Suplemental Filr 6 for ’Monte Carlo analysis of an ODE Model of the Sea Urchin Endomesoderm Network’: Robust- ness to Random Parameter Variations

Result Based on the analysis proposed in the article, we computed the robustness of expression of different genes against random parameter variations using Monte Carlo simulations. To this end, we performed multiple simulation runs with different parameter sets, each generating a distinct result. The resulting mRNA concentrations have been averaged for each time point, also recording the variation. Using the coefficient of variation cv = σ/μ, the variation in expression of different genes can be compared. It indicates whether the expression of a gene is highly affected by or robust against parameter changes. The robustness computed here is not synonymous with robustness as commonly used in biological contexts [1]. In most publications, robustness in a GRN implies that the main features of the system are preserved when small deviations from some natural condition occur (e.g. small changes in individual parameter values). In contrast, we simulate the model using sets of arbitrary parameter values, which might be well out of range of biologically meaningful values. We computed cv for all genes in the model using 800 parameter sets under unperturbed conditions. For each gene, the highest cv (pertaining to the lowest robustness) of all time points is used as an indicator of the genes robustness. Generally, the robustness is higher at earlier measurement points. This is due to