Determination of Condensate Material Properties from Droplet Deformation

Fundamental Aspects of Phase-Separated Biomolecular Condensates

Biomolecular condensates, formed through phase separation, are upending our understanding in much of molecular, cell, and developmental biology. There is an urgent need to elucidate the physicochemical foundations of the behaviors and properties of biomolecular condensates. Here we aim to fill this need by writing a comprehensive, critical, and accessible review on the fundamental aspects of phase-separated biomolecular condensates. We introduce the relevant theoretical background, present the theoretical basis for the computation and experimental measurement of condensate properties, and give mechanistic interpretations of condensate behaviors and properties in terms of interactions at the molecular and residue levels.

Amino Acid-Dependent Material Properties of Tetrapeptide Condensates

Condensates formed by intrinsically disordered proteins mediate a myriad of cellular processes and are linked to pathological conditions including neurodegeneration. Rules of how different types of amino acids (e.g., π-π pairs) dictate the physical properties of biomolecular condensates are emerging, but our understanding of the roles of different amino acids is far from complete. Here we studied condensates formed by tetrapeptides of the form XXssXX, where X is an amino acid and ss represents a disulfide bond along the backbone. Eight peptides form four types of condensates at different concentrations and pH values: droplets (X = F, L, M, P, V, A); amorphous dense liquids (X = L, M, P, V, A); amorphous aggregates (X = W), and gels (X = I, V, A). The peptides exhibit enormous differences in phase equilibrium and material properties, including a 368-fold range in the threshold concentration for phase separation and a 3856-fold range in viscosity. All-atom molecular dynamics simulations provide physical explanations of these results. The present work also reveals widespread critical behaviors, including critical slowing down manifested by the formation of amorphous dense liquids and critical scaling obeyed by fusion speed, with broad implications for condensate function.

Adenosine Triphosphate Mediates Phase Separation of Disordered Basic Proteins by Bridging Intermolecular Interaction Networks

Adenosine triphosphate (ATP) is an abundant molecule with crucial cellular roles as the energy currency and a building block of nucleic acids and for protein phosphorylation. Here we show that ATP mediates the phase separation of basic intrinsically disordered proteins (bIDPs). In the resulting condensates, ATP is highly concentrated (apparent partition coefficients up to 7700) and serves as bridges between bIDP chains. These liquid-like droplets have some of the lowest interfacial tension (∼25 pN/μm) but high zero-shear viscosities (1-15 Pa s) due to the bridged protein networks, and yet their fusion has some of the highest speeds (∼1 μm/ms). The rapid fusion manifests extreme shear thinning, where the apparent viscosity is lower than zero-shear viscosity by over 100-fold, made possible by fast reformation of the ATP bridges. At still higher concentrations, ATP does not dissolve bIDP droplets but results in aggregates and fibrils.

ATP Mediates Phase Separation of Disordered Basic Proteins by Bridging Intermolecular Interaction Networks

ATP is an abundant molecule with crucial cellular roles as the energy currency and a building block of nucleic acids and for protein phosphorylation. Here we show that ATP mediates the phase separation of basic intrinsically disordered proteins (bIDPs). In the resulting condensates, ATP is highly concentrated (apparent partition coefficients at 200-5000) and serves as bridges between bIDP chains. These liquid-like droplets have some of the lowest interfacial tension (~25 pN/μm) but high zero-shear viscosities (1-15 Pa s) due to the bridged protein networks, and yet their fusion has some of the highest speeds (~1 μm/ms). The rapid fusion manifests extreme shear thinning, where the apparent viscosity is lower than zero-shear viscosity by over 100-fold, made possible by fast reformation of the ATP bridges. At still higher concentrations, ATP does not dissolve bIDP droplets but results in aggregates and fibrils.

Determining Thermodynamic and Material Properties of Biomolecular Condensates by Confocal Microscopy and Optical Tweezers

While the roles of biomolecular condensates in health and disease are being intensely studied, it is equally important that their physical properties are characterized in order to achieve mechanistic understanding. Here we share some of the protocols developed in our lab for measuring thermodynamic and materials properties of condensates. These include a simple method for determining the droplet-phase concentrations of condensate components on a confocal microscope, and a method for determining the viscoelasticity of condensates by optical tweezers. These protocols are either generally applicable to biomolecular condensates or are unique for their characterization.

Macromolecular Regulation of the Material Properties of Biomolecular Condensates

Biomolecular condensates inside cells contain dozens to hundreds of macromolecular components and are surrounded by many others. Our computational studies predicted that macromolecular regulators have matching effects on the phase equilibrium and interfacial tension of condensates. Here we validate this prediction experimentally and characterize the effects of macromolecular regulators on other material properties, including viscoelasticity and fusion speed. Local melting due to the heating of a laser beam and turbidity assay both show that Ficoll70 raises the melting temperature of condensates formed by polylysine:heparin mixtures, whereas optical-tweezer measurements reveal parallel increases in interfacial tension. Additional optical-tweezer experiments report elevations in viscosity and shear relaxation time but also fusion speed by Ficoll70. The fusion speed is higher than predicted by modeling the condensates as purely viscous, demonstrating viscoelasticity and shear thinning. These results illustrate the ample opportunities for macromolecular regulators to tune material properties for proper functions of biomolecular condensates.

Liquid-liquid phase separation as an organizing principle of intracellular space: overview of the evolution of the cell compartmentalization concept

At the turn of the twenty-first century, fundamental changes took place in the understanding of the structure and function of proteins and then in the appreciation of the intracellular space organization. A rather mechanistic model of the organization of living matter, where the function of proteins is determined by their rigid globular structure, and the intracellular processes occur in rigidly determined compartments, was replaced by an idea that highly dynamic and multifunctional "soft matter" lies at the heart of all living things. According this "new view", the most important role in the spatio-temporal organization of the intracellular space is played by liquid-liquid phase transitions of biopolymers. These self-organizing cellular compartments are open dynamic systems existing at the edge of chaos. They are characterized by the exceptional structural and compositional dynamics, and their multicomponent nature and polyfunctionality provide means for the finely tuned regulation of various intracellular processes. Changes in the external conditions can cause a disruption of the biogenesis of these cellular bodies leading to the irreversible aggregation of their constituent proteins, followed by the transition to a gel-like state and the emergence of amyloid fibrils. This work represents a historical overview of changes in our understanding of the intracellular space compartmentalization. It also reflects methodological breakthroughs that led to a change in paradigms in this area of science and discusses modern ideas about the organization of the intracellular space. It is emphasized here that the membrane-less organelles have to combine a certain resistance to the changes in their environment and, at the same time, show high sensitivity to the external signals, which ensures the normal functioning of the cell.

Surface tension and super-stoichiometric surface enrichment in two-component biomolecular condensates

Cells can achieve internal organization by exploiting liquid-liquid phase separation to form biomolecular condensates. Here we focus on the surface properties of condensates composed of two multivalent associative polymers held together by one-to-one “sticker” bonds. Using coarse-grained molecular-dynamics simulations, we study the influence of component stoichiometry on condensate surface properties. We find that unequal stoichiometry results in enrichment of the majority species at the interface and a sharp reduction of surface tension. To relate these two effects, we show that the reduction in surface tension scales linearly with the excess concentration of free binding sites at the interface. Our results imply that each excess free site contributes an approximately fixed additional energy and entropy to the interface, with the latter dominating such that enrichment of free majority sites lowers the surface tension. Our work provides insight into novel physical mechanisms by which cells can regulate condensate surface properties.

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Stoichiometry controls the surface tension of two-component biomolecular condensates

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Unequal stoichiometry leads to enrichment of the majority species at the interface

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Enrichment of the free majority binding sites increases the interfacial entropy

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Surface tension is drastically reduced at unequal stoichiometry

Shape recovery of deformed biomolecular droplets: Dependence on condensate viscoelasticity

A theoretical study on the shape dynamics of phase-separated biomolecular droplets is presented, highlighting the importance of condensate viscoelasticity. Previous studies on shape dynamics have modeled biomolecular condensates as purely viscous, but recent data have shown them to be viscoelastic. Here, we present an exact analytical solution for the shape recovery dynamics of deformed biomolecular droplets. The shape recovery of viscous droplets has an exponential time dependence, with the time constant given by the "viscocapillary" ratio, i.e., viscosity over interfacial tension. In contrast, the shape recovery dynamics of viscoelastic droplets is multi-exponential, with shear relaxation yielding additional time constants. During shape recovery, viscoelastic droplets exhibit shear thickening (increase in apparent viscosity) at fast shear relaxation rates but shear thinning (decrease in apparent viscosity) at slow shear relaxation rates. These results highlight the importance of viscoelasticity and expand our understanding of how material properties affect condensate dynamics in general, including aging.

Shear relaxation governs fusion dynamics of biomolecular condensates

Phase-separated biomolecular condensates must respond agilely to biochemical and environmental cues in performing their wide-ranging cellular functions, but our understanding of condensate dynamics is lagging. Ample evidence now indicates biomolecular condensates as viscoelastic fluids, where shear stress relaxes at a finite rate, not instantaneously as in viscous liquids. Yet the fusion dynamics of condensate droplets has only been modeled based on viscous liquids, with fusion time given by the viscocapillary ratio (viscosity over interfacial tension). Here we used optically trapped polystyrene beads to measure the viscous and elastic moduli and the interfacial tensions of four types of droplets. Our results challenge the viscocapillary model, and reveal that the relaxation of shear stress governs fusion dynamics. These findings likely have implications for other dynamic processes such as multiphase organization, assembly and disassembly, and aging.

Viscoelasticity of biomolecular condensates conforms to the Jeffreys model

Biomolecular condensates, largely by virtue of their material properties, are revolutionizing biology, and yet, the physical understanding of these properties is lagging. Here, I show that the viscoelasticity of condensates can be captured by a simple model, comprising a component where shear relaxation is an exponential function (with time constant τ1) and a component with nearly instantaneous shear relaxation (time constant τ0 → 0). Modulation of intermolecular interactions, e.g., by adding salt, can disparately affect the two components such that the τ1 component may dominate at low salt, whereas the τ0 component may dominate at high salt. Condensates have a tendency to fuse, with the dynamics accelerated by interfacial tension and impeded by viscosity. For fast-fusion condensates, shear relaxation on the τ1 timescale may become rate-limiting such that the fusion speed is no longer in direction proportion to the interfacial tension. These insights help narrow the gap in understanding between the biology and physics of biomolecular condensates.

Erratum: Salt-Dependent Rheology and Surface Tension of Protein Condensates Using Optical Traps [Phys. Rev. Lett. 121, 258101 (2018)]

This corrects the article DOI: 10.1103/PhysRevLett.121.258101.