Protein folding, binding, and droplet formation in cell-like conditions

Computational Approaches to Predict Protein-Protein Interactions in Crowded Cellular Environments

Investigating protein-protein interactions is crucial for understanding cellular biological processes because proteins often function within molecular complexes rather than in isolation. While experimental and computational methods have provided valuable insights into these interactions, they often overlook a critical factor: the crowded cellular environment. This environment significantly impacts protein behavior, including structural stability, diffusion, and ultimately the nature of binding. In this review, we discuss theoretical and computational approaches that allow the modeling of biological systems to guide and complement experiments and can thus significantly advance the investigation, and possibly the predictions, of protein-protein interactions in the crowded environment of cell cytoplasm. We explore topics such as statistical mechanics for lattice simulations, hydrodynamic interactions, diffusion processes in high-viscosity environments, and several methods based on molecular dynamics simulations. By synergistically leveraging methods from biophysics and computational biology, we review the state of the art of computational methods to study the impact of molecular crowding on protein-protein interactions and discuss its potential revolutionizing effects on the characterization of the human interactome.

Exploring the dynamics and structure of PpiB in living Escherichia coli cells using electron paramagnetic resonance spectroscopy

The combined effects of the cellular environment on proteins led to the definition of a fifth level of protein structural organization termed quinary structure. To explore the implication of potential quinary structure for globular proteins, we studied the dynamics and conformations of Escherichia coli (E. coli) peptidyl-prolyl cis/trans isomerase B (PpiB) in E. coli cells. PpiB plays a major role in maturation and regulation of folded proteins by catalyzing the cis/trans isomerization of the proline imidic peptide bond. We applied electron paramagnetic resonance (EPR) techniques, utilizing both Gadolinium (Gd(III)) and nitroxide spin labels. In addition to using standard spin labeling approaches with genetically engineered cysteines, we incorporated an unnatural amino acid to achieve Gd(III)-nitroxide orthogonal labeling. We probed PpiB's residue-specific dynamics by X-band continuous wave EPR at ambient temperatures and its structure by double electron-electron resonance (DEER) on frozen samples. PpiB was delivered to E. coli cells by electroporation. We report a significant decrease in the dynamics induced by the cellular environment for two chosen labeling positions. These changes could not be reproduced by adding crowding agents and cell extracts. Concomitantly, we report a broadening of the distance distribution in E. coli, determined by Gd(III)-Gd(III) DEER measurements, as compared with solution and human HeLa cells. This suggests an increase in the number of PpiB conformations present in E. coli cells, possibly due to interactions with other cell components, which also contributes to the reduction in mobility and suggests the presence of a quinary structure.

Protein Association in Solution: Statistical Mechanical Modeling

Protein molecules associate in solution, often in clusters beyond pairwise, leading to liquid phase separations and high viscosities. It is often impractical to study these multi-protein systems by atomistic computer simulations, particularly in multi-component solvents. Instead, their forces and states can be studied by liquid state statistical mechanics. However, past such approaches, such as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, were limited to modeling proteins as spheres, and contained no microscopic structure-property relations. Recently, this limitation has been partly overcome by bringing the powerful Wertheim theory of associating molecules to bear on protein association equilibria. Here, we review these developments.

Crowded Environment Regulates the Coacervation of Biopolymers via Nonspecific Interactions

The membrane-less organelles (MLOs) with subcompartments are formed via liquid-liquid phase separation (LLPS) in the crowded cell interior whose background molecules are up to 400 mg/mL. It is still a puzzle how the background molecules regulate the formation, dynamics, and functions of MLOs. Using biphasic coacervate droplets formed by poly(l-lysine) (PLL), quaternized dextran (Q-dextran), and single-stranded oligonucleotides (ss-oligo) as a model of MLO, we online monitored the LLPS process in Bovine Serine Albumin (BSA) solution up to 200.0 mg/mL. Negatively charged BSA is able to form complex or coacervate with positively charged PLL and Q-dextran and thus participates in the LLPS via nonspecific interactions. Results show that BSA effectively regulates the LLPS by controlling the phase distribution, morphologies, and kinetics. With increasing BSA concentration, the spherical biphasic droplets evolve in sequence into phase-inverted flower-like structure, worm-like chains, network structures, and confined coacervates. Each kind of morphology is formed via its own specific growth and fusion pathway. Our work suggests that MLOs could be controlled solely by the crowded environment and provides a further step toward understanding the life process in cell.

Behaviour of the model antibody fluid constrained by rigid spherical obstacles: Effects of the obstacle-antibody attraction

This study investigates the behaviour of a fluid of monoclonal antibodies (mAbs) when trapped in a confinement represented by rigid spherical obstacles that attract antibodies. The antibody molecule is depicted as an assembly of seven hard spheres (7-bead model), organized to resemble a Y-shaped object. The model antibody has two Fab and one Fc domains located in the corners of letter Y. In this calculation, only the Fab-Fab and Fab-Fc attractive pairs of interactions are effective. The confinement is formed by the randomly distributed hard-spheres fixed in space. The spherical obstacles, besides the size exclusion, interact with beads of the antibody molecules via the Yukawa attractive potential. We applied the combination of the scaled particle theory, replica Ornstein-Zernike equations, Wertheim's thermodynamic perturbation approach and the Flory-Stockmayer theory to calculate: (i) the phase diagram of the liquid-liquid phase separation and the percolation threshold, (ii) the cluster size distributions, and (iii) the second virial coefficient of the protein fluid distributed among the obstacles. All these quantities were calculated as functions of the strength of the attraction between the monoclonal antibodies, and the monoclonal antibodies and obstacles. The conclusion is that while the hard-sphere obstacles decrease the critical density and the critical temperature of the mAbs fluid, the effect of the protein-obstacle attraction is more complex. Adding an attractive potential to the obstacle-mAbs interaction first increases the wideness of the T*-ρ envelope. However, with the further increase of the obstacle-mAbs attraction intensity, we observe reversal of the effect, the T*-ρ curves become narrower. At some point, depending on the obstacle-mAbs interaction, the situation is observed where two different temperatures have the same fluid density (re-entry point). In all the cases shown here the critical point decreases below the value for the neat fluid, but the behaviour with respect to an increase of the strength of the obstacle-mAbs attraction is not monotonic. Yet another interesting phenomenon, known in the literature as an approach toward the "empty liquid" state, is observed. The stability of the "protein droplets", formed by the liquid-liquid phase separation, depends on their local environment and temperature.

Size of the protein-protein energy funnel in crowded environment

Association of proteins to a significant extent is determined by their geometric complementarity. Large-scale recognition factors, which directly relate to the funnel-like intermolecular energy landscape, provide important insights into the basic rules of protein recognition. Previously, we showed that simple energy functions and coarse-grained models reveal major characteristics of the energy landscape. As new computational approaches increasingly address structural modeling of a whole cell at the molecular level, it becomes important to account for the crowded environment inside the cell. The crowded environment drastically changes protein recognition properties, and thus significantly alters the underlying energy landscape. In this study, we addressed the effect of crowding on the protein binding funnel, focusing on the size of the funnel. As crowders occupy the funnel volume, they make it less accessible to the ligands. Thus, the funnel size, which can be defined by ligand occupancy, is generally reduced with the increase of the crowders concentration. This study quantifies this reduction for different concentration of crowders and correlates this dependence with the structural details of the interacting proteins. The results provide a better understanding of the rules of protein association in the crowded environment.

NMR Provides Unique Insight into the Functional Dynamics and Interactions of Intrinsically Disordered Proteins

Intrinsically disordered proteins are ubiquitous throughout all known proteomes, playing essential roles in all aspects of cellular and extracellular biochemistry. To understand their function, it is necessary to determine their structural and dynamic behavior and to describe the physical chemistry of their interaction trajectories. Nuclear magnetic resonance is perfectly adapted to this task, providing ensemble averaged structural and dynamic parameters that report on each assigned resonance in the molecule, unveiling otherwise inaccessible insight into the reaction kinetics and thermodynamics that are essential for function. In this review, we describe recent applications of NMR-based approaches to understanding the conformational energy landscape, the nature and time scales of local and long-range dynamics and how they depend on the environment, even in the cell. Finally, we illustrate the ability of NMR to uncover the mechanistic basis of functional disordered molecular assemblies that are important for human health.

Preferential Interactions of a Crowder Protein with the Specific Binding Site of a Native Protein Complex

Nonspecific binding of crowder proteins with functional proteins is likely prevalent in vivo, yet direct quantitative evidence, let alone residue-specific information, is scarce. Here we present nuclear magnetic resonance (NMR) characterization showing that bovine serum albumin weakly but preferentially interacts with the histidine carrier protein (HPr). Notably, the binding interface overlaps with that for HPr's specific partner protein, EIN, leading to competition. The crowder protein thus decreases the EIN-HPr binding affinity and accelerates the dissociation of the native complex. In contrast, Ficoll-70 stabilizes the native complex and slows its dissociation, as one would expect from excluded-volume and microviscosity effects. Our atomistic modeling of macromolecular crowding rationalizes the experimental data and provides quantitative insights into the energetics of protein-crowder interactions. The integrated NMR and modeling study yields benchmarks for the effects of crowded cellular environments on protein-protein specific interactions, with implications for evolution regarding how nonspecific binding can be minimized or exploited.

From folding to function: complex macromolecular reactions unraveled one-by-one with optical tweezers

Single-molecule manipulation with optical tweezers has uncovered macromolecular behaviour hidden to other experimental techniques. Recent instrumental improvements have made it possible to expand the range of systems accessible to optical tweezers. Beyond focusing on the folding and structural changes of isolated single molecules, optical tweezers studies have evolved into unraveling the basic principles of complex molecular processes such as co-translational folding on the ribosome, kinase activation dynamics, ligand-receptor binding, chaperone-assisted protein folding, and even dynamics of intrinsically disordered proteins (IDPs). In this mini-review, we illustrate the methodological principles of optical tweezers before highlighting recent advances in studying complex protein conformational dynamics - from protein synthesis to physiological function - as well as emerging future issues that are beginning to be addressed with novel approaches.

Charge-driven condensation of RNA and proteins suggests broad role of phase separation in cytoplasmic environments

Phase separation processes are increasingly being recognized as important organizing mechanisms of biological macromolecules in cellular environments. Well-established drivers of phase separation are multi-valency and intrinsic disorder. Here, we show that globular macromolecules may condense simply based on electrostatic complementarity. More specifically, phase separation of mixtures between RNA and positively charged proteins is described from a combination of multiscale computer simulations with microscopy and spectroscopy experiments. Phase diagrams were mapped out as a function of molecular concentrations in experiment and as a function of molecular size and temperature via simulations. The resulting condensates were found to retain at least some degree of internal dynamics varying as a function of the molecular composition. The results suggest a more general principle for phase separation that is based primarily on electrostatic complementarity without invoking polymer properties as in most previous studies. Simulation results furthermore suggest that such phase separation may occur widely in heterogenous cellular environment between nucleic acid and protein components.

Aggregation, liquid-liquid phase separation, and percolation behaviour of a model antibody fluid constrained by hard-sphere obstacles

This study is concerned with the behaviour of proteins within confinement created by hard-sphere obstacles. An individual antibody molecule is depicted as an assembly of seven hard spheres, organized to resemble a Y-shaped (on average) antibody (7-bead model) protein. For comparison with other studies we, in one case, model the protein as a hard sphere decorated by three short-range attractive sites. The antibody has two Fab and one Fc domains located in the corners of the letter Y. In this calculation, only the Fab-Fab and Fab-Fc attractive pair interactions are possible. The confinement is formed by the randomly distributed hard-sphere obstacles fixed in space. Aside from size exclusion, the obstacles do not interact with antibodies, but they affect the protein-protein correlation. We used a combination of the scaled-particle theory, Wertheim's thermodynamic perturbation theory and the Flory-Stockmayer theory to calculate: (i) the second virial coefficient of the protein fluid, (ii) the percolation threshold, (iii) cluster size distributions, and (iv) the liquid-liquid phase separation as a function of the strength of the various pair interactions of the protein and the model parameters, such as protein concentration and the packing fraction of obstacles. The conclusion is that hard-sphere obstacles strongly decrease the critical density and also, but to a much lesser extent, the critical temperature. Also, the confinement enhances clustering, making the percolating region broader. The effect depends on the model parameters, such as the packing fraction of obstacles η0, the inter-site interaction strength εIJ, and the ratio between the size of the obstacle σ0 and the size of one bead of the model antibody σhs; the value of this ratio is varied here from 2 to 5. Interestingly, at low to moderate packing fractions of obstacles, the second virial coefficient first slightly decreases (destabilization), and the slope depends on the observation temperature, but then at higher values of η0 it increases. The calculated values of the second virial coefficient also depend on the size of the obstacles.

In-cell destabilization of a homodimeric protein complex detected by DEER spectroscopy

The complexity of the cellular medium can affect proteins' properties, and, therefore, in-cell characterization of proteins is essential. We explored the stability and conformation of the first baculoviral IAP repeat (BIR) domain of X chromosome-linked inhibitor of apoptosis (XIAP), BIR1, as a model for a homodimer protein in human HeLa cells. We employed double electron-electron resonance (DEER) spectroscopy and labeling with redox stable and rigid Gd³⁺ spin labels at three representative protein residues, C12 (flexible region), E22C, and N28C (part of helical residues 26 to 31) in the N-terminal region. In contrast to predictions by excluded-volume crowding theory, the dimer-monomer dissociation constant K _D was markedly higher in cells than in solution and dilute cell lysate. As expected, this increase was partially recapitulated under conditions of high salt concentrations, given that conserved salt bridges at the dimer interface are critically required for association. Unexpectedly, however, also the addition of the crowding agent Ficoll destabilized the dimer while the addition of bovine serum albumin (BSA) and lysozyme, often used to represent interaction with charged macromolecules, had no effect. Our results highlight the potential of DEER for in-cell study of proteins as well as the complexities of the effects of the cellular milieu on protein structures and stability.

Temperature relaxation in binary hard-sphere mixture system: Molecular dynamics and kinetic theory study

Computational schemes to describe the temperature relaxation in the binary hard-sphere mixture system are given on the basis of molecular dynamics (MD) simulation and renormalized kinetic theory. Event-driven MD simulations are carried out for three model systems in which the initial temperatures and the ratios of diameter and mass of two components are different to study the temporal evolution of each component temperature in nanoscale molecular conditions mimicking those in living cells. On the other hand, the temperature changes of the two components are also described in terms of a mean-field kinetic theory with the correlation functions calculated in the Percus-Yevick approximation. The calculated results by both the computational approaches have shown fair agreement with each other, whereas slight deviations have been found in the temporal range of femto- to picoseconds when the initial temperatures of the two components are significantly different, such as 300 K vs 1000 K. This discrepancy can be ascribed to the fast intra-component temperature relaxation assumed in the kinetic theory, and its violation in the MD simulations can be evaluated in terms of the Kullback-Leibler divergence between the equilibrated Maxwell-Boltzmann distribution at each temperature and the actual non-equilibrium velocity distribution realized in the MD. Thus, the present analysis provides a quantitative basis for addressing the temperature inhomogeneities experimentally observed in nanoscale crowding conditions.

Quantifying Protein-Protein Interactions in Molecular Simulations

Interactions among proteins, nucleic acids, and other macromolecules are essential for their biological functions and shape the physicochemcial properties of the crowded environments inside living cells. Binding interactions are commonly quantified by dissociation constants K_d, and both binding and nonbinding interactions are quantified by second osmotic virial coefficients B₂. As a measure of nonspecific binding and stickiness, B₂ is receiving renewed attention in the context of so-called liquid–liquid phase separation in protein and nucleic acid solutions. We show that K_d is fully determined by B₂ and the fraction of the dimer observed in molecular simulations of two proteins in a box. We derive two methods to calculate B₂. From molecular dynamics or Monte Carlo simulations using implicit solvents, we can determine B₂ from insertion and removal energies by applying Bennett’s acceptance ratio (BAR) method or the (binless) weighted histogram analysis method (WHAM). From simulations using implicit or explicit solvents, one can estimate B₂ from the probability that the two molecules are within a volume large enough to cover their range of interactions. We validate these methods for coarse-grained Monte Carlo simulations of three weakly binding proteins. Our estimates for K_d and B₂ allow us to separate out the contributions of nonbinding interactions to B₂. Comparison of calculated and measured values of K_d and B₂ can be used to (re-)parameterize and improve molecular force fields by calibrating specific affinities, overall stickiness, and nonbinding interactions. The accuracy and efficiency of K_d and B₂ calculations make them well suited for high-throughput studies of large interactomes.

Allostery of multidomain proteins with disordered linkers

Intrinsically disordered regions are often involved in allosteric regulation of multidomain proteins. They can act as disordered linkers to connect and interact with domains, resulting in rather complex allosteric mechanism and novel protein behavior. Therefore, it is necessary to analyze the diverse functions of disordered linkers in order to better understand allostery and relevant regulation process. Here we summarize recent advances in understanding the function of linkers and the advantages of adopting mutlidomain architecture with disorder linkers. It was shown that linkers between domains enhance the local domain concentration and make the allosteric regulation of weakly interacting partners possible, while linkers with only one tethered end cause an entropy effect to reduce binding affinity and prevent aggregation.

Whole-Cell Models and Simulations in Molecular Detail

Comprehensive data about the composition and structure of cellular components have enabled the construction of quantitative whole-cell models. While kinetic network-type models have been established, it is also becoming possible to build physical, molecular-level models of cellular environments. This review outlines challenges in constructing and simulating such models and discusses near- and long-term opportunities for developing physical whole-cell models that can connect molecular structure with biological function.

Calculation of Second Virial Coefficients of Atomistic Proteins Using Fast Fourier Transform

The second virial coefficient, B₂, measures a protein solution's deviation from ideal behavior. It is widely used to predict or explain solubility, crystallization condition, aggregation propensity, and critical temperature for liquid-liquid phase separation. B₂ is determined by the interaction energy between two protein molecules and, specifically, by the integration of the Mayer f-function in the relative configurational space (translation and rotation) of the two molecules. Simple theoretical models, such as one attributed to Derjaguin, Landau, Verwey, and Overbeek (DLVO), can fit the dependence of B₂ on salt concentrations. However, model parameters derived often are physically unrealistic and hardly transferable from protein to protein. Previous B₂ calculations incorporating atomistic details were done with limited sampling in the configurational space, due to enormous computational cost. Our FMAP method, based on fast Fourier transform, can considerably accelerate such calculations, and here we adapt it to calculate B₂ values for proteins represented at the atomic level in implicit solvent. After tuning of a single parameter in the energy function, FMAPB2 predicts well the B₂ values for lysozyme and other proteins over wide ranges of solvent conditions (salt concentration, pH, and temperature). The method is available as a web server at http://pipe.rcc.fsu.edu/fmapb2 .

Novel NMR Avenues to Explore the Conformation and Interactions of Glycans

This perspective article is focused on the presentation of the latest advances in NMR methods and applications that are behind the exciting achievements in the understanding of glycan receptors in molecular recognition events. Different NMR-based methodologies are discussed along with their applications to scrutinize the conformation and dynamics of glycans as well as their interactions with protein receptors.

Quantifying the protein-protein association rate in polymer solutions: crowding-induced diffusion and energy modifications

A theoretical framework is developed to study protein-protein association in polymer solutions under diffusion-limited conditions. Starting from the basal association rate, two fundamental aspects concerning macromolecular crowding are particularly taken into account. One is the effect of microviscosity on protein diffusion. The length-scale dependent relations of translational and rotational diffusion coefficients are incorporated. Another is relevant to the crowding-induced effective interaction between the pair of proteins. The resultant energy modifications to the basal association rate are properly introduced, following an instructive classification with increasing crowder size: repulsive interaction dominant, repulsive and attractive interactions competitive, and attractive interaction prevailing. With specific energy modification terms, we are able to investigate the deviations of the association rate from the Stokes-Einstein (SE) behavior (i.e., the linear relationship with respect to the reciprocal of macroviscosity) in a quantitative manner. Our theory is applied to study the association of TEM1-β-lactamase (TEM) and the β-lactamase inhibitor protein (BLIP) in polyethylene glycol (PEG) solutions, with varying concentration and polymerization. We explicitly evaluate the relative association rate constant as a function of the solution macroviscosity. The theoretical results demonstrate very good agreement with the experimental data. Moreover, the complicated non-trivial deviations, either positive (slower than SE) or negative (faster than SE), are systematically rationalized. The precise role of energy modifications and the microviscosity effect on diffusion, in particular on rotational diffusion, are clearly unraveled.

Unusual crowding-induced chain looping kinetics in hard-sphere fluids: a contrastive study with polymer solutions

A theoretical framework is developed to investigate the looping kinetics of a chain in hard-sphere (HS) fluids, based on a generalized Smoluchowski diffusion-reaction equation. A contrastive study with polymer solutions is performed. The crowding-associated effective viscosity and collapse effects are properly taken into account, which obey different scaling relations in HS and polymer fluids. We examine the dependence of the looping time on both concentration and size of crowders, demonstrating unusual and distinct discrepancies in the two crowded media. Firstly, in the solution of large polymers, the looping rate grows monotonically with polymer concentration. On the other hand, in the solution of large HSs, a caging regime can be observed, where the looping time tends to the value in the absence of crowders. Secondly, polymers in moderate size generally impede chain looping due to the enhanced viscosity. However, in HS fluids, the looping time exhibits a rather complicated variation with increasing HS size. We show a possible mechanism where in the case of small crowders with a relatively strong compaction in the probed chain, the looping kinetics can be facilitated. As the crowder size increases, the collapse effect is reduced and looping is dominated by viscosity-induced inhibition. Simultaneously, our theory rationalizes another possibility of the mechanism observed by recent simulation work. We conclude that the looping kinetics in specific systems actually should be governed by the critical competition between the two crowding factors. By giving reasonable measurements of effective viscosity and collapse, our theoretical framework can provide a unified strategy to analyze crowding effects on the looping rate in a systematic manner.

Computational approaches to macromolecular interactions in the cell

Structural modeling of a cell is an evolving strategic direction in computational structural biology. It takes advantage of new powerful modeling techniques, deeper understanding of fundamental principles of molecular structure and assembly, and rapid growth of the amount of structural data generated by experimental techniques. Key modeling approaches to principal types of macromolecular assemblies in a cell already exist. The main challenge, along with the further development of these modeling approaches, is putting them together in a consistent, unified whole cell model. This opinion piece addresses the fundamental aspects of modeling macromolecular assemblies in a cell, and the state-of-the-art in modeling of the principal types of such assemblies.

Both Ligands and Macromolecular Crowders Preferentially Bind to Closed Conformations of Maltose Binding Protein

In cellular environments, proteins not only interact with their specific partners but also encounter a high concentration of bystander macromolecules, or crowders. Nonspecific interactions with macromolecular crowders modulate the activities of proteins, but our knowledge about the rules of nonspecific interactions is still very limited. In previous work, we presented experimental evidence that macromolecular crowders acted competitively in inhibiting the binding of maltose binding protein (MBP) with its ligand maltose. Competition between a ligand and an inhibitor may result from binding to either the same site or different conformations of the protein. Maltose binds to the cleft between two lobes of MBP, and in a series of mutants, the affinities increased with an increase in the extent of lobe closure. Here we investigated whether macromolecular crowders also have a conformational or site preference when binding to MBP. The affinities of a polymer crowder, Ficoll70, measured by monitoring tryptophan fluorescence were 3-6-fold higher for closure mutants than for wild-type MBP. Competition between the ligand and crowder, as indicated by fitting of titration data and directly by nuclear magnetic resonance spectroscopy, and their similar preferences for closed MBP conformations further suggest the scenario in which the crowder, like maltose, preferentially binds to the interlobe cleft of MBP. Similar observations were made for bovine serum albumin as a protein crowder. Conformational and site preferences in MBP-crowder binding allude to the paradigm that nonspecific interactions can possess hallmarks of molecular recognition, which may be essential for intracellular organizations including colocalization of proteins and liquid-liquid phase separation.

Solvent Composition Effects on the Structural Properties of the Aβ42 Monomer from the 3D-RISM-KH Molecular Theory of Solvation

Structural characterization of amyloid (A)β peptides implicated in Alzheimer's disease is a challenging problem due to their intrinsically disordered nature and their high propensity for aggregation. Only limited information is currently available from experiments on conformational properties and aggregation pathways of the peptides in cellular environments. In silico modeling complements experimental information, providing atomistic insight into structure and dynamics of different Aβ species. All-atom explicit solvent molecular dynamics (MD) simulations with a properly selected force field can deliver reliable structural and dynamic information. In the case of intrinsically disordered Aβ peptides, enhanced sampling simulations beyond the nanosecond time scale are required to obtain statistically meaningful results even for simple solvent conditions. To overcome the challenges of conformational sampling in crowded cellular environments, alternative approaches have to be used, including postprocessing of MD data. In this study, we employ the statistical-mechanical, three-dimensional reference interaction site model with the Kovalenko-Hirata closure integral equation molecular theory of solvation to describe solvent composition effects on the conformational equilibrium in a structural ensemble of the Aβ42 (covering residues 1-42) monomer based on a statistical reweighting technique. The methodology enables a computationally efficient prediction on how different factors in the cellular environment, such as solvent composition, nonpolar solvation, and macromolecular crowding, affect the structural properties of the monomer. Similarities have been identified between changes in the structural ensemble caused by nonpolar solvation and crowded environments modeled by ionic solution with large negative ions. In particular, both solvent conditions reduce the random coil content and enhance the helical structure content of the monomer. In contrast to the previous studies, which reported increased α-helical content of peptides in crowded environments, this work attributes these structural features to the difference in solvent exposure of hydrophilic residues of the monomer for different secondary structure elements, rather than to (entropic) excluded volume effects.

Intrinsically Disordered Protein Exhibits Both Compaction and Expansion under Macromolecular Crowding

Conformational malleability allows intrinsically disordered proteins (IDPs) to respond agilely to their environments, such as nonspecifically interacting with in vivo bystander macromolecules (or crowders). Previous studies have emphasized conformational compaction of IDPs due to steric repulsion by macromolecular crowders, but effects of soft attraction are largely unexplored. Here we studied the conformational ensembles of the IDP FlgM in both polymer and protein crowders by small-angle neutron scattering. As crowder concentrations increased, the mean radius of gyration of FlgM first decreased but then exhibited an uptick. Ensemble optimization modeling indicated that FlgM conformations under protein crowding segregated into two distinct populations, one compacted and one extended. Coarse-grained simulations showed that compacted conformers fit into an interstitial void and occasionally bind to a surrounding crowder, whereas extended conformers snake through interstitial crevices and bind multiple crowders simultaneously. Crowder-induced conformational segregation may facilitate various cellular functions of IDPs.

Macromolecular Crowding Tunes Protein Stability by Manipulating Solvent Accessibility

In all intracellular processes, protein structure and dynamics are subject to the influence of macromolecular crowding (MC). Here, the impact of MC agents of different types and sizes on the model protein Bacillus subtilis Cold shock protein B (BsCspB) during both thermal and chemical denaturation have been comprehensively investigated. We consistently reveal a distinct stabilization of BsCspB in a manner dependent on the MC concentration but not on viscosity, polarity, or size of the MC agent used. This general stabilization has been decoded by use of NMR spectroscopy, through monitoring of chemical shift (CS) perturbations and the intramolecular hydrogen‐bonding networks, as well as local protection of amide protons against exchange with solvent protons. Whereas CSs and hydrogen‐bonding networks are not systematically affected in the presence of MC, we detected a pronounced reduction in exchange in loop regions of BsCspB. We conclude that this reduced accessibility of solvent protons is a key parameter for the increases in protein stability seen under MC.

Biophysical and structural characterization of the small heat shock protein HspA from Thermosynechococcus vulcanus in 2 M urea

Small heat shock proteins (sHSPs) belong to the superfamily of molecular chaperones. They prevent aggregation of partially unfolded or misfolded client proteins, providing protection to organisms under stress conditions. Here, we report the biophysical and structural characterization of a small heat shock protein (HspA) from a thermophilic cyanobacterium Thermosynechococcus vulcanus in the presence of 2 M urea. HspA has been shown to be important for the protection of Photosystem II and the Phycobilisome antenna complex at elevated temperatures. Heterologously expressed HspA requires the presence of 1-2 M urea to maintain its solubility at concentrations required for most characterization methods. Spectroscopic studies reveal the presence of the β-sheet structure and intactness of the tertiary fold in HspA. In vitro assays show that the HspA maintains chaperone-like activity in protecting soluble proteins from thermal aggregation. Chromatography and electron microscopy show that the HspA exists as a mixture of oligomeric forms in the presence of 2 M urea. HspA was successfully crystallized only in the presence of 2 M urea. The crystal structure of HspA shows urea-induced loss of about 30% of the secondary structure without major alteration in the tertiary structure of the protein. The electron density maps reveal changes in the hydrogen bonding network which we attribute to the presence of urea. The crystal structure of HspA demonstrates a mixture of both direct interactions between urea and protein functionalities and interactions between urea and the surrounding solvent that indirectly affect the protein, which are in accordance with previously published studies.

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. Consistent with random phase approximation (RPA) theory and lattice simulations, LLPS propensity as characterized by critical temperature Tcr* increases with increasingly negative SCD for a set of sequences showing a positive correlation between κ and -SCD. Relative to RPA, the simulated sequence-dependent variation in Tcr* is often-though not always-smaller, whereas the simulated critical volume fractions are higher. However, for a set of sequences exhibiting an anti-correlation between κ and -SCD, the simulated Tcr*'s are quite insensitive to either parameter. Additionally, we find that blocky sequences that allow for strong electrostatic repulsion can lead to coexistence curves with upward concavity as stipulated by RPA, but the LLPS propensity of a strictly alternating charge sequence was likely overestimated by RPA and lattice models because interchain stabilization of this sequence requires spatial alignments that are difficult to achieve in real space. These results help delineate the utility and limitations of the charge pattern parameters and of RPA, pointing to further efforts necessary for rationalizing the newly observed subtleties.

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

Human serum albumin (HSA) has been identified as an important regulator of amyloid-β (Aβ) 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 Aβ fibrillization, but the mechanism underlying the interference of fatty acids on Aβ-HSA interactions has been unclear. Here, we used molecular dynamics simulations to gain atomic-level insight on the weak binding of monomeric Aβ40 and Aβ42 peptides with apo and FA·HSA. Consistent with recent NMR data, C-terminal residues of the Aβ peptides have the highest propensities for interacting with apo HSA. Interestingly, the Aβ binding residues of apo and FA·HSA exhibit distinct patterns, which qualitatively correlate with backbone flexibility. In FA·HSA, both flexibilities and Aβ 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 Aβ 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 Aβ-HSA binding and contributes to the understanding of HSA regulation of Aβ aggregation.

Liquid-Liquid Phase Separation of Patchy Particles Illuminates Diverse Effects of Regulatory Components on Protein Droplet Formation

Recently many cellular functions have been associated with membraneless organelles, or protein droplets, formed by liquid-liquid phase separation (LLPS). Proteins in these droplets often contain RNA-binding domains, but the effects of RNA on LLPS have been controversial. To gain better understanding on the roles of RNA and other macromolecular regulators, here we used Gibbs-ensemble simulations to determine phase diagrams of two-component patchy particles, as models for mixtures of proteins with regulatory components. Protein-like particles have four patches, with attraction strength ε_PP; regulatory particles experience mutual steric repulsion but have two attractive patches toward proteins, with the strength ε_PR tunable. At low ε_PR, the regulator, due to steric repulsion, preferentially partitions in the dispersed phase, thereby displacing the protein into the droplet phase and promoting LLPS. At moderate ε_PR, the regulator starts to partition and displace the protein in the droplet phase, but only to weaken bonding networks and thereby suppress LLPS. At ε_PR > ε_PP, the enhanced bonding ability of the regulator initially promotes LLPS, but at higher amounts, the resulting displacement of the protein suppresses LLPS. These results illustrate how RNA can have disparate effects on LLPS, thus able to perform diverse functions in different organelles.

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.

Physical principles of intracellular organization via active and passive phase transitions

Exciting recent developments suggest that phase transitions represent an important and ubiquitous mechanism underlying intracellular organization. We describe key experimental findings in this area of study, as well as the application of classical theoretical approaches for quantitatively understanding these data. We also discuss the way in which equilibrium thermodynamic driving forces may interface with the fundamentally out-of-equilibrium nature of living cells. In particular, time and/or space-dependent concentration profiles may modulate the phase behavior of biomolecules in living cells. We suggest future directions for both theoretical and experimental work that will shed light on the way in which biological activity modulates the assembly, properties, and function of viscoelastic states of living matter.

Markov modeling of peptide folding in the presence of protein crowders

We use Markov state models (MSMs) to analyze the dynamics of a β-hairpin-forming peptide in Monte Carlo (MC) simulations with interacting protein crowders, for two different types of crowder proteins [bovine pancreatic trypsin inhibitor (BPTI) and GB1]. In these systems, at the temperature used, the peptide can be folded or unfolded and bound or unbound to crowder molecules. Four or five major free-energy minima can be identified. To estimate the dominant MC relaxation times of the peptide, we build MSMs using a range of different time resolutions or lag times. We show that stable relaxation-time estimates can be obtained from the MSM eigenfunctions through fits to autocorrelation data. The eigenfunctions remain sufficiently accurate to permit stable relaxation-time estimation down to small lag times, at which point simple estimates based on the corresponding eigenvalues have large systematic uncertainties. The presence of the crowders has a stabilizing effect on the peptide, especially with BPTI crowders, which can be attributed to a reduced unfolding rate ku, while the folding rate kf is left largely unchanged.

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.

Crowding in Cellular Environments at an Atomistic Level from Computer Simulations

The effects of crowding in biological environments on biomolecular structure, dynamics, and function remain not well understood. Computer simulations of atomistic models of concentrated peptide and protein systems at different levels of complexity are beginning to provide new insights. Crowding, weak interactions with other macromolecules and metabolites, and altered solvent properties within cellular environments appear to remodel the energy landscape of peptides and proteins in significant ways including the possibility of native state destabilization. Crowding is also seen to affect dynamic properties, both conformational dynamics and diffusional properties of macromolecules. Recent simulations that address these questions are reviewed here and discussed in the context of relevant experiments.