  Spatially proximate amino acids in a protein tend to coevolve. A protein's
three-dimensional (3D) structure hence leaves an echo of correlations in the
evolutionary record. Reverse engineering 3D structures from such correlations
is an open problem in structural biology, pursued with increasing vigor as more
and more protein sequences continue to fill the data banks. Within this task
lies a statistical inference problem, rooted in the following: correlation
between two sites in a protein sequence can arise from firsthand interaction
but can also be network-propagated via intermediate sites; observed correlation
is not enough to guarantee proximity. To separate direct from indirect
interactions is an instance of the general problem of inverse statistical
mechanics, where the task is to learn model parameters (fields, couplings) from
observables (magnetizations, correlations, samples) in large systems. In the
context of protein sequences, the approach has been referred to as
direct-coupling analysis. Here we show that the pseudolikelihood method,
applied to 21-state Potts models describing the statistical properties of
families of evolutionarily related proteins, significantly outperforms existing
approaches to the direct-coupling analysis, the latter being based on standard
mean-field techniques. This improved performance also relies on a modified
score for the coupling strength. The results are verified using known crystal
structures of specific sequence instances of various protein families. Code
implementing the new method can be found at http://plmdca.csc.kth.se/.
