Figure 2: Evolutionary variables to predict functional asymmetry.

(a) Depiction of an evolutionary event. It shows a loss of gene A in the descendant (d) when both A and B are present in the ancestor (a). (b) Evolutionary variables used for the Bayesian classifier. The evolutionary variables across history of the dependent protein A in an asymmetric pair (A→B) can be expressed via 11 measures, listed in the first columns of two boxes. Of these 11, 6 count the number of times that a dependent protein A is gained or lost independently of B, including 2 that are expected to occur less often and 4 that are expected to occur more often for a dependent protein than for an independent protein. The remaining five measures are fractions that express relative frequencies of two evolutionary scenarios between A and B. f₁, f₂, f₃ and f₄ are expected to be larger than 0.5; f₅, that weighs f₄ with the absolute difference between two gain events of A, is expected to be larger than 0. The six evolutionary and the five relative frequencies all contribute to the prediction of functional asymmetry (Supplementary Fig. S1). (c) Schematic presentation of predicting the functional asymmetry in a protein pair (A–B). A TAN classifier was trained on functionally asymmetric enzyme pairs in the metabolic network¹⁴. For a protein pair (A–B), the 11 evolutionary variables (Fig. 2b) are used to predict the conditional probability that A is functionally independent (α₁) or dependent (α₂). A is likely to be independent if α₁>α₂, or dependent if α₁<α₂. Subsequently, A can be predicted as independent, dependent or unclassified by applying a cutoff on probability (α=max(α_1, α₂), see Methods). The same procedure is applied to protein B. By combining the prediction of both, A–B can be either A→B where A is dependent and B is independent, B→A where A is independent and B is dependent, or no evidence for asymmetry when A and B have any other combination of predicted relationship.