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Demonstration of fitting with Berkeley Madonna
FOCUS Degradation Kinetics, Ton van der Linden, January 27, 2005
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General information
Package
Version
contact
Berkeley Madonna
8.0.1
www.berkeleymadonna.com
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Additional information
• Java 1.1.8 (Sun Microsystems Inc) necessary for using Flowchart editor
• Windows 95 or later• Version for Macintosh available• Free demo version available (full functionality,
except for printing and saving)• User guide and examples available
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Opening screen
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Example
Soil metabolism study, parent + two metabolites
Parent
Metabolite 1
Metabolite 2
Sink
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Steps in the fitting procedure
1. Define model (equations / flow chart)
2. Initial values (substances / parameters)
3. Select parameters for fitting procedure
4. Set restrictions
5. Import datasets
6. Run
7. Export results
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Define model
d/dt (P) = -kp * Pd/dt (M1) = fpm1*kp * P - km1 * M1d/dt (M2) = fm1m2*km1 * M1 - km2 * M2
P = parentM1 = metabolite 1M2 = metabolite 2kx = degradation ratefx = formation fraction
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Flowchart
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Flowchart (simplified)
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Initial values
• Init P = 100• Init M1 = 0• Init M2 = 0• kp = .1• km1 = .1• km2 = .1• fpm1=1• fm1m2=1
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Total user defined code
METHOD RK4
STARTTIME = 0
STOPTIME=119
DT = 0.02
Init P = 100
Init M1 = 0
Init M2 = 0
d/dt (P) = -kp * P
d/dt (M1) = fpm1*kp * P - km1 * M1
d/dt (M2) = fm1m2*km1 * M1 - km2 * M2
kp = .1
km1 = .1
km2 = .1
fpm1=1
fm1m2=1
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Code automatically defined from flowchart
{
{Reservoirs}
d/dt (P) = - JPM1 - JPS
INIT P = 100
d/dt (M1) = + JPM1 - JM1M2 - JM1S
INIT M1 = 0
d/dt (M2) = + JM1M2 - JM2S
INIT M2 = 0
{Flows}
JPM1 = fPM1*kP*P
JM1M2 = fM1M2*kM1*M1
JPS = (1-fPM1)*kP*P
JM1S = (1-fM1M2)*kM1*M1
JM2S = kM2*M2
{Functions}
fPM1 = 1
fM1M2 = 1
kP = 0.1
kM1 = 0.1
kM2 = 0.1
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Parameter selection
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Parameter selection Select parametersrestrict
Import datasetsStart fitting
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Results
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Resultsgraph exported as .bmp
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Results
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Export resultsSave model / graph / table
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Results
• DT50 (parent) 13.8 d
• DT50 (metabolite 1) 6.9 d
• DT50 (metabolite 2) 60.8 d
• f.fraction (metabolite 1) 0.59
Results are very close to results ModelMaker
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Results
Uncertainty of parameters:
Not included in package
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Conclusions
Berkeley Madonna:• Easy to work with• Flexible• Robust• Compatible with many office packages
• Gives similar answers (results) as other packages• Has no built-in statistical routines