Liquid-liquid phase separation is a key organizational principle in eukaryotic cells, on par with intracellular membranes. It allows cells to concentrate specific proteins into condensates, increasing reaction rates and achieving switch-like regulation. However, it is unclear how cells trigger condensate formation or dissolution and regulate their sizes. We predict from first principles two mechanisms of active regulation by post-translational modifications such as phosphorylation: In enrichment-inhibition, the regulating modifying enzyme enriches in condensates and the modifications of proteins inhibit their interactions. Stress granules, Cajal bodies, P granules, splicing speckles, and synapsin condensates obey this model. In localization-induction, condensates form around an immobilized modifying enzyme, whose modifications strengthen protein interactions. Spatially targeted condensates formed during transmembrane signaling, microtubule assembly, and actin polymerization conform to this model. The two models make testable predictions that can guide studies into the many emerging roles of biomolecular condensates.Eukaryotic cells contain numerous types of membraneless organelles, which contain between a few and thousands of protein and RNA species that are highly enriched in comparison to the surrounding nucleoplasm or cytoplasm. These biomolecular condensates are held together by weak, multivalent and highly collaborative interactions, often between intrinsically disordered regions of their constituent proteins (Banani et al., 2017;Shin and Brangwynne, 2017).In contrast to membrane-bound organelles, cells can regulate the formation and size of condensates by posttranslational modifications of one or a few key proteins, most prominently by phosphorylation. The modifications usually lie within intrinsically disordered regions and modulate the strength of attractive interactions with other condensate components (Bah and Forman-Kay, 2016; Fung et al., 2018). Due to the highly cooperative nature of phase transitions, small changes in interaction strengths can result in the formation or dissolution of condensates, and this switch-like, dynamic nature makes them ideal for regulation.For instance the nucleolus, Cajal bodies, splicing speckles, paraspeckles, and PML bodies in the nucleus and P-bodies in the cytoplasm have to be dissolved during mitosis and reformed afterwards to ensure a balanced distribution of their content to daughter cells (Rai et al., 2018;Dundr and Misteli, 2010). Stress granules form upon cellular stress and are dissolved when the stress ceases (Wippich et al., 2013).Whereas these long-known, floating droplet or-ganelles are large enough to be visible using simpler 31 light microscopic techniques, in the past years liquid-32 liquid phase separation has been implicated in mul-33 tifarious processes in which -often sub-micrometer-34 sized -condensates are formed at particular sites in the 35 cell: at sites of DNA repair foci (Altmeyer et al., 2015), 36 Polycomb-mediated chromatin silencing (Tatavo...

Biomolecular condensates are small droplets forming spontaneously in biological cells through phase separation. They play a role in many cellular processes, but it is unclear how cells control them. Cellular regulation often relies on post-translational modifications of proteins. For biomolecular condensates, such chemical modifications could alter the molecular interaction of key condensate components. Here, we test this idea using a theoretical model based on non-equilibrium thermodynamics. In particular, we describe the chemical reactions using transition-state theory, which accounts for the non-ideality of phase separation. We identify that fast control, as in cell signalling, is only possible when external energy input drives the reaction out of equilibrium. If this reaction differs inside and outside the droplet, it is even possible to control droplet sizes. Such an imbalance in the reaction could be created by enzymes localizing to the droplet. Since this situation is typical inside cells, we speculate that our proposed mechanism is used to stabilize multiple droplets with independently controlled size and count. Our model provides a novel and thermodynamically consistent framework for describing droplets subject to non-equilibrium chemical reactions.

Liquid-liquid phase separation is a key organizational principle in eukaryotic cells, on par with intracellular membranes. It allows cells to concentrate specific proteins into condensates, increasing reaction rates and achieving switch-like regulation. However, it is unclear how cells trigger condensate formation or dissolution and regulate their sizes. We predict from first principles two mechanisms of active regulation by post-translational modifications such as phosphorylation: In enrichment-inhibition, the regulating modifying enzyme enriches in condensates and the modifications of proteins inhibit their interactions. Stress granules, Cajal bodies, P granules, splicing speckles, and synapsin condensates obey this model. In localization-induction, condensates form around an immobilized modifying enzyme, whose modifications strengthen protein interactions. Spatially targeted condensates formed during transmembrane signaling, microtubule assembly, and actin polymerization conform to this model. The two models make testable predictions that can guide studies into the many emerging roles of biomolecular condensates. Eukaryotic cells contain numerous types of mem-1 braneless organelles, which contain between a few 2 and thousands of protein and RNA species that are 3 highly enriched in comparison to the surrounding nu-4 cleoplasm or cytoplasm. These biomolecular conden-5 sates are held together by weak, multivalent and highly 6 collaborative interactions, often between intrinsically 7 54 active promoters. Here, we propose two active mecha-55 nisms used by cells for these purposes.56 Phase separation and condensate size behaviour 57 To keep the model simple, we consider only one type of 58 condensate protein. In the dilute regime below the sat-59 1 Cellular control of liquid droplet formation, size, and localization • July 5, 2019 Figure 1: Phase separation and condensate droplet size behaviour. A When protein-protein and solvent-solventinteractions are more favorable than protein-solvent interactions, demixing into two phases can occur, a dilute phase with low protein concentration c out and a dense phase with high concentration c in . This happens when the sum of free energies of the two phases is lower (tip of blue arrow) than the energy of the single phase (base of blue arrow) . B c out is the limiting concentration for infinite condensate droplet radius R. The concentration on the outside of a condensate of radius R is larger the smaller the condensate is (green double-headed arrows), as it cannot hold on to its proteins as well as large ones. This leads to a concentration gradient (∇concentration), which fuels a diffusive flux from small to large condensates (wiggly arrows). (l c is a measure of interaction strength between proteins in comparison to the solvent.) C As a result, condensates below a radius R crit will shrink and larger ones will grow. uration protein concentration c out , condensate droplets 60 cannot form ( Figure 1A). Above c out , in the phase sepa-61 ration regime, condensates can be stable...

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