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page 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, 26-27 January 2005

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- 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) Introduction Regulatory Background page 2

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Introduction Formulation of Kinetic Models Compartment Model: Equation SFO-Model: ParentMetaboliteSink k P->Met k Met->Sink k P->Sink Data points are available and can be used for parameter estimation. Data points are not available OR if they are, with high uncertainty page 3

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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 page 4 Parent Half-life: 35 d Metabolite Half-life: 23 d Sink 60 % ff Met =0.6 40 % 1-ff Met =0.4 100 % 020406080100 0 20 40 60 80 100 SFO model

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Introduction Formation Fraction - Rate Constant - Overall Degradation Rate II Formulation with rate constants: Example (SFO model): Parent: overall degradation rate k P : 0.02 d -1 (Half-life= 35 d) rate constant k P Met : 0.6 * k P = 0.012 d -1 formation fraction ff Met rate constant k P Sink 0.4 * k P = 0.008 d -1 formation fraction 1-ff Met Metabolite: overall degradation rate k Met : 0.03 d -1 (Half-life= 23 d) Formulation with formation fractions: page 5

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Introduction Formation - Plateau - Decline Plateau/Peak k P *P = k Met *Met Decline phase k P *P < k Met *Met Formation phase k P *P > k Met *Met SFO model Parent 100 %> Metabolite 020406080100 0 20 40 60 80 100 page 6 Day 25: 1.2 = 1.2 Day 70: 0.05 < 0.67 Day 5: 4.9 > 0.6

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Introduction Comparison of two Parent-Metabolite Systems 020406080100 0 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) page 7 020406080100 0 20 40 60 80 100 max. amount: 60 % (25 d)

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Types of Kinetic Models for Metabolites I page 8 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) DT 50 values cannot be directly calculated from the model parameters although these trigger values can be derived using an iterative method.

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Bi-phasic models (cont.) FOMC model (First Order Multi Compartment/Gustafson&Holden) 1 st 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 DT 50 calculation of is simple. FOMC model cannot be implemented in complex SW- and GW-models not valid for the determination of modelling endpoints, except PEC soil. Exception: FOMC DT 90 values of terminal metabolites, can be used as conservative estimate of the SFO Half-life by dividing the FOMC DT 90 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! page 9 Types of Kinetic Models for Metabolites II

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page 10 DFOP-model: FMOC (Gustafson&Holden): Types of Kinetic Models for Metabolites III

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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) page 11

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Metabolite Endpoints Trigger Endpoints Trigger Endpoints: Degradation/Dissipation DT 50, DT 90 Derived by best-fit kinetics - unless deviations from SFO kinetics can be attributed to experimental artefacts Trigger DegT 50 and DegT 90 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 DegT 50 and DegT 90 values can be obtained by estimating the disappearance of the metabolite from its observed maximum, by fitting the decline curve (=consideration of the formation) page 12

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020406080100 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 (DissipationT 50 ): Half-life: 114 d (0.006 0.0008) 020406080100 Time after maximum observed 0 20 40 60 80 100 Fit of the metabolite decline curve (SFO) page 13

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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! page 14

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Main recommendations 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 CO 2 ParentMetaboliteSink page 15

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Main recommendations Pathway - Example: Use of sink Parent Sink Metabolite Parent Metabolite page 16 Half-life Parent: 3 d Half-life Metabolite: 38 d Formation fraction ff Met : 0.47 Half-life Parent: 6 d Half-life Metabolite: 16 d Formation fraction ff Met : 1 (fixed) Parent initial amount is not described properly (too low)

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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) page 17

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Main recommendations Kinetic Model - Example 1 (Parent Degradation) Half-life Parent: 21 d Half-life Metabolite: 9 d Formation fraction: 1 Parent SFO DegT 50 Parent: 16 d Half-life: Metabolite: 14 d Formation fraction: 0.65 Parent FOMC page 18

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Main recommendations Kinetic Model - Example 2 (Metabolite Degradation) Half-life Parent: 1 d Half-life Metabolite: 18 d DegT 90 Metabolite: 61 d Metabolite SFO Half-life Parent: 1 d DegT 50 Metabolite: 15 d DegT 90 Metabolite: 95 d Metabolite FOMC page 19

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Main recommendations Weighting Method Data weighting Unweighted fit should be used in the 1 st 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 precursors decline curve, covering formation phase of the metabolite is more important than later time points page 20

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Main recommendations Weighting method - Example Half-life Parent: 13 d Half-life Metabolite 1: 42 d Half-life Metabolite 2: 133 d Unweighted fit - SFO Half-life Parent: 18 d Half-life Metabolite 1: 47 d Half-life Metabolite 2: 369 d Weighted fit (fractional) - SFO page 21

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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 page 22

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Main recommendations Stepwise approach II page 23 1Fit parent substance Met 2 Met 3 Parent SinkSink Met 1 2Add primary metabolite(s), fit with parent parameters fixed to values obtained in 1), check flow to sink and simplify if justified 3Fit parent and primary metabolite(s) using values obtained in 1) and 2) as starting values 4Add 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 ---- nFinal step: fit all substances together using values obtained in n-1) as starting values

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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 page 24

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Procedure to derive endpoints for metabolites Implementation of the conceptual model in a kinetic model II Parent Metabolite1 Metabolite2 Sink (other metabolites, bound residues, CO 2 ) k P * ff Met2 *Pk P * ff Met1 *P k P *(1- ff Met1 - ff Met2 )*P k Met1 * Met1 k Met2 * Met2 Parent: dP/dt = – k P *P Metabolite 1: dM1/dt = k P * ff Met1 *P – k Met1 * Met1 Metabolite 2: dM2/dt = k P * ff Met2 *P – k Met2 * Met2 Sink: dSink/dt = k P *P * (1 – ff Met1 – ff Met2 ) + k Met1 * Met1 + k Met2 * Met2 page 25

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Procedure to derive endpoints for metabolites Flow sheet for Trigger Endpoints PART A page 26 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

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Procedure to derive endpoints for metabolites Flow sheet for Trigger Endpoints PART B page 27 RUN parent best-fit and metabolite FMOC FMOC fit for metabolite acceptable? Case-by-case decision Use estimated SFO trigger endpoints (DT 50 and DT 90 values) Use estimated FMOC trigger endpoints (DT 50 and DT 90 values) SFO fit for metabolite acceptable? yes no

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Procedure to derive endpoints for metabolites Flow sheet for Modelling Endpoints PART A page 28 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 no

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Procedure to derive endpoints for metabolites Flow sheet for Modelling Endpoints PART B page 29 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 yes no RUN parent only with appropriate biphasic model SFO fit acceptabl e? no Parent SFO non-acceptable

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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 r 2 ) 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 page 30

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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) page 31 Goodness-of-fit II

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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 page 32 Goodness-of-fit III

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Conclusions I The half-life or DT 50 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 page 33

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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 page 34

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Conclusions III FOCUS Report: Guidance provided for deriving metabolite kinetic endpoints from studies with parent –Trigger endpoints: degradation/dissipation DT 50 and DT 90 –Modeling endpoints: formation and degradation rate Harmonized approach for reproducible results independent of software tool used –Better acceptance of generated endpoints –Facilitates review process page 35

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