Statistical mechanical properties of sequence space determine the efficiency of the various algorithms to predict interaction energies and native contacts from protein coevolution.

Studying evolutionary correlations in alignments of homologous sequences by means of an inverse Potts model has proven useful to obtain residue-residue contact energies and to predict contacts in proteins. The quality of the results depend much on several choices of the detailed model and on the algorithms used. We built, in a very controlled way, synthetic alignments with statistical properties similar to those of real proteins, and used them to assess the performance of different inversion algorithms and of their variants. Realistic synthetic alignments display typical features of low-temperature phases of disordered systems, a feature that affects the inversion algorithms. We showed that a Boltzmann-learning algorithm is computationally feasible and performs well in predicting the energy of native contacts. However, all algorithms, when applied to alignments of realistic size, suffer of false positives quite equally, making the quality of the prediction of native contacts with the different algorithm much system-dependent.