  The physical chemistry of liquid-liquid phase separation (LLPS) of polymer
solutions bears directly on the assembly of biologically functional
droplet-like bodies from proteins and nucleic acids. These biomolecular
condensates include certain extracellular materials, and intracellular
compartments that are characterized as "membraneless organelles". Analytical
theories are a valuable, computationally efficient tool for addressing general
principles. LLPS of neutral homopolymers are quite well described by theory;
but it has been a challenge to develop general theories for the LLPS of
heteropolymers involving charge-charge interactions. Here we present a novel
theory that combines a random-phase-approximation treatment of polymer density
fluctuations and an account of intrachain conformational heterogeneity based
upon renormalized Kuhn lengths to provide predictions of LLPS properties as a
function of pH, salt, and charge patterning along the chain sequence. Advancing
beyond more limited analytical approaches, our LLPS theory is applicable to a
wide variety of charged sequences ranging from highly charged polyelectrolytes
to neutral or nearly neutral polyampholytes. The new theory should be useful in
high-throughput screening of protein and other sequences for their LLPS
propensities and can serve as a basis for more comprehensive theories that
incorporate non-electrostatic interactions. Experimental ramifications of our
theory are discussed.
