Developments in describing equilibrium phase transitions of multivalent associative macromolecules

Abstract

Biomolecular condensates are distinct cellular bodies that form and dissolve reversibly to organize cellular matter and biochemical reactions in space and time. Condensates are thought to form and dissolve under the influence of spontaneous and driven phase transitions of multivalent associative macromolecules. These include phase separation, which is defined by segregation of macromolecules from the solvent or from one another, and percolation or gelation, which is an inclusive networking transition driven by reversible associations among multivalent macromolecules. Considerable progress has been made to model sequence-specific phase transitions, especially for intrinsically disordered proteins. Here, we summarize the state-of-the-art of theories and computations aimed at understanding and modeling sequence-specific, thermodynamically controlled, coupled associative and segregative phase transitions of archetypal multivalent macromolecules.

Figure 1.. Condensation of multivalent associative macromolecules showing segregative phase separation, associative percolation, and the coupling between the two processes.

Schematics are shown for flexible polymers, but they apply to rigid multivalent macromolecules as well [12]. (A) In a binary mixture comprising a polymer (orange) in a solvent (gray background), can undergo phase separation, which is a segregative transition. This leads to the formation of two distinct coexisting phases delineated by a phase boundary. Chemical potentials of the polymer and solvent as well as the osmotic pressure are equalized across the phase boundary. (B) Multivalent associative macromolecules (MAMs in the main text) feature functional groups or cohesive motifs (shown in yellow). These cohesive motifs are known as stickers, and they form reversible (non-covalent) physical crosslinks. Above a system-specific percolation threshold, which is defined by the valence, interaction strengths, and bond volumes of stickers, the system of MAMs undergoes percolation, which is a continuous associative, networking transition. Note that percolation is an inclusive transition that does not create solvent-rich and MAM-rich coexisting phases. Instead, the solvent is incorporated into the system-spanning network. (C) In a solution of MAMs that feature stickers (yellow) and spacers (orange), phase separation will be coupled to percolation. This gives to a dense, MAM-rich phase, known as a condensate, that is defined by a percolated network of MAMs.

Figure 2.. Oppositely charged MAMs, which can be flexible polyelectrolytes or colloidal macroions, undergo complex coacervation.

The association of oppositely charged MAMs initiates phase separation, which is the driven, in part by the release of counterions from the oppositely charged macromolecules.

Figure 3.. Single-chain coil-to-globule transition of flexible MAMs such as intrinsically disordered proteins (IDPs) is connected to their phase behavior.

(A) For IDPs with an upper critical solution temperature (UCST), a single chain adopts compact conformations below a system-specific transition temperature 𝑇_𝜃 and expanded conformations above 𝑇_𝜃. Below 𝑇_𝜃, phase separation via intermolecular interactions is driven by the same set of interactions that drive chain compaction in the single chain limit. (B) For IDPs with a lower critical solution temperature (LCST), a single chain adopts compact conformations above a system-specific transition temperature 𝑇_𝜃 and expanded conformations below 𝑇_𝜃. Above 𝑇_𝜃, phase separation via intermolecular interactions is driven by the same set of interactions that drive chain compaction in the single chain limit. In panels (A) and (B), the temperatures T_c,UCST and T_c,LCST are the critical temperatures for UCST- and LCST-type of phase separation, respectively. Notice that T_θ > T_c,UCST for the system showing UCST-type phase separation, and T_θ < T_c,LCST for the system showing LCST-type of phase separation. This reflects the continuous nature coil-to-globule transitions, with T_θ being a tricritical point. The theta temperatures approach the critical temperatures for infinitely long polymers.