0. Theory Metabolites Claude Beigel, PhD.
Exposure Assessment Senior Scientist
Research Triangle Park, USA

1. Outline Introduction Kinetic endpoints General fitting recommendations
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

2. 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

3. 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

4. Metabolite Curve Maximum Formation phase Decline phase
kP*ffM*P=kM*M
Formation phase
kP*ffM*P>kM*M
Decline phase
kM*M> kP*ffM*P
Substance (% of applied)
Time (days)

5. Degradation Vs. Dissipation
Metabolite DT50 (decline) = 49.7 d
Metabolite DegT50 = 32.0 d

6. 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

7. 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

8. 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

9. Compartment Models Parent: dP/dt = – FP
Metabolite1
Metabolite2
Sink
(other metabolites, bound residues, CO2)
FP * ffM2
FP * 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

10. 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%)

11. Pathway: Including Flow to Sink
Parent
Others
Metabolite
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

12. 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

13. Always use unweighted data as a first step!
Weighting Method
Unweighted fit
Weighted fit (fractional)
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
Always use unweighted data as a first step!

14. 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

15. Metabolite Kinetic Models
Metabolite SFO
Metabolite DFOP
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

16. Stepwise Approach for Complex Cases
Fit parent substance
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

17. Evaluation of Goodness of Fit
Statistical indices
2 test, minimum 2 error
where C = calculated value O = observed value Ō = mean of observed err = measurement error
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%
T-test for rate constant parameters

18. Evaluation of Goodness of Fit
Graphical Evaluation (Visual Assessment)
Plot of Fitted Vs. Observed with Time
Plot of Residuals (Fitted – Observed)
Statistical Evaluation
Minimum 2 error: 9.2% (parent) and 4.9% (metabolite)

19. 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 parent
yes
no, FOMC better
Biphasic, run DFOP and compare with FOMC
Use Best-fit Model for parent

20. 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 SFO
yes no
Run parent best-fit and test appropriate biphasic model for metabolite (DFOP or FOMC)
Use Biphasic Model
Run parent best-fit with metabolites SFO
Biphasic model acceptable for metabolite

21. Decision Schemes: Modeling Endpoints (2)
Goal: kinetic model compatible with environmental model
First 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 parent
yes no
Run parent with appropriate biphasic model, e.g. DFOP or PEARLneq
Biphasic model good enough ?
Use Biphasic model for parent

22. 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 SFO
yes no
Case-by-case conservative approaches
Run parent with metabolites SFO

23. Conclusions
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