Dynamics Of Condensate Research Articles

Asynchronous quantum Kármán vortex street in two-component Bose-Einstein condensate with PT symmetric potential

The dynamics of a miscible two-component Bose-Einstein condensate (BEC) with PT (parity-time) symmetric potential are investigated numerically. The dynamical behaviors of the system is described by Gross-Pitaevskii (GP) equations under the mean-field theory. Firstly, the ground state of the system is obtained by the imaginary-time propagation method. Then dynamical behaviors are numerically simulated by the time-splitting Fourier pseudo-spectral approach under periodic boundary conditions. By adjusting the width and velocity of the obstacle potential, various patterns such as no vortex, oblique drifting vortex dipole, V-shaped vortex pairs, irregular quantum turbulence and combined modes are studied. It is noted that the shedding vortex pairs in components 1 and 2 are staggered, which is called “the asynchronous quantum Kármán vortex street”. Here, the ratio of the distance between two vortex pairs in one row to the distance between vortex rows is approximately 0.18, which is less than the stability criterion 0.28 of classical fluid. We calculated the drag force acting on the obstacle potential during generation of the asynchronous quantum Kármán vortex street. It is found that periodical oscillation of the drag force is generated via drifting up or down of the vortex pairs. Meanwhile, we analyzed the influence of the imaginary part of the PT symmetric potential with gain-loss for wake. The trajectory and frequency of the vortex are changed, due to the imaginary part breaks the local symmetry of the system. In addition, the imaginary part affects the stability of the asynchronous quantum Kármán vortex street. Lots of numerical simulations are carried out to determine the parameter regions of various vortex shedding modes. We also proposed an experimental protocol to realize the asynchronous quantum Kármán vortex street in the miscible two-component BEC with PT symmetric potential.

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.

Electron Microscopy Analysis of Membraneless Condensates in Plant Cells.

Biomolecular condensates are triggered by multivalent interactions conferred by the intrinsically disordered regions and/or interacting domains within the constituents. While light microscopy has provided powerful tools to study the dynamics of intracellular condensates, electron microscopy (EM) gives more detailed insights into their ultrastructure and spatial connectivity with membrane system. In this chapter, we describe the methods for detecting the membraneless condensates in plant cells by high-pressure freezing -based EM coupled with immuno-gold labeling and correlative light electron microscopy techniques, which may benefit researchers in future studies.

A chaperone-like function of FUS ensures TAZ condensate dynamics and transcriptional activation.

The Hippo pathway has important roles in organ development, tissue homeostasis and tumour growth. Its downstream effector TAZ is a transcriptional coactivator that promotes target gene expression through the formation of biomolecular condensates. However, the mechanisms that regulate the biophysical properties of TAZ condensates to enable Hippo signalling are not well understood. Here using chemical crosslinking combined with an unbiased proteomics approach, we show that FUS associates with TAZ condensates and exerts a chaperone-like effect to maintain their proper liquidity and robust transcriptional activity. Mechanistically, the low complexity sequence domain of FUS targets the coiled-coil domain of TAZ in a phosphorylation-regulated manner, which ensures the liquidity and dynamicity of TAZ condensates. In cells lacking FUS, TAZ condensates transition into gel-like or solid-like assembles with immobilized TAZ, which leads to reduced expression of target genes and inhibition of pro-tumorigenic activity. Thus, our findings identify a chaperone-like function of FUS in Hippo regulation and demonstrate that appropriate biophysical properties of transcriptional condensates are essential for gene activation.

Liquid-Liquid Phase Separation of the Intrinsically Disordered Domain of the Fused in Sarcoma Protein Results in Substantial Slowing of Hydration Dynamics.

Formation of liquid condensates plays a critical role in biology via localization of different components or via altered hydrodynamic transport, yet the hydrogen-bonding environment within condensates, pivotal for solvation, has remained elusive. We explore the hydrogen-bond dynamics within condensates formed by the low-complexity domain of the fused in sarcoma protein. Probing the hydrogen-bond dynamics sensed by condensate proteins using two-dimensional infrared spectroscopy of the protein amide I vibrations, we find that frequency-frequency correlations of the amide I vibration decay on a picosecond time scale. Interestingly, these dynamics are markedly slower for proteins in the condensate than in a homogeneous protein solution, indicative of different hydration dynamics. All-atom molecular dynamics simulations confirm that lifetimes of hydrogen-bonds between water and the protein are longer in the condensates than in the protein in solution. Altered hydrogen-bonding dynamics may contribute to unique solvation and reaction dynamics in such condensates.

On the characterisation of fragmented Bose–Einstein condensation and its emergent effective evolution

Fragmented Bose–Einstein condensates are large systems of identical bosons displaying multiple macroscopic occupations of one-body states, in a suitable sense. The quest for an effective dynamics of the fragmented condensate at the leading order in the number of particles, in analogy to the much more controlled scenario for complete condensation in one single state, is deceptive both because characterising fragmentation solely in terms of reduced density matrices is unsatisfactory and ambiguous, and because as soon as the time evolution starts the rank of the reduced marginals generically passes from finite to infinite, which is a signature of a transfer of occupations on infinitely many more one-body states. In this work we review these difficulties, we refine previous characterisations of fragmented condensates in terms of marginals, and we provide a quantitative rate of convergence to the leading effective dynamics in the double limit of infinitely many particles and infinite energy gap.

Emerging Roles of Ubiquitination in Biomolecular Condensates.

Biomolecular condensates are dynamic non-membrane-bound macromolecular high-order assemblies that participate in a growing list of cellular processes, such as transcription, the cell cycle, etc. Disturbed dynamics of biomolecular condensates are associated with many diseases, including cancer and neurodegeneration. Extensive efforts have been devoted to uncovering the molecular and biochemical grammar governing the dynamics of biomolecular condensates and establishing the critical roles of protein posttranslational modifications (PTMs) in this process. Here, we summarize the regulatory roles of ubiquitination (a major form of cellular PTM) in the dynamics of biomolecular condensates. We propose that these regulatory mechanisms can be harnessed to combat many diseases.

BLM helicase protein negatively regulates stress granule formation through unwinding RNA G-quadruplex structures.

Bloom's syndrome (BLM) protein is a known nuclear helicase that is able to unwind DNA secondary structures such as G-quadruplexes (G4s). However, its role in the regulation of cytoplasmic processes that involve RNA G-quadruplexes (rG4s) has not been previously studied. Here, we demonstrate that BLM is recruited to stress granules (SGs), which are cytoplasmic biomolecular condensates composed of RNAs and RNA-binding proteins. BLM is enriched in SGs upon different stress conditions and in an rG4-dependent manner. Also, we show that BLM unwinds rG4s and acts as a negative regulator of SG formation. Altogether, our data expand the cellular activity of BLM and shed light on the function that helicases play in the dynamics of biomolecular condensates.

ATP-induced cross-linking of a biomolecular condensate

DEAD-box helicases are important regulators of biomolecular condensates. However, the mechanisms through which these enzymes affect the dynamics of biomolecular condensates have not been systematically explored. Here, we demonstrate the mechanism by which the mutation of a DEAD-box helicase’s catalytic core alters ribonucleoprotein condensate dynamics in the presence of ATP. Through altering RNA length within the system, we are able to attribute the altered biomolecular dynamics and material properties to physical cross-linking of RNA facilitated by the mutant helicase. These results suggest that mutant condensates approach a gel transition when RNA length is increased to lengths comparable to eukaryotic mRNA. Lastly, we show that this cross-linking effect is tunable with ATP concentration, uncovering a system whose RNA mobility and material properties vary with enzyme activity. More generally, these findings point to a fundamental mechanism for modulating condensate dynamics and emergent material properties through nonequilibrium, molecular-scale interactions.

Protein compactness and interaction valency define the architecture of a biomolecular condensate across scales.

Non-membrane-bound biomolecular condensates have been proposed to represent an important mode of subcellular organization in diverse biological settings. However, the fundamental principles governing the spatial organization and dynamics of condensates at the atomistic level remain unclear. The Saccharomyces cerevisiae Lge1 protein is required for histone H2B ubiquitination and its N-terminal intrinsically disordered fragment (Lge11-80) undergoes robust phase separation. This study connects single- and multi-chain all-atom molecular dynamics simulations of Lge11-80 with the in vitro behavior of Lge11-80 condensates. Analysis of modeled protein-protein interactions elucidates the key determinants of Lge11-80 condensate formation and links configurational entropy, valency, and compactness of proteins inside the condensates. A newly derived analytical formalism, related to colloid fractal cluster formation, describes condensate architecture across length scales as a function of protein valency and compactness. In particular, the formalism provides an atomistically resolved model of Lge11-80 condensates on the scale of hundreds of nanometers starting from individual protein conformers captured in simulations. The simulation-derived fractal dimensions of condensates of Lge11-80 and its mutants agree with their in vitro morphologies. The presented framework enables a multiscale description of biomolecular condensates and embeds their study in a wider context of colloid self-organization.

Extreme dynamics in a biomolecular condensate.

Proteins and nucleic acids can phase-separate in the cell to form concentrated biomolecular condensates1-4. The functions of condensatesspan many length scales: they modulate interactions and chemical reactions at the molecular scale5, organize biochemical processes at the mesoscale6 and compartmentalize cells4. Understanding the underlying mechanisms of these processeswill require detailed knowledge of the rich dynamics across these scales7. The mesoscopic dynamics of biomolecular condensates have been extensively characterized8, but their behaviour at the molecular scale has remained more elusive. Here, as an example of biomolecular phase separation, we study complexcoacervates of two highly and oppositely charged disordered human proteins9. Their dense phase is 1,000 times more concentrated than the dilute phase, and the resulting percolated interaction network10 leads to a bulk viscosity 300 times greater than that of water. However, single-molecule spectroscopy optimized for measurements within individual droplets reveals that at the molecular scale, the disordered proteins remain exceedingly dynamic, with their chain configurations interconverting on submicrosecond timescales. Massive all-atom moleculardynamics simulations reproduce the experimental observations and explain this apparent discrepancy: the underlying interactions between individual charged side chains are short-lived and exchange on a pico- to nanosecond timescale. Our results indicate that, despite the high macroscopic viscosity of phase-separated systems, local biomolecular rearrangements required for efficient reactions at the molecular scale can remain rapid.

A model for organization and regulation of nuclear condensates by gene activity

Condensation by phase separation has recently emerged as a mechanism underlying many nuclear compartments essential for cellular functions. Nuclear condensates enrich nucleic acids and proteins, localize to specific genomic regions, and often promote gene expression. How diverse properties of nuclear condensates are shaped by gene organization and activity is poorly understood. Here, we develop a physics-based model to interrogate how spatially-varying transcription activity impacts condensate properties and dynamics. Our model predicts that spatial clustering of active genes can enable precise localization and de novo nucleation of condensates. Strong clustering and high activity results in aspherical condensate morphologies. Condensates can flow towards distant gene clusters and competition between multiple clusters lead to stretched morphologies and activity-dependent repositioning. Overall, our model predicts and recapitulates morphological and dynamical features of diverse nuclear condensates and offers a unified mechanistic framework to study the interplay between non-equilibrium processes, spatially-varying transcription, and multicomponent condensates in cell biology.

Dynamical excitation of spin-orbit coupled spin-1 Bose-Einstein condensate in a narrow box trap

We demonstrate the dynamics of a spin-1 ferromagnetic Bose-Einstein condensate (BEC) with Rashba spin-orbit (SO) coupling in a narrow square box trap when an obstacle potential is moving in it. The ground-state energy would be enhanced with the box trap becomes narrower. From the Bogoliubov analytical excitation spectrum lines, we obtain the dependence of critical excitation velocity and momentum on the trap geometry under different SO coupling. Numerically, when the obstacle moves along the direction of plane wave ground state, in addition to spin-density waves being excited periodically, a long density belt accompanied by density island chain is found ahead of the obstacle. Such density distribution is mainly determined by the narrow box trap. A series of density islands arranged more closely are generated as the obstacle moves along opposite direction. There exists another velocity threshold for different density excitation under a larger SO coupling.

Salt-Added Solutions of Markov Polyampholytes: Diagram of States, Antipolyelectrolyte Effect, and Self-Coacervate Dynamics

Field-theoretic and scaling approaches are combined to predict conformational behaviors of single-chain globally neutral polyampholytes (PAs) in the presence of salt, the viscosity of their dilute solutions, and the rheology of condensed self-coacervate phases. To reveal the role of the monomer sequence, we consider PAs with Markov statistics of positive and negative charges. The diagram of globular regimes of single-chain PAs in Θ solvent is constructed with the coordinates of the charge blockiness and salt concentrations. For highly flexible chains, it contains six scaling regimes corresponding to low/high salt concentrations and (i) almost alternating, (ii) random correlated, and (iii) highly blocky sequences of ionic monomers. At increasing salt concentration, PAs of any sequence swell until reaching an ideal-coil size. The amplitude of the salt-induced globule-to-coil transition increases with increasing charge blockiness. So does the change in the viscosity of dilute PA solutions, indicating the sequence specificity in the antipolyelectrolyte effect. The similarity between the internal structure of the globules and macroscopic self-coacervate phases enables prediction of the viscosity of the latter. The respective scaling dependencies for self-coacervates of short unentangled and long entangled PAs are provided. Self-coacervate viscosity is the highest for the most blocky PAs and, for any sequence, decreases with the addition of salt. Our findings serve as important guidelines for understanding the dynamics of intracellular condensates, which form from polyampholytic disordered proteins/regions and exhibit the salt-induced viscosity drop described herein.

Quench-induced chaotic dynamics of Anderson-localized interacting Bose-Einstein condensates in one dimension

We study the effect of atomic interaction on the localization and the associated dynamics of Bose-Einstein condensates in a one-dimensional quasiperiodic optical lattice and random disordered potentials. When the interactions are absent, the condensates exhibit localization, which weakens as we increase the interaction strength beyond a threshold value for both potential types. We inspect the localized and delocalized states by perturbing the system via quenching the interaction strength instantaneously to zero and studying the dynamics of the condensate, which we further corroborate using the out-of-time-order correlator. The temporal behavior of the time correlator displays regular dynamics for the localized state, while it shows temporal chaos for the delocalized state. We confirm this dynamical behavior by analyzing the power spectral density of the time correlator. We further identify that the condensate admits a quasiperiodic route to chaotic dynamics for both the potentials. Finally, we present the variation of the maximal Lyapunov exponents for different nonlinearity and disorder strengths that have a positive value in the regime where the time-correlator function shows chaotic behavior. Through this, we establish the strong connection between the spatially delocalized state of the condensate and its temporal chaos.

From locality to irregularity: introducing local quenches in massive scalar field theory

In this paper, we initiate the study of operator local quenches in non-conformal field theories. We consider the dynamics of excited local states in massive scalar field theory in an arbitrary spacetime dimension and generalize the well-known two-dimensional CFT results. We derive the energy density, U(1)-charge density and ϕ2(x)-condensate post-quench dynamics, and identify different regimes of their evolution depending on the values of the field mass and the quench regularization parameter. For local quenches in higher-dimensional free massless scalar theories, we reproduce the structure of the available holographic results. We also investigate the local quenches in massive scalar field theory on a cylinder and show that they cause an erratic and chaotic-like evolution of observables with a complicated localization/delocalization pattern.

Dynamics and Composition of Small Heat Shock Protein Condensates and Aggregates

Small heat shock proteins (sHSPs) are essential ATP-independent chaperones that protect the cellular proteome. These proteins assemble into polydisperse oligomeric structures, the composition of which dramatically affects their chaperone activity. The biomolecular consequences of variations in sHSP ratios, especially inside living cells, remain elusive. Here, we study the consequences of altering the relative expression levels of HspB2 and HspB3 in HEK293T cells. These chaperones are partners in a hetero-oligomeric complex, and genetic mutations that abolish their mutual interaction are associated with myopathic disorders.HspB2 displays three distinct phenotypes when co-expressed with HspB3 at varying ratios. Expression of HspB2 alone leads to formation of liquid nuclear condensates, while shifting the stoichiometry towards HspB3 resulted in the formation of large solid-like aggregates. Only cells co-expressing HspB2 with a limited amount of HspB3 formed fully soluble complexes that were distributed homogeneously throughout the nucleus. Strikingly, both condensates and aggregates were reversible, as shifting the HspB2:HspB3 balance in situ resulted in dissolution of these structures.To uncover the molecular composition of HspB2 condensates and aggregates, we used APEX-mediated proximity labelling. Most proteins interact transiently with the condensates and were neither enriched nor depleted in these cells. In contrast, we found that HspB2:HspB3 aggregates sequestered several disordered proteins and autophagy factors, suggesting that the cell is actively attempting to clear these aggregates. This study presents a striking example of how changes in the relative expression levels of interacting proteins affects their phase behavior. Our approach could be applied to study the role of protein stoichiometry and the influence of client binding on phase behavior in other biomolecular condensates and aggregates.

In diverse conditions, intrinsic chromatin condensates have liquid-like material properties

Nuclear DNA in eukaryotes is wrapped around histone proteins to form nucleosomes on a chromatin fiber. Dynamic folding of the chromatin fiber into loops and variations in the degree of chromatin compaction regulate essential processes such as transcription, recombination, and mitotic chromosome segregation. Our understanding of the physical properties that allow chromatin to be dynamically remodeled even in highly compacted states is limited. Previously, we reported that chromatin has an intrinsic capacity to phase separate and form dynamic liquid-like condensates, which can be regulated by cellular factors [B. A. Gibson et al., Cell 179, 470-484.e421 (2019)]. Recent contradictory reports claim that a specific set of solution conditions is required for fluidity in condensates that would otherwise be solid [J. C. Hansen, K. Maeshima, M. J. Hendzel, Epigenetics Chromatin 14, 50 (2021); H. Strickfaden et al., Cell 183, 1772-1784.e1713 (2020)]. We sought to resolve these discrepancies, as our ability to translate with confidence these biophysical observations to cells requires their precise characterization. Moreover, whether chromatin assemblies are dynamic or static affects how processes such as transcription, loop extrusion, and remodeling will engage them inside cells. Here, we show in diverse conditions and without specific buffering components that chromatin fragments form phase separated fluids invitro. We also explore how sample preparation and imaging affect the experimental observation of chromatin condensate dynamics. Last, we describe how liquid-like invitro behaviors can translate to the locally dynamic but globally constrained chromatin movement observed in cells.

Correspondence between Dicke-model semiclasscial dynamics in the superradiant dipolar phase and the Euler heavy top

Analytic expression is found for the frequency dependence of the transmission coefficient of a transmission line inductively coupled to the microwave cavity with the superradiant condensate. Sharp transmission drops reflect the condensate's frequencies spectrum. These results pave the way to direct detection of emergence of the superradiant condensates in quantum metamaterials. Results are based on the analytic solutions of the nonlinear semiclassical dynamics of the superradiant photonic condensate in the Dicke model of an ensemble of two-level atoms dipolar coupled to the electromagnetic field in the microwave cavity. In the adiabatic limit with respect to the photon degree of freedom, the system is approximately integrable with evolution being expressed via Jacobi elliptic functions of real time. Depending on the coupling strength, the semiclassical coordinate of the superradiant condensate in the ground state either oscillates in one of the two degenerate minima of the condensate's potential energy or traverses between them over the saddle point. An experimental setup for measuring of the breakdown of the normal phase of the Dicke model via coupling to the transmission line is proposed. A one-to-one mapping of the semiclassical motion of the superradiant condensate on the nodding of unstable Lagrange ``sleeping top'' also turns the Dicke model into an analog device for modeling the dynamics of mechanical systems.

Screen for Modulation of Nucleocapsid Protein Condensation Identifies Small Molecules with Anti-Coronavirus Activity.

Biomolecular condensates formed by liquid-liquid phase separation have been implicated in multiple diseases. Modulation of condensate dynamics by small molecules has therapeutic potential, but so far, few condensate modulators have been disclosed. The SARS-CoV-2 nucleocapsid (N) protein forms phase-separated condensates that are hypothesized to play critical roles in viral replication, transcription, and packaging, suggesting that N condensation modulators might have anti-coronavirus activity across multiple strains and species. Here, we show that N proteins from all seven human coronaviruses (HCoVs) vary in their tendency to undergo phase separation when expressed in human lung epithelial cells. We developed a cell-based high-content screening platform and identified small molecules that both promote and inhibit condensation of SARS-CoV-2 N. Interestingly, these host-targeted small molecules exhibited condensate-modulatory effects across all HCoV Ns. Some have also been reported to exhibit antiviral activity against SARS-CoV-2, HCoV-OC43, and HCoV-229E viral infections in cell culture. Our work reveals that the assembly dynamics of N condensates can be regulated by small molecules with therapeutic potential. Our approach allows for screening based on viral genome sequences alone and might enable rapid paths to drug discovery with value for confronting future pandemics.