Spherical Condenser Research Articles

Noncanonical Amino Acid Incorporation Modulates Condensate States of Intrinsically Disordered Proteins in Escherichia coli Cells.

Biomolecular condensates are distinct subcellular structures with on-demand material states and dynamics in living cells. However, strategies for modulating their material states and physicochemical properties are lacking. Here, we report a chemical strategy for modulating the condensate states of intrinsically disordered proteins in bacterial Escherichia coli cells. This is achieved by noncanonical amino acid (DOPA) incorporation into model resilin-like proteins (RLPs) to endow autonomous oxidative and coordinative cross-linking mechanisms. Biogenesis of spherical gel-like condensates is achieved upon heterologous expression of the DOPA-incorporated RLP in the cells at 30 °C. We reveal that liquid-liquid phase separation underlies the formation of liquid condensates, and this liquid-like state is metastable and its dynamics is compromised by the oxidative and coordinative cross-linkings that ultimately drive the liquid-to-gel transition. Therefore, this study has deepened our understanding of biomolecular condensation and offers a new chemical strategy to expand the landscape of condensation phenotypes of living cells.

Ring solids and supersolids in spherical shell-shaped dipolar Bose-Einstein condensates

Ring solids and supersolids in spherical shell-shaped dipolar Bose-Einstein condensates

Conserved and repetitive motifs in an intrinsically disordered protein drive ⍺-carboxysome assembly

All cyanobacteria and some chemoautotrophic bacteria fix CO2 into sugars using specialized proteinaceous compartments called carboxysomes. Carboxysomes enclose the enzymes Rubisco and carbonic anhydrase inside a layer of shell proteins to increase the CO2 concentration for efficient carbon fixation by Rubisco. In the ⍺-carboxysome lineage, a disordered and highly repetitive protein named CsoS2 is essential for carboxysome formation and function. Without it, the bacteria require high CO2 to grow. How does a protein predicted to be lacking structure serve as the architectural scaffold for such a vital cellular compartment? In this study, we identify key residues present in the repeats of CsoS2, VTG and Y, which are necessary for building functional ⍺-carboxysomes in vivo. These highly conserved and repetitive residues contribute to the multivalent binding interaction and phase separation behavior between CsoS2 and shell proteins. We also demonstrate 3-component reconstitution of CsoS2, Rubisco, and shell proteins into spherical condensates, and show the utility of reconstitution as a biochemical tool to study carboxysome biogenesis. The precise self-assembly of thousands of proteins is crucial for carboxysome formation, and understanding this process could enable their use in alternative biological hosts or industrial processes as effective tools to fix carbon.

Structure-Toxicity Relationship in Intermediate Fibrils from α-Synuclein Condensates.

The aberrant aggregation of α-synuclein (αS) into amyloid fibrils is associated with a range of highly debilitating neurodegenerative conditions, including Parkinson's disease. Although the structural properties of mature amyloids of αS are currently understood, the nature of transient protofilaments and fibrils that appear during αS aggregation remains elusive. Using solid-state nuclear magnetic resonance (ssNMR), cryogenic electron microscopy (cryo-EM), and biophysical methods, we here characterized intermediate amyloid fibrils of αS forming during the aggregation from liquid-like spherical condensates to mature amyloids adopting the structure of pathologically observed aggregates. These transient amyloid intermediates, which induce significant levels of cytotoxicity when incubated with neuronal cells, were found to be stabilized by a small core in an antiparallel β-sheet conformation, with a disordered N-terminal region of the protein remaining available to mediate membrane binding. In contrast, mature amyloids that subsequently appear during the aggregation showed different structural and biological properties, including low levels of cytotoxicity, a rearranged structured core embedding also the N-terminal region, and a reduced propensity to interact with the membrane. The characterization of these two fibrillar forms of αS, and the use of antibodies and designed mutants, enabled us to clarify the role of critical structural elements endowing intermediate amyloid species with the ability to interact with membranes and induce cytotoxicity.

Phase Separation and Fibrillization of Human Annexin A7 Are Mediated by Its Proline-Rich Domain.

Human annexin A7, a calcium- and phospholipid-binding protein, governs calcium homeostasis, plasma membrane repair, apoptosis, and tumor progression. A7 contains an N-terminal proline-rich domain (PRD; 180 residues, ∼24% prolines) that determines its functional specificity. Using microscopy and dye-binding assays, we show that recombinant A7 and its isolated PRD spontaneously phase separate into spherical condensates, which subsequently transform into β-sheet-rich fibrils. We demonstrate that fibrillization of A7-PRD proceeds via primary nucleation and fibril-catalyzed secondary nucleation processes, as determined by chemical kinetics, providing a mechanistic basis for its amyloid assembly. This study confirms and highlights a subclass of eukaryotic PRDs prone to forming aggregates with important physiological and pathological implications.

RAP80 Phase Separation at DNA Double-Strand Break Promotes BRCA1 Recruitment and Tumor Radio-Resistance

RAP80 has been characterized as a component of the BRCA1-A complex and is responsible for the recruitment of BRCA1 to DNA double-strand breaks (DSBs). However, we and others found that the recruitment of RAP80 and BRCA1 are not absolutely temporally synchronized, indicating that other mechanisms, apart from physical interaction, may be implicated. Recently, we and other groups have reported that liquid-liquid phase separation (LLPS) is a pivotal mechanism underlying DNA repair factors condensation at DSBs and their function. In this study, we aim to disclose whether RAP80 undergoes LLPS at DSBs and whether it is required for BRCA1 recruitment. To verify RAP80 is an LLPS protein and its function in DNA damage response (DDR): (1) candidate-mEGFP fusion protein formed condensates in cells and showed fluorescence recovery after photobleaching (FRAP); (2) candidate protein was expressed in Escherichia coli and purified with GST; (3) intrinsically disordered region (IDR) of RAP80 were predicted and tested in cell and in vitro; (4) lentivirus were used to construct RAP80-Knock out (KO) and RAP80 re-expression cell lines; (5) length gradient K63 poly-ubiquitin chains were chemically synthesized and incubated with RAP80 protein in vitro; (6) BRCA1 and RAP80 location were determined through immunofluorescence; (7) RAP80 protein expression in tissue was determined by IHC staining. Thin layer scanning and 3D reconstruction of the RAP80-mEGFP-expressing cells under a fluorescence microscope showed that RAP80-mEGFP formed spherical condensates with fast FRAP. Observation of purified proteins revealed that GST-RAP80-mEGFP protein formed liquid-like droplets, presenting as a FRAP and the fusion event among adjacent droplets. PEG-8000 and Ficol-400 strengthened the formation of GST-RAP80-mEGFP droplets in vitro. Later, we used a previously developed optoIDR tool to verify that IDR1 (1-254aa) is critical for RAP80 LLPS. To investigate whether the interaction between RAP80 and K63 poly-ubiquitin chains could enhance the condensation of RAP80, we chemically synthesized K63 ubiquitin chains and incubated them with purified GST-RAP80-mCherry proteins. The results showed that supplementation of ubiquitin multipolymer (poly-ubiquitin) significantly induced the LLPS of RAP80, and the ability of RAP80 condensates formation potency was positively correlated with the length of the ubiquitin chain. Consistent with their LLPS capacity, RAP80-WT-mEGFP, RAP80-(IDR1+AIR)-mEGFP groups showed prominent BRCA1 foci, while RAP80-IDR1-mEGFP and RAP80-(SIM+UIM)-mEGFP groups showed delayed BRCA1 recruitment. In rectal cancer tissues, positive staining of the RAP80 protein was mainly observed in the nucleus of cancer cells and high RAP80 expression was correlated with a shorter overall survival time. RAP80 undergoes LLPS to form liquid-like condensates at DSB sites, which is important for BRCA1 recruitment and enhances tumor radio-resistance.

A Third Angular Momentum of Photons

Photons that acquire orbital angular momentum move in a helical path and are observed as a light ring. During helical motion, if a force is applied perpendicular to the direction of motion, an additional radial angular momentum is introduced, and alternate dark spots appear on the light ring. Here, a third, centrifugal angular momentum has been added by twisting the helical path further according to the three-step hierarchical assembly of helical organic nanowires. Attaining a third angular momentum is the theoretical limit for a photon. The additional angular momentum converts the dimensionless photon to a hollow spherical photon condensate with interactive dark regions. A stream of these photon condensates can interfere like a wave or disintegrate like matter, similar to the behavior of electrons.

Visualization of Balbiani Body disassembly during human primordial follicle activation.

Dormant human oocytes contain a perinuclear super-organelle, called the Balbiani Body, which is not present in mature oocytes. Here, we use confocal imaging to visualize two Balbiani Body markers-mitochondria and the DEAD-box helicase DDX4-in preantral follicles isolated from a 20-year-old female patient. In primordial follicles, mitochondria were concentrated in a ring near the oocyte nucleus, while DDX4 formed adjacent micron-scale spherical condensates. In primary and secondary follicles, the mitochondria were dispersed throughout the oocyte cytoplasm, and large DDX4 condensates were not visible. Our data suggest that the Balbiani Body breaks down during the primordial to primary follicle transition, thus releasing mitochondria and soluble DDX4 protein into the oocyte cytoplasm.

Molecular organization of the early stages of nucleosome phase separation visualized by cryo-electron tomography

It has been proposed that the intrinsic property of nucleosome arrays to undergo liquid-liquid phase separation (LLPS) invitro is responsible for chromatin domain organization invivo. However, understanding nucleosomal LLPS has been hindered by the challenge to characterize the structure of the resulting heterogeneous condensates. We used cryo-electron tomography and deep-learning-based 3D reconstruction/segmentation to determine the molecular organization of condensates at various stages of LLPS. We show that nucleosomal LLPS involves a two-step process: a spinodal decomposition process yielding irregular condensates, followed by their unfavorable conversion into more compact, spherical nuclei that grow into larger spherical aggregates through accretion of spinodal materials or by fusion with other spherical condensates. Histone H1 catalyzes more than 10-fold the spinodal-to-spherical conversion. We propose that this transition involves exposure of nucleosome hydrophobic surfaces causing modified inter-nucleosome interactions. These results suggest a physical mechanism by which chromatin may transition from interphase to metaphase structures.

Semi-analytical model for the heat conduction resistance of a single spherical condensate droplet

The evolution and heat transfer of a single spherical condensate droplet on a superhydrophobic surface (SHS) can be modeled by the droplet thermal resistance network. The calculation of the heat conduction resistance of a single spherical condensate droplet (Rd) is a fundamental problem in analyzing the droplet thermal resistance network. Till now, the majority of researchers have used Kim's formula to calculate Rd. However, the results from Kim's formula have errors above 85% compared to those from the CFD software (ANSYS Fluent). In this paper, we analyze the reason for inaccuracy of Kim's formula. Taking two-dimensional droplet heat conduction into consideration, we gain the theoretical temperature field function inside the condensate droplet by utilizing the conformal mapping. Basing on calculation of heat transfer rate through the droplet and ANSYS Fluent analysis, we put forward a new semi-analytical model to calculate Rd. We verify and find that the results from our new model have errors less than 13% compared to those from ANSYS Fluent. It means that our new semi-analytical model is more accurate than Kim's formula. We calculate the Rd proportion of the overall heat transfer resistance and find that the application of our model can obviously decrease heat transfer calculation errors for big droplets (r>16μm) with large contact angles (θ>120∘). The new semi-analytical model for the heat conduction resistance of a single spherical condensate droplet is promising in the sense that it might replace Kim's model to become a novel design criterion of enhanced heat transfer SHSs.

In vivo reconstitution finds multivalent RNA-RNA interactions as drivers of mesh-like condensates.

Liquid-like condensates have been thought to be sphere-like. Recently, various condensates with filamentous morphology have been observed in cells. One such condensate is the TIS granule network that shares a large surface area with the rough endoplasmic reticulum and is important for membrane protein trafficking. It has been unclear how condensates with mesh-like shapes but dynamic protein components are formed. In vitro and in vivo reconstitution experiments revealed that the minimal components are a multivalent RNA-binding protein that concentrates RNAs that are able to form extensive intermolecular mRNA-mRNA interactions. mRNAs with large unstructured regions have a high propensity to form a pervasive intermolecular interaction network that acts as condensate skeleton. The underlying RNA matrix prevents full fusion of spherical liquid-like condensates, thus driving the formation of irregularly shaped membraneless organelles. The resulting large surface area may promote interactions at the condensate surface and at the interface with other organelles.

Autophosphorylation-induced self-assembly and STIL-dependent reinforcement underlie Plk4’s ring-to-dot localization conversion around a human centriole

ABSTRACT Polo-like kinase 4 (Plk4) is a key regulator of centriole biogenesis. Studies have shown that Plk4 undergoes dynamic relocalization from a ring-like pattern around a centriole to a dot-like morphology at the procentriole assembly site and this event is central for inducing centriole biogenesis. However, the detailed mechanisms underlying Plk4’s capacity to drive its symmetry-breaking ring-to-dot relocalization remain largely unknown. Here, we showed that Plk4 self-initiates this process in an autophosphorylation–dependent manner and that STIL, its downstream target, is not required for this event. Time-dependent analyses with mEOS-fused photoconvertible Plk4 revealed that a portion of ring-state Plk4 acquires a capacity, presumably through autophosphorylation, to linger around a centriole, ultimately generating a dot-state morphology. Interestingly, Plk4 WT, but not its catalytically inactive mutant, showed the ability to form a nanoscale spherical assembly in the cytosol of human cells or heterologous E. coli, demonstrating its autophosphorylation-dependent self-organizing capacity. At the biochemical level, Plk4 – unlike its N-terminal βTrCP degron motif – robustly autophosphorylated the PC3 SSTT motif within its C-terminal cryptic polo-box, an event critical for inducing its physical clustering. Additional in vivo experiments showed that although STIL was not required for Plk4’s initial ring-to-dot conversion, coexpressed STIL greatly enhanced Plk4’s ability to generate a spherical condensate and recruit Sas6, a major component of the centriolar cartwheel structure. We propose that Plk4’s autophosphorylation-induced clustering is sufficient to induce its ring-to-dot localization conversion and that subsequently recruited STIL potentiates this process to generate a procentriole assembly body critical for Plk4-dependent centriole biogenesis.

Lysine acetyltransferase Tip60 acetylates the APP adaptor Fe65 to increase its transcriptional activity.

Proteolytic processing of the amyloid precursor protein (APP) releases the APP intracellular domain (AICD) from the membrane. Bound to the APP adaptor protein Fe65 and the lysine acetyltransferase (KAT) Tip60, AICD translocates to the nucleus. Here, the complex forms spherical condensates at sites of endogenous target genes, termed AFT spots (AICD-Fe65-Tip60). We show that loss of Tip60 KAT activity prevents autoacetylation, reduces binding of Fe65 and abolishes Fe65-mediated stabilization of Tip60. Autoacetylation is a prerequisite for AFT spot formation, with KAT-deficient Tip60 retained together with Fe65 in speckles. We identify lysine residues 204 and 701 of Fe65 as acetylation targets of Tip60. We do not detect acetylation of AICD. Mutation of Fe65 K204 and K701 toglutamine, mimicking acetylation-induced charge neutralization, increases the transcriptional activity of Fe65 whereas Tip60 inhibition reduces it. The lysine deacetylase (KDAC) class III Sirt1 deacetylates Fe65 and pharmacological modulation of Sirt1 activity regulates Fe65 transcriptional activity. A second acetylation/deacetylation cycle, conducted by CBP and class I/II KDACs atdifferent lysine residues, regulates stability of Fe65. Thisis the first report describing a role for acetylation intheregulation of Fe65 transcriptional activity, with Tip60being the only KAT tested that supports AFT spot formation.

A Multivalent RNA Matrix Drives Formation of Mesh-Like Condensates

The TIS granule network is a constitutively expressed membraneless organelle that is important for trafficking of membrane proteins and is formed through assembly of the RNA-binding protein TIS11B. TIS granules have a mesh-like morphology that allows them to share a lot of surface area with the rough endoplasmic reticulum. It has been unclear how condensates with filamentous shapes, but dynamic protein components are formed. In vitro reconstitution of TIS granule-like condensates revealed that mRNAs with large unstructured regions, that are abundant in a subset of human 3′UTRs, are required for formation of mesh-like condensates. The unstructured regions allow formation of an extensive intermolecular mRNA-mRNA interaction network that acts as condensate skeleton. The underlying RNA matrix prevents full fusion of spherical liquid-like condensates, thus driving the formation of irregularly shaped membraneless organelles. The resulting large surface area promotes interactions at the condensate surface and at the interface with other organelles.

Phase separation of Polo-like kinase 4 by autoactivation and clustering drives centriole biogenesis

Tight control of centriole duplication is critical for normal chromosome segregation and the maintenance of genomic stability. Polo-like kinase 4 (Plk4) is a key regulator of centriole biogenesis. How Plk4 dynamically promotes its symmetry-breaking relocalization and achieves its procentriole-assembly state remains unknown. Here we show that Plk4 is a unique kinase that utilizes its autophosphorylated noncatalytic cryptic polo-box (CPB) to phase separate and generate a nanoscale spherical condensate. Analyses of the crystal structure of a phospho-mimicking, condensation-proficient CPB mutant reveal that a disordered loop at the CPB PB2-tip region is critically required for Plk4 to generate condensates and induce procentriole assembly. CPB phosphorylation also promotes Plk4’s dissociation from the Cep152 tether while binding to downstream STIL, thus allowing Plk4 condensate to serve as an assembling body for centriole biogenesis. This study uncovers the mechanism underlying Plk4 activation and may offer strategies for anti-Plk4 intervention against genomic instability and cancer.

The Effects of Different Catalysts, Substituted Aromatic Aldehydes on One-Pot Three-Component Biginelli Reaction.

The Biginelli reaction, first reported in 1893, is one great example of the important multicomponent reactions reported from 1893. Under the same conditions, the influence of the common catalysts on the yield of the Biginelli reaction was investigated. To a round-bottom flask equipped with a spherical condenser were added 1,3- dicarbonyl compound (1.0 eq), urea (1.45 eq), aromatic aldehyde (1.0 eq), catalyst and methanol. The mixture was heated at reflux for 16 h. After cooling off, the mixture was filtered and washed with cold methanol to give DHPMs. Reaction solution was further purified by recrystallization with petroleum ether and ethyl acetate. Six catalytic systems, different 1,3-dicarbonyl compounds and different substituted aromatic aldehydes with varied substitutions are described for the Biginelli reaction. An analysis was also performed to study the factors that affect the yield of the reaction. When 1,3-dicarbonyl compound was ethyl acetoacetate, the CuCl/ conc.H2SO4 system gave the highest yield (90.5%). While when acetoacetamide was used, the yields of DHPMs in presence of PTSA/conc. HCl, conc. HCl or FeCl3•6H2O were all over 90%. Nine DHPMs with different substituents were obtained. The Lewis acid or mixed catalyst had no significant advantage over a single protonic acid as catalyst. Conc. HCl as the catalyst was found to be the most effective condition for the preparation of DHPMs. The aromatic aldehyde with weak electron-withdrawing substituent such as Br resulted in the best yield.

On local behavior of one class of inverse mappings

As is known, the local behavior of maps is one of the most important problems of analysis. This, in particular, relates to the study of mappings with bounded and finite distortion, which have been actively studied recently. As for this work, here we solve the problem of the behavior of maps, the inverse of which satisfies the Poletsky inequality. The main result is the statement about the equicontinuity of the indicated mappings inside the domain in the case when the majorant corresponding to the distortion of the module under the mapping is integrable in the original domain. It should be emphasized that the proof of this result is largely geometric, at the same time, it uses only the conditions of boundedness of the direct and mapped domains and does not involve any requirements on their boundaries. The study of families of mappings inverse to a given class may turn out to be trivial if we are talking about quasiconformal mappings. In the latter case, we do not go beyond the limits of the class under study in the transition to inverse maps. Nevertheless, when studying mappings with unbounded characteristic, this question is quite substantial, as simple examples of the corresponding classes show. The idea of the proof of the main result is based on the fact that the inner points of an arbitrary domain are weakly flat. The last statement can be called the Väisälä lemma, which was established in his monograph and related to families of curves joining two continua between the plates of a spherical condenser. The proof is also based on the fact that the module of families of curves joining two converging continua in a good domain must tend to infinity. In this case, the neighborhood of some inner point of the mapped domain serves as ''good'' region, in which we check the equicontinuity of the inverse family of maps. The results of this article are applicable to many other classes of mappings such as mappings with a finite distortion in the sense of Iwaniec, Sobolev classes on the plane and in space, and so on.

Three-dimensional splitting dynamics of giant vortices in Bose-Einstein condensates

We study the splitting dynamics of giant vortices in dilute Bose-Einstein condensates by numerically integrating the three-dimensional Gross-Pitaevskii equation in time. By taking advantage of tetrahedral tiling in the spatial discretization, we decrease the error and increase the reliability of the numerical method. An extensive survey of vortex splitting symmetries is presented for different aspect ratios of the harmonic trapping potential. The symmetries of the splitting patterns observed in the simulated dynamics are found to be in good agreement with predictions obtained by solving the dominant dynamical instabilities from the corresponding Bogoliubov equations. Furthermore, we observe intertwining of the split vortices in prolate condensates and a split-and-revival phenomenon in a spherical condensate.

Physics of hollow Bose-Einstein condensates

Bose-Einstein condensate shells, while occurring in ultracold systems of coexisting phases and potentially within neutron stars, have yet to be realized in isolation on Earth due to the experimental challenge of overcoming gravitational sag. Motivated by the expected realization of hollow condensates by the space-based Cold Atomic Laboratory in microgravity conditions, we study a spherical condensate undergoing a topological change from a filled sphere to a hollow shell. We argue that the collective modes of the system show marked and robust signatures of this hollowing transition accompanied by the appearance of a new boundary. In particular, we demonstrate that the frequency spectrum of the breathing modes shows a pronounced depression as it evolves from the filled-sphere limit to the hollowing transition. Furthermore, when the center of the system becomes hollow surface modes show a global restructuring of their spectrum due to the availability of a new, inner, surface for supporting density distortions. We pinpoint universal features of this topological transition as well as analyse the spectral evolution of collective modes in the experimentally relevant case of a bubble-trap.

Particle-number projection in the finite-temperature mean-field approximation

Calculation of statistical properties of nuclei in a finite-temperature mean-field theory requires projection onto good particle number, since the theory is formulated in the grand canonical ensemble. This projection is usually carried out in a saddle-point approximation. Here we derive formulas for an exact particle-number projection of the finite-temperature mean-field solution. We consider both deformed nuclei, in which the pairing condensate is weak and the Hartree-Fock (HF) approximation is the appropriate mean-field theory, and nuclei with strong pairing condensates, in which the appropriate theory is the Hartree-Fock-Bogoliubov (HFB) approximation, a method that explicitly violates particle-number conservation. For the HFB approximation, we present a general projection formula for a condensate that is time-reversal invariant and a simpler formula for the Bardeen-Cooper-Schrieffer (BCS) limit, which is realized in nuclei with spherical condensates. We apply the method to three heavy nuclei: a typical deformed nucleus $^{162}$Dy, a typical spherical nucleus $^{148}$Sm, and a transitional nucleus $^{150}$Sm in which the pairing condensate is deformed. We compare the results of this projection with results from the saddle-point approximation and exact shell model Monte Carlo calculations. We find that the approximate canonical HF entropy in the particle-number projection decreases monotonically to zero in the limit when the temperature goes to zero. However, in a nucleus with a strong pairing condensate, the approximate canonical HFB entropy in the particle-number projection decreases monotonically to a negative value, reflecting the violation of particle-number conservation. Computationally, the exact particle-number projection is more efficient than calculating the derivatives required in the saddle-point approximation.