From Abstract Graphs To (Biophysical) Reality - Graphs In Mutual Information Space Help Identify Highly Correlated Positions In G Protein-Coupled Receptors

G protein-coupled receptors (GPCRs) are a superfamily of seven transmembrane-spanning proteins involved in a wide array of physiological functions and are the most common targets of pharmaceuticals. Are there idiomatic relations between positions on these protein sequences that are evident in their co-evolution? We investigate the semantic graph of the constituent amino acid (AA) positions using an information theoretic approach. Using a multiple sequence alignment of the seven transmembrane (7-TM) domains, we calculated the mutual information (MI) between all pairs of aligned positions. Representing TM positions as vertices and pairing them by their MI we compute the planar acyclic graph that maximizes the total MI. The total MI of this graph is much greater than the total MI of a random planar acyclic graph. From this graph, we identify few positions which have a significantly high degree (edges incident to the vertices) when contrasted with the others. The positions, from class A and class C GPCRs, with the leading degree values are found to be associated with the experimentally determined binding pocket, confirming our previous studies involving MI graphs.