Dynamics Of Condensate Research Articles

Pattern formations and their active manipulation in a Rydberg noisy-dressed Bose-Einstein condensate.

We investigate the formation and manipulation of spatial patterns and their structural phase transitions by examining the effects of laser linewidth on the dynamics of Rydberg noise-dressed Bose-Einstein condensates (RnD BECs). We discover that the homogeneous matter wave can transition into various types of self-organized patterns, which are manipulated by tuning the laser linewidth, control field intensity, and atomic density. Remarkably, the system exhibits stable nonlocal matter-wave solitons, vortices, and soliton molecules under specific laser linewidths.

Optically tuned soliton dynamics in Bose-Einstein condensates within dark traps

Abstract This study investigates the formation and dynamics of solitons in Bose–Einstein condensates (BECs) within dark traps generated by two crossed Laguerre–Gaussian (LG) beams with varying azimuthal indices ℓ . As the index ℓ increases, the potential transitions from a harmonic trap when ℓ = 1 to a square-well potential for larger values of ℓ . This transition allows us to study a range of soliton dynamics under different confinement conditions while maintaining the same BEC volume. Through the derivation of the Gross-Pitaevskii equation (GPE) and under these specific conditions in both one-dimensional and two-dimensional configurations, we explore the dynamics of solitons across multiple scenarios. The study examines two primary methods for solitons generation: the temporal modulation of the scattering length and the implementation of an initial potential barrier that is subsequently removed. The results indicate that the trap shape plays a critical role in the generation and interaction dynamics of solitons. In harmonic traps, solitons exhibit a behavior different from those observed in anharmonic traps, where the dynamics is significantly influenced by the azimuthal index of the trap. The ability to control soliton dynamics in BECs holds significant promise for applications in quantum technologies, precision sensing, and the exploration of fundamental quantum phenomena.

Nucleoprotein Phase-Separation Affinities Revealed via Atomistic Simulations of Short Peptide and RNA Fragments.

Liquid-liquid phase separation of proteins and nucleic acids into condensate phases is a versatile mechanism for ensuring the compartmentalization of cellular biochemistry. RNA molecules play critical roles in these condensates, particularly in transcriptional regulation and stress responses, exhibiting a wide range of thermodynamic and dynamic behaviors. However, deciphering the molecular grammar that governs the stability and dynamics of protein-RNA condensates remains challenging due to the multicomponent and heterogeneous nature of condensates. In this study, we employ atomistic simulations of 20 distinct mixtures containing minimal RNA and peptide fragments which allows us to dissect the phase-separating affinities of all 20 amino acids in the presence of RNA. Our findings elucidate chemically specific interactions, hydration profiles, and ionic effects that synergistically promote or suppress protein-RNA phase separation. We map a ternary phase diagram of interactions, identifying four distinct groups of residues that promote, maintain, suppress, and disrupt protein-RNA clusters.

IGF2BP1 phosphorylation in the disordered linkers regulates ribonucleoprotein condensate formation and RNA metabolism.

The insulin-like growth factor 2 mRNA binding protein 1 (IGF2BP1) is a conserved RNA-binding protein that regulates RNA stability, localization and translation. IGF2BP1 is part of various ribonucleoprotein (RNP) condensates. However, the mechanism that regulates its assembly into condensates remains unknown. By using proteomics, we demonstrate that phosphorylation of IGF2BP1 at S181 in a disordered linker is regulated in a stress-dependent manner. Phosphomimetic mutations in two disordered linkers, S181E and Y396E, modulate RNP condensate formation by IGF2BP1 without impacting its binding affinity for RNA. Intriguingly, the S181E mutant, which lies in linker 1, impairs IGF2BP1 condensate formation in vitro and in cells, whereas a Y396E mutant in the second linker increases condensate size and dynamics. Structural approaches show that the first linker binds RNAs nonspecifically through its RGG/RG motif, an interaction weakened in the S181E mutant. Notably, linker 2 interacts with IGF2BP1's folded domains and these interactions are partially impaired in the Y396E mutant. Importantly, the phosphomimetic mutants impact IGF2BP1's interaction with RNAs and remodel the transcriptome in cells. Our data reveal how phosphorylation modulates low-affinity interaction networks in disordered linkers to regulate RNP condensate formation and RNA metabolism.

Expansion dynamics of Bose-Einstein condensates in a synthetic magnetic field

Expansion dynamics of Bose-Einstein condensates in a synthetic magnetic field

Microscopic Origins of Flow Activation Energy in Biomolecular Condensates.

Material properties of biomolecular condensates dictate their form and function, influencing the diffusion of regulatory molecules and the dynamics of biochemical reactions. The increasing quality and quantity of microrheology experiments on biomolecular condensates necessitate a deeper understanding of the molecular grammar that encodes their material properties. Recent reports have identified a characteristic timescale related to network relaxation dynamics in condensates, which governs their temperature-dependent viscoelastic properties. This timescale is intimately connected to an activated process involving the dissociation of sticker regions, with the energetic barrier referred to as flow activation energy. The microscopic origin of activation energy is a complex function of sequence patterns, component stoichiometry, and external conditions. This study elucidates the microscopic origins of flow activation energy in single and multicomponent condensates composed of model peptide sequences with varying sticker and spacer motifs, with RNA as a secondary component. We dissected the effects of condensate density, RNA stoichiometry, and peptide sequence patterning using extensive sequence-resolved coarse-grained simulations. We found that flow activation energy is closely linked to the lifetime of sticker-sticker pairs under certain conditions, though the presence of multiple competing stickers further complicates this relationship. The insights gained in this study should help establish predictive multiscale models for the material properties and serve as a valuable guide for the programmable design of condensates.

Nucleoprotein phase-separation affinities revealed via atomistic simulations of short peptide and RNA fragments.

Liquid-liquid phase separation of proteins and nucleic acids into condensate phases is a versatile mechanism for ensuring compartmentalization of cellular biochemistry. RNA molecules play critical roles in these condensates, particularly in transcriptional regulation and stress responses, exhibiting a wide range of thermodynamic and dynamic behaviors. However, deciphering the molecular grammar that governs the stability and dynamics of protein-RNA condensates remains challenging due to the multicomponent and heterogeneous nature of these biomolecular mixtures. In this study, we employ atomistic simulations of twenty distinct mixtures containing minimal RNA and peptide fragments to dissect the phase-separating affinities of all twenty amino acids in the presence of RNA. Our findings elucidate chemically specific interactions, hydration profiles, and ionic effects that synergistically promote or suppress protein-RNA phase separation. We map a ternary phase diagram of interactions, identifying four distinct groups of residues that promote, maintain, suppress, or disrupt protein-RNA clusters.

The exchange dynamics of biomolecular condensates.

A hallmark of biomolecular condensates formed via liquid-liquid phase separation is that they dynamically exchange material with their surroundings, and this process can be crucial to condensate function. Intuitively, the rate of exchange can be limited by the flux from the dilute phase or by the mixing speed in the dense phase. Surprisingly, a recent experiment suggests that exchange can also be limited by the dynamics at the droplet interface, implying the existence of an 'interface resistance'. Here, we first derive an analytical expression for the timescale of condensate material exchange, which clearly conveys the physical factors controlling exchange dynamics. We then utilize sticker-spacer polymer models to show that interface resistance can arise when incident molecules transiently touch the interface without entering the dense phase, i.e., the molecules 'bounce' from the interface. Our work provides insight into condensate exchange dynamics, with implications for both natural and synthetic systems.

The exchange dynamics of biomolecular condensates

A hallmark of biomolecular condensates formed via liquid-liquid phase separation is that they dynamically exchange material with their surroundings, and this process can be crucial to condensate function. Intuitively, the rate of exchange can be limited by the flux from the dilute phase or by the mixing speed in the dense phase. Surprisingly, a recent experiment suggests that exchange can also be limited by the dynamics at the droplet interface, implying the existence of an ‘interface resistance’. Here, we first derive an analytical expression for the timescale of condensate material exchange, which clearly conveys the physical factors controlling exchange dynamics. We then utilize sticker-spacer polymer models to show that interface resistance can arise when incident molecules transiently touch the interface without entering the dense phase, i.e., the molecules ‘bounce’ from the interface. Our work provides insight into condensate exchange dynamics, with implications for both natural and synthetic systems.

Predicting Bubble Fragmentation in Superfluids.

In classical fluids, the Weber number is a dimensionless parameter that characterizes the flow of a multiphase fluid. The superfluid analogy of a classical multiphase fluid can be realized in a system of two or more immiscible Bose-Einstein condensates. These superfluid mixtures have been shown to display a wider variety of exotic dynamics than their single component counterparts. Here we systematically study the dynamics of a binary immiscible Bose-Einstein condensate in two dimensions, where a small bubble of the second component is used to "stir" the first component. We begin by rigorously mapping out the critical velocity for vortex shedding as a function of the size of the bubble, in analogy to the critical velocity of a laser spoon. Observing that the dynamics of the system depend on the initial size and velocity of the bubble, we then show that a dimensionless parameter with the same form as the Weber number accurately predicts the resulting bubble fragmentation.

Viscosity Regulation of Chemically Simple Condensates.

This study investigates the viscosity and liquid-solid transition behavior of biomolecular condensates formed by polyarginine chains (Rx) of varying lengths and citric acid (CA) derivatives. By condensing Rx chains of various lengths with CA derivatives, we showed that the shorter Rx chains attenuate the high aggregation tendency of the longer chains when condensed with CA. A mixture of different Rx lengths exhibited uniform intracondensate distribution, while its mobility largely depended on the ratio of the longer Rx chain. Our findings demonstrate a simple method to modulate condensate properties by adjusting the composition of scaffold molecules, shedding light on the role of molecular composition in controlling condensate viscosity and transition dynamics. This research contributes to a deeper understanding of biomolecular condensation processes and offers insights into potential strategies for manipulating condensate properties for various applications, including in the fields of synthetic biology and disease therapeutics in the future.

Interplay of condensate material properties and chromatin heterogeneity governs nuclear condensate ripening.

Nuclear condensates play many important roles in chromatin functions, but how cells regulate their nucleation and growth within the complex nuclear environment is not well understood. Here, we report how condensate properties and chromatin mechanics dictate condensate growth dynamics in the nucleus. We induced condensates with distinct properties using different proteins in human cell nuclei and monitored their growth. We revealed two key physical mechanisms that underlie droplet growth: diffusion-driven or ripening-dominated growth. To explain the experimental observations, we developed a quantitative theory that uncovers the mechanical role of chromatin and condensate material properties in regulating condensate growth in a heterogeneous environment. By fitting our theory to experimental data, we find that condensate surface tension is critical in determining whether condensates undergo elastic or Ostwald ripening. Our model also predicts that chromatin heterogeneity can influence condensate nucleation and growth, which we validated by experimentally perturbing the chromatin organization and controlling condensate nucleation. By combining quantitative experimentation with theoretical modeling, our work elucidates how condensate surface tension and chromatin heterogeneity govern nuclear condensate ripening, implying that cells can control both condensate properties and the chromatin organization to regulate condensate growth in the nucleus.

Sequence-encoded Spatiotemporal Dependence of Viscoelasticity of Protein Condensates Using Computational Microrheology.

Many biomolecular condensates act as viscoelastic complex fluids with distinct cellular functions. Deciphering the viscoelastic behavior of biomolecular condensates can provide insights into their spatiotemporal organization and physiological roles within cells. Though there is significant interest in defining the role of condensate dynamics and rheology in physiological functions, the quantification of their time-dependent viscoelastic properties is limited and mostly done through experimental rheological methods. Here, we demonstrate that a computational passive probe microrheology technique, coupled with continuum mechanics, can accurately characterize the linear viscoelasticity of condensates formed by intrinsically disordered proteins (IDPs). Using a transferable coarse-grained protein model, we first provide a physical basis for choosing optimal values that define the attributes of the probe particle, namely its size and interaction strength with the residues in an IDP chain. We show that the technique captures the sequence-dependent viscoelasticity of heteropolymeric IDPs that differ either in sequence charge patterning or sequence hydrophobicity. We also illustrate the technique's potential in quantifying the spatial dependence of viscoelasticity in heterogeneous IDP condensates. The computational microrheology technique has important implications for investigating the time-dependent rheology of complex biomolecular architectures, resulting in the sequence-rheology-function relationship for condensates.

Nonequilibrium phases of a biomolecular condensate facilitated by enzyme activity.

Biomolecular condensates represent a frontier in cellular organization, existing as dynamic materials driven out of equilibrium by active cellular processes. Here we explore active mechanisms of condensate regulation by examining the interplay between DEAD-box helicase activity and RNA base-pairing interactions within ribonucleoprotein condensates. We demonstrate how the ATP-dependent activity of DEAD-box helicases-a key class of enzymes in condensate regulation-acts as a nonequilibrium driver of condensate properties through the continuous remodeling of RNA interactions. By combining the LAF-1 DEAD-box helicase with a designer RNA hairpin concatemer, we unveil a complex landscape of dynamic behaviors, including time-dependent alterations in RNA partitioning, evolving condensate morphologies, and shifting condensate dynamics. Importantly, we reveal an antagonistic relationship between RNA secondary structure and helicase activity which promotes condensate homogeneity via a nonequilibrium steady state. By elucidating these nonequilibrium mechanisms, we gain a deeper understanding of cellular organization and expand the potential for active synthetic condensate systems.

Quantifying surface tension and viscosity in biomolecular condensates by FRAP-ID

Many proteins with intrinsically disordered regions undergo liquid-liquid phase separation under specific conditions in vitro and in vivo. These complex biopolymers form a metastable phase with distinct mechanical properties defining the timescale of their biological functions. However, determining these properties is nontrivial, even in vitro, and often requires multiple techniques. Here we report the measurement of both viscosity and surface tension of biomolecular condensates via correlative fluorescence microscopy and atomic force microscopy (AFM) in a single experiment (fluorescence recovery after probe-induced dewetting, FRAP-ID). Upon surface tension evaluation via regular AFM-force spectroscopy, controlled AFM indentations induce dry spots in fluorescent condensates on a glass coverslip. The subsequent rewetting exhibits a contact line velocity that is used to quantify the condensed-phase viscosity. Therefore, in contrast with fluorescence recovery after photobleaching (FRAP), where molecular diffusion is observed, in FRAP-ID fluorescence recovery is obtained through fluid rewetting and the subsequent morphological relaxation. We show that the latter can be used to cross-validate viscosity values determined during the rewetting regime. Making use of fluid mechanics, FRAP-ID is a valuable tool to evaluate the mechanical properties that govern the dynamics of biomolecular condensates and determine how these properties impact the temporal aspects of condensate functionality.

All-optical temporal logic gates in localized exciton polaritons

Exciton polaritons—quasi-particle excitations consisting of strongly coupled photons and excitons—present fascinating possibilities for photonic circuits, owing to their strong nonlinearity, ultrafast reaction times and their ability to form macroscopic quantum states at room temperature via non-equilibrium condensation. Past implementations of transistors and logic gates with exciton polaritons have been mostly realized using the spatial propagation of polariton fluids, which place high demands on the fabrication of the microcavities and typically require complex manipulations. In this work we have implemented the full set of logical gate functionalities (that is, temporal AND, OR and NOT gates) in localized exciton polaritons at room temperature, on the basis of precisely controlling the interplay between polariton condensate and exciton reservoir dynamics, using a two-pulse excitation scheme. The dynamics intrinsically covers the cascadability required by the logical operations, enabling efficient information processing without the need for spatial flow. The temporal polariton logic gates demonstrate advantages in ultrafast switching, universality and simplified compatibility with other dimensional controls, showing great potential for building polariton logic networks in strongly coupled light–matter systems.

Self-consistent sharp interface theory of active condensate dynamics

Biomolecular condensates help organize the cell cytoplasm and nucleoplasm into spatial compartments with different chemical compositions. A key feature of such compositional patterning is the local enrichment of enzymatically active biomolecules which, after transient binding via molecular interactions, catalyze reactions among their substrates. Thereby, biomolecular condensates provide a spatial template for nonuniform concentration profiles of substrates. In turn, the concentration profiles of substrates, and their molecular interactions with enzymes, drive enzyme fluxes which can enable novel nonequilibrium dynamics. To analyze this generic class of systems, with a current focus on self-propelled droplet motion, we here develop a self-consistent sharp interface theory. In our theory, we diverge from the usual bottom-up approach, which involves calculating the dynamics of concentration profiles based on a given chemical potential gradient. Instead, reminiscent of control theory, we take the reverse approach by deriving the chemical potential profile and enzyme fluxes required to maintain a desired condensate form and dynamics. The chemical potential profile and currents of enzymes come with a corresponding power dissipation rate, which allows us to derive a thermodynamic consistency criterion for the passive part of the system (here, reciprocal enzyme-enzyme interactions). As a first-use case of our theory, we study the role of reciprocal interactions, where the transport of substrates due to reactions and diffusion is, in part, compensated by redistribution due to molecular interactions. More generally, our theory applies to mass-conserved active matter systems with moving phase boundaries. Published by the American Physical Society 2024

Interference-induced suppression of particle emission from a Bose–Einstein condensate in lattice with time-periodic modulations

Abstract Emission of matter-wave jets from a parametrically driven condensate has attracted significant experimental and theoretical attention due to the appealing visual effects and potential metrological applications. In this work, we investigate the collective particle emission from a Bose–Einstein condensate confined in a one-dimensional lattice with periodically modulated interparticle interactions. We give the regimes for discrete modes, and find that the emission can be distinctly suppressed. The configuration induces a broad band, but few particles are ejected due to the interference of the matter waves. We further qualitatively model the emission process and demonstrate the short-time behaviors. This engineering provides a way to manipulate the propagation of particles and the corresponding dynamics of condensates in lattices, and may find application in the dynamical excitation control of other nonequilibrium problems with time-periodic driving.

Plant Thermosensors.

Plants are exposed to temperature conditions that fluctuate over different time scales, including those inherent to global warming. In the face of these variations, plants sense temperature to adjust their functions and minimize the negative consequences. Transcriptome responses underlie changes in growth, development, and biochemistry (thermomorphogenesis and acclimation to extreme temperatures). We are only beginning to understand temperature sensation by plants. Multiple thermosensors convey complementary temperature information to a given signaling network to control gene expression. Temperature-induced changes in protein or transcript structure and/or in the dynamics of biomolecular condensates are the core sensing mechanisms of known thermosensors, but temperature impinges on their activities via additional indirect pathways. The diversity of plant responses to temperature anticipates that many new thermosensors and eventually novel sensing mechanisms will be uncovered soon.

Sequence-specific interactions determine viscoelasticity and aging dynamics of protein condensates.

Biomolecular condensates are viscoelastic materials. Here, we investigate the determinants of sequence-encoded and age-dependent viscoelasticity of condensates formed by the prion-like low-complexity domain of the protein hnRNP A1 and its designed variants. We find that the dominantly viscous forms of the condensates are metastable Maxwell fluids. A Rouse-Zimm model that accounts for the network-like organization of proteins within condensates reproduces the measured viscoelastic moduli. We show that the strengths of aromatic inter-sticker interactions determine sequence-specific amplitudes of elastic and viscous moduli, and the timescales over which elastic properties dominate. These condensates undergo physical ageing on sequence-specific timescales. This is driven by mutations to spacer residues that weaken the metastability of dominantly viscous phases. The ageing of condensates is accompanied by disorder-to-order transitions, leading to the formation of non-fibrillar, beta-sheet-containing, semi-crystalline, elastic, Kelvin-Voigt solids. Our results suggest that sequence grammars, which refer to amino acid identities of stickers versus spacers in prion-like low-complexity domains, have evolved to afford control over metastabilities of dominantly viscous fluid phases of condensates. This selection is likely to render barriers for conversion from metastable fluids to globally stable solids insurmountable on functionally relevant timescales.