Beyond Pairwise: Higher-order physical interactions affect phase separation in multi-component liquids

Phase separation, crucial for spatially segregating biomolecules in cells, is well-understood in the simple case of a few components with pairwise interactions. Yet, biological cells challenge the simple picture in at least two ways: First, biomolecules, like proteins and nucleic acids, exhibit complex, higher-order interactions, where a single molecule may interact with multiple others simultaneously. Second, cells comprise a myriad of different components that form various droplets. Such multicomponent phase separation has been studied in the simple case of pairwise interactions, but an analysis of higher-order interactions is lacking. We propose such a theory and study the corresponding phase diagrams numerically. We find that interactions between three components are similar to pairwise interactions, whereas composition-dependent higher-order interactions between two components can oppose phase separation. This surprising result can only be revealed from the equilibrium phase diagrams, implying that the often-used stability analysis of homogeneous states is inadequate to study these systems. We thus show that higher-order interactions could play a crucial role in forming droplets in cells, and their manipulation could offer novel approaches to controlling multicomponent phase separation.
Comment: 12 pages, 8 figures, and Appendix