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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

••

•• • •

•

•

•

••

•

•

•

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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••

•• • •

•

• ••

•

••

•0 20 40 60 80 100

0

20

40

60

80

100 max. amount: 60 % (25 d)

•

• • •

•

••

• • ••

•

••

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

80

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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