JAK/STAT signaling model
Reference: Swameye et al. Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by databased modeling. PNAS 100(3), 1028-1033, 2003.
Facts: The model contains 46 data points, 16 free parameters and 1 experimental condition.
In this example application we demonstrate the use of cubic splines are input functions and the use of the fixed measurment noise instead of the parameterized measurement noise function.
After calling the
Setup.m script we see the following figure.
In this model the input
pEpoR is model as strictly posive splines with five knots:
pEpoR C "au" "conc." "spline_pos5(t, 0.0, sp1, 5.0, sp2, 10.0, sp3, 20.0, sp4, 60.0, sp5, 0, 0.0)"
The spline parameters
sp1-5 are estimated together with the model dynamics and the measurement noise.
Using fixed measurment noise
Setup.m script we can switch the flag
useErrorModel = true; if(~useErrorModel) % do not fit error model ar.config.fiterrors = -1; % show error bars instead of error model ar.config.ploterrors = 1; % show, but not fit input data for pEpoR ar.model.data.qFit(3) = 0; % fix parameter for input and error model arSetPars('sp1',,2); […] end
to disable the estimation of the measurement noise. The option
ar.config.fiterrors = -1 indicates that the error model is not used but the experimentally determined measurement errors (standard deviation calculated form triplicates) given in the data sheet in the
_std columns. Also, the weigthed sum of squared residuals is use in the estimation instead of the full likelihood. The option
ar.config.ploterrors = 1 indicates that the conventional error bars on the data points are plotted instead of the error model around the trajectory. The command
ar.model.data.qFit(3) = 0; indicates that third observable should not be used for fitten. This is because no experimentally determined measurement errors are available for this measurement. Correspindings also the spline parameters are fixed by the commands
The results in the following modified figure.