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The physical chemistry of liquid-liquid phase separation (LLPS) of polymersolutions bears directly on the assembly of biologically functionaldroplet-like bodies from proteins and nucleic acids. These biomolecularcondensates include certain extracellular materials, and intracellularcompartments that are characterized as "membraneless organelles". Analyticaltheories are a valuable, computationally efficient tool for addressing generalprinciples. LLPS of neutral homopolymers are quite well described by theory;but it has been a challenge to develop general theories for the LLPS ofheteropolymers involving charge-charge interactions. Here we present a noveltheory that combines a random-phase-approximation treatment of polymer densityfluctuations and an account of intrachain conformational heterogeneity basedupon renormalized Kuhn lengths to provide predictions of LLPS properties as afunction of pH, salt, and charge patterning along the chain sequence. Advancingbeyond more limited analytical approaches, our LLPS theory is applicable to awide variety of charged sequences ranging from highly charged polyelectrolytesto neutral or nearly neutral polyampholytes. The new theory should be useful inhigh-throughput screening of protein and other sequences for their LLPSpropensities and can serve as a basis for more comprehensive theories thatincorporate non-electrostatic interactions. Experimental ramifications of ourtheory are discussed.

A unified analytical theory of heteropolymers for sequence-specific phase behaviors of polyelectrolytes and polyampholytes