1. Theory Metabolites Karin Aden (BVL, Germany)
FOCUS Work Group on Degradation Kinetics
Estimating Persistence and Degradation Kinetics
from Environmental Fate Studies in EU Registration
Brussels, January 2005
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2. Regulatory Background
Introduction
Regulatory Background
- Triggers established in Annex VI of Directive 91/414/EEC must be applied to relevant metabolites
- 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 for relevant metabolites, and for the modelling of the metabolites in the different environmental compartments
- For metabolites applied as test substance, degradation kinetics should be derived following recommendations for parent (treated as parent substance)
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3. Formulation of Kinetic Models
Introduction
Formulation of Kinetic Models
Compartment Model:
Equation SFO-Model:
Parent
Metabolite
Sink
kP->Met
kMet->Sink
kP->Sink
Data points are available and can be used for parameter estimation.
Data points are not available OR
if they are, with high uncertainty
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4. Formation Fraction - Rate Constant - Overall Degradation Rate I
Introduction
Formation Fraction - Rate Constant - Overall Degradation Rate I
Parent
Half-life: 35 d
Metabolite
Half-life: 23 d
Sink
60 %
ffMet=0.6
40 %
1-ffMet=0.4
100 % 20 40 60 80
100
SFO model •
Metabolite formation fraction  Maximum observed!
Sum of formation fractions started from one substance = 1
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5. Formation Fraction - Rate Constant - Overall Degradation Rate II
Introduction
Formation Fraction - Rate Constant - Overall Degradation Rate II
Formulation with rate constants:
Example (SFO model):
Parent:
overall degradation rate kP:
0.02 d-1 (Half-life= 35 d)
rate constant kPMet:
0.6 * kP = d-1
formation fraction ffMet
rate constant kPSink
0.4 * kP = d-1
formation fraction 1-ffMet
Metabolite:
overall degradation rate kMet:
0.03 d-1 (Half-life= 23 d)
Formulation with formation fractions:
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6. Formation - Plateau - Decline
Introduction
Formation - Plateau - Decline
Formation phase
kP*P > kMet*Met
Plateau/Peak
kP*P = kMet*Met
Decline phase
kP*P < kMet*Met 20 40 60 80
100
Day 25:
1.2 = 1.2
Day 70:
0.05 < 0.67
Day 5:
4.9 > 0.6
SFO model
Parent —100 %—> Metabolite
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7. Comparison of two Parent-Metabolite Systems
Introduction
Comparison of two Parent-Metabolite Systems
Example Example 2 20 40 60 80
100
max. amount: 60 % (25 d) • •
max. amount: 30 % (59 d) 20 40 60 80
100 • • • • • • •
Which metabolite degraded faster?
(SFO model, Parent —100 %—> Metabolite)
Metabolite Half-life: 34 d
Parent Half-life: d
Parent Half-life: d
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8. Types of Kinetic Models for Metabolites I
SFO model (Simple First Order)
Robust model, because of limited number of parameters (initial amount and rate constant for parent, formation fraction and rate constant for each metabolite). SFO is implemented in simulation models. The half-life calculation is simple.
Bi-phasic models
Hockey-stick model - should not be used!
Model with its single breakpoint time is not conceptually correct for a metabolite. Due to its continuous formation, deviations from SFO for a metabolite will appear to be gradual and smoothed. Parameter are often uncertain.
bi-exponential DFOP model (Double-First-Order in Parallel)
DT50 values cannot be directly calculated from the model parameters although these trigger values can be derived using an iterative method.
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9. Types of Kinetic Models for Metabolites II
Bi-phasic models (cont.)
FOMC model (First Order Multi Compartment/Gustafson&Holden)
1st Choice
FOMC can be easily implemented for metabolites with a single differential equation. It has only one additional parameter compared to the SFO model. The DT50 calculation of is simple.
FOMC model cannot be implemented in complex SW- and GW-models  not valid for the determination of modelling endpoints, except PECsoil.
Exception: FOMC DT90 values of terminal metabolites, can be used as conservative estimate of the SFO Half-life by dividing the FOMC DT90 by 3.32.
This approach is only valid for terminal metabolites. Otherwise it would affect the kinetics of formation of metabolites further down in the degradation pathway!
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10. Types of Kinetic Models for Metabolites III
DFOP-model: FMOC (Gustafson&Holden):
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11. Distinction needs to be made between:
Metabolite Endpoints
Definition
Distinction needs to be made between:
1.) Kinetics endpoints for metabolites used as triggers for higher tier experiments (“Trigger Endpoints”)
and
2.) Kinetics endpoints used for modelling (“Modelling Endpoints“)
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12. Trigger Endpoints: Degradation/Dissipation DT50, DT90
Metabolite Endpoints
Trigger Endpoints
Trigger Endpoints: Degradation/Dissipation DT50, DT90
Derived by best-fit kinetics - unless deviations from SFO kinetics can be attributed to experimental artefacts
Trigger DegT50 and DegT90 values can be calculated from the estimated degradation rate of the metabolite using the equation corresponding to the best-fit kinetic model (consideration of the degradation only)
A conservative estimate of the trigger DegT50 and DegT90 values can be obtained by estimating the disappearance of the metabolite from its observed maximum, by fitting the decline curve (=consideration of the formation)
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13. Trigger Endpoints - Example
Metabolite Endpoints
Trigger Endpoints - Example 20 40 60 80
100
Time after application
Half-life Parent: -
Decline Metabolite (DissipationT50):
Half-life: 114 d (0.006  ) 20 40 60 80
100
Time after maximum observed
Fit of the metabolite
decline curve (SFO)
Fit of parent - metabolite
system (both SFO)
Half-life Parent: 13 d
Degradation Metabolite:
Half-life: 71 d (0.010  0.002)
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14. Formation rate parameters
Metabolite Endpoints
Modelling Endpoints
The required Modelling Endpoints for an individual metabolite are kinetic parameters and type of kinetic model used:
Formation rate parameters
• degradation rate parameters from precursor(s)
• formation fraction(s) +
Degradation rate parameters
Usually SFO is used for modelling!
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15. Main recommendations Parent Metabolite Sink
Pathway
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
Parent
Metabolite
Sink
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16. Pathway - Example: Use of sink
Main recommendations
Pathway - Example: Use of sink
Parent
Sink
Metabolite
Parent
Metabolite
Half-life Parent: 6 d
Half-life Metabolite: 16 d
Formation fraction ffMet: 1 (fixed)
Half-life Parent: 3 d
Half-life Metabolite: 38 d
Formation fraction ffMet: 0.47
Parent initial amount is not described properly (too low)
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17. For the estimation of parameters it is necessary to identify:
Main recommendations
Kinetic model
For the estimation of parameters it is necessary to identify:
Kinetic model for degradation of precursor(s), e.g. parent
SFO Vs. biphasic models
Appropriate description at least up to 10 % of the initial amount is necessary
Kinetic model for degradation of metabolite
SFO Vs. biphasic models (FOMC, DFOP)
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18. Kinetic Model - Example 1 (Parent Degradation)
Main recommendations
Kinetic Model - Example 1 (Parent Degradation)
Parent SFO
DegT50 Parent: 16 d
Half-life: Metabolite: 14 d
Formation fraction: 0.65
Parent FOMC
Half-life Parent: 21 d
Half-life Metabolite: 9 d
Formation fraction: 1
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19. Kinetic Model - Example 2 (Metabolite Degradation)
Main recommendations
Kinetic Model - Example 2 (Metabolite Degradation)
Metabolite SFO
Half-life Parent: 1 d
DegT50 Metabolite: 15 d
DegT90 Metabolite: 95 d
Metabolite FOMC
Half-life Parent: 1 d
Half-life Metabolite: 18 d
DegT90 Metabolite: 61 d
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20. Unweighted fit should be used in the 1st step
Main recommendations
Weighting Method
Data weighting
Unweighted fit should be used in the 1st step
In special cases data weighting can be useful. But sufficient information for a weighting, e. g. information about the quality of data points within a data set, is usually not present
First part of the precursor’s decline curve, covering formation phase of the metabolite is more important than later time points
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21. Weighting method - Example
Main recommendations
Weighting method - Example
Unweighted fit - SFO
Half-life Parent: 18 d
Half-life Metabolite 1: 47 d
Half-life Metabolite 2: 369 d
Weighted fit (fractional) - SFO
Half-life Parent: 13 d
Half-life Metabolite 1: 42 d
Half-life Metabolite 2: 133 d
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22. A stepwise parameter fit is recommended in the following cases:
Main recommendations
Stepwise approach I
A stepwise parameter fit is recommended in the following
cases:
Complex systems with several metabolites
The pathway is not fully defined with regards to the formation of minor metabolites and bound residues
Non-SFO kinetic models are considered
Data sets with scattered or limited data points
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23. Main recommendations Parent Fit parent substance
Stepwise approach II
Fit parent substance
Met 2
Met 3
Parent S i n k
Met 1
Add primary metabolite(s), fit with parent parameters fixed to values obtained in 1), check flow to sink and simplify if justified
Fit parent and primary metabolite(s) using values obtained in 1) and 2) as starting values
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
----
Final step: fit all substances together using values obtained in n-1) as starting values
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24. Procedure to derive endpoints for metabolites
Implementation of the conceptual model in a kinetic model I
Combine parent kinetics (SFO, FOMC, DFOP or other model), metabolite formation fraction and metabolite kinetics (SFO, FOMC, DFOP or other)
- Selected kinetic models must be consistent with intended use (trigger Vs. modeling)
- Use of Metabolites decision flow charts
Integrated equations with analytical solution exist for simple cases or
Use sets of differential equations in compartment models with software tool for solving, e. g. ModelMaker
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25. Procedure to derive endpoints for metabolites
Implementation of the conceptual model in a kinetic model II
Parent
kP* ffMet1*P
kP* ffMet2*P
Metabolite1
kP*(1- ffMet1- ffMet2)*P
Metabolite2
kMet1* Met1
kMet2* Met2
Sink
(other metabolites, bound residues, CO2)
Parent: dP/dt = – kP*P
Metabolite 1: dM1/dt = kP* ffMet1*P – kMet1* Met1
Metabolite 2: dM2/dt = kP* ffMet2*P – kMet2* Met2
Sink: dSink/dt = kP*P * (1 – ffMet1 – ffMet2) + kMet1* Met1 + kMet2* Met2
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26. Procedure to derive endpoints for metabolites
Flow sheet for Trigger Endpoints PART A
RUN parent only SFO, FOMC
Data entry
SFO fit acceptable and statistically more appropriate than FOMC
RUN parent best-fit and metabolite
RUN parent only DFOP
FOMC and/or DFOP fit acceptable? Determine best-fit model
Case-by-case decision
see next slide no
yes
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27. Procedure to derive endpoints for metabolites
Flow sheet for Trigger Endpoints PART B
RUN parent best-fit and metabolite FMOC
FMOC fit for metabolite acceptable?
Case-by-case
decision
Use estimated SFO trigger endpoints
(DT50 and DT90 values)
Use estimated FMOC trigger endpoints
SFO fit for metabolite acceptable?
yes no
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28. Procedure to derive endpoints for metabolites
Flow sheet for Modelling Endpoints PART A
RUN parent only SFO
Data entry
SFO fit acceptable?
RUN parent and metabolites all-SFO
Parent SFO acceptable
SFO fit for metabolites acceptable?
Use estimated SFO endpoints for fate modelling
Case-by-case
decision
yes no
see next slide
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29. Procedure to derive endpoints for metabolites
Flow sheet for Modelling Endpoints PART B
Biphasic fit acceptable?
Case-by-case
decision
RUN parent biphasic and metabolites all-SFO
SFO fit for metabolites acceptable?
Use estimated endpoints for fate modelling
yes no
RUN parent only with appropriate biphasic model
SFO fit acceptable?
Parent SFO non-acceptable
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30. Main tool for assessing goodness-of-fit: Visual assessment of
Goodness-of-fit I
Main tool for assessing goodness-of-fit: Visual assessment of
Sampling points and fitted curves
Plots of residuals
- determination that the residuals are randomly distributed
- systematic error  indication that the pathway or kinetic
model used is maybe not appropriate
Overall-Fit (determination coefficient r2)
Parent and metabolites with the highest measured levels carry
more weight than metabolites at lower level
 an overall fit may still appear acceptable while one or more of the metabolites may not be well fitted
 For that reason, overall goodness-of-fit is not performed,
instead each substance is evaluated, separately
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31. Tool for model comparison
Goodness-of-fit II
2 test
Tool for model comparison
Tool for assessing the Goodness-of-fit of an individual substance
2 error value should be calculated for each metabolite
(using all data used in the fit, including the sampling points below LOD or LOQ before the formation phase and after the decline phase that are included as ½ LOD or ½ (LOQ+LOD). The time-0 sample however, if set to 0 should not be used in the 2 error determination)
Error value at which the 2-test is passed for the metabolite should be below 15 % (not an absolute cut-off criterion)
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32. Reliability of the individual rate parameter
Goodness-of-fit III
Reliability of the individual rate parameter
Reliability of individual rate parameter estimates based on
- t-test or
- confidence intervals of the parameters
Important for metabolites that do not show a clear decline
 to discern between metabolites that are persistent and
metabolites that are degrading and forming at the same
time at a similar rate
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33. Conclusions I
The half-life or DT50 value of a metabolite is not sufficient for the description of the fate of a metabolite!
Rate of formation must be considered in addition to rate of degradation
Formation and degradation are linked, and the parameters can be highly correlated
Degradation of the precursor(s) must be described properly to be able to describe the degradation of the metabolite
Number of data points for metabolites and their concentrations are often lower than for parent substances
The maximum amount and the decline phase of the metabolite are not reached during the study in some cases
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34. — Complexity increases with complexity of pathway
Conclusions II
Metabolites kinetics is more complex than for parent because formation and degradation occur simultaneously
— Complexity increases with complexity of pathway
Number of precursors (e.g. parent, metabolites)
Number of successive degradation steps
— Complexity increases with complexity of kinetic models
Formation
Degradation
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35. Trigger endpoints: degradation/dissipation DT50 and DT90
Conclusions III
FOCUS Report:
Guidance provided for deriving metabolite kinetic endpoints from studies with parent
Trigger endpoints: degradation/dissipation DT50 and DT90
Modeling endpoints: formation and degradation rate
Harmonized approach for reproducible results independent of software tool used
Better acceptance of generated endpoints
Facilitates review process
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