  Information processing and decision making is based upon logic operations,
which in cellular networks has been well characterized at the level of
transcription. In recent years however, both experimentalists and theorists
have begun to appreciate that cellular decision making can also be performed at
the level of a single protein, giving rise to the notion of protein logic. Here
we systematically explore protein logic using a well known statistical
mechanical model. As an example system, we focus on receptors which bind either
one or two ligands, and their associated dimers. Notably, we find that a single
heterodimer can realize any of the 16 possible logic gates, including the XOR
gate, by variation of biochemical parameters. We then introduce the novel idea
that a set of receptors with fixed parameters can encode functionally unique
logic gates simply by forming different dimeric combinations. An exhaustive
search reveals that the simplest set of receptors (two single-ligand receptors
and one double-ligand receptor) can realize several different groups of three
unique gates, a result for which the parametric analysis of single receptors
and dimers provides a clear interpretation. Both results underscore the
surprising functional freedom readily available to cells at the single-protein
level.
