  In allosteric proteins, the binding of a ligand modifies function at a
distant active site. Such allosteric pathways can be used as target for drug
design, generating considerable interest in inferring them from sequence
alignment data. Currently, different methods lead to conflicting results, in
particular on the existence of long-range evolutionary couplings between
distant amino-acids mediating allostery. Here we propose a resolution of this
conundrum, by studying epistasis and its inference in models where an
allosteric material is evolved in silico to perform a mechanical task. We find
in our model the four types of epistasis (Synergistic, Sign, Antagonistic,
Saturation), which can be both short or long-range and have a simple mechanical
interpretation. We perform a Direct Coupling Analysis (DCA) and find that DCA
predicts well the cost of point mutations but is a rather poor generative
model. Strikingly, it can predict short-range epistasis but fails to capture
long-range epistasis, in consistence with empirical findings. We propose that
such failure is generic when function requires subparts to work in concert. We
illustrate this idea with a simple model, which suggests that other methods may
be better suited to capture long-range effects.
