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Sequences of nucleotides (for DNA and RNA) or amino acids (for proteins) arecentral objects in biology. Among the most important computational problems isthat of sequence alignment, i.e. arranging sequences from different organismsin such a way to identify similar regions, to detect evolutionary relationshipsbetween sequences, and to predict biomolecular structure and function. This istypically addressed through profile models, which captureposition-specificities like conservation in sequences, but assume anindependent evolution of different positions. Over the last years, it has beenwell established that coevolution of different amino-acid positions isessential for maintaining three-dimensional structure and function. Modelingapproaches based on inverse statistical physics can catch the coevolutionsignal in sequence ensembles; and they are now widely used in predictingprotein structure, protein-protein interactions, and mutational landscapes.Here, we present DCAlign, an efficient alignment algorithm based on anapproximate message-passing strategy, which is able to overcome the limitationsof profile models, to include coevolution among positions in a general way, andto be therefore universally applicable to protein- and RNA-sequence alignmentwithout the need of using complementary structural information. The potentialof DCAlign is carefully explored using well-controlled simulated data, as wellas real protein and RNA sequences.

Aligning biological sequences by exploiting residue conservation and coevolution