Differential Effects of Sequence-Local versus Nonlocal Charge Patterns on Phase Separation and Conformational Dimensions of Polyampholytes as Model Intrinsically Disordered Proteins.

Conformational properties of intrinsically disordered proteins (IDPs) are governed by a sequence-ensemble relationship. To differentiate the impact of sequence-local versus sequence-nonlocal features of an IDP's charge pattern on its conformational dimensions and its phase-separation propensity, the charge "blockiness" κ and the nonlocality-weighted sequence charge decoration (SCD) parameters are compared for their correlations with isolated-chain radii of gyration (s) and upper critical solution temperatures (UCSTs) of polyampholytes modeled by random phase approximation, field-theoretic simulation, and coarse-grained molecular dynamics. SCD is superior to κ in predicting because SCD accounts for effects of contact order, i.

Biological condensates form percolated networks with molecular motion properties distinctly different from dilute solutions.

Formation of membraneless organelles or biological condensates via phase separation and related processes hugely expands the cellular organelle repertoire. Biological condensates are dense and viscoelastic soft matters instead of canonical dilute solutions. To date, numerous different biological condensates have been discovered, but mechanistic understanding of biological condensates remains scarce.

Analytical Formulation and Field-Theoretic Simulation of Sequence-Specific Phase Separation of Protein-Like Heteropolymers with Short- and Long-Spatial-Range Interactions.

A theory for sequence-dependent liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) in the study of biomolecular condensates is formulated by extending the random phase approximation (RPA) and field-theoretic simulation (FTS) of heteropolymers with spatially long-range Coulomb interactions to include the fundamental effects of short-range, hydrophobic-like interactions between amino acid residues. To this end, short-range effects are modeled by Yukawa interactions between multiple nonelectrostatic charges derived from an eigenvalue decomposition of pairwise residue-residue contact energies. Chain excluded volume is afforded by incompressibility constraints.

Numerical Techniques for Applications of Analytical Theories to Sequence-Dependent Phase Separations of Intrinsically Disordered Proteins.

Biomolecular condensates, physically underpinned to a significant extent by liquid-liquid phase separation (LLPS), are now widely recognized by numerous experimental studies to be of fundamental biological, biomedical, and biophysical importance. In the face of experimental discoveries, analytical formulations emerged as a powerful yet tractable tool in recent theoretical investigations of the role of LLPS in the assembly and dissociation of these condensates. The pertinent LLPS often involves, though not exclusively, intrinsically disordered proteins engaging in multivalent interactions that are governed by their amino acid sequences.

Field theory description of ion association in re-entrant phase separation of polyampholytes.

Phase separation of several different overall neutral polyampholyte species (with zero net charge) is studied in solution with two oppositely charged ion species that can form ion pairs through an association reaction. Hereby, a field theory description of the system, which treats polyampholyte charge sequence dependent electrostatic interactions as well as excluded volume effects, is given. Interestingly, analysis of the model using random phase approximation and field theoretic simulation consistently shows evidence of a re-entrant polyampholyte phase separation at high ion concentrations when there is an overall decrease of volume upon ion association.

Effects of Cosolvents and Crowding Agents on the Stability and Phase Transition Kinetics of the SynGAP/PSD-95 Condensate Model of Postsynaptic Densities.

The SynGAP/PSD-95 binary protein system serves as a simple mimicry of postsynaptic densities (PSDs), which are protein assemblies based largely on liquid-liquid phase separation (LLPS), that are located underneath the plasma membrane of excitatory synapses. Surprisingly, the LLPS of the SynGAP/PSD-95 system is much more pressure sensitive than typical folded states of proteins or nucleic acids. It was found that phase-separated SynGAP/PSD-95 droplets dissolve into a homogeneous solution at a pressure of tens to hundred bar.

Assembly of model postsynaptic densities involves interactions auxiliary to stoichiometric binding.

The assembly of functional biomolecular condensates often involves liquid-liquid phase separation (LLPS) of proteins with multiple modular domains, which can be folded or conformationally disordered to various degrees. To understand the LLPS-driving domain-domain interactions, a fundamental question is how readily the interactions in the condensed phase can be inferred from interdomain interactions in dilute solutions. In particular, are the interactions leading to LLPS exclusively those underlying the formation of discrete interdomain complexes in homogeneous solutions? We address this question by developing a mean-field LLPS theory of two stoichiometrically constrained solute species.

Small-Angle X-ray Scattering Signatures of Conformational Heterogeneity and Homogeneity of Disordered Protein Ensembles.

An accurate account of disordered protein conformations is of central importance to deciphering the physicochemical basis of biological functions of intrinsically disordered proteins and the folding-unfolding energetics of globular proteins. Physically, disordered ensembles of nonhomopolymeric polypeptides are expected to be heterogeneous, i.e.

Subcompartmentalization of polyampholyte species in organelle-like condensates is promoted by charge-pattern mismatch and strong excluded-volume interaction.

Polyampholyte field theory and explicit-chain molecular dynamics models of sequence-specific phase separation of a system with two intrinsically disordered protein (IDP) species indicate consistently that a substantial polymer excluded volume and a significant mismatch of the IDP sequence charge patterns can act in concert, but not in isolation, to demix the two IDP species upon condensation. This finding reveals an energetic-geometric interplay in a stochastic, "fuzzy" molecular recognition mechanism that may facilitate subcompartmentalization of membraneless organelles.

A Simple Explicit-Solvent Model of Polyampholyte Phase Behaviors and Its Ramifications for Dielectric Effects in Biomolecular Condensates.

Biomolecular condensates such as membraneless organelles, underpinned by liquid-liquid phase separation (LLPS), are important for physiological function, with electrostatics, among other interaction types, being a prominent force in their assembly. Charge interactions of intrinsically disordered proteins (IDPs) and other biomolecules are sensitive to the aqueous dielectric environment. Because the relative permittivity of protein is significantly lower than that of water, the interior of an IDP condensate is expected to be a relatively low-dielectric regime, which aside from its possible functional effects on client molecules should facilitate stronger electrostatic interactions among the scaffold IDPs.

Comparative roles of charge, , and hydrophobic interactions in sequence-dependent phase separation of intrinsically disordered proteins.

Endeavoring toward a transferable, predictive coarse-grained explicit-chain model for biomolecular condensates underlain by liquid-liquid phase separation (LLPS) of proteins, we conducted multiple-chain simulations of the N-terminal intrinsically disordered region (IDR) of DEAD-box helicase Ddx4, as a test case, to assess roles of electrostatic, hydrophobic, cation-π, and aromatic interactions in amino acid sequence-dependent LLPS. We evaluated three different residue-residue interaction schemes with a shared electrostatic potential. Neither a common hydrophobicity scheme nor one augmented with arginine/lysine-aromatic cation-π interactions consistently accounted for available experimental LLPS data on the wild-type, a charge-scrambled, a phenylalanine-to-alanine (FtoA), and an arginine-to-lysine (RtoK) mutant of Ddx4 IDR.

Analytical Theory for Sequence-Specific Binary Fuzzy Complexes of Charged Intrinsically Disordered Proteins.

Intrinsically disordered proteins (IDPs) are important for biological functions. In contrast to folded proteins, molecular recognition among certain IDPs is "fuzzy" in that their binding and/or phase separation are stochastically governed by the interacting IDPs' amino acid sequences, while their assembled conformations remain largely disordered. To help elucidate a basic aspect of this fascinating yet poorly understood phenomenon, the binding of a homo or heterodimeric pair of polyampholytic IDPs is modeled statistical mechanically using cluster expansion.

A unified analytical theory of heteropolymers for sequence-specific phase behaviors of polyelectrolytes and polyampholytes.

The physical chemistry of liquid-liquid phase separation (LLPS) of polymer solutions bears directly on the assembly of biologically functional dropletlike bodies from proteins and nucleic acids. These biomolecular condensates include certain extracellular materials and intracellular compartments that are characterized as "membraneless organelles." Analytical theories are a valuable, computationally efficient tool for addressing general principles.

Pressure Sensitivity of SynGAP/PSD-95 Condensates as a Model for Postsynaptic Densities and Its Biophysical and Neurological Ramifications.

Biomolecular condensates consisting of proteins and nucleic acids can serve critical biological functions, so that some condensates are referred as membraneless organelles. They can also be disease-causing, if their assembly is misregulated. A major physicochemical basis of the formation of biomolecular condensates is liquid-liquid phase separation (LLPS).

Temperature, Hydrostatic Pressure, and Osmolyte Effects on Liquid-Liquid Phase Separation in Protein Condensates: Physical Chemistry and Biological Implications.

Liquid-liquid phase separation (LLPS) of proteins and other biomolecules play a critical role in the organization of extracellular materials and membrane-less compartmentalization of intra-organismal spaces through the formation of condensates. Structural properties of such mesoscopic droplet-like states were studied by spectroscopy, microscopy, and other biophysical techniques. The temperature dependence of biomolecular LLPS has been studied extensively, indicating that phase-separated condensed states of proteins can be stabilized or destabilized by increasing temperature.

Pressure-Sensitive and Osmolyte-Modulated Liquid-Liquid Phase Separation of Eye-Lens γ-Crystallins.

Biomolecular condensates can be functional (e.g., as membrane-less organelles) or dysfunctional (e.

Coarse-grained residue-based models of disordered protein condensates: utility and limitations of simple charge pattern parameters.

Biomolecular condensates undergirded by phase separations of proteins and nucleic acids serve crucial biological functions. To gain physical insights into their genetic basis, we study how liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs) depends on their sequence charge patterns using a continuum Langevin chain model wherein each amino acid residue is represented by a single bead. Charge patterns are characterized by the "blockiness" measure κ and the "sequence charge decoration" (SCD) parameter.

Pressure-Induced Dissolution and Reentrant Formation of Condensed, Liquid-Liquid Phase-Separated Elastomeric α-Elastin.

We investigated the combined effects of temperature and pressure on liquid-liquid phase separation (LLPS) phenomena of α-elastin up to the multi-kbar regime. FT-IR spectroscopy, CD, UV/Vis absorption, phase-contrast light and fluorescence microscopy techniques were employed to reveal structural changes and mesoscopic phase states of the system. A novel pressure-induced reentrant LLPS was observed in the intermediate temperature range.

Theories for Sequence-Dependent Phase Behaviors of Biomolecular Condensates.

Liquid-liquid phase separation and related condensation processes of intrinsically disordered proteins (IDPs), proteins with intrinsically disordered regions, and nucleic acids underpin various condensed-liquid droplets or gel-like assemblies in the cellular environment. Collectively referred to as condensates, these bodies provide spatial/temporal compartmentalization, often serving as hubs for regulated biomolecular interactions. Examples include certain extracellular materials, transcription complexes, and membraneless organelles such as germ and stress granules and the nucleolus.

A Lattice Model of Charge-Pattern-Dependent Polyampholyte Phase Separation.

In view of recent intense experimental and theoretical interests in the biophysics of liquid-liquid phase separation (LLPS) of intrinsically disordered proteins (IDPs), heteropolymer models with chain molecules configured as self-avoiding walks on the simple cubic lattice are constructed to study how phase behaviors depend on the sequence of monomers along the chains. To address pertinent general principles, we focus primarily on two fully charged 50-monomer sequences with significantly different charge patterns. Each monomer in our models occupies a single lattice site, and all monomers interact via a screened pairwise Coulomb potential.

Molecular recognition and packing frustration in a helical protein.

Biomolecular recognition entails attractive forces for the functional native states and discrimination against potential nonnative interactions that favor alternate stable configurations. The challenge posed by the competition of nonnative stabilization against native-centric forces is conceptualized as frustration. Experiment indicates that frustration is often minimal in evolved biological systems although nonnative possibilities are intuitively abundant.

Structural and hydrodynamic properties of an intrinsically disordered region of a germ cell-specific protein on phase separation.

Membrane encapsulation is frequently used by the cell to sequester biomolecules and compartmentalize their function. Cells also concentrate molecules into phase-separated protein or protein/nucleic acid "membraneless organelles" that regulate a host of biochemical processes. Here, we use solution NMR spectroscopy to study phase-separated droplets formed from the intrinsically disordered N-terminal 236 residues of the germ-granule protein Ddx4.