Abstract
Condensate formation of biopolymer solutions, prominently those of various intrinsically disordered proteins (IDPs), is often driven by “sticky” interactions between associating residues, multivalently present along the polymer backbone. Using a ternary mean-field “stickers-and-spacers” model, we demonstrate that if sticker association is of the order of a few times the thermal energy, a delicate balance between specific binding and nonspecific polymer–solvent interactions gives rise to a particularly rich ternary phase behavior under physiological circumstances. For a generic system represented by a solution comprising multiassociative scaffold and client polymers, the difference in solvent compatibility between the polymers modulates the nature of isothermal liquid–liquid phase separation (LLPS) between associative and segregative. The calculations reveal regimes of dualistic phase behavior, where both types of LLPS occur within the same phase diagram, either associated with the presence of multiple miscibility gaps or a flip in the slope of the tie-lines belonging to a single coexistence region.
Highlights
A recent paradigm shift has shown important eukaryotic cellular functions to be regulated by concentrated liquid-like biomolecular condensates that form in coexistence with the surrounding cytoplasm or nucleoplasm.[1−4] These “membraneless organelles” (MLOs), of which nucleoli, stress granules, Pbodies, and Cajal bodies are examples, exist as suspended, dense droplets, typically containing multiple species of biomacromolecules, such as proteins and RNA
As in the original single polymer model by Semenov and Rubinstein,[29] sticker association is “specific” in that it occurs between designated sites on the polymer chains, but not “orientational” in the sense that structural rigidity limits the directional freedom of the noncovalent bonds, as, for instance, seen for patchy globular species[49] and folded amino acid sequences.[50]
To predict how the interplay between sticker association, nonspecific interaction, and chain length determines the phase diagram, we extend the classical Flory−Huggins (FH) mixing free energy for a ternary mixture of polymer-A, polymer-B, and solvent, as we used in previous studies,[51,52] by a contribution from the presence and association of/between stickers (ST)
Summary
A recent paradigm shift has shown important eukaryotic cellular functions to be regulated by concentrated liquid-like biomolecular condensates that form in coexistence with the surrounding cytoplasm or nucleoplasm.[1−4] These “membraneless organelles” (MLOs), of which nucleoli, stress granules, Pbodies, and Cajal bodies are examples, exist as suspended, dense droplets, typically containing multiple species of biomacromolecules, such as proteins and RNA. IDPs or IDRs may demix from their environment through a noncovalent association between specific amino acid sequences that occur along the backbone in a multivalent manner.[10] The nature of such “sticky interactions” may, for instance, be hydrogen-bonding,[11] electrostatic,[12] π−π stacking,[13] and π−cation interactions[14,15] and due to the hydrophobic effect[16−18] or a combination of binding motifs.[11,19] MLOs may comprise complex multicomponent mixtures, the phase behavior often seems determined by a few or even a single species acting as a “scaffold” to which secondary components associate as “clients” or ligands,[20] which, depending on the interaction strength, modulate the driving force for condensate formation.[21,22] in vitro approaches targeting the phase behavior of reduced, experimentally accessible solutions of native,[9,11,23] mutant,[24] or engineered[25−27] associating biomacromolecules are effective experimental tools in the elucidation of complex cellular mechanisms
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