  Intrinsically disordered proteins (IDPs) are important for biological
functions. In contrast to folded proteins, molecular recognition among certain
IDPs is "fuzzy" in that their binding and/or phase separation are
stochastically governed by the interacting IDPs' amino acid sequences while
their assembled conformations remain largely disordered. To help elucidate a
basic aspect of this fascinating yet poorly understood phenomenon, the binding
of a homo- or hetero-dimeric pair of polyampholytic IDPs is modeled statistical
mechanically using cluster expansion. We find that the binding affinities of
binary fuzzy complexes in the model correlate strongly with a newly derived
simple "jSCD" 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 polyelectrostatic
interactions.

Biomolecules