Add reformulated Fiedler_BMCSystBiol2016

[m-philipps]

The authors used an identifiable, reformulated version of the model for Raf/MEK/ERK signaling after release from S-phase arrest:

The model for the relative phosphorylation levels does not depend explicitly on the total abundances $\text{[Raf}]_0$, $\text{[MEK}]_0$ and $\text{[ERK}]_0$ but only on products and ratios of these parameters with other parameters, e.g., $k_3\text{[Raf}]_0$. Defining these products and ratios as new parameters eliminates non-identifiabilities and reduces the number of parameters.

Compared to the existing implementation the state variables of the model are now the relative phosphorylation levels
$x_1 = \text{[pRaf] / [Raf}]_0, x_2 = \text{[pMEK] / [MEK}]_0, x_3 = \text{[pERK] / [ERK}]_0$.
Therefore, the PEtab observables are now $x2$ (pMEK_rel) and $x3$ (pERK_rel)

The interpretation of the scaling factors changes to the product of the scaling factor and $\text{[MEK}]_0$ for pMEK_rel, and the product of scaling factors and $\text{[ERK}]_0$ for pERK_rel.

[m-philipps]

The parameter table nominalValues were taken from parameter estimation. 1000 starts with the fides optimiser resulted in a convergence in objective and parameter values.

Waterfall plot

Parameter vectors for the 200 best models

Best model fit

Intensities were rescaled by the maximum value per western blot gel, dashed line is the simulation, different colours correspond to different western blot gels.