Reference: Swameye et al. Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by databased modeling. PNAS 100(3), 1028-1033, 2003.

Folder: /Examples/Swameye_PNAS2003.

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 measurement 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.

In the 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 arSetPars('sp1-5',[],2);.

The results in the following modified figure.