Before revision: Many intrinsically disordered proteins (IDPs) , proteinsthat do not fold into a unique tertiary structure in isolation because of their depletion in hydrophobicity whereas enrichment in charge and aromaticity, retain their structural disorderness when participating in IDP-IDP binding andIDP phase separation via a sequence-specific "fuzzy  " molecular recognition mechanism. We implement the cluster expansion method in statistical mechanics to develop an analytical theory for elucidating the nature of the fuzzy Coulomb interaction between two charged IDPs . We apply the theory to calculate binding affinities between various pairs of IDP sequences, and extract a parameter jSCDencompassing the sequence-specific IDP-IDP interaction.
After revision: Many intrinsically disordered proteins (IDPs) , proteinsthat do not fold into a unique tertiary structure in isolation because of their depletion in hydrophobicity whereas enrichment in charge and aromaticity, retain their structural disorderness when participating in IDP-IDP binding andIDP phase separation via a sequence-specific "fuzzy " parameter readily calculable from the pair of IDPs' sequence charge patterns. Predictions by our analytical theory are in essential agreement with coarse-grained explicit-chain simulations. This computationally efficient theoretical framework is expected to be broadly applicable to rationalizing and predicting sequence-specific IDP-IDP interaction.