Dynamics of network fluids

Biomolecular condensates form spatially inhomogeneous network fluids

The functions of biomolecular condensates are thought to be influenced by their material properties, and these will be determined by the internal organization of molecules within condensates. However, structural characterizations of condensates are challenging, and rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that are formed by macromolecules from nucleolar granular components (GCs). We show that these minimal facsimiles of GCs form condensates that are network fluids featuring spatial inhomogeneities across different length scales that reflect the contributions of distinct protein and peptide domains. The network-like inhomogeneous organization is characterized by a coexistence of liquid- and gas-like macromolecular densities that engenders bimodality of internal molecular dynamics. These insights suggest that condensates formed by multivalent proteins share features with network fluids formed by systems such as patchy or hairy colloids.

Biomolecular condensates form spatially inhomogeneous network fluids

The functions of biomolecular condensates are thought to be influenced by their material properties, and these will be determined by the internal organization of molecules within condensates. However, structural characterizations of condensates are challenging, and rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that are formed by macromolecules from nucleolar granular components (GCs). We show that these minimal facsimiles of GCs form condensates that are network fluids featuring spatial inhomogeneities across different length scales that reflect the contributions of distinct protein and peptide domains. The network-like inhomogeneous organization is characterized by a coexistence of liquid- and gas-like macromolecular densities that engenders bimodality of internal molecular dynamics. These insights suggest that condensates formed by multivalent proteins share features with network fluids formed by systems such as patchy or hairy colloids.

Phase separation of a magnetic fluid: Asymptotic states and nonequilibrium kinetics

We study self-assembly in a colloidal suspension of magnetic particles by performing comprehensive molecular dynamics simulations of the Stockmayer (SM) model, which comprises spherical particles decorated by a magnetic moment. The SM potential incorporates dipole-dipole interactions along with the usual Lennard-Jones interaction and exhibits a gas-liquid phase coexistence observed experimentally in magnetic fluids. When this system is quenched from the high-temperature homogeneous phase to the coexistence region, the nonequilibrium evolution to the condensed phase proceeds with the development of spatial as well as magnetic order. We observe density-dependent coarsening mechanisms-a diffusive growth law ℓ(t)∼t^{1/3} in the nucleation regime and hydrodynamics-driven inertial growth law ℓ(t)∼t^{2/3} in the spinodal regimes. [ℓ(t) is the average size of the condensate at time t after the quench.] While the spatial growth is governed by the expected conserved order parameter dynamics, the growth of magnetic order in the spinodal regime exhibits unexpected nonconserved dynamics. The asymptotic morphologies have density-dependent shapes which typically include the isotropic sphere and spherical bubble morphologies in the nucleation region, and the anisotropic cylinder, planar slab, cylindrical bubble morphologies in the spinodal region. The structures are robust and nonvolatile, and exhibit characteristic magnetic properties. For example, the oppositely magnetized hemispheres in the spherical morphology impart the characteristics of a Janus particle to it. The observed structures have versatile applications in catalysis, drug delivery systems, memory devices, and magnetic photonic crystals, to name a few.

Nucleolar dynamics are determined by the ordered assembly of the ribosome

Ribosome biogenesis is coordinated within the nucleolus, a biomolecular condensate that exhibits dynamic material properties that are thought to be important for nucleolar function. However, the relationship between ribosome assembly and nucleolar dynamics is not clear. Here, we screened 364 genes involved in ribosome biogenesis and RNA metabolism for their impact on dynamics of the nucleolus, as measured by automated, high-throughput fluorescence recovery after photobleaching (FRAP) of the nucleolar scaffold protein NPM1. This screen revealed that gene knockdowns that caused accumulation of early rRNA intermediates were associated with nucleolar rigidification, while accumulation of late intermediates led to increased fluidity. These shifts in dynamics were accompanied by distinct changes in nucleolar morphology. We also found that genes involved in mRNA processing impact nucleolar dynamics, revealing connections between ribosome biogenesis and other RNA processing pathways. Together, this work defines mechanistic ties between ribosome assembly and the biophysical features of the nucleolus, while establishing a toolbox for understanding how molecular dynamics impact function across other biomolecular condensates.

Deciphering how naturally occurring sequence features impact the phase behaviours of disordered prion-like domains

Prion-like low-complexity domains (PLCDs) have distinctive sequence grammars that determine their driving forces for phase separation. Here we uncover the physicochemical underpinnings of how evolutionarily conserved compositional biases influence the phase behaviour of PLCDs. We interpret our results in the context of the stickers-and-spacers model for the phase separation of associative polymers. We find that tyrosine is a stronger sticker than phenylalanine, whereas arginine is a context-dependent auxiliary sticker. In contrast, lysine weakens sticker-sticker interactions. Increasing the net charge per residue destabilizes phase separation while also weakening the strong coupling between single-chain contraction in dilute phases and multichain interactions that give rise to phase separation. Finally, glycine and serine residues act as non-equivalent spacers, and thus make the glycine versus serine contents an important determinant of the driving forces for phase separation. The totality of our results leads to a set of rules that enable comparative estimates of composition-specific driving forces for PLCD phase separation.

The rise and fall of branching: A slowing down mechanism in relaxing wormlike micellar networks

A mean-field kinetic model suggests that the relaxation dynamics of wormlike micellar networks is a long and complex process due to the problem of reducing the number of free end-caps (or dangling ends) while also reaching an equilibrium level of branching after an earlier overgrowth. The model is validated against mesoscopic molecular dynamics simulations and is based on kinetic equations accounting for scission and synthesis processes of blobs of surfactants. A long relaxation time scale is reached with both thermal quenches and small perturbations of the system. The scaling of this relaxation time is exponential with the free energy of an end cap and with the branching free energy. We argue that the subtle end-recombination dynamics might yield effects that are difficult to detect in rheology experiments, with possible underestimates of the typical time scales of viscoelastic fluids.

Programmable viscoelasticity in protein-RNA condensates with disordered sticker-spacer polypeptides

Liquid-liquid phase separation of multivalent proteins and RNAs drives the formation of biomolecular condensates that facilitate membrane-free compartmentalization of subcellular processes. With recent advances, it is becoming increasingly clear that biomolecular condensates are network fluids with time-dependent material properties. Here, employing microrheology with optical tweezers, we reveal molecular determinants that govern the viscoelastic behavior of condensates formed by multivalent Arg/Gly-rich sticker-spacer polypeptides and RNA. These condensates behave as Maxwell fluids with an elastically-dominant rheological response at shorter timescales and a liquid-like behavior at longer timescales. The viscous and elastic regimes of these condensates can be tuned by the polypeptide and RNA sequences as well as their mixture compositions. Our results establish a quantitative link between the sequence- and structure-encoded biomolecular interactions at the microscopic scale and the rheological properties of the resulting condensates at the mesoscale, enabling a route to systematically probe and rationally engineer biomolecular condensates with programmable mechanics.

Aging of living polymer networks: a model with patchy particles

Microrheology experiments show that viscoelastic media composed by wormlike micellar networks display complex relaxations lasting seconds even at the scale of micrometers. By mapping a model of patchy colloids with suitable mesoscopic elementary motifs to a system of worm-like micelles, we are able to simulate its relaxation dynamics, upon a thermal quench, spanning many decades, from microseconds up to tens of seconds. After mapping the model to real units and to experimental scission energies, we show that the relaxation process develops through a sequence of non-local and energetically challenging arrangements. These adjustments remove undesired structures formed as a temporary energetic solution for stabilizing the thermodynamically unstable free caps of the network. We claim that the observed scale-free nature of this stagnant process may complicate the correct quantification of experimentally relevant time scales as the Weissenberg number.

Making the Case for Disordered Proteins and Biomolecular Condensates in Bacteria

Intrinsically disordered proteins/regions (IDPs/IDRs) contribute to a diverse array of molecular functions in eukaryotic systems. There is also growing recognition that membraneless biomolecular condensates, many of which are organized or regulated by IDPs/IDRs, can enable spatial and temporal regulation of complex biochemical reactions in eukaryotes. Motivated by these findings, we assess if (and how) membraneless biomolecular condensates and IDPs/IDRs are functionally involved in key cellular processes and molecular functions in bacteria. We summarize the conceptual underpinnings of condensate assembly and leverage these concepts by connecting them to recent findings that implicate specific types of condensates and IDPs/IDRs in important cellular level processes and molecular functions in bacterial systems.

Physical Principles Underlying the Complex Biology of Intracellular Phase Transitions

Many biomolecular condensates appear to form via spontaneous or driven processes that have the hallmarks of intracellular phase transitions. This suggests that a common underlying physical framework might govern the formation of functionally and compositionally unrelated biomolecular condensates. In this review, we summarize recent work that leverages a stickers-and-spacers framework adapted from the field of associative polymers for understanding how multivalent protein and RNA molecules drive phase transitions that give rise to biomolecular condensates. We discuss how the valence of stickers impacts the driving forces for condensate formation and elaborate on how stickers can be distinguished from spacers in different contexts. We touch on the impact of sticker- and spacer-mediated interactions on the rheological properties of condensates and show how the model can be mapped to known drivers of different types of biomolecular condensates.

Human Antiviral Protein MxA Forms Novel Metastable Membraneless Cytoplasmic Condensates Exhibiting Rapid Reversible Tonicity-Driven Phase Transitions

Phase-separated biomolecular condensates of proteins and nucleic acids form functional membrane-less organelles (e.g., stress granules and P-bodies) in the mammalian cell cytoplasm and nucleus. In contrast to the long-standing belief that interferon (IFN)-inducible human myxovirus resistance protein A (MxA) associated with the endoplasmic reticulum (ER) and Golgi apparatus, we report that MxA formed membraneless metastable (shape-changing) condensates in the cytoplasm. In our studies, we used the same cell lines and methods as those used by previous investigators but concluded that wild-type MxA formed variably sized spherical or irregular bodies, filaments, and even a reticulum distinct from that of ER/Golgi membranes. Moreover, in Huh7 cells, MxA structures associated with a novel cytoplasmic reticular meshwork of intermediate filaments. In live-cell assays, 1,6-hexanediol treatment led to rapid disassembly of green fluorescent protein (GFP)-MxA structures; FRAP revealed a relative stiffness with a mobile fraction of 0.24 ± 0.02 within condensates, consistent with a higher-order MxA network structure. Remarkably, in intact cells, GFP-MxA condensates reversibly disassembled/reassembled within minutes of sequential decrease/increase, respectively, in tonicity of extracellular medium, even in low-salt buffers adjusted only with sucrose. Condensates formed from IFN-α-induced endogenous MxA also displayed tonicity-driven disassembly/reassembly. In vesicular stomatitis virus (VSV)-infected Huh7 cells, the nucleocapsid (N) protein, which participates in forming phase-separated viral structures, associated with spherical GFP-MxA condensates in cells showing an antiviral effect. These observations prompt comparisons with the extensive literature on interactions between viruses and stress granules/P-bodies. Overall, the new data correct a long-standing misinterpretation in the MxA literature and provide evidence for membraneless MxA biomolecular condensates in the uninfected cell cytoplasm.IMPORTANCE There is a long-standing belief that interferon (IFN)-inducible human myxovirus resistance protein A (MxA), which displays antiviral activity against several RNA and DNA viruses, associates with the endoplasmic reticulum (ER) and Golgi apparatus. We provide data to correct this misinterpretation and further report that MxA forms membraneless metastable (shape-changing) condensates in the cytoplasm consisting of variably sized spherical or irregular bodies, filaments, and even a reticulum. Remarkably, MxA condensates showed the unique property of rapid (within 1 to 3 min) reversible disassembly and reassembly in intact cells exposed sequentially to hypotonic and isotonic conditions. Moreover, GFP-MxA condensates included the VSV nucleocapsid (N) protein, a protein previously shown to form liquid-like condensates. Since intracellular edema and ionic changes are hallmarks of cytopathic effects of a viral infection, the tonicity-driven regulation of MxA condensates may reflect a mechanism for modulation of MxA function during viral infection.

LASSI: A lattice model for simulating phase transitions of multivalent proteins

Many biomolecular condensates form via spontaneous phase transitions that are driven by multivalent proteins. These molecules are biological instantiations of associative polymers that conform to a so-called stickers-and-spacers architecture. The stickers are protein-protein or protein-RNA interaction motifs and / or domains that can form reversible, non-covalent crosslinks with one another. Spacers are interspersed between stickers and their preferential interactions with solvent molecules determine the cooperativity of phase transitions. Here, we report the development of an open source computational engine known as LASSI (LAttice simulation engine for Sticker and Spacer Interactions) that enables the calculation of full phase diagrams for multicomponent systems comprising of coarse-grained representations of multivalent proteins. LASSI is designed to enable computationally efficient phenomenological modeling of spontaneous phase transitions of multicomponent mixtures comprising of multivalent proteins and RNA molecules. We demonstrate the application of LASSI using simulations of linear and branched multivalent proteins. We show that dense phases are best described as droplet-spanning networks that are characterized by reversible physical crosslinks among multivalent proteins. We connect recent observations regarding correlations between apparent stoichiometry and dwell times of condensates to being proxies for the internal structural organization, specifically the convolution of internal density and extent of networking, within condensates. Finally, we demonstrate that the concept of saturation concentration thresholds does not apply to multicomponent systems where obligate heterotypic interactions drive phase transitions. This emerges from the ellipsoidal structures of phase diagrams for multicomponent systems and it has direct implications for the regulation of biomolecular condensates in vivo.

Optimal number of linkers per monomer in linker-mediated aggregation

We study the dynamics of diffusion-limited irreversible aggregation of monomers, where bonds are mediated by linkers. We combine kinetic Monte Carlo simulations of a lattice model with a mean-field theory to study the dynamics when the diffusion of aggregates is negligible and only monomers diffuse. We find two values of the number of linkers per monomer which maximize the size of the largest aggregate. We explain the existence of the two maxima based on the distribution of linkers per monomer. This observation is well described by a simple mean-field model. We also show that a relevant parameter is the ratio of the diffusion coefficients of monomers and linkers. In particular, when this ratio is close to ten, the two maxima merge at a single maximum.

Crossover from three- to six-fold symmetry of colloidal aggregates in circular traps

At sufficiently low temperatures and high densities, repulsive spherical particles in two-dimensions (2d) form close-packed structures with six-fold symmetry. By contrast, when the interparticle interaction has an attractive anisotropic component, the structure may exhibit the symmetry of the interaction. We consider a suspension of spherical particles interacting through an isotropic repulsive potential and a three-fold symmetric attractive interaction, confined in circular potential traps in 2d. We find that, due to the competition between the interparticle and the external potentials, the particles self-organize into structures with three- or six-fold symmetry, depending on the width of the traps. For intermediate trap widths, a core-shell structure is formed, where the core has six-fold symmetry and the shell is three-fold symmetric. When the width of the trap changes periodically in time, the symmetry of the colloidal structure also changes, but it does not necessarily follow that of the corresponding static trap.

Phase Separation of Intrinsically Disordered Proteins

There is growing interest in the topic of intracellular phase transitions that lead to the formation of biologically regulated biomolecular condensates. These condensates are membraneless bodies formed by phase separation of key protein and nucleic acid molecules from the cytoplasmic or nucleoplasmic milieus. The drivers of phase separation are referred to as scaffolds whereas molecules that preferentially partition into condensates formed by scaffolds are known as clients. Recent advances have shown that it is possible to generate physical and functional facsimiles of many biomolecular condensates in vitro. This is achieved by titrating the concentration of key scaffold proteins and solution parameters such as salt concentration, pH, or temperature. The ability to reproduce phase separation in vitro allows one to compare the relationships between information encoded in the sequences of scaffold proteins and the driving forces for phase separation. Many scaffold proteins include intrinsically disordered regions whereas others are entirely disordered. Our focus is on comparative assessments of phase separation for different scaffold proteins, specifically intrinsically disordered linear multivalent proteins. We highlight the importance of coexistence curves known as binodals for quantifying phase behavior and comparing driving forces for sequence-specific phase separation. We describe the information accessible from full binodals and highlight different methods for-and challenges associated with-mapping binodals. In essence, we provide a wish list for in vitro characterization of phase separation of intrinsically disordered proteins. Fulfillment of this wish list through key advances in experiment, computation, and theory should bring us closer to being able to predict in vitro phase behavior for scaffold proteins and connect this to the functions and features of biomolecular condensates.

Tuning the order of colloidal monolayers: assembly of heterogeneously charged colloids close to a patterned substrate

We study the behavior of negatively charged colloids with two positively charged polar caps close to a planar patterned surface. The competition between the different anisotropic components of the particle-particle interaction is able by itself to give rise to a rich assembly scenario: colloids with charged surface patterns already form different crystalline domains when adsorbed to a homogeneously charged substrate. Here we consider substrates composed of alternating (negative/neutral, positive/neutral and positive/negative) parallel stripes and, by means of Monte Carlo simulations, we investigate the ordering of the colloids on changing the number of the stripes. We show that the additional competition between the two different lengths scales characterizing the system (i.e., the particle interaction range and the size of the stripes) gives rise to a plethora of distinct particle arrangements, where some well-defined trends can be observed. By accurately tuning the substrate charged motif it is possible to, e.g., promote specific particle arrangements, disfavor crystalline domains or induce the formation of extended, open clusters.

Physico-chemical foundations of particle-laden fluid interfaces

Particle-laden interfaces are ubiquitous nowadays. The understanding of their properties and structure is essential for solving different problems of technological and industrial relevance; e.g. stabilization of foams, emulsions and thin films. These rely on the response of the interface to mechanical perturbations. The complex mechanical response appearing in particle-laden interfaces requires deepening on the understanding of physico-chemical mechanisms underlying the assembly of particles at interface which plays a central role in the distribution of particles at the interface, and in the complex interfacial dynamics appearing in these systems. Therefore, the study of particle-laden interfaces deserves attention to provide a comprehensive explanation on the complex relaxation mechanisms involved in the stabilization of fluid interfaces.

Percolation of functionalized colloids on patterned substrates

We study the percolation properties for a system of functionalized colloids on patterned substrates via Monte Carlo simulations. The colloidal particles are modeled as hard disks with three equally-distributed attractive patches on their perimeter. We describe the patterns on the substrate as circular potential wells of radius Rp arranged in a regular square or hexagonal lattice. We find a nonmonotonic behavior of the percolation threshold (packing fraction) as a function of Rp. For attractive wells, the percolation threshold is higher than the one for clean (non-patterned) substrates if the circular wells are non-overlapping and can only be lower if the wells overlap. For repulsive wells we find the opposite behavior. In addition, at high packing fractions the formation of both structural and bond defects suppress percolation. As a result, the percolation diagram is reentrant with the non-percolated state occurring at very low and intermediate densities.

Annealing cycles and the self-organization of functionalized colloids

The self-assembly of functionalized (patchy) particles with directional interactions into target structures is still a challenge, despite the significant experimental advances in their synthesis. Self-assembly pathways are typically characterized by high energy barriers that hinder access to stable (equilibrium) structures. A possible strategy to tackle this challenge is to perform annealing cycles. By periodically switching on and off the inter-particle bonds, one expects to smooth-out the kinetic pathways and favor the assembly of targeted structures. Preliminary results have shown that the efficiency of annealing cycles depends strongly on their frequency. Here, we study numerically how this frequency-dependence scales with the strength of the directional interactions (size of the patch σ). We use analytical arguments to show that the scaling results from the statistics of a random walk in configurational space.

Dynamics of Patchy Particles in and out of Equilibrium

We combine particle-based simulations, mean-field rate equations, and Wertheim's theory to study the dynamics of patchy particles in and out of equilibrium, at different temperatures and densities. We consider an initial random distribution of nonoverlapping three-patch particles, with no bonds, and analyze the time evolution of the breaking and bonding rates of a single bond. We find that the asymptotic (equilibrium) dynamics differs from the initial (out of equilibrium) one. These differences are expected to depend on the initial conditions, temperature, and density.