claude beigel, phd. exposure assessment senior scientist research triangle park, usa theory...
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Claude Beigel, PhD.Exposure Assessment Senior ScientistResearch Triangle Park, USA
Theory Metabolites
Outline
Introduction Kinetic endpoints
– Degradation Vs. Dissipation endpoints
– Trigger Vs. Modeling endpoints
General fitting recommendations
– Description of metabolic pathway
– Data handling
– Selected kinetic models
– Evaluation of goodness of fit
– Decision schemes
Conclusions
Introduction
Metabolites need to be considered in environmental assessment
The assessment of the relevancy of a metabolite normally involves performing an exposure analysis (soil, groundwater, water-sediment-systems)
Kinetic endpoints are needed as triggers for subsequent studies, and for the modeling of the metabolites in the different environmental compartments
Introduction
More complex than for parent because formation and degradation occur simultaneously
Complexity increases with complexity of pathway
– Number of successive degradation steps, number of metabolites formed at each step & number of precursors
Complexity increases with complexity of kinetic models
– Formation & degradation
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Parent
MetaboliteMaximum
kP*ffM*P=kM*MFormation phase
kP*ffM*P>kM*MDecline phase
kM*M> kP*ffM*P
Time (days)
Subs
tanc
e (%
of
app
lied
)
Metabolite Curve
Degradation Vs. Dissipation
Aerobic Soil Metabolism Metabolite Decline
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Su
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Parent
Metabolite
Metabolite DT50 (decline) = 49.7 d
Aerobic Soil Metabolism Parent + Metabolite
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Metabolite DegT50 = 32.0 d
Trigger Vs. Modeling Endpoints for Metabolites
Trigger endpoints (degradation or dissipation DT50/DT90)
Triggers for further studies, as provided in Annex II, III and VI of Dir. 91/414/EEC and in Guidance Documents on Aquatic and Terrestrial Ecotoxicology
– Use best-fit model kinetics based on statistical and visual analysis
Trigger Vs. Modeling Endpoints for Metabolites
Modeling endpoints (formation rate, formation fraction and degradation rate parameters)
No restriction on kinetic model (e.g. PEC soil)
– Use best-fit model kinetics based on statistical and visual analysis
Restricted to specific kinetic model(s) (e.g. FOCUS groundwater models)
– Standard versions of most fate models use SFO
– Preference for SFO when an adequate SFO fit is obtained based on statistical and visual analysis
– Correction procedures or higher-Tier approaches if an adequate SFO fit is not obtained
General Fitting Recommendations
Metabolites applied as test substance and decline of metabolite from max. are treated as parent
Kinetic endpoints for metabolites from studies with parent or precursor can be determined with help of compartment models
Substances are represented by different compartments
Flows between substances (formation/degradation) are described with differential equations
Overall flow from one compartment (e.g. parent) to several compartments (e.g. metabolites + sink) is split using formation fractions
Compartment Models
Parent
Metabolite1 Metabolite2
Sink(other metabolites, bound residues, CO2)
FP * ffM2FP * ffM1
FP*(1-ffM1-ffM2)
FM1 FM2
Parent: dP/dt = – FP
Metabolite 1: dM1/dt = FP · ffM1 – FM1
Metabolite 2: dM2/dt = FP · ffM2 – FM2
Sink: dS/dt = FP · (1 – ffM1 – ffM2) + FM1 + FM2
Description of Metabolic Pathway
Formation and degradation of metabolite are linked, and the parameters can be highly correlated
Formation of metabolite = degradation of precursor x formation fraction
Pathway
Conceptual model must reflect actual degradation or dissipation pathway
Flows to sink are initially included for formation of other metabolites (identified or not), bound residues and CO2
Essential to describe precursor correctly (especially first 90%)
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Metabolite
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Metabolite
ParentOthers
Metabolite
Parent Metabolite
DT50 Parent: 5.8 d
DT50 Metabolite: 16 d
Formation fraction: 1
DT50 Parent: 3.3 d
DT50 Metabolite: 38 d
Formation fraction: 0.466
Pathway: Including Flow to Sink
Data Handling
Follow general guidance with regard to replicates, experimental artifacts and outliers
Correction of time-zero data
Add metabolites + bound residues to parent, set metabolites and sink time-zero to 0
Data points below LOQ/LOD
Set concentrations between LOD and LOQ to measured value or 0.5 x (LOD+LOQ)
Set samples < LOD to 0.5 x LOD
Omit all but one < LOD samples before first detect
Omit samples after first non-detect unless later samples > LOQ
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(%
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) ParentMetabolite1Metabolite2
DT50 Parent: 12.7 d
DT50 Metabolite 1: 41.5 d
DT50 Metabolite 2: 133 d
DT50 Parent: 17.6 d
DT50 Metabolite 1: 47.3 d
DT50 Metabolite 2: 369 d
Unweighted fit Weighted fit (fractional)
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Time (days)S
ub
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ce (
% A
R) Parent
Metabolite1Metabolite2
Always use unweighted data as a first step!
Weighting Method
Selected Kinetic Models for Metabolites
SFO model
Preferred model, constitutive autonomous differential equation available
Common problem with biphasic models: differential equations include time, not suitable for metabolites that are formed over time
FOMC model may only be used in integrated form, cannot be implemented in environmental models
DFOP model can still be implemented with system of differential equations using two sub-compartments biphasic model of choice
HS model not appropriate for metabolites because of breakpoint
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Time (days)
Su
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(%
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Parent
Metabolite
DT50 Parent: 0.94 d
DT50 Metabolite: 18.3 d
DT90 Metabolite: 60.9 d
DT50 Parent: 0.94 d
DT50 Metabolite: 15.6 d
DT90 Metabolite: 113 d
Metabolite SFO Metabolite DFOP
Metabolite Kinetic Models
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Stepwise Approach for Complex Cases
1) Fit parent substance
2) Add primary metabolite(s), fit with parent parameters fixed to values obtained in 1), check flow to sink and simplify if justified
3) Fit parent and primary metabolite(s) using values obtained in 1) and 2) as starting values
4) Add secondary metabolite(s), fit with parent and primary metabolite(s) parameters fixed to values obtained in 3), check flow to sink and simplify if justified
----
n) Final step: fit all substances together using values obtained in n-1) as starting values
Evaluation of Goodness of Fit
Statistical indices
2
22
)O x 100/err(
)OC(where C = calculated value O = observed value Ō = mean of observed err = measurement error
T-test for rate constant parameters
If 2 > 2m, then the model is not appropriate at the chosen significance level
where m = degrees of freedom (No. of obs. used in the fitting – No. of optimized model parameters)
= level of significance, typically 5%
2 test, minimum 2 error
Evaluation of Goodness of Fit
Graphical Evaluation (Visual Assessment)
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-20
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(% A
R)
Baseline
Parent
Metabolite
Minimum 2 error: 9.2% (parent) and 4.9% (metabolite)
Plot of Residuals (Fitted – Observed)Plot of Fitted Vs. Observed with Time
Statistical Evaluation
Decision Schemes: Trigger Endpoints (1)
Goal: find best-fit model (same approach for PEC soil)
Start with parent, compare SFO to most simple biphasic model (FOMC)
If SFO same or better, and SFO acceptable, keep SFO model
If FOMC better, compare with DFOP, keep best-fit model
Run parent SFO Vs. FOMC
SFO better and acceptable Use SFO for parentyes
no, FOMC better
Biphasic, run DFOP and compare with FOMC Use Best-fitModel for parent
Decision Schemes: Trigger Endpoints (2)
Add metabolites, stepwise for complex cases, run parent best-fit and metabolites SFO
If SFO acceptable for metabolites, keep SFO model
If not, run appropriate biphasic model for metabolite (DFOP or FOMC), if acceptable, use best-fit model for metabolite
SFO acceptable for metabolites Use SFOyes
noRun parent best-fit and test appropriate biphasicmodel for metabolite (DFOP or FOMC)
Use BiphasicModel
Run parent best-fit with metabolites SFO
Biphasic model acceptable for metaboliteyes
Decision Schemes: Modeling Endpoints (2)
Goal: kinetic model compatible with environmental modelFirst step: check if SFO is acceptable, if yes use SFO model
If not, higher-Tier options to implement biphasic degradation pattern
Start with parent, is SFO acceptable for at least first 90% of dissipation?
Run parent SFO
SFO good enough ? Use SFO for parentyesno
Run parent with appropriate biphasic model, e.g. DFOP or PEARLneq
Biphasic model good enough ? Use Biphasic modelfor parent
yes
Decision Schemes: Modeling Endpoints (2)
Add metabolites, stepwise for complex cases, run with metabolites SFO
If SFO acceptable for metabolites, keep SFO model
If not, use conservative approaches, on case-by-case basis
– Degradation rate constant of metabolite not significantly 0, use conservative default of 1000 days
– Metabolite biphasic, use higher-tier approach (DFOP or PEARLneq), or set SFO DT50 to DFOP DT90/3.32 if terminal metabolite
SFO acceptable for metabolites Use SFOyes
noCase-by-case conservative approaches
Run parent with metabolites SFO
Guidance provided for deriving kinetic endpoints for metabolites
Trigger endpoints: degradation/dissipation DT50 and DT90
Modeling endpoints: formation fraction, formation and degradation rates
Harmonized approach for reproducible results independent of software tool used
Better acceptance of generated endpoints
Facilitates review process
Conclusions
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