Centrosomes are autocatalytic droplets of pericentriolar material organized by centrioles

Design principles and feedback mechanisms in organelle size control

Intracellular organelles are essential for cellular architecture and function, and their size regulation is critical for maintaining cellular homeostasis. Organelle size often scales with cell size, governed by mechanisms that integrate resource allocation, stochastic dynamics, and feedback controls. Here we review these underlying biophysical principles of organelle size control, including the limiting pool hypothesis, stochastic assembly processes, and feedback-driven growth dynamics. We discuss how negative feedback motifs stabilize size, while positive feedback can amplify growth and maintain size under specific conditions. Additionally, we discuss recent advances in modeling size control for organelles with nucleation and fission-fusion dynamics. By integrating experimental observations with theoretical insights, this review provides a conceptual understanding of the design principles governing organelle size regulation in dynamic cellular environments.

Maximum entropy inference of reaction-diffusion models

Reaction-diffusion equations are commonly used to model a diverse array of complex systems, including biological, chemical, and physical processes. Typically, these models are phenomenological, requiring the fitting of parameters to experimental data. In the present work, we introduce a novel formalism to construct reaction-diffusion models that is grounded in the principle of maximum entropy. This new formalism aims to incorporate various types of experimental data, including ensemble currents, distributions at different points in time, or moments of such. To this end, we expand the framework of Schrödinger bridges and maximum caliber problems to nonlinear interacting systems. We illustrate the usefulness of the proposed approach by modeling the evolution of (i) a morphogen across the fin of a zebrafish and (ii) the population of two varieties of toads in Poland, so as to match the experimental data.

Molecular simulations of enzymatic phosphorylation of disordered proteins and their condensates

Condensation and aggregation of disordered proteins in cellular non-equilibrium environments are shaped decisively by enzymes. Enzymes called kinases phosphorylate proteins, consuming the chemical fuel ATP. Protein phosphorylation by kinases such as Casein kinase 1 delta (CK1δ) determines the interactions of neurodegeneration-linked proteins such as TDP-43. Hyperphosphorylation of TDP-43 by CK1δ may be a cytoprotective mechanism for neurons, but how CK1δ interacts with protein condensates is not known. Molecular dynamics simulations hold the promise to resolve how kinases interact with disordered proteins and their condensates, and how this shapes the phosphorylation dynamics. In practice, it is difficult to verify whether implementations of chemical-fuel driven coarse-grained simulations are thermodynamically consistent, which we address by a generally applicable and automatic Markov state modeling approach. In this work, we thus elucidate with coarse-grained simulations, drivers of how TDP-43 is phosphorylated by CK1δ and how this leads to the dissolution of TDP-43 condensates upon hyperphosphorylation.

Activity-Induced Droplet Inversion in Multicomponent Liquid-Liquid Phase Separation

Liquid-liquid phase separation (LLPS) is a vital process in forming membrane-free organelles, crucial for cell physiology and recently gaining significant attention. However, the effects of nonequilibrium factors, which are common in real life, on the process of LLPS have not been fully explored. To address this issue, we developed a model for nonequilibrium phase separation involving three components (A, B, and C) by integrating a nonequilibrium term into the chemical potential for active component B. We find significant changes in the morphology and dynamics of nonequilibrium phase-separated droplets compared to their equilibrium counterparts. Remarkably, with a large enough activity, the B-A-C structure (B at the center, surrounded by A, then enveloped by C) under equilibrium conditions may change to a C-A-B structure. Further simulations give a global picture of the system under both active and passive conditions, revealing the shifts of the phase boundaries and unraveling the effect of activity on different droplet structures. We derived an effective free energy for the active LLPS system to provide a qualitative understanding of our observations. Our study presents a basic model for nonequilibrium phase separation processes, providing crucial insights into LLPS alongside intracellular nonequilibrium phenomena.

Catalytic growth in a shared enzyme pool ensures robust control of centrosome size

Accurate regulation of centrosome size is essential for ensuring error-free cell division, and dysregulation of centrosome size has been linked to various pathologies, including developmental defects and cancer. While a universally accepted model for centrosome size regulation is lacking, prior theoretical and experimental works suggest a centrosome growth model involving autocatalytic assembly of the pericentriolar material. Here, we show that the autocatalytic assembly model fails to explain the attainment of equal centrosome sizes, which is crucial for error-free cell division. Incorporating latest experimental findings into the molecular mechanisms governing centrosome assembly, we introduce a new quantitative theory for centrosome growth involving catalytic assembly within a shared pool of enzymes. Our model successfully achieves robust size equality between maturing centrosome pairs, mirroring cooperative growth dynamics observed in experiments. To validate our theoretical predictions, we compare them with available experimental data and demonstrate the broad applicability of the catalytic growth model across different organisms, which exhibit distinct growth dynamics and size scaling characteristics.

Nucleocapsid assembly drives Ebola viral factory maturation and dispersion

Replication and genome encapsidation of many negative-sense RNA viruses take place in virus-induced membraneless organelles termed viral factories (VFs). Although liquid properties of VFs are believed to control the transition from genome replication to nucleocapsid (NC) assembly, VF maturation and interactions with the cellular environment remain elusive. Here, we apply in situ cryo-correlative light and electron tomography to follow NC assembly and changes in VF morphology and their liquid properties during Ebola virus infection. We show that viral NCs transition from loosely packed helical assemblies in early VFs to compact cylinders that arrange into highly organized parallel bundles later in infection. Early VFs associate with intermediate filaments and are devoid of other host material but become progressively accessible to cellular components. Our data suggest that this process is coupled to VF solidification, loss of sphericity, and dispersion and promotes cytoplasmic exposure of NCs to facilitate their transport to budding sites.

Reactive Brownian Dynamics of Chemically Fueled Droplets: Roles of Attraction and Deactivation Modes

The self-assembly of biological membraneless organelles can be mimicked by active droplets resulting from chemically fueled microphase separation. However, how the nonequilibrium, transient structure of these active droplets can be controlled through the physicochemical input parameters is not yet well understood. In our work, a chemically fueled two-state chemical reaction and subsequent droplet growth and decay are modeled with a reactive Brownian dynamics simulation in two spatial dimensions. In our model, particles that are activated via the consumption of fuel become attractive and can accumulate into droplets. A local-density-dependent distinction of the droplet's 'internal' and 'external' particles allows for structural feedback by giving further control over the deactivation process. The simulation shows that the deactivation of only external particles slows down the decay and stabilizes the droplets, whereas the deactivation of only internal particles can lead to a temporary encapsulation of deactivated particles (in nonequilibrium 'core-shell' structures) where the chemically active particles serve as an outer shell. Additionally, the role of hydrophobicity resembled by the attraction energy ε and the dependency of the nonequilibrium droplet formation on the various parameters of the chemical reaction are investigated. For example, a high attraction energy can lead to transient finite-size crystalline droplets, while other parameter choices indicate bimodal droplet size distributions at specific times. Similarities and differences to related experiments are discussed.

Catalytic growth in a shared enzyme pool ensures robust control of centrosome size

Accurate regulation of centrosome size is essential for ensuring error-free cell division, and dysregulation of centrosome size has been linked to various pathologies, including developmental defects and cancer. While a universally accepted model for centrosome size regulation is lacking, prior theoretical and experimental works suggest a centrosome growth model involving autocatalytic assembly of the pericentriolar material. Here we show that the autocatalytic assembly model fails to explain the attainment of equal centrosome sizes, which is crucial for error-free cell division. Incorporating latest experimental findings into the molecular mechanisms governing centrosome assembly, we introduce a new quantitative theory for centrosome growth involving catalytic assembly within a shared pool of enzymes. Our model successfully achieves robust size equality between maturing centrosome pairs, mirroring cooperative growth dynamics observed in experiments. To validate our theoretical predictions, we compare them with available experimental data and demonstrate the broad applicability of the catalytic growth model across different organisms, which exhibit distinct growth dynamics and size scaling characteristics.

Carboxy-terminal polyglutamylation regulates signaling and phase separation of the Dishevelled protein

Polyglutamylation is a reversible posttranslational modification that is catalyzed by enzymes of the tubulin tyrosine ligase-like (TTLL) family. Here, we found that TTLL11 generates a previously unknown type of polyglutamylation that is initiated by the addition of a glutamate residue to the free C-terminal carboxyl group of a substrate protein. TTLL11 efficiently polyglutamylates the Wnt signaling protein Dishevelled 3 (DVL3), thereby changing the interactome of DVL3. Polyglutamylation increases the capacity of DVL3 to get phosphorylated, to undergo phase separation, and to act in the noncanonical Wnt pathway. Both carboxy-terminal polyglutamylation and the resulting reduction in phase separation capacity of DVL3 can be reverted by the deglutamylating enzyme CCP6, demonstrating a causal relationship between TTLL11-mediated polyglutamylation and phase separation. Thus, C-terminal polyglutamylation represents a new type of posttranslational modification, broadening the range of proteins that can be modified by polyglutamylation and providing the first evidence that polyglutamylation can modulate protein phase separation.

Active RNA synthesis patterns nuclear condensates

Biomolecular condensates are membraneless compartments that organize biochemical processes in cells. In contrast to well-understood mechanisms describing how condensates form and dissolve, the principles underlying condensate patterning - including their size, number and spacing in the cell - remain largely unknown. We hypothesized that RNA, a key regulator of condensate formation and dissolution, influences condensate patterning. Using nucleolar fibrillar centers (FCs) as a model condensate, we found that inhibiting ribosomal RNA synthesis significantly alters the patterning of FCs. Physical theory and experimental observations support a model whereby active RNA synthesis generates a non-equilibrium state that arrests condensate coarsening and thus contributes to condensate patterning. Altering FC condensate patterning by expression of the FC component TCOF1 impairs ribosomal RNA processing, linking condensate patterning to biological function. These results reveal how non-equilibrium states driven by active chemical processes regulate condensate patterning, which is important for cellular biochemistry and function.

Liquid-liquid phase transition as a basis for novel materials for skin repair and regeneration

Inorganic materials are of increasing interest not only for bone repair but also for other applications in regenerative medicine. In this study, the combined effects of energy-providing, regeneratively active inorganic polyphosphate (polyP) and also morphogenetically active pearl powder on wound healing were investigated. Aragonite, the mineralic constituent of pearl nacre and thermodynamically unstable form of crystalline calcium carbonate, was found to be converted into a soluble state in the presence of a Ca2+-containing wound exudate, particularly upon addition of sodium polyP (Na-polyP), driven by the transfer of Ca2+ ions from aragonite to polyP, leading to liquid-liquid phase separation to form an aqueous Ca-polyP coacervate. This process is further enhanced in the presence of Ca-polyP nanoparticles (Ca-polyP-NP). Kinetic studies revealed that the coacervation of polyP and nacre aragonite in wound exudate is a very rapid process that results in the formation of a stronger gel with a porous structure compared to polyP alone. Coacervate formation, enabled by phase transition of crystalline aragonite in the presence of Na-polyP/Ca-polyP-NP and wound exudate, could also be demonstrated in a hydroxyethyl cellulose-based hydrogel used for wound treatment. Furthermore, it is shown that Na-polyP/Ca-polyP-NP together with nacre aragonite strongly enhances the proliferation of mesenchymal stem cells and promotes microtube formation in the in vitro angiogenesis assay with HUVEC endothelial cells. The latter effect was confirmed by gene expression studies, applying real-time polymerase chain reaction, using the biomarker genes VEGF (vascular endothelial growth factor) and hypoxia-inducible factor-1 α (HIF-1α). Division of Escherichia coli is suppressed when suspended in a matrix containing Na-polyP/Ca-polyP-NP and aragonite. The potential medical relevance of these findings is supported by an animal study on genetically engineered diabetic mice (db/db), which demonstrated a marked increase in granulation tissue and microvessel formation in regenerating experimental wounds treated with Ca-polyP-NP compared to controls. Co-administration of aragonite significantly accelerated the wound healing-promoting effect of polyP in db/db mice. Based on these results, we propose that the ability of polyP to form a mixed coacervate with aragonite, in addition to its energy (ATP)-generating function, can decisively contribute to the regenerative activity of this polymer in wound repair.

Droplet Differentiation by a Chemical Switch

A fundamental question about biomolecular condensates is how distinct condensates can emerge from the interplay of different components. Here we present a minimal model of droplet differentiation where phase separated droplets demix into two types with different chemical modifications triggered by enzymatic reactions. We use numerical solutions to Cahn-Hilliard equations with chemical reactions and an effective droplet model to reveal the switchlike behavior. Our work shows how condensate identities in cells could result from competing enzymatic actions.

Reaction-Driven Diffusiophoresis of Liquid Condensates: Potential Mechanisms for Intracellular Organization

The cellular environment, characterized by its intricate composition and spatial organization, hosts a variety of organelles, ranging from membrane-bound ones to membraneless structures that are formed through liquid-liquid phase separation. Cells show precise control over the position of such condensates. We demonstrate that organelle movement in external concentration gradients, diffusiophoresis, is distinct from the one of colloids because fluxes can remain finite inside the liquid-phase droplets and movement of the latter arises from incompressibility. Within cellular domains diffusiophoresis naturally arises from biochemical reactions that are driven by a chemical fuel and produce waste. Simulations and analytical arguments within a minimal model of reaction-driven phase separation reveal that the directed movement stems from two contributions: Fuel and waste are refilled or extracted at the boundary, resulting in concentration gradients, which (i) induce product fluxes via incompressibility and (ii) result in an asymmetric forward reaction in the droplet's surroundings (as well as asymmetric backward reaction inside the droplet), thereby shifting the droplet's position. We show that the former contribution dominates and sets the direction of the movement, toward or away from fuel source and waste sink, depending on the product molecules' affinity toward fuel and waste, respectively. The mechanism thus provides a simple means to organize condensates with different composition. Particle-based simulations and systems with more complex reaction cycles corroborate the robustness and universality of this mechanism.

Multivalent coiled-coil interactions enable full-scale centrosome assembly and strength

The outermost layer of centrosomes, called pericentriolar material (PCM), organizes microtubules for mitotic spindle assembly. The molecular interactions that enable PCM to assemble and resist external forces are poorly understood. Here, we use crosslinking mass spectrometry (XL-MS) to analyze PLK-1-potentiated multimerization of SPD-5, the main PCM scaffold protein in C. elegans. In the unassembled state, SPD-5 exhibits numerous intramolecular crosslinks that are eliminated after phosphorylation by PLK-1. Thus, phosphorylation induces a structural opening of SPD-5 that primes it for assembly. Multimerization of SPD-5 is driven by interactions between multiple dispersed coiled-coil domains. Structural analyses of a phosphorylated region (PReM) in SPD-5 revealed a helical hairpin that dimerizes to form a tetrameric coiled-coil. Mutations within this structure and other interacting regions cause PCM assembly defects that are partly rescued by eliminating microtubule-mediated forces, revealing that PCM assembly and strength are interdependent. We propose that PCM size and strength emerge from specific, multivalent coiled-coil interactions between SPD-5 proteins.

Coiled-coil domains are sufficient to drive liquid-liquid phase separation in protein models

Liquid-liquid phase separation (LLPS) is thought to be a main driving force in the formation of membraneless organelles. Examples of such organelles include the centrosome, central spindle, and stress granules. Recently, it has been shown that coiled-coil (CC) proteins, such as the centrosomal proteins pericentrin, spd-5, and centrosomin, might be capable of LLPS. CC domains have physical features that could make them the drivers of LLPS, but it is unknown if they play a direct role in the process. We developed a coarse-grained simulation framework for investigating the LLPS propensity of CC proteins, in which interactions that support LLPS arise solely from CC domains. We show, using this framework, that the physical features of CC domains are sufficient to drive LLPS of proteins. The framework is specifically designed to investigate how the number of CC domains, as well as the multimerization state of CC domains, can affect LLPS. We show that small model proteins with as few as two CC domains can phase separate. Increasing the number of CC domains up to four per protein can somewhat increase LLPS propensity. We demonstrate that trimer-forming and tetramer-forming CC domains have a dramatically higher LLPS propensity than dimer-forming coils, which shows that multimerization state has a greater effect on LLPS than the number of CC domains per protein. These data support the hypothesis of CC domains as drivers of protein LLPS, and have implications in future studies to identify the LLPS-driving regions of centrosomal and central spindle proteins.

Active osmoticlike pressure on permeable inclusions

We use a standard minimal active Brownian model to investigate the osmotic-like effective pressure generated by active fluids on fixed hollow inclusions. These inclusions are enclosed by a permeable (albeit nonflexible) membrane, and the interior and exterior regions of the inclusions have different particle motility strengths. We consider both rectangular and disklike inclusions and analyze the effects of various system parameters, such as excluded volume interaction between active particles, hardness of membrane, and active particle density, on the effective pressure produced on the enclosing membrane. We focus on the range of intermediate to high motility strengths and analyze the effective pressure in the steady state. Our findings for the active pressure produced in the interior and exterior regions of the inclusion indicate that the pressure is higher in the region with lower motility due to the relatively stronger accumulation of active particles.

NAGPKin: Nucleation-and-growth parameters from the kinetics of protein phase separation

The assembly of biomolecular condensate in eukaryotic cells and the accumulation of amyloid deposits in neurons are processes involving the nucleation and growth (NAG) of new protein phases. To therapeutically target protein phase separation, drug candidates are tested in in vitro assays that monitor the increase in the mass or size of the new phase. Limited mechanistic insight is, however, provided if empirical or untestable kinetic models are fitted to these progress curves. Here we present the web server NAGPKin that quantifies NAG rates using mass-based or size-based progress curves as the input data. A report is generated containing the fitted NAG parameters and elucidating the phase separation mechanisms at play. The NAG parameters can be used to predict particle size distributions of, for example, protein droplets formed by liquid-liquid phase separation (LLPS) or amyloid fibrils formed by protein aggregation. Because minimal intervention is required from the user, NAGPKin is a good platform for standardized reporting of LLPS and protein self-assembly data. NAGPKin is useful for drug discovery as well as for fundamental studies on protein phase separation. NAGPKin is freely available (no login required) at https://nagpkin.i3s.up.pt.

Interplay between posttranslational modifications and liquid‒liquid phase separation in tumors

Liquid‒liquid phase separation (LLPS) is a general phenomenon recently recognized to be critically involved in the regulation of a variety of cellular biological processes, such as transcriptional regulation, heterochromatin formation and signal transduction, through the compartmentalization of proteins or nucleic acids into droplet-like condensates. These processes are directly or indirectly related to tumor initiation and treatment. Posttranslational modifications (PTMs), which represent a rapid and reversible mechanism involved in the functional regulation of proteins, have emerged as key events in modulating LLPS under physiological or pathophysiological conditions, including tumorigenesis and antitumor therapy. In this review, we introduce the biological functions participated in cancer-associated LLPS, discuss the potential roles of LLPS during tumor onset or therapy, and emphasize the mechanistic characteristics of LLPS regulated by PTMs and its effects on tumor progression. We then provide a perspective on further studies on LLPS and its regulation by PTMs in cancer research. This review aims to broaden the understanding of the functions of LLPS and its regulation by PTMs under normal or aberrant cellular conditions.

Regulation of centrosome size by the cell-cycle oscillator in Drosophila embryos

Mitotic centrosomes assemble when centrioles recruit large amounts of pericentriolar material (PCM) around themselves. In early C. elegans embryos, mitotic centrosome size appears to be set by the limiting amount of a key component. In Drosophila syncytial embryos, thousands of mitotic centrosomes are assembled as the embryo proceeds through 13 rounds of rapid nuclear division, driven by a core cell cycle oscillator. These divisions slow during nuclear cycles 11-13, and we find that centrosomes respond by reciprocally decreasing their growth rate, but increasing their growth period-so that they grow to a relatively consistent size at each cycle. At the start of each cycle, moderate CCO activity initially promotes centrosome growth, in part by stimulating Polo/PLK1 recruitment to centrosomes. Later in each cycle, high CCO activity inhibits centrosome growth by suppressing the centrosomal recruitment and/or maintenance of centrosome proteins. Thus, in fly embryos, mitotic centrosome size appears to be regulated predominantly by the core cell cycle oscillator, rather than by the depletion of a limiting component.

Biomolecular Condensates: Structure, Functions, Methods of Research

The term "biomolecular condensates" is used to describe membraneless compartments in eukaryotic cells, accumulating proteins and nucleic acids. Biomolecular condensates are formed as a result of liquid-liquid phase separation (LLPS). Often, they demonstrate properties of liquid-like droplets or gel-like aggregates; however, some of them may appear to have a more complex structure and high-order organization. Membraneless microcompartments are involved in diverse processes both in cytoplasm and in nucleus, among them ribosome biogenesis, regulation of gene expression, cell signaling, and stress response. Condensates properties and structure could be highly dynamic and are affected by various internal and external factors, e.g., concentration and interactions of components, solution temperature, pH, osmolarity, etc. In this review, we discuss variety of biomolecular condensates and their functions in live cells, describe their structure variants, highlight domain and primary sequence organization of the constituent proteins and nucleic acids. Finally, we describe current advances in methods that characterize structure, properties, morphology, and dynamics of biomolecular condensates in vitro and in vivo.

Irreversibility across a Nonreciprocal PT-Symmetry-Breaking Phase Transition

Nonreciprocal interactions are commonplace in continuum-level descriptions of both biological and synthetic active matter, yet studies addressing their implications for time reversibility have so far been limited to microscopic models. Here, we derive a general expression for the average rate of informational entropy production in the most generic mixture of conserved phase fields with nonreciprocal couplings and additive conservative noise. For the particular case of a binary system with Cahn-Hilliard dynamics augmented by nonreciprocal cross-diffusion terms, we observe a nontrivial scaling of the entropy production rate across a parity-time symmetry breaking phase transition. We derive a closed-form analytic expression in the weak-noise regime for the entropy production rate due to the emergence of a macroscopic dynamic phase, showing it can be written in terms of the global polar order parameter, a measure of parity-time symmetry breaking.

Biomolecular condensates in kidney physiology and disease

The regulation and preservation of distinct intracellular and extracellular solute microenvironments is crucial for the maintenance of cellular homeostasis. In mammals, the kidneys control bodily salt and water homeostasis. Specifically, the urine-concentrating mechanism within the renal medulla causes fluctuations in extracellular osmolarity, which enables cells of the kidney to either conserve or eliminate water and electrolytes, depending on the balance between intake and loss. However, relatively little is known about the subcellular and molecular changes caused by such osmotic stresses. Advances have shown that many cells, including those of the kidney, rapidly (within seconds) and reversibly (within minutes) assemble membraneless, nano-to-microscale subcellular assemblies termed biomolecular condensates via the biophysical process of hyperosmotic phase separation (HOPS). Mechanistically, osmotic cell compression mediates changes in intracellular hydration, concentration and molecular crowding, rendering HOPS one of many related phase-separation phenomena. Osmotic stress causes numerous homo-multimeric proteins to condense, thereby affecting gene expression and cell survival. HOPS rapidly regulates specific cellular biochemical processes before appropriate protective or corrective action by broader stress response mechanisms can be initiated. Here, we broadly survey emerging evidence for, and the impact of, biomolecular condensates in nephrology, where initial concentration buffering by HOPS and its subsequent cellular escalation mechanisms are expected to have important implications for kidney physiology and disease.

Polyelectrolytes: From Seminal Works to the Influence of the Charge Sequence

We propose a selected tour of the physics of polyelectrolytes (PE) following the line initiated by de Gennes and coworkers in their seminal 1976 paper. The early works which used uniform charge distributions along the PE backbone achieved tremendous progress and set most milestones in the field. Recently, the focus has shifted to the role of the charge sequence. Revisited topics include PE complexation and polyampholytes (PA). We develop the example of a random PE in poor solvent forming pearl-necklace structures. It is shown that the pearls typically adopt very asymmetric mass and charge distributions. Individual sequences do not necessarily reflect the ensemble statistics and a rich variety of behaviors emerges (specially for PA). Pearl necklaces are dynamic structures and switch between various types of pearl-necklace structures, as described for both PE and PA.

Chemical reaction motifs driving non-equilibrium behaviours in phase separating materials

Chemical reactions that couple to systems that phase separate have been implicated in diverse contexts from biology to materials science. However, how a particular set of chemical reactions (chemical reaction network, CRN) would affect the behaviours of a phase separating system is difficult to fully predict theoretically. In this paper, we analyse a mean field theory coupling CRNs to a combined system of phase separating and non-phase separating materials and analyse how the properties of the CRNs affect different classes of non-equilibrium behaviour: microphase separation or temporally oscillating patterns. We examine the problem of achieving microphase separated condensates by statistical analysis of the Jacobians, of which the most important motifs are negative feedback of the phase separating component and combined inhibition/activation by the non-phase separating components. We then identify CRN motifs that are likely to yield microphase by examining randomly generated networks and parameters. Molecular sequestration of the phase separating motif is shown to be the most robust towards yielding microphase separation. Subsequently, we find that dynamics of the phase separating species is promoted most easily by inducing oscillations in the diffusive components coupled to the phase separating species. Our results provide guidance towards the design of CRNs that manage the formation, dissolution and organization of compartments.

An ESCRT grommet cooperates with a diffusion barrier to maintain nuclear integrity

The molecular mechanisms by which the endosomal sorting complexes required for transport (ESCRT) proteins contribute to the integrity of the nuclear envelope (NE) barrier are not fully defined. We leveraged the single NE hole generated by mitotic extrusion of the Schizosaccharomyces pombe spindle pole body to reveal two modes of ESCRT function executed by distinct complements of ESCRT-III proteins, both dependent on CHMP7/Cmp7. A grommet-like function is required to restrict the NE hole in anaphase B, whereas replacement of Cmp7 by a sealing module ultimately closes the NE in interphase. Without Cmp7, nucleocytoplasmic compartmentalization remains intact despite NE discontinuities of up to 540 nm, suggesting mechanisms to limit diffusion through these holes. We implicate spindle pole body proteins as key components of a diffusion barrier acting with Cmp7 in anaphase B. Thus, NE remodelling mechanisms cooperate with proteinaceous diffusion barriers beyond nuclear pore complexes to maintain the nuclear compartment.

Amphiphiles Formed from Synthetic DNA-Nanomotifs Mimic the Stepwise Dispersal of Transcriptional Clusters in the Cell Nucleus

Stem cells exhibit prominent clusters controlling the transcription of genes into RNA. These clusters form by a phase-separation mechanism, and their size and shape are controlled via an amphiphilic effect of transcribed genes. Here, we construct amphiphile-nanomotifs purely from DNA, and we achieve similar size and shape control for phase-separated droplets formed from fully synthetic, self-interacting DNA-nanomotifs. Increasing amphiphile concentrations induce rounding of droplets, prevent droplet fusion, and, at high concentrations, cause full dispersal of droplets. Super-resolution microscopy data obtained from zebrafish embryo stem cells reveal a comparable transition for transcriptional clusters with increasing transcription levels. Brownian dynamics and lattice simulations further confirm that the addition of amphiphilic particles is sufficient to explain the observed changes in shape and size. Our work reproduces key aspects of transcriptional cluster formation in biological cells using relatively simple DNA sequence-programmable nanostructures, opening novel ways to control the mesoscopic organization of synthetic nanomaterials.

Quantification of Surface Tension Effects and Nucleation-and-Growth Rates during Self-Assembly of Biological Condensates

Liquid-solid and liquid-liquid phase separation (PS) drives the formation of functional and disease-associated biological assemblies. Principles of phase equilibrium are here employed to derive a general kinetic solution that predicts the evolution of the mass and size of biological assemblies. Thermodynamically, protein PS is determined by two measurable concentration limits: the saturation concentration and the critical solubility. Due to surface tension effects, the critical solubility can be higher than the saturation concentration for small, curved nuclei. Kinetically, PS is characterized by the primary nucleation rate constant and a combined rate constant accounting for growth and secondary nucleation. It is demonstrated that the formation of a limited number of large condensates is possible without active mechanisms of size control and in the absence of coalescence phenomena. The exact analytical solution can be used to interrogate how the elementary steps of PS are affected by candidate drugs.

Coiled-coil domains are sufficient to drive liquid-liquid phase separation of proteins in molecular models

Liquid-liquid phase separation (LLPS) is thought to be a main driving force in the formation of membraneless organelles. Examples of such organelles include the centrosome, central spindle, and stress granules. Recently, it has been shown that coiled-coil (CC) proteins, such as the centrosomal proteins pericentrin, spd-5, and centrosomin, might be capable of LLPS. CC domains have physical features that could make them the drivers of LLPS, but it is unknown if they play a direct role in the process. We developed a coarse-grained simulation framework for investigating the LLPS propensity of CC proteins, in which interactions which support LLPS arise solely from CC domains. We show, using this framework, that the physical features of CC domains are sufficient to drive LLPS of proteins. The framework is specifically designed to investigate how the number of CC domains, as well as multimerization state of CC domains, can affect LLPS. We show that small model proteins with as few as two CC domains can phase separate. Increasing the number of CC domains up to four per protein can somewhat increase LLPS propensity. We demonstrate that trimer-forming and tetramer-forming CC domains have a dramatically higher LLPS propensity than dimer-forming coils, which shows that multimerization state has a greater effect on LLPS than the number of CC domains per protein. These data support the hypothesis of CC domains as drivers of protein LLPS, and has implications in future studies to identify the LLPS-driving regions of centrosomal and central spindle proteins.

Shedding light on reovirus assembly-Multimodal imaging of viral factories

Avian (ortho)reovirus (ARV), which belongs to Reoviridae family, is a major domestic fowl pathogen and is the causative agent of viral tenosynovitis and chronic respiratory disease in chicken. ARV replicates within cytoplasmic inclusions, so-called viral factories, that form by phase separation and thus belong to a wider class of biological condensates. Here, we evaluate different optical imaging methods that have been developed or adapted to follow formation, fluidity and composition of viral factories and compare them with the complementary structural information obtained by well-established transmission electron microscopy and electron tomography. The molecular and cellular biology aspects for setting up and following virus infection in cells by imaging are described first. We then demonstrate that a wide-field version of fluorescence recovery after photobleaching is an effective tool to measure fluidity of mobile viral factories. A new technique, holotomographic phase microscopy, is then used for imaging of viral factory formation in live cells in three dimensions. Confocal Raman microscopy of infected cells provides "chemical" contrast for label-free segmentation of images and addresses important questions about biomolecular concentrations within viral factories and other biological condensates. Optical imaging is complemented by electron microscopy and tomography which supply higher resolution structural detail, including visualization of individual virions within the three-dimensional cellular context.

Nucleation of Chemically Active Droplets

Driven chemical reactions can control the macroscopic properties of droplets, like their size. Such active droplets are critical in structuring the interior of biological cells. Cells also need to control where and when droplets appear, so they need to control droplet nucleation. Our numerical simulations demonstrate that reactions generally suppress nucleation if they stabilize the homogeneous state. An equilibrium surrogate model reveals that reactions increase the effective energy barrier of nucleation, enabling quantitative predictions of the increased nucleation times. Moreover, the surrogate model allows us to construct a phase diagram, which summarizes how reactions affect the stability of the homogeneous phase and the droplet state. This simple picture provides accurate predictions of how driven reactions delay nucleation, which is relevant for understanding droplets in biological cells and chemical engineering.

Designing negative feedback loops in enzymatic coacervate droplets

Membraneless organelles within the living cell use phase separation of biomolecules coupled with enzymatic reactions to regulate cellular processes. The diverse functions of these biomolecular condensates motivate the pursuit of simpler in vitro models that exhibit primitive forms of self-regulation based on internal feedback mechanisms. Here, we investigate one such model based on complex coacervation of the enzyme catalase with an oppositely charge polyelectrolyte DEAE-dextran to form pH-responsive catalytic droplets. Upon addition of hydrogen peroxide "fuel", enzyme activity localized within the droplets causes a rapid increase in the pH. Under appropriate conditions, this reaction-induced pH change triggers coacervate dissolution owing to its pH-responsive phase behavior. Notably, this destabilizing effect of the enzymatic reaction on phase separation depends on droplet size owing to the diffusive delivery and removal of reaction components. Reaction-diffusion models informed by the experimental data show that larger drops support larger changes in the local pH thereby enhancing their dissolution relative to smaller droplets. Together, these results provide a basis for achieving droplet size control based on negative feedback between pH-dependent phase separation and pH-changing enzymatic reactions.

Self-assembly coupled to liquid-liquid phase separation

Liquid condensate droplets with distinct compositions of proteins and nucleic acids are widespread in biological cells. While it is known that such droplets, or compartments, can regulate irreversible protein aggregation, their effect on reversible self-assembly remains largely unexplored. In this article, we use kinetic theory and solution thermodynamics to investigate the effect of liquid-liquid phase separation on the reversible self-assembly of structures with well-defined sizes and architectures. We find that, when assembling subunits preferentially partition into liquid compartments, robustness against kinetic traps and maximum achievable assembly rates can be significantly increased. In particular, both the range of solution conditions leading to productive assembly and the corresponding assembly rates can increase by orders of magnitude. We analyze the rate equation predictions using simple scaling estimates to identify effects of liquid-liquid phase separation as a function of relevant control parameters. These results may elucidate self-assembly processes that underlie normal cellular functions or pathogenesis, and suggest strategies for designing efficient bottom-up assembly for nanomaterials applications.

Sensitive and selective polymer condensation at membrane surface driven by positive co-operativity

Biomolecular phase separation has emerged as an essential mechanism for cellular organization. How cells respond to environmental stimuli in a robust and sensitive manner to build functional condensates at the proper time and location is only starting to be understood. Recently, lipid membranes have been recognized as an important regulatory center for biomolecular condensation. However, how the interplay between the phase behaviors of cellular membranes and surface biopolymers may contribute to the regulation of surface condensation remains to be elucidated. Using simulations and a mean-field theoretical model, we show that two key factors are the membrane's tendency to phase-separate and the surface polymer's ability to reorganize local membrane composition. Surface condensate forms with high sensitivity and selectivity in response to features of biopolymer when positive co-operativity is established between coupled growth of the condensate and local lipid domains. This effect relating the degree of membrane-surface polymer co-operativity and condensate property regulation is shown to be robust by different ways of tuning the co-operativity, such as varying membrane protein obstacle concentration, lipid composition, and the affinity between lipid and polymer. The general physical principle emerged from the current analysis may have implications in other biological processes and beyond.

A membrane reticulum, the centriculum, affects centrosome size and function in Caenorhabditis elegans

Centrosomes are cellular structures that nucleate microtubules. At their core is a pair of centrioles that recruit pericentriolar material (PCM). Although centrosomes are considered membraneless organelles, in many cell types, including human cells, centrosomes are surrounded by endoplasmic reticulum (ER)-derived membranes of unknown structure and function. Using volume electron microscopy (vEM), we show that centrosomes in the Caenorhabditis elegans (C. elegans) early embryo are surrounded by a three-dimensional (3D), ER-derived membrane reticulum that we call the centriculum, for centrosome-associated membrane reticulum. The centriculum is adjacent to the nuclear envelope in interphase and early mitosis and fuses with the fenestrated nuclear membrane at metaphase. Centriculum formation is dependent on the presence of an underlying centrosome and on microtubules. Conversely, increasing centriculum size by genetic means led to the expansion of the PCM, increased microtubule nucleation capacity, and altered spindle width. The effect of the centriculum on centrosome function suggests that in the C. elegans early embryo, the centrosome is not membraneless. Rather, it is encased in a membrane meshwork that affects its properties. We provide evidence that the centriculum serves as a microtubule "filter," preventing the elongation of a subset of microtubules past the centriculum. Finally, we propose that the fusion between the centriculum and the nuclear membrane contributes to nuclear envelope breakdown by coupling spindle elongation to nuclear membrane fenestration.

Effective simulations of interacting active droplets

Droplets form a cornerstone of the spatiotemporal organization of biomolecules in cells. These droplets are controlled using physical processes like chemical reactions and imposed gradients, which are costly to simulate using traditional approaches, like solving the Cahn-Hilliard equation. To overcome this challenge, we here present an alternative, efficient method. The main idea is to focus on the relevant degrees of freedom, like droplet positions and sizes. We derive dynamical equations for these quantities using approximate analytical solutions obtained from a sharp interface limit and linearized equations in the bulk phases. We verify our method against fully-resolved simulations and show that it can describe interacting droplets under the influence of chemical reactions and external gradients using only a fraction of the computational costs of traditional methods. Our method can be extended to include other processes in the future and will thus serve as a relevant platform for understanding the dynamics of droplets in cells.

Actin filaments form a size-dependent diffusion barrier around centrosomes

The centrosome, a non-membranous organelle, constrains various soluble molecules locally to execute its functions. As the centrosome is surrounded by various dense components, we hypothesized that it may be bordered by a putative diffusion barrier. After quantitatively measuring the trapping kinetics of soluble proteins of varying size at centrosomes by a chemically inducible diffusion trapping assay, we find that centrosomes are highly accessible to soluble molecules with a Stokes radius of less than 5.8 nm, whereas larger molecules rarely reach centrosomes, indicating the existence of a size-dependent diffusion barrier at centrosomes. The permeability of this barrier is tightly regulated by branched actin filaments outside of centrosomes and it decreases during anaphase when branched actin temporally increases. The actin-based diffusion barrier gates microtubule nucleation by interfering with γ-tubulin ring complex recruitment. We propose that actin filaments spatiotemporally constrain protein complexes at centrosomes in a size-dependent manner.

Affinity and Valence Impact the Extent and Symmetry of Phase Separation of Multivalent Proteins

Biomolecular self-assembly spatially segregates proteins with a limited number of binding sites (valence) into condensates that coexist with a dilute phase. We develop a many-body lattice model for a three-component system of proteins with fixed valence in a solvent. We compare the predictions of the model to experimental phase diagrams that we measure in vivo, which allows us to vary specifically a binding site's affinity and valency. We find that the extent of phase separation varies exponentially with affinity and increases with valency. Valency alone determines the symmetry of the phase diagram.

Intermittent attractive interactions lead to microphase separation in nonmotile active matter

Nonmotile active matter exhibits a wide range of nonequilibrium collective phenomena yet examples are crucially lacking in the literature. We present a microscopic model inspired by the bacteria Neisseria meningitidis in which diffusive agents feel intermittent attractive forces. Through a formal coarse-graining procedure, we show that this truly scalar model of active matter exhibits the time-reversal-symmetry breaking terms defining the Active Model B+ class. In particular, we confirm the presence of microphase separation by solving the kinetic equations numerically. We show that the switching rate controlling the interactions provides a regulation mechanism tuning the typical cluster size, e.g., in populations of bacteria interacting via type IV pili.

A combined in silico and in vivo approach to the structure-function annotation of SPD-2 provides mechanistic insight into its functional diversity

Centrosomes are organelles that function as hubs of microtubule nucleation and organization, with key roles in organelle positioning, asymmetric cell division, ciliogenesis, and signaling. Aberrant centrosome number, structure or function is linked to neurodegenerative diseases, developmental abnormalities, ciliopathies, and tumor development. A major regulator of centrosome biogenesis and function in C. elegans is the conserved Spindle-defective protein 2 (SPD-2), a homolog of the human CEP-192 protein. CeSPD-2 is required for centrosome maturation, centriole duplication, spindle assembly and possibly cell polarity establishment. Despite its importance, the specific molecular mechanism of CeSPD-2 regulation and function is poorly understood. Here, we combined computational analysis with cell biology approaches to uncover possible structure-function relationships of CeSPD-2 that may shed mechanistic light on its function. Domain prediction analysis corroborated and refined previously identified coiled-coils and ASH (Aspm-SPD-2 Hydin) domains and identified new domains: a GEF domain, an Ig-like domain, and a PDZ-like domain. In addition to these predicted structural features, CeSPD-2 is also predicted to be intrinsically disordered. Surface electrostatic maps identified a large basic region unique to the ASH domain of CeSPD-2. This basic region overlaps with most of the residues predicted to be involved in protein-protein interactions. In vivo, ASH::GFP localized to centrosomes and centrosome-associated microtubules. Our analysis groups ASH domains, PapD, Usher chaperone domains, and Major Sperm Protein (MSP) domains into a single superfold within the larger Immunoglobulin superfamily. This study lays the groundwork for designing rational hypothesis-based experiments to uncover the mechanisms of CeSPD-2 function in vivo.Abbreviations: AIR, Aurora kinase; ASH, Aspm-SPD-2 Hydin; ASP, Abnormal Spindle Protein; ASPM, Abnormal Spindle-like Microcephaly-associated Protein; CC, coiled-coil; CDK, Cyclin-dependent Kinase; Ce, Caenorhabditis elegans; CEP, Centrosomal Protein; CPAP, centrosomal P4.1-associated protein; D, Drosophila; GAP, GTPase activating protein; GEF, GTPase guanine nucleotide exchange factor; Hs, Homo sapiens/Human; Ig, Immunoglobulin; MAP, Microtubule associated Protein; MSP, Major Sperm Protein; MDP, Major Sperm Domain-Containing Protein; OCRL-1, Golgi endocytic trafficking protein Inositol polyphosphate 5-phosphatase; PAR, abnormal embryonic PARtitioning of the cytosol; PCM, Pericentriolar material; PCMD, pericentriolar matrix deficient; PDZ, PSD95/Dlg-1/zo-1; PLK, Polo like kinase; RMSD, Root Mean Square Deviation; SAS, Spindle assembly abnormal proteins; SPD, Spindle-defective protein; TRAPP, TRAnsport Protein Particle; Xe, Xenopus; ZYG, zygote defective protein.

Rheology and Viscoelasticity of Proteins and Nucleic Acids Condensates

Phase separation is as familiar as watching vinegar separating from oil in vinaigrette. The observation that phase separation of proteins and nucleic acids is widespread in living cells has opened an entire field of research into the biological significance and the biophysical mechanisms of phase separation and protein condensation in biology. Recent evidence indicates that certain proteins and nucleic acids condensates are not simple liquids and instead display both viscous and elastic behaviors, which in turn may have biological significance. The aim of this Perspective is to review the state-of-the-art of this quickly emerging field focusing on the material and rheological properties of protein condensates. Finally, we discuss the different techniques that can be employed to quantify the viscoelasticity of condensates and highlight potential future directions and opportunities for interdisciplinary cross-talk between chemists, physicists, and biologists.

A unified statistical potential reveals that amino acid stickiness governs nonspecific recruitment of client proteins into condensates

Membraneless organelles are cellular compartments that form by liquid-liquid phase separation of one or more components. Other molecules, such as proteins and nucleic acids, will distribute between the cytoplasm and the liquid compartment in accordance with the thermodynamic drive to lower the free energy of the system. The resulting distribution colocalizes molecular species to carry out a diversity of functions. Two factors could drive this partitioning: the difference in solvation between the dilute versus dense phase and intermolecular interactions between the client and scaffold proteins. Here, we develop a set of knowledge-based potentials that allow for the direct comparison between stickiness, which is dominated by desolvation energy, and pairwise residue contact propensity terms. We use these scales to examine experimental data from two systems: protein cargo dissolving within phase-separated droplets made from FG repeat proteins of the nuclear pore complex and client proteins dissolving within phase-separated FUS droplets. These analyses reveal a close agreement between the stickiness of the client proteins and the experimentally determined values of the partition coefficients (R > 0.9), while pairwise residue contact propensities between client and scaffold show weaker correlations. Hence, the stickiness of client proteins is sufficient to explain their differential partitioning within these two phase-separated systems without taking into account the composition of the condensate. This result implies that selective trafficking of client proteins to distinct membraneless organelles requires recognition elements beyond the client sequence composition. STATEMENT: Empirical potentials for amino acid stickiness and pairwise residue contact propensities are derived. These scales are unique in that they enable direct comparison of desolvation versus contact terms. We find that partitioning of a client protein to a condensate is best explained by amino acid stickiness.

Size regulation of multiple organelles competing for a limiting subunit pool

How cells regulate the size of intracellular structures and organelles is a longstanding question. Recent experiments suggest that size control of intracellular structures is achieved through the depletion of a limiting subunit pool in the cytoplasm. While the limiting pool model ensures organelle-to-cell size scaling, it does not provide a mechanism for robust size control of multiple co-existing structures. Here we develop a generalized theory for size-dependent growth of intracellular structures to demonstrate that robust size control of multiple intracellular structures, competing for a limiting subunit pool, is achieved via a negative feedback between the growth rate and the size of the individual structure. This design principle captures size maintenance of a wide variety of subcellular structures, from cytoskeletal filaments to three-dimensional organelles. We identify the feedback motifs for structure size regulation based on known molecular processes, and compare our theory to existing models of size regulation in biological assemblies. Furthermore, we show that positive feedback between structure size and growth rate can lead to bistable size distribution and spontaneous size selection.

Organelle size control is essential for the proper physiological functioning of eukaryotic cells, but the underlying mechanisms of size regulation remain poorly understood. By developing a general theory for organelle size control, we show that robust size control of intracellular structures and organelles is achieved via a negative feedback between individual organelle size and their net growth rates. This design principle not only describes size maintenance of single organelles, but also ensures size stability of multiple co-existing organelles that are built from a limiting pool of subunits. Our results delineate the role of limiting pool as a size scaling mechanism rather than a size control mechanism, supporting the idea that negative feedback control of organelle size via depletion of a limiting subunit pool is not sufficient to maintain the size of multiple competing organelles. In the case of positive feedback between organelle size and growth rate, our model reproduces phenomena such as bistability in organelle size distribution and spontaneous emergence of cell polarity.

Centrioles generate a local pulse of Polo/PLK1 activity to initiate mitotic centrosome assembly

Mitotic centrosomes are formed when centrioles start to recruit large amounts of pericentriolar material (PCM) around themselves in preparation for mitosis. This centrosome "maturation" requires the centrioles and also Polo/PLK1 protein kinase. The PCM comprises several hundred proteins and, in Drosophila, Polo cooperates with the conserved centrosome proteins Spd-2/CEP192 and Cnn/CDK5RAP2 to assemble a PCM scaffold around the mother centriole that then recruits other PCM client proteins. We show here that in Drosophila syncytial blastoderm embryos, centrosomal Polo levels rise and fall during the assembly process-peaking, and then starting to decline, even as levels of the PCM scaffold continue to rise and plateau. Experiments and mathematical modelling indicate that a centriolar pulse of Polo activity, potentially generated by the interaction between Polo and its centriole receptor Ana1 (CEP295 in humans), could explain these unexpected scaffold assembly dynamics. We propose that centrioles generate a local pulse of Polo activity prior to mitotic entry to initiate centrosome maturation, explaining why centrioles and Polo/PLK1 are normally essential for this process.

Centrosome maturation requires phosphorylation-mediated sequential domain interactions of SPD-5

Centrosomes consist of two centrioles and surrounding pericentriolar material (PCM). PCM expands during mitosis in a process called centrosome maturation, in which PCM scaffold proteins play pivotal roles to recruit other centrosomal proteins. In C. elegans, the scaffold protein SPD-5 forms PCM scaffold in a PLK-1 phosphorylation-dependent manner. However, how phosphorylation of SPD-5 promotes PCM scaffold assembly is unclear. Here, we identified three functional domains of SPD-5 through in vivo domain analyses, and propose that sequential domain interactions of SPD-5 are required for mitotic PCM scaffold assembly. Firstly, SPD-5 is targeted to centrioles through direct interaction between its centriole localization (CL) domain and a centriolar protein PCMD-1. Then, intra- and intermolecular interaction between SPD-5 phospho-regulated multimerization (PReM) domain and the PReM association (PA) domain is enhanced by phosphorylation by PLK-1, which leads to PCM scaffold expansion. Our findings suggest that the sequential domain interactions of scaffold proteins mediated by Polo/PLK-1 phosphorylation is an evolutionarily conserved mechanism of PCM scaffold assembly.

Microenvironment-mediated cancer dormancy: Insights from metastability theory

Dormancy is an evolutionarily conserved protective mechanism widely observed in nature. A pathological example is found during cancer metastasis, where cancer cells disseminate from the primary tumor, home to secondary organs, and enter a growth-arrested state, which could last for decades. Recent studies have pointed toward the microenvironment being heavily involved in inducing, preserving, or ceasing this dormant state, with a strong focus on identifying specific molecular mechanisms and signaling pathways. Increasing evidence now suggests the existence of an interplay between intracellular as well as extracellular biochemical and mechanical cues in guiding such processes. Despite the inherent complexities associated with dormancy, proliferation, and growth of cancer cells and tumor tissues, viewing these phenomena from a physical perspective allows for a more global description, independent from many details of the systems. Building on the analogies between tissues and fluids and thermodynamic phase separation concepts, we classify a number of proposed mechanisms in terms of a thermodynamic metastability of the tumor with respect to growth. This can be governed by interaction with the microenvironment in the form of adherence (wetting) to a substrate or by mechanical confinement of the surrounding extracellular matrix. By drawing parallels with clinical and experimental data, we advance the notion that the local energy minima, or metastable states, emerging in the tissue droplet growth kinetics can be associated with a dormant state. Despite its simplicity, the provided framework captures several aspects associated with cancer dormancy and tumor growth.

Protein Aggregation and Disaggregation in Cells and Development

Protein aggregation is a feature of numerous neurodegenerative diseases. However, regulated, often reversible, formation of protein aggregates, also known as condensates, helps control a wide range of cellular activities including stress response, gene expression, memory, cell development and differentiation. This review presents examples of aggregates found in biological systems, how they are used, and cellular strategies that control aggregation and disaggregation. We include features of the aggregating proteins themselves, environmental factors, co-aggregates, post-translational modifications and well-known aggregation-directed activities that influence their formation, material state, stability and dissolution. We highlight the emerging roles of biomolecular condensates in early animal development, and disaggregation processing proteins that have recently been shown to play key roles in gametogenesis and embryogenesis.

Self-organized protein patterns: The MinCDE and ParABS systems

Self-organized protein patterns are of tremendous importance for biological decision-making processes. Protein patterns have been shown to identify the site of future cell division, establish cell polarity, and organize faithful DNA segregation. Intriguingly, several key concepts of pattern formation and regulation apply to a variety of different protein systems. Herein, we explore recent advances in the understanding of two prokaryotic pattern-forming systems: the MinCDE system, positioning the FtsZ ring precisely at the midcell, and the ParABS system, distributing newly synthesized DNA along with the cell. Despite differences in biological functionality, these two systems have remarkably similar molecular components, mechanisms, and strategies to achieve biological robustness.

Biophysical and Quantitative Principles of Centrosome Biogenesis and Structure

The centrosome is a main orchestrator of the animal cellular microtubule cytoskeleton. Dissecting its structure and assembly mechanisms has been a goal of cell biologists for over a century. In the last two decades, a good understanding of the molecular constituents of centrosomes has been achieved. Moreover, recent breakthroughs in electron and light microscopy techniques have enabled the inspection of the centrosome and the mapping of its components with unprecedented detail. However, we now need a profound and dynamic understanding of how these constituents interact in space and time. Here, we review the latest findings on the structural and molecular architecture of the centrosome and how its biogenesis is regulated, highlighting how biophysical techniques and principles as well as quantitative modeling are changing our understanding of this enigmatic cellular organelle. Expected final online publication date for the Annual Review of Cell and Developmental Biology, Volume 37 is October 2021. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.