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It has been proposed that during the early steps in the origin of life, small droplets could have formed via the segregation of molecules from complex mixtures by phase separation. These droplets could have provided chemical reaction centres. However, whether these droplets could divide and propagate is unclear. Here we examine the behaviour of droplets in systems that are maintained away from thermodynamic equilibrium by an external supply of energy. In these systems, droplets grow by the addition of droplet material generated by chemical reactions. Surprisingly, we find that chemically driven droplet growth can lead to shape instabilities that trigger the division of droplets into two smaller daughters. Therefore, chemically active droplets can exhibit cycles of growth and division that resemble the proliferation of living cells. Dividing active droplets could serve as a model for prebiotic protocells, where chemical reactions in the droplet play the role of a prebiotic metabolism. Droplets are an appealing picture for protocells in origin-of-life studies, but it’s unclear how they would have propagated by growth and division. Theory suggests that chemically active droplets spontaneously split into equal daughter droplets.

Liquid-liquid phase separation yields spherical droplets that eventually coarsen to one large, stable droplet governed by the principle of minimal free energy. In chemically fueled phase separation, the formation of phase-separating molecules is coupled to a fuel-driven, non-equilibrium reaction cycle. It thus yields dissipative structures sustained by a continuous fuel conversion. Such dissipative structures are ubiquitous in biology but are poorly understood as they are governed by non-equilibrium thermodynamics. Here, we bridge the gap between passive, close-to-equilibrium, and active, dissipative structures with chemically fueled phase separation. We observe that spherical, active droplets can undergo a morphological transition into a liquid, spherical shell. We demonstrate that the mechanism is related to gradients of short-lived droplet material. We characterize how far out of equilibrium the spherical shell state is and the chemical power necessary to sustain it. Our work suggests alternative avenues for assembling complex stable morphologies, which might already be exploited to form membraneless organelles by cells. Dissipative structures are governed by non-equilibrium thermodynamics. Here, the authors describe a size-dependent transition from active droplets to active spherical shells—a dissipative structure that arises from reaction diffusion gradients.

In living cells, protein-rich condensates can wet the cell membrane and surfaces of membrane-bound organelles. Interestingly, many phase-separating proteins also bind to membranes leading to a molecular layer of bound molecules. Here we investigate how binding to membranes affects wetting, prewetting and surface phase transitions. We derive a thermodynamic theory for a three-dimensional bulk in the presence of a two-dimensional, flat membrane. At phase coexistence, we find that membrane binding facilitates complete wetting and thus lowers the wetting angle. Moreover, below the saturation concentration, binding facilitates the formation of a thick layer at the membrane and thereby shifts the prewetting phase transition far below the saturation concentration. The distinction between bound and unbound molecules near the surface leads to a large variety of surface states and complex surface phase diagrams with a rich topology of phase transitions. Our work suggests that surface phase transitions combined with molecular binding represent a versatile mechanism to control the formation of protein-rich domains at intra-cellular surfaces.

Oscillations in the formation and dissolution of molecular assemblies inside living cells are pivotal in orchestrating various cellular functions and processes. However, designing such rhythmic patterns in synthetic cells remains a challenge. Here, we demonstrate the spontaneous emergence of spatio-temporal oscillations in the number of droplets, size, and their spatial distribution within a synthetic cell. The coacervate-based droplets in these synthetic cells sediment and fuse at the cell’s bottom. Through a size control mechanism, the sedimented, large droplets shrink by expelling droplet material. The expelled molecules nucleate new droplets at the top of the synthetic cell, which grow and sediment again. These oscillations are sustained by converting chemical fuel into waste and can continue for hundreds of periods without evidence of fatigue. Strikingly, the period of the oscillation is in the minute’s regime and tunable. The design of oscillating artificial organelles in synthetic cells brings us closer to creating more life-like materials and de novo life. Oscillations in the formation and dissolution of molecular assemblies inside living cells are essential for various cellular functions and processes, but difficult to design in synthetic cells. Here, the authors show spontaneous emergence of spatio-temporal oscillations in the number of droplets, size, and their spatial distribution within a synthetic cell.

Biomolecules, such as proteins and nucleic acids, can phase separate in the cytoplasm of cells to form biomolecular condensates. Such condensates are often liquid-like droplets that can wet biological surfaces such as membranes. Many molecules that participate in phase separation can also reversibly bind to membrane surfaces. When a droplet wets a surface, molecules can diffuse inside and outside of the droplet or in the bound state on the surface. How the interplay between surface binding, diffusion in surface and bulk affects the wetting kinetics is not well understood. Here, we derive the governing equations using non-equilibrium thermodynamics by relating the thermodynamic fluxes and forces at the surface coupled to the bulk. We study the spreading dynamics in the presence of surface binding and find that binding speeds up wetting by nucleating a droplet inside the surface. Our results suggest that the wetting dynamics of droplets can be regulated by two-dimensional surface droplets in the surface-bound layer through changing the binding affinity to the surfaces. These findings are relevant both to engineering life-like systems with condensates and vesicles, and biomolecular condensates in living cells.

A simple system for studying self-organization in biology comprises driven actin filaments, thought to interact primarily via binary collisions. Angle-resolved statistics suggest that the transition to polar order is driven by multi-filament events. From the self-organization of the cytoskeleton to the synchronous motion of bird flocks, living matter has the extraordinary ability to behave in a concerted manner 1 , 2 , 3 , 4 . The Boltzmann equation for self-propelled particles is frequently used in silico to link a system’s meso- or macroscopic behaviour to the microscopic dynamics of its constituents 5 , 6 , 7 , 8 , 9 , 10 . But so far such studies have relied on an assumption of simplified binary collisions owing to a lack of experimental data suggesting otherwise. We report here experimentally determined binary-collision statistics by studying a recently introduced molecular system, the high-density actomyosin motility assay 11 , 12 , 13 . We demonstrate that the alignment induced by binary collisions is too weak to account for the observed ordering transition. The transition density for polar pattern formation decreases quadratically with filament length, indicating that multi-filament collisions drive the observed ordering phenomenon and that a gas-like picture cannot explain the transition of the system to polar order. Our findings demonstrate that the unique properties of biological active-matter systems require a description that goes well beyond that developed in the framework of kinetic theories.

In this paper we discuss current challenges to the sustainability concept. This article focuses on seven dimensions of the concept. These dimensions are crucial for understanding sustainability. Even today, the literature contains basic misunderstandings about these seven dimensions. This article sketches such fallacies in the context of global and planetary sustainability. The sustainability concept has been criticized as a content-empty ‘fuzzy notion’ or non-committal ‘all-purpose glue’. This article thus has a critical intention of reflecting the sustainability concept accurately. The aim is to contribute a better understanding of the concept. This paper focuses on questions related to the normative content of sustainability. Even today, the literature contains basic misunderstandings about this content. So, this article sketches seven such fallacies in the context of global and planetary sustainability. They are partly to blame for the recent discourse about the environment and development ending up in a cul-de-sac, discrediting the term sustainability. This article thus has a critical intention of reflecting the sustainability concept accurately by discussing current challenges. The aim is to contribute a better understanding of the normative aspects of sustainability. By presenting a differentiated analysis of its content the article will provide a reflected version of the sustainability concept, characterized by the following dimensions: (1) ecological: reflection on the conditions and consequences of human activities; (2) political: sustainability as a cross-sectional political guideline; (3) ethical: intergenerational and global responsibility; (4) socio-economic: operationalizing the principle of sustainability; (5) democratic: pluralism, participation and democratic innovation; (6) cultural: lifestyle and a new model of wealth; (7) theological: belief in creation and sustainability. We do not want to offer limited definitions, but rather to stimulate a debate about rehabilitating the sustainability concept. Therefore, these dimensions are crucial for understanding sustainability.

The last decades have shown a tendency towards higher central bank transparency. This leads to the question of how central bank transparency is entangled with price stability and inflation volatility. A plethora of studies analysed the relationship from a theoretical point of view and came to contradictory results. Thus, the article aims to analyse this question empirically and to better understand the mechanism behind it. Firstly, the results show that transparency reduces inflation expectations and inflation even if we control for other determinants. However, transparency alone is not sufficient to produce stable prices. Secondly, the paper proves that the effect on inflation mainly comes from reduced inflation expectations. Thirdly, we show that central bank transparency seems to diminish inflation uncertainty. This confirms the economic importance of central bank transparency.

Most central banks have increased their transparency in the recent past. The question is whether higher transparency comes at some cost. Firstly, the article shows in a theoretical model that transparency does not necessarily lead to higher unemployment. Secondly, the paper analyses the main theoretical results of other authors that transparency leads to higher wages and unemployment (volatility). The empirical results show no evidence for these conjectures. In fact, the analyses show that transparency can reduce the detrimental effect that central bank independence has on employment. Furthermore, the estimations confirm that transparency does not lead to higher unemployment volatility.

Living cells use phase separation and concentration gradients to organize chemical compartments in space. Here, we present a theoretical study of droplet dynamics in gradient systems. We derive the corresponding growth law of droplets and find that droplets exhibit a drift velocity and position dependent growth. As a consequence, the dissolution boundary moves through the system, thereby segregating droplets to one end. We show that for steep enough gradients, the ripening leads to a transient arrest of droplet growth that is induced by a narrowing of the droplet size distribution.