Phase Transitions of Associative Biomacromolecules

Abstract

Multivalent proteins and nucleic acids, collectively referred to as multivalent associative biomacromolecules, provide the driving forces for the formation and compositional regulation of biomolecular condensates. Here, we review the key concepts of phase transitions of aqueous solutions of associative biomacromolecules, specifically proteins that include folded domains and intrinsically disordered regions. The phase transitions of these systems come under the rubric of coupled associative and segregative transitions. The concepts underlying these processes are presented, and their relevance to biomolecular condensates is discussed.

Figure 1:. Hard sphere fluids can undergo density transitions viz., phase separation.

(A) System of hard spheres. The arrows indicate that the collisions among the molecules are purely elastic. (B) Potential for a pair of hard spheres. (C) A segregative density transition gives rise to two coexisting phases of different densities separated by an interface, as depicted here.

Figure 2:

Systems of hard aspherical molecules including rods, ellipsoids, and discoids can also undergo segregative transitions.

Figure 3:

Entropically-driven phase separation helps explain bacterial chromosomal segregation.

Figure 4:. Example of movement-induced (motility-induced) phase separation .

The figure shows active Brownian particles that are self-propelled in an external field. Propulsion creates flows and local inhomogeneities that can drive segregative transitions.

Figure 5:. Scenarios for phase separation.

(A) The coexistence of two phases, one that is polymer-rich and another that is solvent-rich. (B) A scenario that is reminiscent of the ternary PEG, dextran, water system whereby two phases, rich in different types of polymers, coexist with one another. (C) The formation of distinct phases, each enriched in a specific type of polymer.

Figure 6:. Coexistence curves for different types of thermoresponsive phase transitions.

The systems depicted in (A) and (B) have an upper critical solution temperature (UCST) and a lower critical solution temperature (LCST), respectively. (C) shows a system with both a UCST and an LCST, where the two-phase regime exists between these critical temperatures, resulting in a closed loop. (D) shows a system with both a UCST and an LCST, with a two-phase regime above the UCST and below the LCST, resulting in an hourglass shape.

Figure 7:. Patchy particles and the structures they form through site-specific interactions.

(A) Particle with a single patch. (B) Dimer formed by the interaction of particles, each with a single patch. (C) Particles with two, three, and four patches. (D) System spanning network formed by particles with three and four patches.

Figure 8:. Clusters versus percolation.

(A) A dimer forms that cannot grow into a network. (B) and (C) Trimers of different topologies featuring unsatisfied stickers that poise the system to grow and become a percolated network.

Figure 9:. Mapping of proteins onto different physical instantiations of associative macromolecules.

(A) shows how intrinsically foldable domains (IFDs) may be mapped onto patchy colloids. (B) shows how intrinsically disordered regions (IDRs) may be mapped onto flexible, linear associative polymers. (C) shows how full-length proteins with IFDs and IDRs may be mapped onto specific combinations of patchy colloids and linear polymers. In all cases, black regions indicate spacers, and red and green regions indicate different types of stickers. Blue regions in (C) indicate oligomerization domains that behave as strong stickers.

Figure 10:

Schematic of an exponentially bounded (black dashed curve) versus heavy-tailed (red solid curve) version of p(n_cluster|c_bulk).

Figure 11:. Schematics summarizing the physical principles of complex coacervation.

(A) Two polyelectrolytes, a polycation (left) and polyanion (right) can form a complex driven by a combination of complementary electrostatic interactions and the release of counterions. (B) and (C) show the formation of coexisting dilute and dense phase (coacervate) from the vantage point of the salt (B) and the polyelectrolytes (C). (D) The charge states of ionizable residues will be sensitive to pH and this can affect the complexation and coacervation of polyelectrolytes and polyampholytes (schematic shows the latter).

Figure 12:. Coexistence curve or phase boundary in the (c_am, c_an)-plane.

The phase boundary is in blue, the two-phase region is in pale blue, and the coexisting phases are joined by dashed red lines, which are tie lines. Tie lines may have positive slopes, implying an accumulation of the analyte in the dense phase, negative slopes, implying a depletion of the analyte from the dense phase, or horizontal slopes, implying equal preference of the analyte for the dense and dilute phases. Note that the slopes of tie lines can change sign as the critical point is approached, which is what we depict in this schematic.

Figure 13:. Coexistence curve (blue) and percolation line (dashed and solid green) for a solution of associative polymers undergoing UCST-style phase separation coupled to percolation.

The red lines are tie lines (see section 6.1) that connect coexisting dilute and dense phases. There are two critical temperatures, T_cs for the segregative transition and T_cp for the percolation transition. For temperatures below T_cs and above T_cp there is the formal possibility of phase separation without percolation. Whether this regime is accessible or not will depend on the gap between the two critical temperatures T_cs and T_cp.

Figure 14:. Pressure-temperature phase diagram of a substance that can be in a liquid, solid, or vapor phase.

The red circle indicates the triple point where all three phases coexist. The green circle indicates the critical point where the vapor-liquid coexistence curve terminates. Beyond this critical point, the system forms a single fluid phase.

Figure 15:. Shapes of phase boundaries for systems with A and B macromolecules.

The solution conditions are fixed. The top left panel shows the case of a system where the phase behavior is driven purely by heterotypic interactions. The top middle panel shows the case where homotypic interactions among A molecules are equivalent to or outcompeting the heterotypic interactions. The bottom left panel shows the converse scenario. The bottom middle and bottom right panels show phase boundaries for the mixture where the drivers of phase transitions are purely A-A or B-B homotypic interactions. In all cases, the yellow circles designate coexisting dilute phases, and the blue circles are coexisting dense phases. Intercepts drawn from the yellow and blue circles to the abscissa and ordinate will quantify the concentrations of the coexisting dilute and dense phases, respectively. In each panel, the red lines are the tie lines.

Figure 16:. Ellipsoidal phase boundary for a system with three associative macromolecules in a solvent.

If three phases can coexist, as would be the case for the nucleolus or nuclear speckle , then the tie simplex is a 2-simplex, which is a triangle. The concentrations of the macromolecules in the three coexisting phases will be determined by the direction cosines that define each side of the triangle.

Figure 17:. Adsorption and wetting of a polymer onto a solid surface.

The solvent is shown in blue and the solid surface is shown in gray. The red chains indicate a polymeric species able to undergo phase separation at the proper conditions. The yellow dashed curves outline the adsorbing or wetting polymers. In (A), the polymer is in the one-phase regime and adsorbs onto the substrate. In (B) and (C), the polymer has undergone phase separation and the nascent dense phase partially wets the surface. The contact angle, θ_Y, may be above 90°, indicating poor wetting (B), or below 90°, indicating good wetting (C). In (D), the polymer-rich dense phase completely wets the surface.