claude beigel, phd. exposure assessment senior scientist research triangle park, usa practical...
TRANSCRIPT
Claude Beigel, PhD.
Exposure Assessment Senior Scientist
Research Triangle Park, USA
Practical session metabolitesPart I: curve fitting
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Using Compartment Models for Metabolite Curve Fitting
Parent + metabolite(s) data sets can be fitted with compartment models based on the same principles shown for parent substance
Model parameters are defined
A compartment is added for each metabolite
Flows are added between parent and metabolite(s), and metabolite(s) and sink
Each flow is defined with differential equation corresponding to appropriate kinetic model, using defined parameters
Model is fitted to parent and metabolite measured data
If metabolite was applied to test system, data set treated as for parent substance
Metabolite decline treated as parent substance, with time 0 starting as time of maximum, and initial amount (estimated) as maximum amount of metabolite
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Two Approaches to Defining FlowsIndividual Rate Constants and Formation Fractions
Overall degradation rate of a substance is defined by differential equation corresponding to selected model (SFO, FOMC, DFOP)
Basic simplifying assumption: degradation to different compartments (metabolite(s) and sink) follows same kinetic model
Overall rate is split between metabolite(s) formed and sink
Substance SFO, two options:
– Use individual first-order rate constant for each flow with sum = overall degradation rate constant (because first-order rates are additive)
– Multiply overall rate constant by formation fraction for each metabolite, and 1-ffMi for sink
Substance biphasic
– Multiply overall rate equation by formation fraction for each metabolite, and 1-ffMi for sink
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Metabolite Curve-fittingSummary of required steps to follow (1)
Always build simplest model representative of pathway
Follow metabolic pathway
Initially include all flows to sink, reduce when applicable
Data handling
Set metabolite time-0 to 0 and eventually correct parent time-0
Deal with metabolite <LOD/LOQ data as recommended
– Set first data point <LOD/LOQ before first detect and after last detect to half of LOD or half (LOQ+LOD)
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Ask yourself: what type of endpoints are needed?
Trigger DT50/90 best-fit kinetics
PEC soil endpoints (formation + degradation rate parameters, formation fraction) best-fit kinetics
Modeling endpoints (formation + degradation rate parameters, formation fraction) restricted kinetic models
Use stepwise approach for complex cases
Determine parent kinetics first
Add metabolites stepwise
Free all parameters in final fit
Metabolite Curve-fittingSummary of required steps to follow (2)
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Hands-on Example 1
Exercise 1
Same substance 1 as fitted yesterday in parent session
Proposed pathway shows substance degrading to primary metabolite 1
Measured data for metabolite 1 given in Excel spreadsheet 2.2_metabolites examples input.xls
Derive trigger and modeling endpoints for metabolite 1
Trigger endpoints: metabolite DT50/90
Modeling endpoints: parent degradation rate, metabolite formation fraction and metabolite degradation rate
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Building the Compartment Model Step-by-step
Results from yesterday’s exercise showed that SFO model was appropriate for both trigger and modeling endpoints for parent
We will add metabolite 1 using a model formulation with formation fraction
We will follow the stepwise approach to fitting
1. Fix parent parameters and fit metabolite parameters
2. Use fitted parameters as initial values, and fit parent and metabolite parameters together
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Building the Compartment Model Step-by-step
Start from parent – sink model with appropriate kinetic model for endpoints of interest (here SFO)
– Open 2.2_Example1_parent.mod ModelMaker file provided
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Building the Compartment Model Step-by-step
Define SFO parameters for primary metabolite(s)
– In this example, formation fraction ffM1 and first-order rate constant kM1
– Select initial value of 0.5 for ffM1 and constrain between 0 and 1
– Select initial value of 0.01 for kM1 (unconstrained)
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Building the Compartment Model Step-by-step
Add metabolite compartment(s)
– Here create one compartment for Metabolite 1 (no space in symbol/name)
– Leave metabolite initial value set to 0.0
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Building the Compartment Model Step-by-step
Add flows from parent to metabolite compartment(s) and metabolite(s) to sink
– Here create flow parent to Metabolite 1 and Metabolite 1 to Sink
– Red arrows mean that flows are not defined yet
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Building the Compartment Model Step-by-step
Define flow from parent to metabolite with appropriate differential equation for kinetic model (multiplied by formation fraction)
– Here define fP_M1 with SFO equation = ffM1*kP*Parent
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Building the Compartment Model Step-by-step
Define flow from metabolite to sink with differential equation for SFO model
– Here define fM1_S with SFO equation = kM1*Metabolite1
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Building the Compartment Model Step-by-step
Modify flow from parent to sink to account for formation of metabolite(s) (multiply by 1-ffMi)
– Here modify fP_S to equation = (1-ffM1)*kP*Parent
– Compartment model is now fully defined
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Building the Compartment Model Step-by-step
Create variables for calculating metabolite DT50/90 values
– In main page, click on variable icon, create DT50_M1 = LN(2)/kM1 and DT90_M1 = LN(10)/kM1
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Building the Compartment Model Step-by-step
Add Metabolite1 compartment and DT50/90 variables to Table
– In table page, right-click and go to selection, add the components to selection by double-clicking in component list or use >> and << buttons to select and unselect components
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Building the Compartment Model Step-by-step
Add metabolite data to model data
– Type or paste metabolite data in “Not Used” column, if necessary, “insert” column, highlight column and define as Metabolite1
– Always check that data correspond to correct times, ModelMaker tends to disregard empty cells and move data up or left
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Building the Compartment Model Step-by-step
Add metabolite to graph
– In graph page, right-click and go to “selection” window, add Metabolite 1 from components by double-clicking on component or use >> button
– Modify series appearance by right-clicking and go to “series” window, you can remove error bar and change line and symbol
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Building the Compartment Model Step-by-step
Run model (model – integrate)
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Building the Compartment Model Step-by-step
Optimize metabolite parameters
– In parameters page, select metabolite parameters by clicking on “optimize”, leave parent parameters unchecked at this point
– Fit to data by clicking on Model - Optimize
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Building the Compartment Model Step-by-step
Repeat optimization changing initial parameter values to check that results do not change
Your results should be the following (minimal variation if different initial values used):
Update parameters (in parameter results page, select parameters,right-click outside of selection, and update)
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Building the Compartment Model Step-by-step
Run model with optimized parameters (model – integrate)
ParentMetabolite1
Example 1 data set (SFO)
0 10 20 30 40 50 60 70 80 90 100 110 120
Time (days)
0
10
20
30
40
50
60
70
80
90
100
110
Su
bst
ance
(%
AR
)
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Building the Compartment Model Step-by-step
Final step: optimize parent and metabolite parameters together
– In parameters page, select all parameters by clicking on “optimize”, keep initial values to previously optimized values
– Fit to data by clicking on Model – Optimize
– Update all parameters, run model and save
– Write-down final optimization results, and calculated DT50/90 values
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Additional Notes on Example 1
The Modelmaker file for the equivalent model formulated with individual rate constants is provided in your training material (2.2_Example1_individualrates.mod file). You can check that you obtain similar results with the two model formulations (minimal variation due to initial value of parameters).
The stepwise approach is recommended for complex cases, and would not be necessary for a well-behaved data set such as this. You can try a simultaneous fit approach by changing the initial parameter values to reasonable estimates such as Pini = 100, kP = 0.1, ffM1 = 0.5 and kM1 = 0.01 and fit all parameters together. You should obtain similar results as in the stepwise final fit (minimal variation due to initial value of parameters).
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Hands-on Example 2
Exercise 2
Same substance 2 as fitted yesterday in parent session
Proposed pathway shows substance degrading to one metabolite
Measured data for metabolite of substance 2 given in Excel spreadsheet 2.2_metabolites examples input.xls
Derive trigger and modeling endpoints for metabolite
Trigger endpoints: metabolite DT50/90
Modeling endpoints: parent degradation rate, metabolite formation fraction and metabolite degradation rate
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Hands-on Example 2 General Guidance
Parent substance
Results from yesterday’s exercise on parent showed that parent degradation is biphasic
– FOMC model of choice for parent trigger endpoints
– DFOP model may be used for modeling endpoints
Add metabolite using a model formulation with formation fraction
Follow the stepwise approach to fitting
1. Fix parent parameters and fit metabolite parameters
2. Use fitted parameters as initial values, and fit parent and metabolite parameters together
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Hands-on Example 2Guidance for Deriving Trigger Endpoints
Start from parent FOMC fit
Use 2.2_Example2_parentFOMC.mod ModelMaker file provided
Add metabolite parameters and compartment (same as for example 1)
Split parent flow with metabolite formation fraction:
– kP_M1 = ffM1*alphaP/betaP*Parent/(t/betaP+1)
– kP_S = (1-ffM1)*alphaP/betaP*Parent/(t/betaP+1)
Further steps same as for example 1
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Hands-on Example 2Guidance for Deriving Modeling Endpoints
Start from parent DFOP fit
Use 2.2_Example2_parentDFOP.mod ModelMaker file provided
Add metabolite parameters and compartment (same as for example 1)
Split parent flow with metabolite formation fraction:
– kP_M1 = ffM1*(k1*g*exp(-k1*t)+k2*(1-g)*exp(-k2*t))/(g*exp(-k1*t)+(1-g)*exp(-k2*t))*Parent
– kP_S = (1-ffM1)*(k1*g*exp(-k1*t)+k2*(1-g)*exp(-k2*t))/(g*exp(-k1*t)+(1-g)*exp(-k2*t))*Parent
(tip: use copy/paste, ctrl-c/ctrl-v)
Further steps same as for example 1
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For Those Who Have Time to Go Further
Exercise 1 (continued)
Add second metabolite (metabolite 2) formed from metabolite 1 and derive trigger and modeling endpointsMeasured data for metabolite 2 of substance 1 given in Excel spreadsheet examplesinput.xls
Exercise 2 (continued)
Fit metabolite decline data (from maximum onward) with SFO modelto derive decline rate constant and DT50 value