  To confer high specificity and affinity in binding, contacts at interfaces
between two interacting macromolecules are expected to exhibit pair preferences
for types of atoms or residues. Here we quantify these preferences by measuring
the mutual information of contacts for 895 protein-protein interfaces. The
information content is significant and is highest at the atomic resolution. A
simple phenomenological theory reveals a connection between information at
interfaces and the free energy spectrum of association. The connection is
presented in the form of a relation between mutual information and the energy
gap of the native bound state to off-target bound states. Measurement of
information content in designed lattice interfaces show the predicted scaling
behavior to the energy gap. Our theory also suggests that mutual information in
contacts emerges by a selection mechanism, and that strong selection, or high
conservation, of residues should lead to correspondingly high mutual
information. Amino acids which contribute more heavily to information content
are then expected to be more conserved. We verify this by showing a
statistically significant correlation between the conservation of each of the
twenty amino acids and their individual contribution to the information content
at protein-protein interfaces
