition coefficients & body size have similarities & interactions
Bas KooijmanDept theoretical biology
Vrije Universiteit [email protected]
http://www.bio.vu.nl/thb/
Lyon, 2006/05/10
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Contents
• toxicokinetic models one-compartment, film
• toxic effects
• DEB theory
• QSARs
• body size scaling
• similarities
• interactions
Lyon, 2006/05/10
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1-compartment model
For a given external concentration as function of time:
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1,1-compartment model
compound can cross interface between media with different rates vice versa
interface
medium i
medium j
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1,1 compartment model
Suppose andwhile
Conclusion: relationship between par values follows from model structure
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n,n-compartment models
compound can cross interface between media with different rates vice versa sub-layers with equal rates for all sub-layers
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film models
Steady flux approximation
Kooijman et al 2004Chemosphere 57: 745-753
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Elimination rate & partition coeff
log P01 log P01
log
10%
sat
urat
ion
tim
e
1 film 2 filmdiffusivities
low
high
Transition: film 1,1-compartment model
slope = 0.5slope = 0.5
Kooijman et al 2004Chemosphere 57: 745-753
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Concentration ranges of chemicals
• 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
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Effects on organisms
• Chemicals, parasites, noise, temperature affect organisms via changes of parameters values of their dynamic energy budget these values are functions of internal concentrations
• Primary target: individuals some effects at sub-organism level can be compensated (NEC) • Effects on populations are derived from that on individuals individuals interact via competition, trophic relationships
• Parameters of the energy budget model individual-specific and (partly) under genetic control
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Models for toxic effects
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
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Dynamic Energy Budget theoryfor metabolic organisationUptake of substrates (nutrients, light, food) by organisms and their use (maintenance, growth, development, reproduction) during life cycle (dynamic)
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
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1- maturitymaintenance
maturityoffspring
maturationreproduction
Standard DEB scheme
food faecesassimilation
reserve
feeding defecation
structurestructure
somaticmaintenance
growth
Def “standard”:• 1 type of food• 1 type of reserve• 1 type structure• isomorphy
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1- maturitymaintenance
maturityoffspring
maturationreproduction
Modes of action of toxicants
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
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Simplest basis: Change internal conc that exceeds internal NEC
or
with
Change in target parameter
Rationale
• effective molecules operate independently
• approximation for small effects
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Effect on survival
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
Hazard model for survival:• one compartment kinetics• hazard rate linear in internal concentration
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QSARs for tox parameters
10lo
g N
EC
, m
M
10lo
g el
im r
ate,
d-1
10lo
g ki
ll ra
te,
mM
-1 d
-1
10log Pow 10log Pow10log Pow
Slope = -1 Slope = 1Slope = -0.5
Hazard model for survival:• one compartment kinetics• hazard rate linear in internal concentration
Alkyl benzenes in PimephalesData from Geiger et al 1990
Assumption:Each molecule has same effect
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QSARs for tox parameters
10lo
g N
EC
, m
M
10lo
g el
im r
ate,
d-1
10lo
g ki
ll ra
te,
mM
-1 d
-1
10log Pow 10log Pow10log Pow
Slope = -1 Slope = 1Slope = -0.5
Benzenes, alifates, phenols in PimephalesData from Mackay et al 1992,
Hawker & Connell 1985
Assumption:Each molecule has same effect
Hazard model for survival:• one compartment kinetics• hazard rate linear in internal concentration
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Covariation of tox parameters1
0log
NE
C, m
M
10log killing rate, mM-1 d-1
Slope = -1
PimephalesData from Gerritsen 1997
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QSARs for LC50’s
10log Pow10log Pow
10lo
g LC
50.1
4d, M
LC50.14d of chlorinated hydrocarbons for Poecilia. Data: Könemann, 1980
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Primary scaling relationships
Dependent on max size
K saturation constant
Lb length at birth
Lp length at puberty
{pAm} max spec assim rate
Independent of max size
yEX yield of reserve on food
v energy conductance
[pM] volume-spec maint. costs
{pT} surface-spec maint. costs
[EG] spec structure costs
ha aging acceleration
partitioning fraction
R reproduction efficiency
maximum length Lm = {pAm} / [pM] Kooijman 1986J. Theor. Biol. 121: 269-282
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Scaling of metabolic rate
intra-species inter-species
maintenance
growth
weight
nrespiratio3
32
dl
llls
43
32
ldld
lll
EV
h
structure
reserve
32 vll
l0l
0
3lllh
Respiration: contributions from growth and maintenanceWeight: contributions from structure and reserveStructure ; = length; endotherms 3l l
3lllh
0hl
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Metabolic rate
Log weight, gLo
g m
etab
olic
rat
e,
w
endotherms
ectotherms
unicellulars
slope = 1
slope = 2/3
Length, cm
O2 c
onsu
mpt
ion,
l
/h
Inter-speciesIntra-species
0.0226 L2 + 0.0185 L3
0.0516 L2.44
2 curves fitted:
(Daphnia pulex)
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Von Bertalanffy growth rate
vVkr MB /3/3 3/11
At 25 °C : maint rate coeff kM = 400 a-1
energy conductance v = 0.3 m a-1
25 °CTA = 7 kK
10log ultimate length, mm 10log ultimate length, mm
10lo
g vo
n B
ert
grow
th r
ate
, a-1
)exp()()( 3/13/13/13/1 arVVVaV Bb
3/1V
a
3/1V
3/1bV
1Br
↑
↑0
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SimilaritiesQSAR body size scaling
1-compartment model: partition coefficient (= state) is ratio between uptake and elimination rate
DEB-model: maximum length (= state) is ratio between assimilation and maintenance rate
Parameters are constant for a system, but vary between systems in a way that follows from the model structure
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• uptake, elimination fluxes, food uptake surface area (intra-specifically) elimination rate length-1 (exposure time should depend on size) food uptake structural volume (inter-specifically)
• dilution by growth affects toxicokinetics max growth length2 (inter-specifically)
• elimination via reproduction: max reprod mass flux length2 (inter-specifically)
• chemical composition: reserve capacity length4 (inter-specifically) in some taxa reserve are enriched in lipids
• chemical transformation, excretion is coupled to metabolic rate metabolic rate scales between length2 and length3
• juvenile period length, abundance length-3 , pop growth rate length-1
links with risk assessment strategies
InteractionsQSAR body size scaling
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DEB tele course 2007
http://www.bio.vu.nl/thb/deb/
Free of financial costs; some 250 h effort investment
Feb-April 2007; target audience: PhD students
We encourage participation in groups that organize local meetings weekly French group of participants of the DEB tele course 2005: special issue of J. Sea Res. 2006 on DEB applications to bivalves
Software package DEBtool for Octave/ Matlab freely downloadable
Slides of this presentation are downloadable from http://www.bio.vu.nl/thb/users/bas/lectures/
Cambridge Univ Press 2000
Audience: thank you for your attention
Organizers: thank you for the invitation