What does this equation mean?

The fix is to fit a global model that explains the observed column statistics with the smallest number of direct couplings. In the maximum-entropy formulation used in this literature, the probability of a full sequence takes a Potts form, $P(a_1,\ldots,a_L) = \frac{1}{Z}\exp\!\left[\sum_{i} h_i(a_i) + \sum_{i<j} e_{ij}(a_i,a_j)\right]$. with single-site fields $h_i$ and pair couplings $e_{ij}$ fitted so that the model reproduces the single-column and pairwise frequencies of the alignment. Marks and colleagues reported that the strength of the inferred couplings is a strong predictor of residue proximity in the folded structure, and that the top-scoring couplings are accurate and well-distributed enough to define a three-dimensional fold [ 5 ] . Morcos and colleagues developed a computationally efficient direct-coupling analysis that disentangled direct from indirect correlations and evaluated contact-prediction accuracy across a large number of protein domain families from sequence information alone [ 6 ] .