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)

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Metabolite Curve

Degradation Vs. Dissipation

Aerobic Soil Metabolism Metabolite Decline

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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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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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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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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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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

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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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Baseline

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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