Fig 5. Prediction of epistasis by DCA.

A: Running average of the absolute value of epistasis $\Delta \Delta {\mathcal{F}}_{ij}$ and of DCA prediction $\Delta \Delta {\mathcal{E}}_{ij}$ for 1.5 × 10³ configurations as a function of the distance between link i and j. The trends are nearly identical at short distances but at long distance DCA underestimates epistasis. Inset: Top 400 inferred couplings. They are mostly short range with only a few long-range couplings connecting the allosteric and the active site. Next we assess the prediction of epistasis in single configurations by these top 400 couplings. We consider separately long-range (> 7) and short-range (< 7) pairs of links, and rank them respectively in terms of the epistasis magnitude $|\Delta \Delta {\mathcal{F}}_{ij}|$. B shows which fraction of these pairs—averaged over 100 configurations randomly chosen—belongs to the 400 largest couplings, as a function of the number of pairs with maximal epistasis considered. Clearly coupling magnitude has less predictive power at large distances than at short ones. The random expectations for these mean predicted fractions are 0.0041 for short-range pairs and 0.0009 for long-range ones (they are both significantly lower than the values reported here). This feature stays robust also if we increase, e.g. up to 1000, the number of top couplings for prediction (see Panel A in Fig. D, S1 Text).