Fig. 2.

Failure of straightforward optimization. Optimal combination values found by the single-player algorithm, a neural network which minimizes the Coefficient of Regulation with unconstrained shuffling (CR, Eq. 5, ζ(⋅)≡1). This algorithm was fed with time traces of the three proteins, with the ratio $\raisebox{1ex}{$P_2$}\!\left/ \!\raisebox{-1ex}{$P_1$}\right.$ being the conserved combination. The network output is displayed as an arbitrary-value colormap in the (P₁, P₂) plane. Shuffles that fall within the boundaries of the data (the white lines) have a practically fixed value, while shuffles outside these boundaries attain values that are correlated with their distance from the boundaries. The found combination has a CR of almost zero (0.004 ± 0.003). However, its Pearson correlation with the ground truth conserved combination is 0.11 ± 0.08.