This thermodynamically safe parameterization relies on the definition of a reference state upon which feasible parameter sets can be efficiently sampled.

For the aforementioned cases, the sums of the blue and red areas represent the 95% confidence region of all the thermodynamically feasible parameter sets .

Such increased area point to a greater diversity of feasible parameter sets under more thermodynamically favourable conditions.

On the contrary, more homogeneous parameter sets can be found closer to equilibrium, i.e.

All use simplified kinetic expressions (loss of generality) and most ignore intrinsic thermodynamic constraints between kinetic parameters, hence they will sample infeasible parameter sets .

This sampling strategy ensures that any parameter set sampled satisfies both pattern and kinetic constraints (Fig.

Parameter set accuracy check

The sampling procedure generates only feasible parameter sets .

Since this parameterization is built upon a reference point, this can be validated by confirming that the parameter set produces the reference flux at the reference point, i.e.

Using evolutionary optimization, we found parameter sets that show excellent agreement with the fluorescence in situ hybridization (FISH) data for sna, vnd, 50g, and zen (Fig.

.p15]N, are evaluated and compared to the data using a residual sum of squares calculation: where th = dl-Venus data, clth 2 measurement uncertainty—both corresponding to simulated nucleus h and timepoint k—and SN is the ordinary least squares estimate of the scale factor that minimizes the difference between X and Y across all time and space coordinates and for parameter set N. Um“; and Wnuc are the dimensionless versions of nuclear dl and nuclear dl/ Cact complex, respectively (see Equations (1) and (3)).

After the 25th generation, we keep the top 100 parameter sets as the end product of each evolutionary optimization run.

A similar method is used to find parameter sets for simulations of gene eXpression, with l = 250, [,4 = 50.

Each evolutionary optimization run that was used to fit our model to the dl-Venus data set resulted in 100 closely-clustered parameter sets .

We represent each evolutionary optimization run by an average parameter set , in which we calculate the mean and standard deviation (weighted by RSS error; see Methods and 81 Text) for each parameter, across all 100 sets.

We collected 254 such runs, resulting in 254 average parameter sets that are nearly indistinguishable in terms of their average RSS error (see Methods and 81 Text), yet vary in the values of their parameters, as has been observed previously for biological models [25, 26].

We thus fit the sum of free nuclear d1 (1) and nuclear dl/Cact complex (3) in our extended model to the dl-Venus data set in both space and time, revealing parameter sets that show an excellent fit to the data (see Fig.

The correlation with tumor survival in this case is lower than the correlation of tumor survival with MP1 across the entire parameter set (Fig.

The correlation with tumor survival in this case is higher than that observed across the entire parameter set .

This movie shows a representative simulation that results in tumor survival under the base parameter set .

With a few exceptions (detailed in the caption of SS Fig), the sensitivity of simulation outcomes to the parameters was found to be less informative over this larger parameter set, and for this reason we focused our analysis on the initial parameter set (above).

To find the optimal parameter sets that describe the experimental data for each model structure, we performed parameter estimations.

To prove the validity of our optimization procedure, a Latin hypercube sampling approach with 1000 initial parameter sets has been performed (S7 Fig).

Therefore, the best performing model structure in combination with the estimated parameter set is described by the lowest -Zlog(L).

Multistart optimization with 1000 initial parameter sets for model 4_8_12.

A) Mul-tistart optimization has been performed With 1000 initial parameter sets .

In neuronal modeling, it has become clear that different combinations of conductance parameter sets can give rise to the same activity pattern and that using average values of the conductances may fail to generate that pattern [10,11,37].

Finally, the iterative optimization approach [31] refined our in silico parameter estimation by decreasing the spread of the returned parameter sets , which caused the prediction error to again decrease by an order of magnitude.

Although the optimized model action potential matches the optimization objective to a very high degree, the estimated parameter set does not match that of the FR model (Fig 1E).