Author summaryLiquid-liquid phase separation describes the de-mixing of a fluid into 'compartments' with different compositions, such as the separation of oil and water. Liquid-liquid phase separation occurs within biological cells, allowing different chemical reactions to occur within different compartments. One such reaction is self-assembly, in which proteins and other biomolecules organize into larger, more complex structures, such as a virus particle. It has recently been shown that many viruses self-assemble in liquid-liquid phase-separated compartments within their host cells. However, the effects of liquid-liquid phase separation on self-assembly, and how it may facilitate the formation of virus particles or other biological complexes, are not understood. We develop theoretical models, which show that liquid-liquid phase separation can make self-assembly occur significantly faster, and make it more likely to result in properly assembled particles. The models also reveal the mechanisms underlying these effects, showing that by locally concentrating subunits, phase separation can accelerate assembly while simultaneously preventing the system from running out of subunits before assembly completes. These findings could enable new strategies to prevent or treat viral infections. More broadly, these insights can be applied to understand other self-assembly reactions in biological cells. Liquid condensate droplets with distinct compositions of proteins and nucleic acids are widespread in biological cells. While it is known that such droplets, or compartments, can regulate irreversible protein aggregation, their effect on reversible self-assembly remains largely unexplored. In this article, we use kinetic theory and solution thermodynamics to investigate the effect of liquid-liquid phase separation on the reversible self-assembly of structures with well-defined sizes and architectures. We find that, when assembling subunits preferentially partition into liquid compartments, robustness against kinetic traps and maximum achievable assembly rates can be significantly increased. In particular, both the range of solution conditions leading to productive assembly and the corresponding assembly rates can increase by orders of magnitude. We analyze the rate equation predictions using simple scaling estimates to identify effects of liquid-liquid phase separation as a function of relevant control parameters. These results may elucidate self-assembly processes that underlie normal cellular functions or pathogenesis, and suggest strategies for designing efficient bottom-up assembly for nanomaterials applications.
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