Cluster-expansion theory for sequence-specific "fuzzy” interaction between a pair of intrinsically disordered proteins*

Intrinsically disordered proteins (IDPs) do not fold into a unique tertiary structure in isolation, likely because they are depleted in hydrophobic but enriched in polar, charged, and aromatic amino acids. While many IDPs become ordered upon binding to folded proteins, several IDPs have been recently discovered to retain their structural disorder when binding with each other via a so-called "fuzzy" mechanism. Just like interactions between folded proteins, such a fuzzy mechanism must be determined by the amino acid sequences of the IDPs. Here, we implement the cluster expansion method in statistical mechanics to develop an analytical theory for calculating the sequence-specific IDP-IDP binding affinity. We apply the theory to various IDP pairs selected from a set of 30 polyampholytic IDP sequences with the same amino acid composition but different charge patterns. The sequence-specific correlation between the double-chain binding affinities and single-chain conformations are systematically investigated. Our analytical theory provides a concise and powerful tool for high-throughput proteomic analysis of IDP-IDP interaction.