Stoichiometry Controls the Dynamics of Liquid Condensates of Associative Proteins

Prewetting couples membrane and protein phase transitions to greatly enhance coexistence in models and cells

Both membranes and biopolymers can individually separate into coexisting liquid phases. Here we explore biopolymer prewetting at membranes, a phase transition that emerges when these two thermodynamic systems are coupled. In reconstitution, we couple short poly-L-Lysine and poly-L-Glutamic Acid polyelectrolytes to membranes of saturated lipids, unsaturated lipids, and cholesterol, and detect coexisting prewet and dry surface phases well outside of the region of coexistence for each individual system. Notability, polyelectrolyte prewetting is highly sensitive to membrane lipid composition, occurring at 10 fold lower polymer concentration in a membrane close to its phase transition compared to one without a phase transition. In cells, protein prewetting is achieved using an optogenetic tool that enables titration of condensing proteins and tethering to the plasma membrane inner leaflet. Here we show that protein prewetting occurs for conditions well outside those where proteins condense in the cytoplasm, and that the stability of prewet domains is sensitive to perturbations of plasma membrane composition and structure. Our work presents an example of how thermodynamic phase transitions can impact cellular structure outside their individual coexistence regions, suggesting new possible roles for phase-separation-prone systems in cell biology.

Mechanistic insights into condensate formation of human liver-type phosphofructokinase by stochastic modeling approaches

Human liver-type phosphofructokinase 1 (PFKL) has been shown to regulate glucose flux as a scaffolder arranging glycolytic and gluconeogenic enzymes into a multienzyme metabolic condensate, the glucosome. However, it has remained elusive of how phase separation of PFKL is governed and initiates glucosome formation in living cells, thus hampering to understand a mechanism of glucosome formation and its functional contribution to human cells. In this work, we developed a stochastic model in silico using the principle of Langevin dynamics to investigate how biological properties of PFKL contribute to the condensate formation. The significance of an intermolecular interaction between PFKLs, an effective concentration of PFKL at a region of interest, and its own self-assembled filaments in formation of PFKL condensates and control of their sizes were demonstrated by molecular dynamics simulation using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS). Such biological properties that define intracellular dynamics of PFKL appear to be essential for phase separation of PFKL, which may represent an initiation step for the formation of glucosome condensates. Collectively, our computational study provides mechanistic insights of glucosome formation, particularly an initial stage through the formation of PFKL condensates in living human cells.

Peptide diffusion in biomolecular condensates

Diffusion determines the turnover of biomolecules in liquid-liquid phase-separated condensates. We considered the mean square displacement and thus the diffusion constant for simple model systems of peptides GGGGG, GGQGG, and GGVGG in aqueous solutions after phase separation by simulating atomic-level models. These solutions readily separate into aqueous and peptide-rich droplet phases. We noted the effect of the peptides being in a solvated, surface, or droplet state on the peptide's diffusion coefficients. Both sequence and peptide conformational distribution were found to influence diffusion and condensate turnover in these systems, with sequence dominating the magnitude of the differences. We found that the most compact structures for each sequence diffused the fastest in the peptide-rich condensate phase. This model result may have implications for turnover dynamics in signaling systems.

Interfacial exchange dynamics of biomolecular condensates are highly sensitive to client interactions

Phase separation of biomolecules can facilitate their spatiotemporally regulated self-assembly within living cells. Due to the selective yet dynamic exchange of biomolecules across condensate interfaces, condensates can function as reactive hubs by concentrating enzymatic components for faster kinetics. The principles governing this dynamic exchange between condensate phases, however, are poorly understood. In this work, we systematically investigate the influence of client-sticker interactions on the exchange dynamics of protein molecules across condensate interfaces. We show that increasing affinity between a model protein scaffold and its client molecules causes the exchange of protein chains between the dilute and dense phases to slow down and that beyond a threshold interaction strength, this slowdown in exchange becomes substantial. Investigating the impact of interaction symmetry, we found that chain exchange dynamics are also considerably slower when client molecules interact equally with different sticky residues in the protein. The slowdown of exchange is due to a sequestration effect, by which there are fewer unbound stickers available at the interface to which dilute phase chains may attach. These findings highlight the fundamental connection between client-scaffold interaction networks and condensate exchange dynamics.

Sequence-dependent material properties of biomolecular condensates and their relation to dilute phase conformations

Material properties of phase-separated biomolecular condensates, enriched with disordered proteins, dictate many cellular functions. Contrary to the progress made in understanding the sequence-dependent phase separation of proteins, little is known about the sequence determinants of condensate material properties. Using the hydropathy scale and Martini models, we computationally decipher these relationships for charge-rich disordered protein condensates. Our computations yield dynamical, rheological, and interfacial properties of condensates that are quantitatively comparable with experimentally characterized condensates. Interestingly, we find that the material properties of model and natural proteins respond similarly to charge segregation, despite different sequence compositions. Molecular interactions within the condensates closely resemble those within the single-chain ensembles. Consequently, the material properties strongly correlate with molecular contact dynamics and single-chain structural properties. We demonstrate the potential to harness the sequence characteristics of disordered proteins for predicting and engineering the material properties of functional condensates, with insights from the dilute phase properties.

Sequence-Dependent Material Properties of Biomolecular Codensates and their Relation to Dilute Phase Conformations

Material properties of phase-separated biomolecular assemblies, enriched with disordered proteins, dictate their ability to participate in many cellular functions. Despite the significant effort dedicated to understanding how the sequence of the disordered protein drives its phase separation to form condensates, little is known about the sequence determinants of condensate material properties. Here, we computationally decipher these relationships for charged disordered proteins using model sequences comprised of glutamic acid and lysine residues as well as naturally occurring sequences of LAF1's RGG domain and DDX4's N-terminal domain. We do so by delineating how the arrangement of oppositely charged residues within these sequences influences the dynamical, rheological, and interfacial properties of the condensed phase through equilibrium and non-equilibrium molecular simulations using the hydropathy scale and Martini models. Our computations yield material properties that are quantitatively comparable with experimentally characterized condensate systems. Interestingly, we find that the material properties of both the model and natural proteins respond similarly to the segregation of charges, despite their very different sequence compositions. Condensates of the highly charge-segregated sequences exhibit slower dynamics than the uniformly charge-patterned sequences, because of their comparatively long-lived molecular contacts between oppositely charged residues. Surprisingly, the molecular interactions within the condensate are highly similar to those within a single-chain for all sequences. Consequently, the condensate material properties of charged disordered proteins are strongly correlated with their dense phase contact dynamics and their single-chain structural properties. Our findings demonstrate the potential to harness the sequence characteristics of disordered proteins for predicting and engineering the material properties of functional condensates, with insights from the dilute phase properties.

Dynamical control enables the formation of demixed biomolecular condensates

Cellular matter can be organized into compositionally distinct biomolecular condensates. For example, in Ashbya gossypii, the RNA-binding protein Whi3 forms distinct condensates with different RNA molecules. Using criteria derived from a physical framework for explaining how compositionally distinct condensates can form spontaneously via thermodynamic considerations, we find that condensates in vitro form mainly via heterotypic interactions in binary mixtures of Whi3 and RNA. However, within these condensates, RNA molecules become dynamically arrested. As a result, in ternary systems, simultaneous additions of Whi3 and pairs of distinct RNA molecules lead to well-mixed condensates, whereas delayed addition of an RNA component results in compositional distinctness. Therefore, compositional identities of condensates can be achieved via dynamical control, being driven, at least partially, by the dynamical arrest of RNA molecules. Finally, we show that synchronizing the production of different RNAs leads to more well-mixed, as opposed to compositionally distinct condensates in vivo.

Glutamate helps unmask the differences in driving forces for phase separation versus clustering of FET family proteins in sub-saturated solutions

Multivalent proteins undergo coupled segregative and associative phase transitions. Phase separation, a segregative transition, is driven by macromolecular solubility, and this leads to coexisting phases above system-specific saturation concentrations. Percolation is a continuous transition that is driven by multivalent associations among cohesive motifs. Contributions from percolation are highlighted by the formation of heterogeneous distributions of clusters in sub-saturated solutions, as was recently reported for Fused in sarcoma (FUS) and FET family proteins. Here, we show that clustering and phase separation are defined by a separation of length- and energy-scales. This is unmasked when glutamate is the primary solution anion. Glutamate is preferentially excluded from protein sites, and this enhances molecular associations. Differences between glutamate and chloride are manifest at ultra-low protein concentrations. These differences are amplified as concentrations increase, and they saturate as the micron-scale is approached. Therefore, condensate formation in supersaturated solutions and clustering in sub-saturated are governed by distinct energy and length scales. Glutamate, unlike chloride, is the dominant intracellular anion, and the separation of scales, which is masked in chloride, is unmasked in glutamate. Our work highlights how components of cellular milieus and sequence-encoded interactions contribute to amplifying distinct contributions from associative versus segregative phase transitions.

Glutamate helps unmask the differences in driving forces for phase separation versus clustering of FET family proteins in sub-saturated solutions

Multivalent proteins undergo coupled segregative and associative phase transitions. Phase separation, a segregative transition, is driven by macromolecular solubility, and this leads to coexisting phases above system-specific saturation concentrations. Percolation is a continuous transition that is driven by multivalent associations among cohesive motifs. Contributions from percolation are highlighted by the formation of heterogeneous distributions of clusters in sub-saturated solutions, as was recently reported for Fused in sarcoma (FUS) and FET family proteins. Here, we show that clustering and phase separation are defined by a separation of length- and energy-scales. This is unmasked when glutamate is the primary solution anion. Glutamate is preferentially excluded from protein sites, and this enhances molecular associations. Differences between glutamate and chloride are manifest at ultra-low protein concentrations. These differences are amplified as concentrations increase, and they saturate as the micron-scale is approached. Therefore, condensate formation in supersaturated solutions and clustering in sub-saturated are governed by distinct energy and length scales. Glutamate, unlike chloride, is the dominant intracellular anion, and the separation of scales, which is masked in chloride, is unmasked in glutamate. Our work highlights how components of cellular milieus and sequence-encoded interactions contribute to amplifying distinct contributions from associative versus segregative phase transitions.

Effects of linker length on phase separation: lessons from the Rubisco-EPYC1 system of the algal pyrenoid

Biomolecular condensates are membraneless organelles formed via phase separation of macromolecules, typically consisting of bond-forming "stickers" connected by flexible "linkers". Linkers have diverse roles, such as occupying space and facilitating interactions. To understand how linker length relative to other lengths affects condensation, we focus on the pyrenoid, which enhances photosynthesis in green algae. Specifically, we apply coarse-grained simulations and analytical theory to the pyrenoid proteins of Chlamydomonas reinhardtii: the rigid holoenzyme Rubisco and its flexible partner EPYC1. Remarkably, halving EPYC1 linker lengths decreases critical concentrations by ten-fold. We attribute this difference to the molecular "fit" between EPYC1 and Rubisco. Varying Rubisco sticker locations reveals that the native sites yield the poorest fit, thus optimizing phase separation. Surprisingly, shorter linkers mediate a transition to a gas of rods as Rubisco stickers approach the poles. These findings illustrate how intrinsically disordered proteins affect phase separation through the interplay of molecular length scales.

Developments in describing equilibrium phase transitions of multivalent associative macromolecules

Biomolecular condensates are distinct cellular bodies that form and dissolve reversibly to organize cellular matter and biochemical reactions in space and time. Condensates are thought to form and dissolve under the influence of spontaneous and driven phase transitions of multivalent associative macromolecules. These include phase separation, which is defined by segregation of macromolecules from the solvent or from one another, and percolation or gelation, which is an inclusive networking transition driven by reversible associations among multivalent macromolecules. Considerable progress has been made to model sequence-specific phase transitions, especially for intrinsically disordered proteins. Here, we summarize the state-of-the-art of theories and computations aimed at understanding and modeling sequence-specific, thermodynamically controlled, coupled associative and segregative phase transitions of archetypal multivalent macromolecules.

Dynamical control enables the formation of demixed biomolecular condensates

Macromolecular phase separation underlies the regulated formation and dissolution of biomolecular condensates. What is unclear is how condensates of distinct and shared macromolecular compositions form and coexist within cellular milieus. Here, we use theory and computation to establish thermodynamic criteria that must be satisfied to achieve compositionally distinct condensates. We applied these criteria to an archetypal ribonucleoprotein condensate and discovered that demixing into distinct protein-RNA condensates cannot be the result of purely thermodynamic considerations. Instead, demixed, compositionally distinct condensates arise due to asynchronies in timescales that emerge from differences in long-lived protein-RNA and RNA-RNA crosslinks. This type of dynamical control is also found to be active in live cells whereby asynchronous production of molecules is required for realizing demixed protein-RNA condensates. We find that interactions that exert dynamical control provide a versatile and generalizable way to influence the compositions of coexisting condensates in live cells.

Dynamics of protein condensates in weak-binding regime

Weak complementary interactions between proteins and nucleic acids are the main driving forces of intracellular liquid-liquid phase separation. The sticker-spacer model has emerged as a unifying principle for understanding the phase behavior of these multivalent molecules. It remains elusive how specific interactions mediated by stickers contribute to the rheological properties of the liquid condensates. Previous studies have revealed that for strong binding strength ɛ_{b}, the bulk diffusivity D depends on the effective bond lifetime τ, viz., D∝τ^{-1}. Consequently, equal concentrations of the complementary stickers induce a slow down in the dynamics of the condensates D∝e^{-1.5ɛ_{b}}. However, for weak-binding strength, it is expected that the resulting condensates are dynamic, loose network liquids rather than kinetically arrested, compact clusters. We develop a mean-field theory using the thermodynamics of the associative polymers and perform molecular-dynamics simulations based on the sticker-spacer model to study the controlling factors in the structure and dynamics of such condensates in the weak-binding regime. Through scaling analysis, we delineate how the free sticker fraction W_{f} and the bulk diffusivity D decrease with increasing binding energy and find that the internal dynamics of such network liquids are controlled by the free sticker fraction D∝W_{f}∝e^{-0.5ɛ_{b}} rather than the effective bond lifetime. Referred to as the free-sticker-dominated diffusivity, the microscopic slowdown due to a gradual loss of the free stickers affects the viscosity of the condensates as well, with the scaling of the zero-shear viscosity η∝e^{0.5ɛ_{b}}. Therefore, the way of controlling the structure, diffusivity, and viscosity of the condensates through the binding energy can be tested experimentally.

Tuning Protein Hydrogel Mechanics through Modulation of Nanoscale Unfolding and Entanglement in Postgelation Relaxation

Globular folded proteins are versatile nanoscale building blocks to create biomaterials with mechanical robustness and inherent biological functionality due to their specific and well-defined folded structures. Modulating the nanoscale unfolding of protein building blocks during network formation (in situ protein unfolding) provides potent opportunities to control the protein network structure and mechanics. Here, we control protein unfolding during the formation of hydrogels constructed from chemically cross-linked maltose binding protein using ligand binding and the addition of cosolutes to modulate protein kinetic and thermodynamic stability. Bulk shear rheology characterizes the storage moduli of the bound and unbound protein hydrogels and reveals a correlation between network rigidity, characterized as an increase in the storage modulus, and protein thermodynamic stability. Furthermore, analysis of the network relaxation behavior identifies a crossover from an unfolding dominated regime to an entanglement dominated regime. Control of in situ protein unfolding and entanglement provides an important route to finely tune the architecture, mechanics, and dynamic relaxation of protein hydrogels. Such predictive control will be advantageous for future smart biomaterials for applications which require responsive and dynamic modulation of mechanical properties and biological function.

Rheology and Viscoelasticity of Proteins and Nucleic Acids Condensates

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

Controlling cluster size in 2D phase-separating binary mixtures with specific interactions

By varying the concentration of molecules in the cytoplasm or on the membrane, cells can induce the formation of condensates and liquid droplets, similar to phase separation. Their thermodynamics, much studied, depends on the mutual interactions between microscopic constituents. Here, we focus on the kinetics and size control of 2D clusters, forming on membranes. Using molecular dynamics of patchy colloids, we model a system of two species of proteins, giving origin to specific heterotypic bonds. We find that concentrations, together with valence and bond strength, control both the size and the growth time rate of the clusters. In particular, if one species is in large excess, it gradually saturates the binding sites of the other species; the system then becomes kinetically arrested and cluster coarsening slows down or stops, thus yielding effective size selection. This phenomenology is observed both in solid and fluid clusters, which feature additional generic homotypic interactions and are reminiscent of the ones observed on biological membranes.