Liquid-liquid phase separation (LLPS), especially coacervation, plays a crucial role in cell biology, as it forms numerous membraneless organelles in cells. Coacervates play an indispensable role in regulating intracellular biochemistry, and their dysfunction is associated with several diseases. Understanding of the LLPS dynamics would greatly benefit from controlled in vitro assays that mimic cells. Here, we use a microfluidics-based methodology to form coacervates inside cell-sized (~10 µm) liposomes, allowing control over the dynamics. Protein-pore-mediated permeation of small molecules into liposomes triggers LLPS passively or via active mechanisms like enzymatic polymerization of nucleic acids. We demonstrate sequestration of proteins (FtsZ) and supramolecular assemblies (lipid vesicles), as well as the possibility to host metabolic reactions ( β - galactosidase activity) inside coacervates. This coacervate-in-liposome platform provides a versatile tool to understand intracellular phase behavior, and these hybrid systems will allow engineering complex pathways to reconstitute cellular functions and facilitate bottom-up creation of synthetic cells.

Length regulation of microtubules (MTs) is essential for many cellular processes. Molecular motors like kinesin-8, which move along MTs and also act as depolymerases, are known as key players in MT dynamics. However, the regulatory mechanisms of length control remain elusive. Here, we investigate a stochastic model accounting for the interplay between polymerization kinetics and motor-induced depolymerization. We determine the dependence of MT length and variance on rate constants and motor concentration. Moreover, our analyses reveal how collective phenomena lead to a well-defined MT length.

The assembly and disassembly dynamics of microtubules (MTs) is tightly controlled by MT-associated proteins. Here, we investigate how plus-end-directed depolymerases of the kinesin-8 family regulate MT depolymerization dynamics. Using an individual-based model, we reproduce experimental findings. Moreover, crowding is identified as the key regulatory mechanism of depolymerization dynamics. Our analysis reveals two qualitatively distinct regimes. For motor densities above a particular threshold, a macroscopic traffic jam emerges at the plus-end and the MT dynamics become independent of the motor concentration. Below this threshold, microscopic traffic jams at the tip arise that cancel out the effect of the depolymerization kinetics such that the depolymerization speed is solely determined by the motor density. Because this density changes over the MT length, length-dependent regulation is possible. Remarkably, motor cooperativity affects only the end-residence time of depolymerases and not the depolymerization speed.

The cytoskeleton is regulated by a plethora of enzymes that influence the stability and dynamics of cytoskeletal filaments. How microtubules (MTs) are controlled is of particular importance for mitosis, during which dynamic MTs are responsible for proper segregation of chromosomes. Molecular motors of the kinesin-8 protein family have been shown to depolymerize MTs in a length-dependent manner, and recent experimental and theoretical evidence suggests a possible role for kinesin-8 in the dynamic regulation of MTs. However, so far the detailed molecular mechanisms of how these molecular motors interact with the growing MT tip remain elusive. Here we show that two distinct scenarios for the interactions of kinesin-8 with the MT tip lead to qualitatively different MT dynamics, including accurate length control as well as intermittent dynamics. We give a comprehensive analysis of the regimes where length regulation is possible and characterize how the stationary length depends on the biochemical rates and the bulk concentrations of the various proteins. For a neutral scenario, where MTs grow irrespective of whether the MT tip is occupied by a molecular motor, length regulation is possible only for a narrow range of biochemical rates, and, in particular, limited to small polymerization rates. By contrast, for an inhibition scenario, where the presence of a motor at the MT tip inhibits MT growth, the regime where length regulation is possible is extremely broad and includes high growth rates. These results also apply to situations where a polymerizing enzyme like XMAP215 and kinesin-8 mutually exclude each other from the MT tip. Moreover, we characterize the differences in the stochastic length dynamics between the two scenarios. While for the neutral scenario length is tightly controlled, length dynamics is intermittent for the inhibition scenario and exhibits extended periods of MT growth and shrinkage. On a broader perspective, the set of models established in this work quite generally suggest that mutual exclusion of molecules at the ends of cytoskeletal filaments is an important factor for filament dynamics and regulation.

Coacervates are polymer-rich droplets that form through liquid−liquid phase separation in polymer solutions. Liquid−liquid phase separation and coacervation have recently been shown to play an important role in the organization of biological systems. Such systems are highly dynamic and under continuous influence of enzymatic and chemical processes. However, it is still unclear how enzymatic and chemical reactions affect the coacervation process. Here, we present and characterize a system of enzymatically active coacervates containing spermine, RNA, free nucleotides, and the template independent RNA (de)polymerase PNPase. We find that these RNA coacervates display transient nonspherical shapes, and we systematically study how PNPase concentration, UDP concentration, and temperature affect coacervate morphology. Furthermore, we show that PNPase localizes predominantly into the coacervate phase and that its depolymerization activity in high-phosphate buffer causes coacervate degradation. Our observations of nonspherical coacervate shapes may have broader implications for the relationship between (bio)chemical activity and coacervate biology.

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Molecular spiders are synthetic molecular motors based on DNA nanotechnology. While natural molecular motors have evolved towards very high efficiency, it remains a major challenge to develop efficient designs for man-made molecular motors. Inspired by biological motor proteins such as kinesin and myosin, molecular spiders comprise a body and several legs. The legs walk on a lattice that is coated with substrate which can be cleaved catalytically. We propose a molecular spider design in which n spiders form a team. Our theoretical considerations show that coupling several spiders together alters the dynamics of the resulting team significantly. Although spiders operate at a scale where diffusion is dominant, spider teams can be tuned to behave nearly ballistic, which results in fast and predictable motion. Based on the separation of time scales of substrate and product dwell times, we develop a theory which utilizes equivalence classes to coarse-grain the microstate space. In addition, we calculate diffusion coefficients of the spider teams, employing a mapping of an n-spider team to an n-dimensional random walker on a confined lattice. We validate these results with Monte Carlo simulations and predict optimal parameters of the molecular spider team architecture which makes their motion most directed and maximally predictable.

The availability of protein is an important factor for the determination of the size of the mitotic spindle. Involved in spindle-size regulation is kinesin-8, a molecular motor and microtubule (MT) depolymerase, which is known to tightly control MT length. Here, we propose and analyze a theoretical model in which kinesin-induced MT depolymerization competes with spontaneous polymerization while supplies of both tubulin and kinesin are limited. In contrast to previous studies where resources were unconstrained, we find that, for a wide range of concentrations, MT length regulation is bistable. We test our predictions by conducting in vitro experiments and find that the bistable behavior manifests in a bimodal MT length distribution. DOI: 10.1103/PhysRevLett.120.148101 The absolute and relative abundance of particular sets of proteins is important for a wide range of processes in cells. For example, during Xenopus laevis embryogenesis, importin α becomes progressively localized to the cell membrane [1]. As a consequence of importin's depletion from the cytoplasm, the protein kif2a escapes inactivation and decreases the size of the mitotic spindle. Similarly, formation of the mitotic spindle reduces the concentration of free tubulin dimers, the building blocks of microtubules (MTs). Thus, up to 60% of all tubulin heterodimers [2,3] may be incorporated into the spindle [4]. In addition, it has been shown in vivo and in vitro that both spindle size [4,5] and the lengths of its constituent MTs [6] scale with cytoplasmic volume.Assembly and disassembly of MTs are regulated by a set of proteins that interact with the plus ends of protofilaments [7,8]. One of these factors, the molecular motor kinesin-8, acts as a depolymerase [8,9]. As a consequence, spindle size increases in its absence [10] and decreases upon overexpression of the protein [11]. Moreover, the kinesin-8 homolog Kip3 from Saccharomyces cerevisiae has been shown to depolymerize MTs in a length-dependent fashion [9,12]. This is facilitated by a density gradient on the MT, caused by the interplay between the processive motion of Kip3 along the MT and its depolymerase activity at the plus end, which effectively enables the MT to "sense" its own length [12,13]. In combination with spontaneous MT polymerization, the Kip3 gradient leads to a length regulation mechanism [14,15].Here, we explore the combined effect of limited resources and Kip3-induced depolymerization on the length regulation of MTs. As seen in theoretical studies on the collective motion of molecular motors, resource limitation affects the density profile on the MT: regions of low and high motor density separate, as a localized domain wall emerges on the MT [16][17][18][19]. This is a direct result of resource limitation and does not rely on the existence of a motor density gradient, as necessary for domain wall localization in the presence of unlimited resources [20][21][22][23]. So far, most work on the role of limited resources has focused on single components of the relevant system [17][...