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.

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.

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.

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.

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.

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.

Glutamate dehydrogenase: Structure of a hyperinsulinism mutant, corrections to the atomic model, and insights into a regulatory site.

Mammalian glutamate dehydrogenase (GDH) has complex allosteric regulation and the loss of GTP inhibition causes the hyperinsulinism/hyperammonemia syndrome (HHS) where insulin is hypersecreted upon consumption of protein. The archetypical HHS lesion is H454Y and lies in the GTP binding pocket. To better understand the mechanism of HHS, we determined the crystal structure of H454Y. When the bovine GDH crystal structures were minimized to prepare for further computational analysis, unusually large deviations were found at the allosteric NADH binding site due to chemical sequence errors. Notably, 387 lies in an allosteric where several activators and inhibitors bind and should be lysine rather than asparagine. All structures were re-refined and the consequence of this sequence error on NADH binding was calculated using free energy perturbation. The binding free energy penalty going from the correct to incorrect sequence found is +5 kcal/mol per site and therefore has a significant impact on drug development. BROADER AUDIENCE ABSTRACT: Glutamate dehydrogenase is a key enzyme involved in amino acid catabolism. As such, it is heavily regulated in animals by a wide array of metabolites. The importance of this regulation is most apparent in a genetic disorder called hyperinsulinism/hyperammonemia (HHS) where patients hypersecrete insulin upon the consumption of protein. We determined the atomic structure of one of these HHS mutants to better understand the disease and also analyzed an allosteric regulatory site.

Influence of DNA sequence on the structure of minicircles under torsional stress.

The sequence dependence of the conformational distribution of DNA under various levels of torsional stress is an important unsolved problem. Combining theory and coarse-grained simulations shows that the DNA sequence and a structural correlation due to topology constraints of a circle are the main factors that dictate the 3D structure of a 336 bp DNA minicircle under torsional stress. We found that DNA minicircle topoisomers can have multiple bend locations under high torsional stress and that the positions of these sharp bends are determined by the sequence, and by a positive mechanical correlation along the sequence. We showed that simulations and theory are able to provide sequence-specific information about individual DNA minicircles observed by cryo-electron tomography (cryo-ET). We provided a sequence-specific cryo-ET tomogram fitting of DNA minicircles, registering the sequence within the geometric features. Our results indicate that the conformational distribution of minicircles under torsional stress can be designed, which has important implications for using minicircle DNA for gene therapy.

Thermodynamics of Conformational Transitions in a Disordered Protein Backbone Model.

Conformational entropy is expected to contribute significantly to the thermodynamics of structural transitions in intrinsically disordered proteins or regions in response to protein/ligand binding, posttranslational modifications, and environmental changes. We calculated the backbone (dihedral) conformational entropy of oligoglycine (GlyN), a protein backbone mimic and model intrinsically disordered region, as a function of chain length (N=3, 4, 5, 10, and 15) from simulations using three different approaches. The backbone conformational entropy scales linearly with chain length with a slope consistent with the entropy of folding of well-structured proteins. The entropic contributions of second-order dihedral correlations are predominantly through intraresidue ϕ-ψ pairs, suggesting that oligoglycine may be thermodynamically modeled as a system of independent glycine residues. We find the backbone conformational entropy to be largely independent of global structural parameters, like the end-to-end distance and radius of gyration. We introduce a framework referred to herein as "ensemble confinement" to estimate the loss (gain) of conformational free energy and its entropic component when individual residues are constrained to (released from) particular regions of the ϕ-ψ map. Quantitatively, we show that our protein backbone model resists ordering/folding with a significant, unfavorable ensemble confinement free energy because of the loss of a substantial portion of the absolute backbone entropy. Proteins can couple this free-energy reservoir to distal binding events as a regulatory mechanism to promote or suppress binding.

Phage-like packing structures with mean field sequence dependence.

Packing of double-stranded DNA in phages must overcome both electrostatic repulsions and the problem of persistence length. We consider coarse-grained models with the ability to kink and with randomly generated disorder. We show that the introduction of kinking into configurations of the DNA polymer packaged within spherical confinement results in significant reductions of the overall energies and pressures. We use a kink model which has the ability to deform every 24 bp, close to the average length predicted from phage sequence. The introduction of such persistence length defects even with highly random packing models increases the local nematic ordering of the packed DNA polymer segments. Such local ordering allowed by kinking not only reduces the total bending energy of confined DNA due to nonlinear elasticity but also reduces the electrostatic component of the energy and pressure. We show that a broad ensemble of polymer configurations is consistent with the structural data. © 2016 Wiley Periodicals, Inc.

Optimal updating magnitude in adaptive flat-distribution sampling.

We present a study on the optimization of the updating magnitude for a class of free energy methods based on flat-distribution sampling, including the Wang-Landau (WL) algorithm and metadynamics. These methods rely on adaptive construction of a bias potential that offsets the potential of mean force by histogram-based updates. The convergence of the bias potential can be improved by decreasing the updating magnitude with an optimal schedule. We show that while the asymptotically optimal schedule for the single-bin updating scheme (commonly used in the WL algorithm) is given by the known inverse-time formula, that for the Gaussian updating scheme (commonly used in metadynamics) is often more complex. We further show that the single-bin updating scheme is optimal for very long simulations, and it can be generalized to a class of bandpass updating schemes that are similarly optimal. These bandpass updating schemes target only a few long-range distribution modes and their optimal schedule is also given by the inverse-time formula. Constructed from orthogonal polynomials, the bandpass updating schemes generalize the WL and Langfeld-Lucini-Rago algorithms as an automatic parameter tuning scheme for umbrella sampling.

Effects of geometry and chemistry on hydrophobic solvation.

Inserting an uncharged van der Waals (vdw) cavity into water disrupts the distribution of water and creates attractive dispersion interactions between the solvent and solute. This free-energy change is the hydrophobic solvation energy (ΔG(vdw)). Frequently, it is assumed to be linear in the solvent-accessible surface area, with a positive surface tension (γ) that is independent of the properties of the molecule. However, we found that γ for a set of alkanes differed from that for four configurations of decaalanine, and γ = -5 was negative for the decaalanines. These findings conflict with the notion that ΔG(vdw) favors smaller A. We broke ΔG(vdw) into the free energy required to exclude water from the vdw cavity (ΔG(rep)) and the free energy of forming the attractive interactions between the solute and solvent (ΔG(att)) and found that γ < 0 for the decaalanines because -γ(att) > γ(rep) and γ(att) < 0. Additionally, γ(att) and γ(rep) for the alkanes differed from those for the decaalanines, implying that none of ΔG(att), ΔG(rep), and ΔG(vdw) can be computed with a constant surface tension. We also showed that ΔG(att) could not be computed from either the initial or final water distributions, implying that this quantity is more difficult to compute than is sometimes assumed. Finally, we showed that each atom's contribution to γ(rep) depended on multibody interactions with its surrounding atoms, implying that these contributions are not additive. These findings call into question some hydrophobic models.

DNA Shape versus Sequence Variations in the Protein Binding Process.

The binding process of a protein with a DNA involves three stages: approach, encounter, and association. It has been known that the complexation of protein and DNA involves mutual conformational changes, especially for a specific sequence association. However, it is still unclear how the conformation and the information in the DNA sequences affects the binding process. What is the extent to which the DNA structure adopted in the complex is induced by protein binding, or is instead intrinsic to the DNA sequence? In this study, we used the multiscale simulation method to explore the binding process of a protein with DNA in terms of DNA sequence, conformation, and interactions. We found that in the approach stage the protein can bind both the major and minor groove of the DNA, but uses different features to locate the binding site. The intrinsic conformational properties of the DNA play a significant role in this binding stage. By comparing the specific DNA with the nonspecific in unbound, intermediate, and associated states, we found that for a specific DNA sequence, ∼40% of the bending in the association forms is intrinsic and that ∼60% is induced by the protein. The protein does not induce appreciable bending of nonspecific DNA. In addition, we proposed that the DNA shape variations induced by protein binding are required in the early stage of the binding process, so that the protein is able to approach, encounter, and form an intermediate at the correct site on DNA.

Solvation Thermodynamics of Oligoglycine with Respect to Chain Length and Flexibility.

Oligoglycine is a backbone mimic for all proteins and is prevalent in the sequences of intrinsically disordered proteins. We have computed the absolute chemical potential of glycine oligomers at infinite dilution by simulation with the CHARMM36 and Amber ff12SB force fields. We performed a thermodynamic decomposition of the solvation free energy (ΔG(sol)) of Gly2-5 into enthalpic (ΔH(sol)) and entropic (ΔS(sol)) components as well as their van der Waals and electrostatic contributions. Gly2-5 was either constrained to a rigid/extended conformation or allowed to be completely flexible during simulations to assess the effects of flexibility on these thermodynamic quantities. For both rigid and flexible oligoglycine models, the decrease in ΔG(sol) with chain length is enthalpically driven with only weak entropic compensation. However, the apparent rates of decrease of ΔG(sol), ΔH(sol), ΔS(sol), and their elec and vdw components differ for the rigid and flexible models. Thus, we find solvation entropy does not drive aggregation for this system and may not explain the collapse of long oligoglycines. Additionally, both force fields yield very similar thermodynamic scaling relationships with respect to chain length despite both force fields generating different conformational ensembles of various oligoglycine chains.

Solvation and cavity occupation in biomolecules.

BACKGROUND: Solvation density locations are important for protein dynamics and structure. Knowledge of the preferred hydration sites at biomolecular interfaces and those in the interior of cavities can enhance understanding of structure and function. While advanced X-ray diffraction methods can provide accurate atomic structures for proteins, that technique is challenged when it comes to providing accurate hydration structures, especially for interfacial and cavity bound solvent molecules. METHODS: Advances in integral equation theories which include more accurate methods for calculating the long-ranged Coulomb interaction contributions to the three-dimensional distribution functions make it possible to calculate angle dependent average solvent structure, accurately, around and inside irregular molecular conformations. The proximal radial distribution method provides another approximate method to determine average solvent structures for biomolecular systems based on a proximal or near neighbor solvent distribution that can be constructed from previously collected solvent distributions. These two approximate methods, along with all-atom molecular dynamics simulations are used to determine the solvent density inside the myoglobin heme cavity. DISCUSSION AND RESULTS: Myoglobin is a good test system for these methods because the cavities are many and one is large, tens of Å(3), but is shown to have only four hydration sites. These sites are not near neighbors which implies that the large cavity must have more than one way in and out. CONCLUSIONS: Our results show that main solvation sites are well reproduced by all three methods. The techniques also produce a clearly identifiable solvent pathway into the interior of the protein. GENERAL SIGNIFICANCE: The agreement between molecular dynamics and less computationally demanding approximate methods is encouraging. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

Systematic identification of single amino acid variants in glioma stem-cell-derived chromosome 19 proteins.

Novel proteoforms with single amino acid variations represent proteins that often have altered biological functions but are less explored in the human proteome. We have developed an approach, searching high quality shotgun proteomic data against an extended protein database, to identify expressed mutant proteoforms in glioma stem cell (GSC) lines. The systematic search of MS/MS spectra using PEAKS 7.0 as the search engine has recognized 17 chromosome 19 proteins in GSCs with altered amino acid sequences. The results were further verified by manual spectral examination, validating 19 proteoforms. One of the novel findings, a mutant form of branched-chain aminotransferase 2 (p.Thr186Arg), was verified at the transcript level and by targeted proteomics in several glioma stem cell lines. The structure of this proteoform was examined by molecular modeling in order to estimate conformational changes due to mutation that might lead to functional modifications potentially linked to glioma. Based on our initial findings, we believe that our approach presented could contribute to construct a more complete map of the human functional proteome.

Force field-dependent solution properties of glycine oligomers.

Molecular simulations can be used to study disordered polypeptide systems and to generate hypotheses on the underlying structural and thermodynamic mechanisms that govern their function. As the number of disordered protein systems investigated with simulations increase, it is important to understand how particular force fields affect the structural properties of disordered polypeptides in solution. To this end, we performed a comparative structural analysis of Gly(3) and Gly(10) in aqueous solution from all atom, microsecond molecular dynamics (MD) simulations using the CHARMM 27 (C27), CHARMM 36 (C36), and Amber ff12SB force fields. For each force field, Gly(3) and Gly(10) were simulated for at least 300 ns and 1 µs, respectively. Simulating oligoglycines of two different lengths allows us to evaluate how force field effects depend on polypeptide length. Using a variety of structural metrics (e.g., end-to-end distance, radius of gyration, dihedral angle distributions), we characterize the distribution of oligoglycine conformers for each force field and show that each sample conformation space differently, yielding considerably different structural tendencies of the same oligoglycine model in solution. Notably, we find that C36 samples more extended oligoglycine structures than both C27 and ff12SB.

Computation of virial coefficients from integral equations.

A polynomial-time method of computing the virial coefficients from an integral equation framework is presented. The method computes the truncated density expansions of the correlation functions by series transformations, and then extracts the virial coefficients from the density components. As an application, the method was used in a hybrid-closure integral equation with a set of self-consistent conditions, which produced reasonably accurate virial coefficients for the hard-sphere fluid and Gaussian model in high dimensions.

Physico-chemical foundations underpinning microarray and next-generation sequencing experiments.

Hybridization of nucleic acids on solid surfaces is a key process involved in high-throughput technologies such as microarrays and, in some cases, next-generation sequencing (NGS). A physical understanding of the hybridization process helps to determine the accuracy of these technologies. The goal of a widespread research program is to develop reliable transformations between the raw signals reported by the technologies and individual molecular concentrations from an ensemble of nucleic acids. This research has inputs from many areas, from bioinformatics and biostatistics, to theoretical and experimental biochemistry and biophysics, to computer simulations. A group of leading researchers met in Ploen Germany in 2011 to discuss present knowledge and limitations of our physico-chemical understanding of high-throughput nucleic acid technologies. This meeting inspired us to write this summary, which provides an overview of the state-of-the-art approaches based on physico-chemical foundation to modeling of the nucleic acids hybridization process on solid surfaces. In addition, practical application of current knowledge is emphasized.

Modeling DNA thermodynamics under torsional stress.

Negatively twisted DNA is essential to many biological functions. Due to torsional stress, duplex DNA can have local, sequence-dependent structural defects. In this work, a thermodynamic model of DNA was built to qualitatively predict the local sequence-dependent mechanical instabilities under torsional stress. The results were compared to both simulation of a coarse-grained model and experiment results. By using the Kirkwood superposition approximation, we built an analytical model to represent the free energy difference ΔW of a hydrogen-bonded basepair between the B-form helical state and the basepair opened (or locally melted) state, within a given sequence under torsional stress. We showed that ΔW can be well approximated by two-body interactions with its nearest-sequence-neighbor basepairs plus a free energy correction due to long-range correlations. This model is capable of rapidly predicting the position and thermodynamics of local defects in a given sequence. The result qualitatively matches with an in vitro experiment for a long DNA sequence (>4000 basepairs). The 12 parameters used in this model can be further quantitatively refined when more experimental data are available.