Fig. 1. The limitation of the covariance-based methods in estimating inter-residue distances.
a Two artifactual proteins P1 and P2. In protein P1, two residues R1 and R2 are close, whereas in protein P2, they are far from each other. b The MSAs constructed for the two proteins show considerable difference. c The covariance matrices calculated from these two MSAs are totally identical; thus, the covariance-based methods give the same estimation of inter-residue distances for protein P1 and P2. This is contradict the true inter-residue distances. d Unlike the covariance matrices, the conditional joint-residue distribution P(R1, R2∣R3) could effectively distinguish these two MSAs.