Control of condensate shape and composition via chemical reaction networks

Interactions among the multitude of macromolecules populating the cytoplasm can lead to the emergence of coexisting phases formed via phase separation. This phenomenon plays a crucial role in the spatial organization of cells and the regulation of their functions. Many of the molecules that drive phase separation can undergo transitions among different states. Proteins, for example, can go through conformational transitions and switch among different phosphorylation states. In addition, proteins that are relevant for phase separation can assemble into oligomers of different sizes. Both molecular transitions and oligomerization can be described as chemical reactions in the context of theories that account for phase separation in multicomponent mixtures. In this work, we discuss how chemical reactions can be used to control coexisting phase composition and shape. In particular, focusing on molecular transitions among two states of a protein, we find a discontinuous thermodynamic phase transition in the composition of the protein-dense phase, as a function of temperature. Breaking detailed balance of the molecular transition by continuous fuel addition can also be used to control the number of distinct coexisting phases and their composition. Additionally, fuel turnover can lead to the emergence of novel patterns as the system approaches a non-equilibrium stationary state. We focus on the mechanism that leads to the formation of ring-like patterns, motivated by the observation of similar shapes in experiments with chemical reaction cycles coupled to a fuel reservoir. We propose that, due to chemical reactions, the composition at the centre of the dense phase can be altered, leading to an instability that drives the formation of a new interface. Controlling the composition of coexisting phases becomes crucial when the number of components and the number of reactions among them rises. This is the case in mixtures containing proteins that can be found in a monomeric state but also form aggregates of arbitrary size. We characterise the equilibrium of such systems in the limit of maximum aggregate size going to infinity. For systems that phase separate, we show that the aggregate size distribution can be different in each of the coexisting phases and is determined by the temperature and the energy of bonds between monomers. Mixtures composed of disk-like or spherical aggregates can undergo a gelation transition. Gelation can be considered as a special case of phase coexistence between a dilute phase (the 'sol') containing aggregates of finite size, and a 'gel' phase, corresponding to an aggregate of infinite size. Lowering the temperature leads to a transition from two coexisting ''sol' phases to the coexistence of a 'sol' phase and a ''gel'' phase. In summary, this work provides a theoretical framework to study phase-separating systems composed of many components that undergo chemical reactions. Furthermore, we discuss how to exploit such reactions to control the composition of coexisting phases

Thermodynamics of wetting, prewetting and surface phase transitions with surface binding

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

Liquid spherical shells are a non-equilibrium steady state of active 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

Selection of prebiotic oligonucleotides by cyclic phase separation

The emergence of functional oligonucleotides on early Earth required a molecular selection mechanism to screen for specific sequences with prebiotic functions. Cyclic processes such as daily temperature oscillations were ubiquitous in this environment and could trigger oligonucleotide phase separation. Here, we propose sequence selection based on phase separation cycles realized through sedimentation in a system subjected to the feeding of oligonucleotides. Using theory and experiments with DNA, we show sequence-specific enrichment in the sedimented dense phase, in particular of short 22-mer DNA sequences. The underlying mechanism selects for complementarity, as it enriches sequences that tightly interact in the condensed phase through base-pairing. Our mechanism also enables initially weakly biased pools to enhance their sequence bias or to replace the most abundant sequences as the cycles progress. Our findings provide an example of a selection mechanism that may have eased screening for the first auto-catalytic self-replicating oligonucleotides

Notulae to the Italian native vascular flora: 5.

In this contribution, new data concerning the distribution of native vascular flora in Italy are presented. It includes new records and confirmations to the Italian administrative regions for taxa in the genera Allium, Arabis, Campanula, Centaurea, Chaerophyllum, Crocus, Dactylis, Dianthus, Festuca, Galanthus, Helianthemum, Lysimachia, Milium, Pteris, and Quercus. Nomenclature and distribution updates, published elsewhere, and corrections are provided as supplementary material

Notulae to the Italian alien vascular flora 6

In this contribution, new data concerning the distribution of vascular flora alien to Italy are presented. It includes new records, confirmations, exclusions, and status changes for Italy or for Italian administrative regions of taxa in the genera Acalypha, Acer, Canna, Cardamine, Cedrus, Chlorophytum, Citrus, Cyperus, Epilobium, Eucalyptus, Euphorbia, Gamochaeta, Hesperocyparis, Heteranthera, Lemna, Ligustrum, Lycium, Nassella, Nothoscordum, Oenothera, Osteospermum, Paspalum, Pontederia, Romulea, Rudbeckia, Salvia, Sesbania, Setaria, Sicyos, Styphnolobium, Symphyotrichum, and Tradescantia. Nomenclature and distribution updates, published elsewhere, and corrigenda are provided as supplementary material

Notulae to the Italian native vascular flora: 10

In this contribution, new data concerning the distribution of native vascular flora in Italy are presented. It includes new records, confirmations, exclusions, and status changes to the Italian administrative regions for taxa in the genera Artemisia, Chaetonychia, Cirsium, Cynanchum, Genista, Hieracium, Iberis, Melica, Misopates, Myosotis, Thalictrum, Trifolium, Utricularia, Veronica, and Vicia. Nomenclatural and distribution updates, published elsewhere, and corrigenda are provided as supplementary material

Notulae to the Italian alien vascular flora: 12

In this contribution, new data concerning the distribution of vascular flora alien to Italy are presented. It includes new records, confirmations, exclusions, and status changes for Italy or for Italian administrative regions. Nomenclatural and distribution updates published elsewhere are provided as Suppl. material 1

Notulae to the Italian alien vascular flora: 14

In this contribution, new data concerning the distribution of vascular flora alien to Italy are presented. It includes new records, confirmations, and status changes for Italy or for Italian administrative regions. Nomenclatural and distribution updates, published elsewhere, and corrections are provided as Suppl. materia