A conceptual framework for understanding phase separation and addressing open questions and challenges

Abstract

Macromolecular phase separation is being recognized for its potential importance and relevance as a driver of spatial organization within cells. Here, we describe a framework based on synergies between networking (percolation or gelation) and density (phase separation) transitions. Accordingly, the phase transitions in question are referred to as phase separation coupled to percolation (PSCP). The condensates that result from PSCP are viscoelastic network fluids. Such systems have sequence-, composition-, and topology-specific internal network structures that give rise to time-dependent interplays between viscous and elastic properties. Unlike pure phase separation, the process of PSCP gives rise to sequence-, chemistry-, and structure-specific distributions of clusters that can form at concentrations that lie well below the threshold concentration for phase separation. PSCP, influenced by specific versus solubility-determining interactions, also provides a bridge between different observations and helps answer questions and address challenges that have arisen regarding the role of macromolecular phase separation in biology.

Keywords: associative polymers; biomolecular condensate; biophysics; cell biology; cluster; membraneless organelle; network fluid; percolation; phase separation; saturation concentration; viscoelasticity.

Figure 1:. Phase separation is a density transition.

(Left) In an aqueous two-phase system (ATPS), the interactions of A and B are incompatible with one another, but both macromolecules make favorable interactions with the solvent S. The mixture separates into two coexisting phases, one that is rich in A, the other rich in B. The density of B (ρ_B) in the A-rich phase is low and the density of A (ρ_A) in the B-rich phase is low. In this case, the solvent density is the same across the two phases, but in general it is governed by the ratio of A:B, the volumes taken up by the A- and B-rich phases, and the extent to which it prefers to interact with A vs. B. (Right) For a binary mixture comprising a macromolecule and solvent, the radial density profile from the center of a condensate shows a sharp, χ-dependent decrease in macromolecular density as the phase boundary is crossed.

Figure 2:. Coupling and decoupling of phase separation and percolation in multivalent proteins.

Here, we consider a system in which two proteins interact via repeats of interaction domains and motifs, e.g., via repeats of SH3 domains in protein A and repeats of proline-rich motifs (PRMs) in protein B (top); hot spots on SH3 domains and PRMs are the stickers. The multivalent interactions mediate percolation above the percolation threshold, c_perc. The solubility of individual protein molecules and complexes, which are strongly influenced by the linker compositions, determine whether percolation is coupled to phase separation (c_sat < c_perc, on the left) or proceeds without phase separation (if c_perc < c_sat, on the right). Clusters coexist in the dilute phase. The figure was adapted from the work of Harmon et al. (Harmon et al., 2017).

Figure 3:. Consequences of condensates being viscoelastic network fluids.

The properties of the multivalent macromolecules that form condensates through PSCP determine network structure and dynamics, the material properties, the properties of interfaces, and the size distributions of pre-percolation clusters.

Figure 4:. Dilute phase concentrations of macromolecules are determined by whether phase separation is driven by homotypic vs. heterotypic interactions.

(A) Shape of the phase boundary that results from a binary system of a macromolecule P and solvent. For a given total concentration P, the system separates into a dilute phase and a dense phase, and their densities are temperature dependent. The tie lines are horizontal because the temperatures are equal across the phase boundary. (B) For increasing total concentration P, the soluble concentration increases up to the saturation concentration (indicated by the red broken line). Additional increase of the total protein concentration beyond the saturation concentration is incorporated into the growing dense phase volume fraction, and the dilute phase remains at c_sat. (C) Shape of the phase boundary that results from a system where phase separation is driven purely by heterotypic interactions between macromolecules A and B. The black envelope is the phase boundary. The black lines are tie lines of constant chemical potentials and they connect points corresponding to the joint concentrations of A and B in the coexisting dilute and dense phases. One can perform a thought experiment to ask how the concentration in the sol or dilute phase designated as [A]_sol varies with the total concentration of [A] as the total concentration of B is held fixed. This would be a typical experiment to perform to test for the validity of phase separation by asking if [A]_sol shows plateauing behavior above some value of [A]. (D) The dashed line is the 1:1 line between [A]_sol and [A]. Within the two-phase regime, [A]_sol (blue line) deviates from the 1:1 line, and it does not show the plateauing behavior expected of phase separation driven exclusively by homotypic interactions. Notice that even though the bulk concentration of B is held fixed, the concentrations of B in the dilute vs. dense phase are set by the tie line, and not by the expression level of B. Therefore, along a tie line, the saturation of the dilute phase is set jointly by the concentrations of the A and B macromolecules, and the joint concentrations in the coexisting dilute phase change depending on the slopes of the tie lines.