Fig 3. Potts model is predictive of higher-order marginals in the sequence MSA.

For each subsequence of length 2 to 14, marginal frequencies are determined by counting the occurrences in the MSA and computed for 500 randomly picked subsequences. They are compared with the corresponding predictions of marginal probabilities by the Potts model (blue) and a site-independent model (gray). The Spearman ρ² between the dataset marginal frequencies and the Potts and independent model predictions for all marginal frequencies above 2% are shown for subsequences picked at random from different combinations of 36 Protease-inhibitor or PI-associated positions in PR (A), 24 Nucleoside-reverse-transcriptase-inhibitor or NRTI-associated positions in RT (C), and 31 Integrase-strand-transfer-inhibitor or INSTI-associated positions in IN (E). Shown in (B), (D), (F), are the same but the subsequences are picked at random from non resistance-associated sites in PR, RT, and IN, respectively. The blue dashed line represents perfect correlation of ρ² = 1. In all, the Potts model accurately captures the higher-order marginals in the dataset; the independent model however gets progressively worse in capturing the higher-order marginals for resistance-associated sites in (A), (C), and (E). The role of epistatic interactions is strongly manifested in the effect on drug-resistance-associated positions (DRAPs) (indicating the strong role of correlations at functional positions within the protein). For residue positions not associated with drug resistance, epistatic interactions between sites appear to play a less important role and the site-independent model is sufficient to model the higher-order marginals in the MSA.