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.

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.

Surface Charge Can Modulate Phase Separation of Multidomain Proteins.

Phase separation has emerged as an important mechanism explaining the formation of certain biomolecular condensates. Biological phase separation is often driven by the multivalent interactions of modular protein domains. Beyond valency, the physical features of folded domains that promote phase separation are poorly understood. We used a model system─the small ubiquitin modifier (SUMO) and its peptide ligand, the SUMO interaction motif (SIM)─to examine how domain surface charge influences multivalency-driven phase separation. Phase separation of polySUMO and polySIM was altered by pH via a change in the protonation state of SUMO surface histidines. These effects were recapitulated by histidine mutations, which modulated SUMO solubility and polySUMO-polySIM phase separation in parallel and were quantitatively explained by atomistic modeling of weak interactions among proteins in the system. Thus, surface charge can tune the phase separation of multivalent proteins, suggesting a means of controlling phase separation biologically, evolutionarily, and therapeutically.

Protamine-Mediated Tangles Produce Extreme Deoxyribonucleic Acid Compaction.

In sperm cells, protamine replaces histones to compact DNA 10-20 times more than in somatic cells. To characterize the extreme compaction, we employed confocal microscopy and optical tweezers to determine the conformations and stability of protamine-bound λ-DNA. Confocal images show increasing compaction of λ-DNA at increasing protamine concentration. In the presence of protamine, single λ-DNA molecules form tangles that withstand forces strong enough (∼55 pN) for strand separation and shorten the contour length by up to 40% even at high forces, as well as bends and loops that rupture at 10-40 pN forces. Strand separation nucleates tangles, implicating protamine interactions with DNA bases. Molecular dynamics simulations show that Arg sidechains of protamine each form hydrogen bonds with multiple bases, frequently in the form of a wedge between the two strands of DNA. Protamine may participate in both local and higher-order chromatin organization, leading to extreme compaction and global transcription silencing.

Power law in a bounded range: Estimating the lower and upper bounds from sample data.

Power law distributions are widely observed in chemical physics, geophysics, biology, and beyond. The independent variable x of these distributions has an obligatory lower bound and, in many cases, also an upper bound. Estimating these bounds from sample data is notoriously difficult, with a recent method involving O(N3) operations, where N denotes sample size. Here I develop an approach for estimating the lower and upper bounds that involve O(N) operations. The approach centers on calculating the mean values, x̂min and x̂max, of the smallest x and the largest x in N-point samples. A fit of x̂min or x̂max as a function of N yields the estimate for the lower or upper bound. Application to synthetic data demonstrates the accuracy and reliability of this approach.

N-WASP is competent for downstream signaling before full release from autoinhibition.

Allosteric regulation of intrinsically disordered proteins (IDPs) is still vastly understudied compared to the counterpart of structured proteins. Here, we used molecular dynamics simulations to characterize the regulation of the IDP N-WASP by the binding of its basic region with inter- and intramolecular ligands (PIP2 and an acidic motif, respectively). The intramolecular interactions keep N-WASP in an autoinhibited state; PIP2 binding frees the acidic motif for interacting with Arp2/3 and thereby initiating actin polymerization. We show that PIP2 and the acidic motif compete in binding with the basic region. However, even when PIP2 is present at 30% in the membrane, the acidic motif is free of contact with the basic region ("open" state) in only 8.5% of the population. The very C-terminal three residues of the A motif are crucial for Arp2/3 binding; conformations where only the A tail is free are present at a much higher population than the open state (40- to 6-fold, depending on the PIP2 level). Thus, N-WASP is competent for Arp2/3 binding before it is fully freed from autoinhibition.

Functional stability of water wire-carbonyl interactions in an ion channel.

Water wires are critical for the functioning of many membrane proteins, as in channels that conduct water, protons, and other ions. Here, in liquid crystalline lipid bilayers under symmetric environmental conditions, the selective hydrogen bonding interactions between eight waters comprising a water wire and a subset of 26 carbonyl oxygens lining the antiparallel dimeric gramicidin A channel are characterized by 17O NMR spectroscopy at 35.2 T (or 1,500 MHz for 1H) and computational studies. While backbone 15N spectra clearly indicate structural symmetry between the two subunits, single site 17O labels of the pore-lining carbonyls report two resonances, implying a break in dimer symmetry caused by the selective interactions with the water wire. The 17O shifts document selective water hydrogen bonding with carbonyl oxygens that are stable on the millisecond timescale. Such interactions are supported by density functional theory calculations on snapshots taken from molecular dynamics simulations. Water hydrogen bonding in the pore is restricted to just three simultaneous interactions, unlike bulk water environs. The stability of the water wire orientation and its electric dipole leads to opposite charge-dipole interactions for K+ ions bound at the two ends of the pore, thereby providing a simple explanation for an ∼20-fold difference in K+ affinity between two binding sites that are ∼24 Šapart. The 17O NMR spectroscopy reported here represents a breakthrough in high field NMR technology that will have applications throughout molecular biophysics, because of the acute sensitivity of the 17O nucleus to its chemical environment.

Why Do Disordered and Structured Proteins Behave Differently in Phase Separation?

Intracellular membraneless organelles and their myriad cellular functions have garnered tremendous recent interest. It is becoming well accepted that they form via liquid-liquid phase separation (LLPS) of protein mixtures (often including RNA), where the organelles correspond to a protein-rich droplet phase coexisting with a protein-poor bulk phase. The major protein components contain disordered regions and often also RNA-binding domains, and the disordered fragments on their own easily undergo LLPS. By contrast, LLPS for structured proteins has been observed infrequently. The contrasting phase behaviors can be explained by modeling disordered and structured proteins, respectively, as polymers and colloids. These physical models also provide a better understanding of the regulation of droplet formation by cellular signals and its dysregulation leading to diseases.

Binding free energy decomposition and multiple unbinding paths of buried ligands in a PreQ1 riboswitch.

Riboswitches are naturally occurring RNA elements that control bacterial gene expression by binding to specific small molecules. They serve as important models for RNA-small molecule recognition and have also become a novel class of targets for developing antibiotics. Here, we carried out conventional and enhanced-sampling molecular dynamics (MD) simulations, totaling 153.5 µs, to characterize the determinants of binding free energies and unbinding paths for the cognate and synthetic ligands of a PreQ1 riboswitch. Binding free energy analysis showed that two triplets of nucleotides, U6-C15-A29 and G5-G11-C16, contribute the most to the binding of the cognate ligands, by hydrogen bonding and by base stacking, respectively. Mg2+ ions are essential in stabilizing the binding pocket. For the synthetic ligands, the hydrogen-bonding contributions of the U6-C15-A29 triplet are significantly compromised, and the bound state resembles the apo state in several respects, including the disengagement of the C15-A14-A13 and A32-G33 base stacks. The bulkier synthetic ligands lead to significantly loosening of the binding pocket, including extrusion of the C15 nucleobase and a widening of the C15-C30 groove. Enhanced-sampling simulations further revealed that the cognate and synthetic ligands unbind in almost opposite directions. Our work offers new insight for designing riboswitch ligands.

Multiphase organization is a second phase transition within multi-component biomolecular condensates.

We present a mean-field theoretical model, along with molecular dynamics simulations, to show that the multiphase organization of multi-component condensates is a second phase transition. Whereas the first phase transition that leads to the separation of condensates from the bulk phase is driven by the overall attraction among the macromolecular components, the second phase transition can be driven by the disparity in the strength between the self- and cross-species attraction. At a fixed level of disparity in interaction strengths, both of the phase transitions can be observed by decreasing the temperature, leading first to the separation of condensates from the bulk phase and then to component demixing inside condensates. The existence of a critical temperature for demixing and predicted binodals are verified by molecular dynamics simulations of model mixtures.

Three archetypical classes of macromolecular regulators of protein liquid-liquid phase separation.

Membraneless organelles, corresponding to the droplet phase upon liquid-liquid phase separation (LLPS) of protein or protein-RNA mixtures, mediate myriad cellular functions. Cells use a variety of biochemical signals such as expression level and posttranslational modification to regulate droplet formation and dissolution, but the physical basis of the regulatory mechanisms remains ill-defined and quantitative assessment of the effects is largely lacking. Our computational study predicted that the strength of attraction by droplet-forming proteins dictates whether and how macromolecular regulators promote or suppress LLPS. We experimentally tested this prediction, using the pentamers of SH3 domains and proline-rich motifs (SH35 and PRM5) as droplet-forming proteins. Determination of the changes in phase boundary and the partition coefficients in the droplet phase over a wide range of regulator concentrations yielded both a quantitative measure and a mechanistic understanding of the regulatory effects. Three archetypical classes of regulatory effects were observed. Ficoll 70 at high concentrations indirectly promoted SH35-PRM5 LLPS, by taking up volume in the bulk phase and thereby displacing SH35 and PRM5 into the droplet phase. Lysozyme had a moderate partition coefficient and suppressed LLPS by substituting weaker attraction with SH35 for the stronger SH35-PRM5 attraction in the droplet phase. By forming even stronger attraction with PRM5, heparin at low concentrations partitioned heavily into the droplet phase and promoted LLPS. These characteristics were recapitulated by computational results of patchy particle models, validating the identification of the 3 classes of macromolecular regulators as volume-exclusion promotors, weak-attraction suppressors, and strong-attraction promotors.

Oligomer Formation by Amyloid-ß42 in a Membrane-Mimicking Environment in Alzheimer's Disease.

The brains of Alzheimer's disease (AD) patients contain numerous amyloid plaques that are diagnostic of the disease. The plaques are primarily composed of the amyloidogenic peptides proteins Aß40 and Aß42, which are derived by the processing of the amyloid pre-cursor protein (APP) by two proteases called ß-secretase and γ-secretase. Aß42 differs from Aß40 in having two additional hydrophobic amino acids, ILE and ALA, at the C-terminus. A small percentage of AD is autosomal dominant (ADAD) and linked either to the genes for the presenilins, which are part of γ-secretase, or APP. Because ADAD shares most pathogenic features with widespread late-onset AD, Aß peptides have become the focus of AD research. Fibrils formed by the aggregation of these peptides are the major component of plaques and were initially targeted in AD therapy. However, the fact that the abundance of plaques does not correlate well with cognitive decline in AD patients has led investigators to examine smaller Aß aggregates called oligomers. The low levels and heterogeneity of Aß oligomers have made the determination of their structures difficult, but recent structure determinations of oligomers either formed or initiated in detergents have been achieved. We report here on the structures of these oligomers and suggest how they may be involved in AD.

Machine Learning-Enabled Pipeline for Large-Scale Virtual Drug Screening.

Virtual screening is receiving renewed attention in drug discovery, but progress is hampered by challenges on two fronts: handling the ever-increasing sizes of libraries of drug-like compounds and separating true positives from false positives. Here, we developed a machine learning-enabled pipeline for large-scale virtual screening that promises breakthroughs on both fronts. By clustering compounds according to molecular properties and limited docking against a drug target, the full library was trimmed by 10-fold; the remaining compounds were then screened individually by docking; and finally, a dense neural network was trained to classify the hits into true and false positives. As illustration, we screened for inhibitors against RPN11, the deubiquitinase subunit of the proteasome, and a drug target for breast cancer.

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.

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.

Membrane Association and Functional Mechanism of Synaptotagmin-1 in Triggering Vesicle Fusion.

Upon Ca2+ influx, synaptic vesicles fuse with the presynaptic plasma membrane (PM) to release neurotransmitters. Membrane fusion is triggered by synaptotagmin-1, a transmembrane protein in the vesicle membrane (VM), but the mechanism is under debate. Synaptotagmin-1 contains a single transmembrane helix (TM) and two tandem C2 domains (C2A and C2B). This study aimed to use molecular dynamics simulations to elucidate how Ca2+-bound synaptotagmin-1, by simultaneously associating with VM and PM, brings them together for fusion. Although C2A stably associates with VM via two Ca2+-binding loops, C2B has a propensity to partially dissociate. Importantly, an acidic motif in the TM-C2A linker competes with VM for interacting with C2B, thereby flipping its orientation to face PM. Subsequently, C2B readily associates with PM via a polybasic cluster and a Ca2+-binding loop. The resulting mechanistic model for the triggering of membrane fusion by synaptotagmin-1 reconciles many experimental observations.

Tug of War between Condensate Phases in a Minimal Macromolecular System.

Membraneless organelles, comprising dozens to hundreds of macromolecular components, form heterogeneous phases in space and evolve over time in material properties. Here, using four macromolecules, we demonstrate a range of phase behaviors associated with membraneless organelles and uncover the underlying physicochemical rules. The macromolecules are SH35 (S) and PRM5 (P), two pentameric, oppositely charged protein constructs; heparin (H), an anionic polymer; and lysozyme (L), a cationic single-domain protein. The S:P, S:L, and P:H binaries form droplets, but the H:L binary forms network-like precipitates, therefore setting up a tug of war between different condensate phases within the S:P:H:L quaternary. The H:L exception can partly be attributed to the compactness of L, as supported by ThT binding data. Increasing amounts of P alone or both S and P, but not S alone, can dissolve H:L precipitates into droplets. These differential effects can be explained by the order of the strengths of pairwise attraction: H:L > P:H > S:P > S:L, deduced from the shapes of ternary phase boundaries. When S and P are at subdissolution concentrations, S:P:H:L precipitates change over time to become droplet-like in appearance, although not completely fluidic according to fluorescence recovery after photobleaching. In fact, confocal microscopy reveals separated S:L-rich and P:H-rich foci inside the droplet-like condensates. Therefore, complex phase behaviors of membraneless organelles, including rescue of aberrant phase transitions, demixing of condensates, and time evolution of material properties, can all be reconstituted and understood via a minimal macromolecular system.

Electrostatic Interactions in Protein Structure, Folding, Binding, and Condensation.

Charged and polar groups, through forming ion pairs, hydrogen bonds, and other less specific electrostatic interactions, impart important properties to proteins. Modulation of the charges on the amino acids, e.g., by pH and by phosphorylation and dephosphorylation, have significant effects such as protein denaturation and switch-like response of signal transduction networks. This review aims to present a unifying theme among the various effects of protein charges and polar groups. Simple models will be used to illustrate basic ideas about electrostatic interactions in proteins, and these ideas in turn will be used to elucidate the roles of electrostatic interactions in protein structure, folding, binding, condensation, and related biological functions. In particular, we will examine how charged side chains are spatially distributed in various types of proteins and how electrostatic interactions affect thermodynamic and kinetic properties of proteins. Our hope is to capture both important historical developments and recent experimental and theoretical advances in quantifying electrostatic contributions of proteins.

Determinants for Fusion Speed of Biomolecular Droplets.

Biomolecular droplets formed through phase separation have a tendency to fuse. The speed with which fusion occurs is a direct indicator of condensate liquidity, which is key to both cellular functions and diseases. Using a dual-trap optical tweezers setup, we found the fusion speeds of four types of droplets to differ by two orders of magnitude. The order of fusion speed correlates with the fluorescence of thioflavin T, which in turn reflects the macromolecular packing density inside droplets. Unstructured protein or polymer chains pack loosely and readily rearrange, leading to fast fusion. In contrast, structured protein domains pack more closely and have to break extensive contacts before rearrangement, corresponding to slower fusion. This molecular interpretation for disparate fusion speeds provides mechanistic insight into the assembly and aging of biomolecular droplets.

Fatty Acids Compete with Aß in Binding to Serum Albumin by Quenching Its Conformational Flexibility.

Human serum albumin (HSA) has been identified as an important regulator of amyloid-ß (Aß) fibrillization both in blood plasma and in cerebrospinal fluid. Fatty acids bind to HSA, and high serum levels of fatty acids increase the risk of Alzheimer's disease. In vitro, fatty-acid-loaded HSA (FA·HSA) loses the protective effect against Aß fibrillization, but the mechanism underlying the interference of fatty acids on Aß-HSA interactions has been unclear. Here, we used molecular dynamics simulations to gain atomic-level insight on the weak binding of monomeric Aß40 and Aß42 peptides with apo and FA·HSA. Consistent with recent NMR data, C-terminal residues of the Aß peptides have the highest propensities for interacting with apo HSA. Interestingly, the Aß binding residues of apo and FA·HSA exhibit distinct patterns, which qualitatively correlate with backbone flexibility. In FA·HSA, both flexibilities and Aß binding propensities are relatively even among the three domains. In contrast, in apo HSA, domain III shows the highest flexibility and is the primary target for Aß binding. Specifically, deformation of apo HSA creates strong binding sites within subdomain IIIb, around the interface between subdomains IIIa and IIIb, and at the cleft between domains III and I. Therefore, much like disordered proteins, HSA can take advantage of flexibility in forming promiscuous interactions with partners, until the flexibility is quenched by fatty-acid binding. Our work explains the effect of fatty acids on Aß-HSA binding and contributes to the understanding of HSA regulation of Aß aggregation.