In this section we present the computation schemes for finding the time
derivatives of the output function. In case of the theoretical examples we
used the Mathematica@ function Interpolation to a set of theoretical data
points 
to obtain a spline version of the distribution
distorted cosine function (24, 26 and 28). This
function can be given the extra argument ''InterpolationOrder'' which
denotes the polynomial order of the splines functions used. We set this
value equal to the highest value of the derivative we want in the
transformation functions (4, 7, and 8).
Next the Mathematica@ function Derivative[order][function] was used to
compute the time derivatives of the interpolation function at the time
points 
.
For the experimental data we proceeded a little different. Since the data have some additional sample stochasticity we fitted polynomials using the Mathematica@ function Fit to various parts of the CLN2 mRNA time series. The order of the polynomials and the parts used were judged by eye. Again the function Derivative was used to compute the time derivatives.
The Mathematica code used can be obtained upon request to the authors.