Peptide diffusion in biomolecular condensates.

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

Parameter Dependence of the Solubility Limit for Disodium Phosphate.

The solubility limit was calculated for supersaturated solutions of disodium phosphate in water as a function of the sodium-oxygen Lennard-Jones radius parameter Rmin. We found that changes in the sodium-oxygen Rmin were clearly exponentially related to the concentration of the solubility limit. Starting from standard force fields more suited to nucleic acids and phospholipids, only relatively small changes were required to achieve the experimentally known solubility limit. Simultaneously, we found that it was possible to achieve the solubility limit and the osmotic pressure with the same model parameters. Based on transferability, the adjusted Rmin parameter can be used to more accurately model phosphorylated proteins.

Transition Mutations in the hTERT Promoter Are Unrelated to Potential i-motif Formation in the C-Rich Strand.

Increased expression of the human telomere reverse transcriptase (hTERT) in tumors promotes tumor cell survival and diminishes the survival of patients. Cytosine-to-thymine (C-to-T) transition mutations (C250T or C228T) in the hTERT promoter create binding sites for transcription factors, which enhance transcription. The G-rich strand of the hTERT promoter can form G-quadruplex structures, whereas the C-rich strand can form an i-motif in which multiple cytosine residues are protonated. We considered the possibility that i-motif formation might promote cytosine deamination to uracil and C-to-T mutations. We computationally probed the accessibility of cytosine residues in an i-motif to attack by water. We experimentally examined regions of the C-rich strand to form i-motifs using pH-dependent UV and CD spectra. We then incubated the C-rich strand with and without the G-rich complementary strand DNA under various conditions, followed by deep sequencing. Surprisingly, deamination rates did not vary substantially across the 46 cytosines examined, and the two mutation hotspots were not deamination hotspots. The appearance of mutational hotspots in tumors is more likely the result of the selection of sequences with increased promoter binding affinity and hTERT expression.

Direct measurements of biomolecular electrostatics through experiments.

Biomolecular electrostatics has been a subject of computational investigations based on 3D structures. This situation is changing because emerging experimental tools allow us to quantitatively investigate biomolecular electrostatics without any use of structure information. Now, electrostatic potentials around biomolecules can directly be measured for many residues simultaneously by nuclear magnetic resonance (NMR) spectroscopy. This NMR method can be used to study electrostatic aspects of various processes, including macromolecular association and liquid-liquid phase separation. Applications to structurally flexible biomolecules such as intrinsically disordered proteins are particularly useful. The new tools also facilitate examination of theoretical models and methods for biomolecular electrostatics.

Effects of Conformational Constraint on Peptide Solubility Limits.

Liquid-liquid phase separation of proteins preferentially involves intrinsically disordered proteins or disordered regions. Understanding the solution chemistry of these phase separations is key to learning how to quantify and manipulate systems that involve such processes. Here, we investigate the effect of cyclization on the liquid-liquid phase separation of short polyglycine peptides. We simulated separate aqueous systems of supersaturated cyclic and linear GGGGG and observed spontaneous liquid-liquid phase separation in each of the solutions. The cyclic GGGGG phase separates less robustly than linear GGGGG and has a higher aqueous solubility, even though linear GGGGG has a more favorable single molecule solvation free energy. The versatile and abundant interpeptide contacts formed by the linear GGGGG stabilize the condensed droplet phase, driving the phase separation in this system. In particular, we find that van der Waals close contact interactions are enriched in the droplet phase as opposed to electrostatic interactions. An analysis of the change in backbone conformational entropy that accompanies the phase transition revealed that cyclic peptides lose significantly less entropy in this process as expected. However, we find that the enhanced interaction enthalpy of linear GGGGG in the droplet phase is enough to compensate for a larger decrease in conformational entropy.

Assessment of the Components of the Electrostatic Potential of Proteins in Solution: Comparing Experiment and Theory.

In this work, the components of the protein electrostatic potentials in solution are analyzed with NMR paramagnetic relaxation enhancement experiments and compared with continuum solution theory, and multiscale simulations. To determine the contributions of the solution components, we analyze them at different ionic strengths from 0 to 745 mM. A theoretical approximation allows the determination of the electrostatic potential at a given proton without reference to the protein structure given the ratio of paramagnetic relaxation enhancements rates between a cationic and an anionic probe. The results derived from simulations show good agreement with experiment and simple continuum solvent theory for many of the residues. A discrepancy including a switch of sign of the electrostatic potential was observed for particular residues. By considering the components of the potential, we found the discrepancy is mainly caused by angular correlations of the probe molecules with these residues. The correction for the correlations allows a more accurate analysis of the experiments determining the electrostatic potential of proteins in solution.

The Effects of Flexibility on dsDNA-dsDNA Interactions.

A detailed understanding of the physical mechanism of ion-mediated dsDNA interactions is important in biological functions such as DNA packaging and homologous pairing. We report the potential of mean force (PMF) or the effective solvent mediated interactions between two parallel identical dsDNAs as a function of interhelical separation in 0.15 M NaCl solution. Here, we study the influence of flexibility of dsDNAs on the effective interactions by comparing PMFs between rigid models and flexible ones. The role of flexibility of dsDNA pairs in their association is elucidated by studying the energetic properties of Na+ ions as well as the fluctuations of ions around dsDNAs. The introduction of flexibility of dsDNAs softens the vdW contact wall and induces more counterion fluctuations around dsDNAs. In addition, flexibility facilitates the Na+ ions dynamics affecting their distribution. The results quantify the extent of attraction influenced by dsDNA flexibility and further emphasize the importance of non-continuum solvation approaches.

Structural Studies on the Shapeshifting Murine Norovirus.

Noroviruses are responsible for almost a fifth of all cases of gastroenteritis worldwide. The calicivirus capsid is composed of 180 copies of VP1 with a molecular weight of ~58 kDa. This coat protein is divided into the N-terminus (N), the shell (S) and C-terminal protruding (P) domains. The S domain forms a shell around the viral RNA genome, while the P domains dimerize to form protrusions on the capsid surface. The P domain is subdivided into P1 and P2 subdomains, with the latter containing the binding sites for cellular receptors and neutralizing antibodies. Reviewed here are studies on murine norovirus (MNV) showing that the capsid responds to several physiologically relevant cues; bile, pH, Mg2+, and Ca2+. In the initial site of infection, the intestinal tract, high bile and metal concentrations and low pH cause two significant conformational changes: (1) the P domain contracts onto the shell domain and (2) several conformational changes within the P domain lead to enhanced receptor binding while blocking antibody neutralization. In contrast, the pH is neutral, and the concentrations of bile and metals are low in the serum. Under these conditions, the loops at the tip of the P domain are in the open conformation with the P domain floating on a linker or tether above the shell. This conformational state favors antibody binding but reduces interactions with the receptor. In this way, MNV uses metabolites and environmental cues in the intestine to optimize cellular attachment and escape antibody binding but presents a wholly different structure to the immune system in the serum. To our knowledge, this is the first example of a virus shapeshifting in this manner to escape the immune response.

Multiple Signals in the Gut Contract the Mouse Norovirus Capsid To Block Antibody Binding While Enhancing Receptor Affinity.

Human norovirus is the leading cause of gastroenteritis worldwide, with no approved vaccine or antiviral treatment to mitigate infection. These plus-strand RNA viruses have T = 3 icosahedral protein capsids with 90 pronounced protruding (P) domain dimers, to which antibodies and cellular receptors bind. We previously demonstrated that bile binding to the capsid of mouse norovirus (MNV) causes several major conformational changes; the entire P domain rotates by ∼90° and contracts onto the shell, the P domain dimers rotate about each other, and the structural equilibrium of the epitopes at the top of the P domain shifts toward the closed conformation, which favors receptor binding while blocking antibody binding. Here, we demonstrate that MNV undergoes reversible conformational changes at pH 5.0 that are nearly identical to those observed when bile binds. Notably, at low pH or when metals bind, a cluster of acidic resides in the G'-H' loop interact and distort the G'-H' loop, and this may drive C'-D' loop movement toward the closed conformation. Enzyme-linked immunosorbent assays with infectious virus particles at low pH or in the presence of metals demonstrated that all tested antibodies do not bind to this contracted form, akin to what was observed with the MNV-bile complex. Therefore, low pH, cationic metals, and bile salts are physiological triggers in the gut for P domain contraction and structural rearrangement, which synergistically prime the virus for receptor binding while blocking antibody binding. IMPORTANCE The protruding domains on the calicivirus capsids are recognized by cell receptors and antibodies. We demonstrated that MNV P domains are highly mobile, and bile causes contraction onto the shell surface while allosterically blocking antibody binding. We present the near-atomic cryo-electron microscopy structures of infectious MNV at pH 5.0 and pH 7.5. Surprisingly, low pH is sufficient to cause the same conformational changes as when bile binds. A cluster of acidic residues on the G'-H' loop were most likely involved in the pH effects. These residues also bound divalent cations and had the same conformation as observed here at pH 5. Binding assays demonstrated that low pH and metals block antibody binding, and thus the G'-H' loop might be driving the conformational changes. Therefore, low pH, cationic metals, and bile salts in the gut synergistically prime the virus for receptor binding while blocking antibody binding.

Contributions of higher-order proximal distribution functions to solvent structure around proteins.

The proximal distribution function (pDF) quantifies the probability of finding a solvent molecule in the vicinity of solutes. The approach constitutes a hierarchically organized theory for constructing approximate solvation structures around solutes. Given the assumption of universality of atom cluster-specific solvation, reconstruction of the solvent distribution around arbitrary molecules provides a computationally convenient route to solvation thermodynamics. Previously, such solvent reconstructions usually considered the contribution of the nearest-neighbor distribution only. We extend the pDF reconstruction algorithm to terms including next-nearest-neighbor contribution. As a test, small molecules (alanine and butane) are examined. The analysis is then extended to include the protein myoglobin in the P6 crystal unit cell. Molecular dynamics simulations are performed, and solvent density distributions around the solute molecules are compared with the results from different pDF reconstruction models. It is shown that the next-nearest-neighbor modification significantly improves the reconstruction of the solvent number density distribution in concave regions and between solute molecules. The probability densities are then used to calculate the solute-solvent non-bonded interaction energies including van der Waals and electrostatic, which are found to be in good agreement with the simulated values.

Thermodynamic Compensation in Peptides Following Liquid-Liquid Phase Separation.

Liquid-liquid phase separation of proteins often incorporates intrinsically disordered proteins or those with disordered regions. Examining these processes via the entropy change is desirable for establishing a quantitative foundation with which to probe and understand these phase transitions. Of interest is the effect of residue sequence on the entropy of the peptide backbone. In this work we model these systems via all atom simulations of liquid-liquid phase separation of peptides. Systems of supersaturated pentapeptides separate into a peptide-dense liquid droplet phase as well as a dilute (saturated) aqueous phase. An analysis of the change in backbone conformational entropy associated with the phase transition was performed. We examined systems of four different pentapeptides (GGGGG, GGQGG, GGNGG, and GGVGG) in order to explore the effect of sequence variation on the conformational entropy, as well as the effect of side chain variation on the physical characteristics of the droplet phases. We find that the loss of conformational entropy that accompanies aqueous → droplet transitions is more than compensated by a decrease in interaction enthalpy as contributions to the free energy change for the process.

De novo determination of near-surface electrostatic potentials by NMR.

Electrostatic potentials computed from three-dimensional structures of biomolecules by solving the Poisson-Boltzmann equation are widely used in molecular biophysics, structural biology, and medicinal chemistry. Despite the approximate nature of the Poisson-Boltzmann theory, validation of the computed electrostatic potentials around biological macromolecules is rare and methodologically limited. Here, we present a unique and powerful NMR method that allows for straightforward and extensive comparison with electrostatic models for biomolecules and their complexes. This method utilizes paramagnetic relaxation enhancement arising from analogous cationic and anionic cosolutes whose spatial distributions around biological macromolecules reflect electrostatic potentials. We demonstrate that this NMR method enables de novo determination of near-surface electrostatic potentials for individual protein residues without using any structural information. We applied the method to ubiquitin and the Antp homeodomain-DNA complex. The experimental data agreed well with predictions from the Poisson-Boltzmann theory. Thus, our experimental results clearly support the validity of the theory for these systems. However, our experimental study also illuminates certain weaknesses of the Poisson-Boltzmann theory. For example, we found that the theory predicts stronger dependence of near-surface electrostatic potentials on ionic strength than observed in the experiments. Our data also suggest that conformational flexibility or structural uncertainties may cause large errors in theoretical predictions of electrostatic potentials, particularly for highly charged systems. This NMR-based method permits extensive assessment of near-surface electrostatic potentials for various regions around biological macromolecules and thereby may facilitate improvement of the computational approaches for electrostatic potentials.

Quantitative description of a contractile macromolecular machine.

Contractile injection systems (CISs) [type VI secretion system (T6SS), phage tails, and tailocins] use a contractile sheath-rigid tube machinery to breach cell walls and lipid membranes. The structures of the pre- and postcontraction states of several CISs are known, but the mechanism of contraction remains poorly understood. Combining structural information of the end states of the 12-megadalton R-type pyocin sheath-tube complex with thermodynamic and force spectroscopy analyses and an original modeling procedure, we describe the mechanism of pyocin contraction. We show that this nanomachine has an activation energy of 160 kilocalories/mole (kcal/mol), and it releases 2160 kcal/mol of heat and develops a force greater than 500 piconewtons. Our combined approach provides a quantitative and experimental description of the membrane penetration process by a CIS.

A Norovirus Uses Bile Salts To Escape Antibody Recognition While Enhancing Receptor Binding.

Noroviruses, members of the Caliciviridae family, are the major cause of epidemic gastroenteritis in humans, causing ∼20 million cases annually. These plus-strand RNA viruses have T=3 icosahedral protein capsids with 90 pronounced protruding (P) domain dimers to which antibodies and cellular receptors bind. In the case of mouse norovirus (MNV), bile salts have been shown to enhance receptor (CD300lf) binding to the P domain. We demonstrated previously that the P domains of several genotypes are markedly flexible and "float" over the shell, but the role of this flexibility was unclear. Recently, we demonstrated that bile causes a 90° rotation and collapse of the P domain onto the shell surface. Since bile binds distally to the P-shell interface, it was not at all clear how it could cause such dramatic changes. Here, we present the near-atomic resolution cryo-electron microscopy (cryo-EM) structure of the MNV protruding domain complexed with a neutralizing Fab. On the basis of previous results, we show here that bile salts cause allosteric conformational changes in the P domain that block antibody recognition of the top of the P domain. In addition, bile causes a major rearrangement of the P domain dimers that is likely responsible for the bile-induced collapse of the P domain onto the shell. In the contracted shell conformation, antibodies to the P1 and shell domains are not expected to bind. Therefore, at the site of infection in the gut, the host's own bile allows the virus to escape antibody-mediated neutralization while enhancing cell attachment. IMPORTANCE The major feature of calicivirus capsids is the 90 protruding domains (P domains) that are the site of cell receptor attachment and antibody epitopes. We demonstrated previously that these P domains are highly mobile and that bile causes these "floating" P domains in mouse norovirus (MNV) to contract onto the shell surface. Here, we present the near-atomic cryo-EM structure of the isolated MNV P domain complexed with a neutralizing Fab fragment. Our data show that bile causes two sets of changes. First, bile causes allosteric conformational changes in the epitopes at the top of the P domain that block antibody binding. Second, bile causes the P domain dimer subunits to rotate relative to each other, causing a contraction of the P domain that buries epitopes at the base of the P and shell domains. Taken together, the results show that MNV uses the host's own metabolites to enhance cell receptor binding while simultaneously blocking antibody recognition.

Effects of Model Shape, Volume, and Softness of the Capsid for DNA Packaging of phi29.

Double-stranded DNA is under extreme confinement when packed in phage phi29 with osmotic pressures approaching 60 atm and densities near liquid crystalline. The shape of the capsid determined from experiment is elongated. We consider the effects of the capsid shape and volume on the DNA distribution. We propose simple models for the capsid of phage phi29 to capture volume, shape, and wall flexibility, leading to an accurate DNA density profile. The effect of the packaging motor twisting the DNA on the resulting density distribution has been explored. We find packing motor induced twisting leads to a greater numbers of defects formed. The emergence of defects such as bubbles or large roll angles along the DNA shows a sequence dependence, and the resulting flexibility leads to an inhomogeneous distribution of defects occurring more often at TpA steps and AT-rich regions. In conjunction with capsid elongation, this has effects on the global DNA packing structures.

Dynamics of Ionic Interactions at Protein-Nucleic Acid Interfaces.

Molecular association of proteins with nucleic acids is required for many biological processes essential to life. Electrostatic interactions via ion pairs (salt bridges) of nucleic acid phosphates and protein side chains are crucial for proteins to bind to DNA or RNA. Counterions around the macromolecules are also key constituents for the thermodynamics of protein-nucleic acid association. Until recently, there had been only a limited amount of experiment-based information about how ions and ionic moieties behave in biological macromolecular processes. In the past decade, there has been significant progress in quantitative experimental research on ionic interactions with nucleic acids and their complexes with proteins. The highly negatively charged surfaces of DNA and RNA electrostatically attract and condense cations, creating a zone called the ion atmosphere. Recent experimental studies were able to examine and validate theoretical models on ions and their mobility and interactions with macromolecules. The ionic interactions are highly dynamic. The counterions rapidly diffuse within the ion atmosphere. Some of the ions are released from the ion atmosphere when proteins bind to nucleic acids, balancing the charge via intermolecular ion pairs of positively charged side chains and negatively charged backbone phosphates. Previously, the release of counterions had been implicated indirectly by the salt-concentration dependence of the association constant.Recently, direct detection of counterion release by NMR spectroscopy has become possible and enabled more accurate and quantitative analysis of the counterion release and its entropic impact on the thermodynamics of protein-nucleic acid association. Recent studies also revealed the dynamic nature of ion pairs of protein side chains and nucleic acid phosphates. These ion pairs undergo transitions between two major states. In one of the major states, the cation and the anion are in direct contact and form hydrogen bonds. In the other major state, the cation and the anion are separated by water. Transitions between these states rapidly occur on a picosecond to nanosecond time scale. When proteins interact with nucleic acids, interfacial arginine (Arg) and lysine (Lys) side chains exhibit considerably different behaviors. Arg side chains show a higher propensity to form rigid contacts with nucleotide bases, whereas Lys side chains tend to be more mobile at the molecular interfaces. The dynamic ionic interactions may facilitate adaptive molecular recognition and play both thermodynamic and kinetic roles in protein-nucleic acid interactions.

Physical Chemistry of the Protein Backbone: Enabling the Mechanisms of Intrinsic Protein Disorder.

Over the last two decades it has become clear that well-defined structure is not a requisite for proteins to properly function. Rather, spectra of functionally competent, structurally disordered states have been uncovered requiring canonical paradigms in molecular biology to be revisited or reimagined. It is enticing and oftentimes practical to divide the proteome into structured and unstructured, or disordered, proteins. While function, composition, and structural properties largely differ, these two classes of protein are built upon the same scaffold, namely, the protein backbone. The versatile physicochemical properties of the protein backbone must accommodate structural disorder, order, and transitions between these states. In this review, we survey these properties through the conceptual lenses of solubility and conformational populations and in the context of protein-disorder mediated phenomena (e.g., phase separation, order-disorder transitions, allostery). Particular attention is paid to the results of computational studies, which, through thermodynamic decomposition and dissection of molecular interactions, can provide valuable mechanistic insight and testable hypotheses to guide further solution experiments. Lastly, we discuss changes in the dynamics of side chains and order-disorder transitions of the protein backbone as two modes or realizations of "entropic reservoirs" capable of tuning coupled thermodynamic processes.

Interactions between identical DNA double helices.

The molecular mechanism of specific interactions between double stranded DNA molecules has been investigated for many years. Problems remain in how confinement, ions, and condensing agents change the interactions. We consider how the orientational alignment of DNAs contributes to the interactions via free energy simulations. Here we report on the effective interactions between two parallel DNA double helices in 150-mM NaCl solution using all atom models. We calculate the potential of mean force (PMF) of DNA-DNA interactions as a function of two coordinates, interhelical separation of parallel double helices and relative rotation of a DNA molecule with respect to the other about the helical axis. We generate the two-dimensional PMF to better understand the effective interactions when a DNA molecule is in juxtaposition with another. The analysis of the ion and solvent distributions around the DNA and particularly in the interface region shows that certain alignments of the DNA pair enhance the interactions. At local free energy minima in distance and alignment, water molecules and Na^{+} ions form a hydrogen bonded network with the phosphates from each DNA. This network contributes an attractive energy component to the DNA-DNA interactions. Our results provide a molecular mechanism whereby local DNA-DNA interactions, depending on the helical orientation, give a potential mechanism for stabilizing pairing of much larger lengths of homologous DNA that have been seen experimentally. The study suggests an atomically detailed local picture of relevance to certain aspects of DNA condensation or aggregation.

Structure and the role of filling rate on model dsDNA packed in a phage capsid.

The conformation of DNA inside bacteriophages is of paramount importance for understanding packaging and ejection mechanisms. Models describing the structure of the confined macromolecule have depicted highly ordered conformations, such as spooled or toroidal arrangements that focus on reproducing experimental results obtained by averaging over thousands of configurations. However, it has been seen that more disordered states, including DNA kinking and the presence of domains with different DNA orientation can also accurately reproduce many of the structural experiments. In this work we have compared the results obtained through different simulated filling rates. We find a rate dependence for the resulting constrained states showing different anisotropic configurations. We present a quantitative analysis of the density distribution and the DNA orientation across the capsid showing excellent agreement with structural experiments. Second, we have analyzed the correlations within the capsid, finding evidence of the presence of domains characterized by aligned segments of DNA characterized by the structure factor. Finally, we have measured the number and distribution of DNA defects such as the emergence of bubbles and kinks as function of the filling rate. We find the slower the rate the fewer kink defects that appear and they would be unlikely at experimental filling rates with our model parameters. DNA domains of various orientation get larger with slower rates.