page 1 theory metabolites karin aden (bvl, germany) focus work group on degradation kinetics...
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Theory MetabolitesKarin Aden (BVL, Germany)
FOCUS Work Group on Degradation Kinetics
Estimating Persistence and Degradation Kineticsfrom Environmental Fate Studies in EU Registration
Brussels, 26-27 January 2005
- 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)
IntroductionRegulatory Background
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IntroductionFormulation of Kinetic Models
MetkPkdt
dSink
MetkPkdt
dMet
PkPkdt
dP
SinkMetSinkP
SinkMetMetP
SinkPMetP
Compartment Model:
Equation SFO-Model:
Parent Metabolite SinkkP->Met kMet->Sink
kP->Sink
Data points are available and can be used for parameter estimation.
Data points are not available ORif they are, with high uncertainty
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Introduction Formation Fraction - Rate Constant - Overall Degradation Rate I
• Metabolite formation fraction Maximum observed!• Sum of formation fractions started from one substance = 1
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ParentHalf-life: 35 d
MetaboliteHalf-life: 23 d
Sink
60 %ffMet=0.6
40 %1-ffMet=0.4
100 %
0 20 40 60 80 1000
20
40
60
80
100 SFO model
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Introduction Formation Fraction - Rate Constant - Overall Degradation Rate II
MetkPkdt
dSink
MetkPkdt
dMet
PkPkdt
dP
SinkMetSinkP
SinkMetMetP
SinkPMetP
Formulation with rate constants: Example (SFO model):
Parent:overall degradation rate kP: 0.02 d-1 (Half-life= 35 d)
rate constant kPMet:0.6 * kP = 0.012 d-1
formation fraction ffMet
rate constant kPSink
0.4 * kP = 0.008 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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MetkPkffdt
dSink
MetkPkffdt
dMet
Pkdt
dP
MetPMet
MetPMet
P
1
Introduction Formation - Plateau - Decline
Plateau/Peak
kP*P = kMet*Met
Decline phase
kP*P < kMet*Met
Formation phase
kP*P > kMet*Met
SFO model
Parent —100 %—> Metabolite
0 20 40 60 80 1000
20
40
60
80
100
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Day 25:1.2 = 1.2
Day 70:0.05 < 0.67
Day 5:4.9 > 0.6
IntroductionComparison of two Parent-Metabolite Systems
0 20 40 60 80 1000
20
40
60
80
100
Example 1 Example 2
max. amount: 30 % (59 d)
Metabolite Half-life: 34 d
Parent Half-life: 10 d
Metabolite Half-life: 34 d
Parent Half-life: 50 d
Which metabolite degraded faster? (SFO model, Parent —100 %—> Metabolite)
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20
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100 max. amount: 60 % (25 d)
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Types of Kinetic Models for Metabolites I
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• 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.
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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Types of Kinetic Models for Metabolites II
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DFOP-model: FMOC (Gustafson&Holden):
Types of Kinetic Models for Metabolites III
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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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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0 20 40 60 80 100
Time after application
0
20
40
60
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100
Metabolite Endpoints Trigger Endpoints - Example
Half-life Parent: 13 d
Degradation Metabolite:
Half-life: 71 d (0.010 0.002)
Fit of parent - metabolite system (both SFO)
Half-life Parent: -
Decline Metabolite (DissipationT50):
Half-life: 114 d (0.006 0.0008)
0 20 40 60 80 100
Time after maximum observed
0
20
40
60
80
100Fit of the metabolite decline curve (SFO)
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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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Main recommendationsPathway
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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Main recommendationsPathway - Example: Use of sink
Parent Sink
MetaboliteParent Metabolite
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Half-life Parent: 3 dHalf-life Metabolite: 38 dFormation fraction ffMet: 0.47
Half-life Parent: 6 dHalf-life Metabolite: 16 dFormation fraction ffMet: 1 (fixed)
Parent initial amount is not described properly (too low)
Main recommendationsKinetic 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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Main recommendationsKinetic Model - Example 1 (Parent Degradation)
Half-life Parent: 21 dHalf-life Metabolite: 9 dFormation fraction: 1
Parent SFO
DegT50 Parent: 16 d
Half-life: Metabolite: 14 dFormation fraction: 0.65
Parent FOMC
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Main recommendationsKinetic Model - Example 2 (Metabolite Degradation)
Half-life Parent: 1 dHalf-life Metabolite: 18 dDegT90 Metabolite: 61 d
Metabolite SFO
Half-life Parent: 1 dDegT50 Metabolite: 15 d
DegT90 Metabolite: 95 d
Metabolite FOMC
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Main recommendationsWeighting 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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Main recommendationsWeighting method - Example
Half-life Parent: 13 dHalf-life Metabolite 1: 42 dHalf-life Metabolite 2: 133 d
Unweighted fit - SFO
Half-life Parent: 18 dHalf-life Metabolite 1: 47 dHalf-life Metabolite 2: 369 d
Weighted fit (fractional) - SFO
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Main recommendationsStepwise approach I
A stepwise parameter fit is recommended in the followingcases:
• 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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Main recommendationsStepwise approach II
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1 Fit parent substance
Met 2
Met 3
Parent
Sink
Met 12 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
Procedure to derive endpoints for metabolitesImplementation 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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Procedure to derive endpoints for metabolitesImplementation of the conceptual model in a kinetic model II
Parent
Metabolite1 Metabolite2
Sink(other metabolites, bound residues, CO2)
kP* ffMet2*PkP* ffMet1*P
kP*(1- ffMet1- ffMet2)*P
kMet1* Met1 kMet2* Met2
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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Procedure to derive endpoints for metabolitesFlow sheet for Trigger Endpoints PART A
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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
no
yes
Procedure to derive endpoints for metabolitesFlow sheet for Trigger Endpoints PART B
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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 (DT50 and DT90
values)
SFO fit for metabolite
acceptable?
yes
yes
no
no
Procedure to derive endpoints for metabolitesFlow sheet for Modelling Endpoints PART A
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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
yesno
see next slideno
Procedure to derive endpoints for metabolitesFlow sheet for Modelling Endpoints PART B
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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
Case-by-case decision
yesno
RUN parent only with appropriate biphasic model
SFO fit acceptabl
e?
no
noParent SFO
non-acceptable
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 carrymore 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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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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Goodness-of-fit II
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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Goodness-of-fit III
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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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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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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