  Proteins employ the information stored in the genetic code and translated
into their sequences to carry out well-defined functions in the cellular
environment. The possibility to encode for such functions is controlled by the
balance between the amount of information supplied by the sequence and that
left after that the protein has folded into its structure. We developed a
computational algorithm to evaluate the amount of information necessary to
specify the protein structure, keeping into account the thermodynamic
properties of protein folding. We thus show that the information remaining in
the protein sequence after encoding for its structure (the 'information gap')
is very close to what needed to encode for its function and interactions. Then,
by predicting the information gap directly from the protein sequence, we show
that it may be possible to use these insights from information theory to
discriminate between ordered and disordered proteins, to identify unknown
functions, and to optimize designed proteins sequences.
