  Proteins created by combinatorial methods in vitro are an important source of
information for understanding sequence-structure-function relationships.
Alignments of folded proteins from combinatorial libraries can be analyzed
using methods developed for naturally occurring proteins, but this neglects the
information contained in the unfolded sequences of the library. We introduce
two algorithms, logistic regression and excess information analysis, that use
both the folded and unfolded sequences and compare them against contingency
table and statistical coupling analysis, which only use the former. The test
set for this benchmark study is a library of fictitious proteins that fold
according to a hypothetical energy model. Of the four methods studied, only
logistic regression is able to correctly recapitulate the energy model from the
sequence alignment. The other algorithms predict spurious interactions between
alignment positions with strong but individual influences on protein stability.
When present in the same protein, stabilizing amino acids tend to lower the
energy below the threshold needed for folding. As a result, their frequencies
in the alignment can be correlated even if the positions do not interact. We
believe any algorithm that neglects the nonlinear relationship between folding
and energy is susceptible to this error.
