Abstract
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.
Highlights
Biomolecular condensates are small droplets that structure the cell interior of eukaryotes [1,2] and prokaryotes [3,4,5]
We introduced a model that explains how chemical reactions can control liquid-like droplets
We identified three ingredients necessary for effective size control: (i) the chemical modification of the droplet material must convert it to a soluble form, (ii) this modification must involve a driven reaction using a chemical fuel, and (iii) the reaction dynamics must differ inside and outside the droplet, e.g. by localizing enzymes appropriately
Summary
Biomolecular condensates are small droplets that structure the cell interior of eukaryotes [1,2] and prokaryotes [3,4,5]. Transcriptional condensates actively regulate gene expression [18] In all these examples, the cell controls the size, position or count of the biomolecular condensates [2,19]. Theoretical studies of active droplets, which combine phase separation and chemical reactions, suggest that chemical reactions can suppress Ostwald ripening, leading to coexisting droplets of similar size [30,31] and even droplet division [32] These studies described chemical reactions using fixed rate laws, which do not include the molecular interactions necessary for phase separation. We present a minimal model of active droplets that combines non-equilibrium thermodynamics [36,37] and transition state theory [38,39] to describe the chemical reactions It focuses on chemical potentials as key quantities and describes the non-equilibrium driving explicitly. We build up the complete model by starting from passive liquid–liquid phase separation and successively adding the reaction, the driving and enzymatic control
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