Crystal lattice properties fully determine short-range interaction parameters for alkali and halide ions

Biomolecular condensates are characterized by interphase electric potentials

Biomolecular condensates form via processes that combine phase separation and reversible associations of multivalent macromolecules. Condensates can be two- or multi-phase systems defined by coexisting dense and dilute phases. Here, we show that solution ions can partition asymmetrically across coexisting phases defined by condensates formed by intrinsically disordered proteins or homopolymeric RNA molecules. Our findings were enabled by direct measurements of the activities of cations and anions within coexisting phases of protein and RNA condensates. Asymmetries in ion partitioning between coexisting phases vary with protein sequence, condensate type, salt concentration, and ion type. The Donnan equilibrium set up by asymmetrical partitioning of solution ions generates interphase electric potentials known as Donnan and Nernst potentials. Our measurements show that the interphase potentials of condensates are of the same order of magnitude as membrane potentials of membrane-bound organelles. Interphase potentials quantify the degree to which microenvironments of coexisting phases are different from one another. Importantly, and based on condensate-specific interphase electric potentials, which are membrane-like potentials of membraneless bodies, we reason that condensates are mesoscale capacitors that store charge. Interphase potentials lead to electric double layers at condensate interfaces. This helps explain recent observations of condensate interfaces being electrochemically active.

Phosphorylation of disordered proteins tunes local and global intramolecular interactions

Protein post-translational modifications, such as phosphorylation, are important regulatory signals for diverse cellular functions. In particular, intrinsically disordered protein regions (IDRs) are subject to phosphorylation as a means to modulate their interactions and functions. Toward understanding the relationship between phosphorylation in IDRs and specific functional outcomes, we must consider how phosphorylation affects the IDR conformational ensemble. Various experimental techniques are suited to interrogate the features of IDR ensembles; molecular simulations can provide complementary insights and even illuminate ensemble features that may be experimentally inaccessible. Therefore, we sought to expand the tools available to study phosphorylated IDRs by all-atom Monte Carlo simulations. To this end, we implemented parameters for phosphoserine (pSer) and phosphothreonine (pThr) into the OPLS version of the continuum solvent model, ABSINTH, and assessed their performance in all-atom simulations compared to published findings. We simulated short (< 20 residues) and long (> 80 residues) phospho-IDRs that, collectively, survey both local and global phosphorylation-induced changes to the ensemble. Our simulations of four well-studied phospho-IDRs show near-quantitative agreement with published findings for these systems via metrics including changes to radius of gyration, transient helicity, and persistence length. We also leveraged the inherent advantage of sequence control in molecular simulations to explore the conformational effects of diverse combinations of phospho-sites in two multi-phosphorylated IDRs. Our results support and expand on prior observations that connect phosphorylation to changes in the IDR conformational ensemble. Herein, we describe phosphorylation as a means to alter sequence chemistry, net charge and charge patterning, and intramolecular interactions, which can collectively modulate the local and global IDR ensemble features.

Biomolecular condensates form spatially inhomogeneous network fluids

The functions of biomolecular condensates are thought to be influenced by their material properties, and these will be determined by the internal organization of molecules within condensates. However, structural characterizations of condensates are challenging, and rarely reported. Here, we deploy a combination of small angle neutron scattering, fluorescence recovery after photobleaching, and coarse-grained molecular dynamics simulations to provide structural descriptions of model condensates that are formed by macromolecules from nucleolar granular components (GCs). We show that these minimal facsimiles of GCs form condensates that are network fluids featuring spatial inhomogeneities across different length scales that reflect the contributions of distinct protein and peptide domains. The network-like inhomogeneous organization is characterized by a coexistence of liquid- and gas-like macromolecular densities that engenders bimodality of internal molecular dynamics. These insights suggest that condensates formed by multivalent proteins share features with network fluids formed by systems such as patchy or hairy colloids.

Macromolecular condensation organizes nucleolar sub-phases to set up a pH gradient

Nucleoli are multicomponent condensates defined by coexisting sub-phases. We identified distinct intrinsically disordered regions (IDRs), including acidic (D/E) tracts and K-blocks interspersed by E-rich regions, as defining features of nucleolar proteins. We show that the localization preferences of nucleolar proteins are determined by their IDRs and the types of RNA or DNA binding domains they encompass. In vitro reconstitutions and studies in cells showed how condensation, which combines binding and complex coacervation of nucleolar components, contributes to nucleolar organization. D/E tracts of nucleolar proteins contribute to lowering the pH of co-condensates formed with nucleolar RNAs in vitro. In cells, this sets up a pH gradient between nucleoli and the nucleoplasm. By contrast, juxta-nucleolar bodies, which have different macromolecular compositions, featuring protein IDRs with very different charge profiles, have pH values that are equivalent to or higher than the nucleoplasm. Our findings show that distinct compositional specificities generate distinct physicochemical properties for condensates.

Labile assembly of a tardigrade protein induces biostasis

Tardigrades are microscopic animals that survive desiccation by inducing biostasis. To survive drying tardigrades rely on intrinsically disordered CAHS proteins, which also function to prevent perturbations induced by drying in vitro and in heterologous systems. CAHS proteins have been shown to form gels both in vitro and in vivo, which has been speculated to be linked to their protective capacity. However, the sequence features and mechanisms underlying gel formation and the necessity of gelation for protection have not been demonstrated. Here we report a mechanism of fibrillization and gelation for CAHS D similar to that of intermediate filament assembly. We show that in vitro, gelation restricts molecular motion, immobilizing and protecting labile material from the harmful effects of drying. In vivo, we observe that CAHS D forms fibrillar networks during osmotic stress. Fibrillar networking of CAHS D improves survival of osmotically shocked cells. We observe two emergent properties associated with fibrillization; (i) prevention of cell volume change and (ii) reduction of metabolic activity during osmotic shock. We find that there is no significant correlation between maintenance of cell volume and survival, while there is a significant correlation between reduced metabolism and survival. Importantly, CAHS D's fibrillar network formation is reversible and metabolic rates return to control levels after CAHS fibers are resolved. This work provides insights into how tardigrades induce reversible biostasis through the self-assembly of labile CAHS gels.

Computation of Electrical Conductivities of Aqueous Electrolyte Solutions: Two Surfaces, One Property

In this work, we computed electrical conductivities under ambient conditions of aqueous NaCl and KCl solutions by using the Einstein-Helfand equation. Common force fields (charge q = ±1 e) do not reproduce the experimental values of electrical conductivities, viscosities, and diffusion coefficients. Recently, we proposed the idea of using different charges to describe the potential energy surface (PES) and the dipole moment surface (DMS). In this work, we implement this concept. The equilibrium trajectories required to evaluate electrical conductivities (within linear response theory) were obtained by using scaled charges (with the value q = ±0.75 e) to describe the PES. The potential parameters were those of the Madrid-Transport force field, which accurately describe viscosities and diffusion coefficients of these ionic solutions. However, integer charges were used to compute the conductivities (thus describing the DMS). The basic idea is that although the scaled charge describes the ion-water interaction better, the integer charge reflects the value of the charge that is transported due to the electric field. The agreement obtained with experiments is excellent, as for the first time electrical conductivities (and the other transport properties) of NaCl and KCl electrolyte solutions are described with high accuracy for the whole concentration range up to their solubility limit. Finally, we propose an easy way to obtain a rough estimate of the actual electrical conductivity of the potential model under consideration using the approximate Nernst-Einstein equation, which neglects correlations between different ions.

Scaled charges for ions: An improvement but not the final word for modeling electrolytes in water

In this work, we discuss the use of scaled charges when developing force fields for NaCl in water. We shall develop force fields for Na⁺ and Cl^- using the following values for the scaled charge (in electron units): ±0.75, ±0.80, ±0.85, and ±0.92 along with the TIP4P/2005 model of water (for which previous force fields were proposed for q = ±0.85 and q = ±1). The properties considered in this work are densities, structural properties, transport properties, surface tension, freezing point depression, and maximum in density. All the developed models were able to describe quite well the experimental values of the densities. Structural properties were well described by models with charges equal to or larger than ±0.85, surface tension by the charge ±0.92, maximum in density by the charge ±0.85, and transport properties by the charge ±0.75. The use of a scaled charge of ±0.75 is able to reproduce with high accuracy the viscosities and diffusion coefficients of NaCl solutions for the first time. We have also considered the case of KCl in water, and the results obtained were fully consistent with those of NaCl. There is no value of the scaled charge able to reproduce all the properties considered in this work. Although certainly scaled charges are not the final word in the development of force fields for electrolytes in water, its use may have some practical advantages. Certain values of the scaled charge could be the best option when the interest is to describe certain experimental properties.

The material properties of a bacterial-derived biomolecular condensate tune biological function in natural and synthetic systems

Intracellular phase separation is emerging as a universal principle for organizing biochemical reactions in time and space. It remains incompletely resolved how biological function is encoded in these assemblies and whether this depends on their material state. The conserved intrinsically disordered protein PopZ forms condensates at the poles of the bacterium Caulobacter crescentus, which in turn orchestrate cell-cycle regulating signaling cascades. Here we show that the material properties of these condensates are determined by a balance between attractive and repulsive forces mediated by a helical oligomerization domain and an expanded disordered region, respectively. A series of PopZ mutants disrupting this balance results in condensates that span the material properties spectrum, from liquid to solid. A narrow range of condensate material properties supports proper cell division, linking emergent properties to organismal fitness. We use these insights to repurpose PopZ as a modular platform for generating tunable synthetic condensates in human cells.

“Intracellular phase separation is emerging as a universal principle for organizing biochemical reactions in time and space. Here the authors show that PopZ condensate dynamics support cell division and using PopZ modular architecture, the tunable PopTag platform was developed to enable designer condensates.”

Competing interactions give rise to two-state behavior and switch-like transitions in charge-rich intrinsically disordered proteins

The most commonly occurring intrinsically disordered proteins (IDPs) are polyampholytes, which are defined by the duality of low net charge per residue and high fractions of charged residues. Recent experiments have uncovered nuances regarding sequence–ensemble relationships of model polyampholytic IDPs. These include differences in conformational preferences for sequences with lysine vs. arginine and the suggestion that well-mixed sequences form a range of conformations, including globules, conformations with ensemble averages that are reminiscent of ideal chains, or self-avoiding walks. Here, we explain these observations by analyzing results from atomistic simulations. We find that polyampholytic IDPs generally sample two distinct stable states, namely, globules and self-avoiding walks. Globules are favored by electrostatic attractions between oppositely charged residues, whereas self-avoiding walks are favored by favorable free energies of hydration of charged residues. We find sequence-specific temperatures of bistability at which globules and self-avoiding walks can coexist. At these temperatures, ensemble averages over coexisting states give rise to statistics that resemble ideal chains without there being an actual counterbalancing of intrachain and chain-solvent interactions. At equivalent temperatures, arginine-rich sequences tilt the preference toward globular conformations whereas lysine-rich sequences tilt the preference toward self-avoiding walks. We also identify differences between aspartate- and glutamate-containing sequences, whereby the shorter aspartate side chain engenders preferences for metastable, necklace-like conformations. Finally, although segregation of oppositely charged residues within the linear sequence maintains the overall two-state behavior, compact states are highly favored by such systems.

Adaptable P body physical states differentially regulate bicoid mRNA storage during early Drosophila development

Ribonucleoprotein condensates can exhibit diverse physical states in vitro and in vivo. Despite considerable progress, the relevance of condensate physical states for in vivo biological function remains limited. Here, we investigated the physical properties of processing bodies (P bodies) and their impact on mRNA storage in mature Drosophila oocytes. We show that the conserved DEAD-box RNA helicase Me31B forms viscous P body condensates, which adopt an arrested physical state. We demonstrate that structurally distinct proteins and protein-protein interactions, together with RNA, regulate the physical properties of P bodies. Using live imaging and in situ hybridization, we show that the arrested state and integrity of P bodies support the storage of bicoid (bcd) mRNA and that egg activation modulates P body properties, leading to the release of bcd for translation in the early embryo. Together, this work provides an example of how physical states of condensates regulate cellular function in development.

Differing biophysical properties underpin the unique signaling potentials within the plant phytochrome photoreceptor families

Many aspects of photoperception by plants and microorganisms are initiated by the phytochrome (Phy) family of photoreceptors that detect light through interconversion between red light- (Pr) and far-red light-absorbing (Pfr) states. Plants synthesize a small family of Phy isoforms (PhyA to PhyE) that collectively regulate photomorphogenesis and temperature perception through redundant and unique actions. While the selective roles of these isoforms have been partially attributed to their differing abundances, expression patterns, affinities for downstream partners, and turnover rates, we show here from analysis of recombinant Arabidopsis chromoproteins that the Phy isoforms also display distinct biophysical properties. Included are a hypsochromic shift in the Pr absorption for PhyC and varying rates of Pfr to Pr thermal reversion, part of which can be attributed to the core photosensory module in each. Most strikingly, PhyB combines strong temperature dependence of thermal reversion with an order-of-magnitude faster rate to likely serve as the main physiological thermosensor, whereby thermal reversion competes with photoconversion. In addition, comparisons of Pfr occupancies for PhyA and PhyB under a range of red- and white-light fluence rates imply that low-light environments are effectively sensed by PhyA, while high-light environments, such as full sun, are effectively sensed by PhyB. Parallel analyses of the Phy isoforms from potato and maize showed that the unique features within the Arabidopsis family are conserved, thus indicating that the distinct biophysical properties among plant Phy isoforms emerged early in Phy evolution, likely to enable full interrogation of their light and temperature environments.

Parametrization of Trivalent and Tetravalent Metal Ions for the OPC3, OPC, TIP3P-FB, and TIP4P-FB Water Models

Commonly seen in rare-earth chemistry and materials science, highly charged metal ions play key roles in many chemical processes. Computer simulations have become an important tool for scientific research nowadays. Meaningful simulations require reliable parameters. In the present work, we parametrized 18 M(III) and 6 M(IV) metal ions for four new water models (OPC3, OPC, TIP3P-FB, TIP4P-FB) in conjunction with each of the 12-6 and 12-6-4 nonbonded models. Similar to what was observed previously, issues with the 12-6 model can be fixed by using the 12-6-4 model. Moreover, the four new water models showed comparable performance or considerable improvement over the previous water models (TIP3P, SPC/E, and TIP4P_EW) in the same category (3-point or 4-point water models, respectively). Finally, we reported a study of a metalloprotein system demonstrating the capability of the 12-6-4 model to model metalloproteins. The reported parameters will facilitate accurate simulations of highly charged metal ions in aqueous solution.

The SARS-CoV-2 nucleocapsid protein is dynamic, disordered, and phase separates with RNA

The SARS-CoV-2 nucleocapsid (N) protein is an abundant RNA-binding protein critical for viral genome packaging, yet the molecular details that underlie this process are poorly understood. Here we combine single-molecule spectroscopy with all-atom simulations to uncover the molecular details that contribute to N protein function. N protein contains three dynamic disordered regions that house putative transiently-helical binding motifs. The two folded domains interact minimally such that full-length N protein is a flexible and multivalent RNA-binding protein. N protein also undergoes liquid-liquid phase separation when mixed with RNA, and polymer theory predicts that the same multivalent interactions that drive phase separation also engender RNA compaction. We offer a simple symmetry-breaking model that provides a plausible route through which single-genome condensation preferentially occurs over phase separation, suggesting that phase separation offers a convenient macroscopic readout of a key nanoscopic interaction.

The Influence of Spectator Cations on Solvent Reorganization Energy Is a Short-Range Effect

In this manuscript, we use classical molecular dynamics simulation to explore the origin of specific cation effects on the rates of bulk-phase aqueous electron transfer (ET) reactions. We consider 0.6 M solutions of Cl^- and a series of different cations: Li⁺, Na⁺, K⁺, Rb⁺, and Cs⁺. We evaluate the collective electrostatic fluctuations that drive Marcus-like ET and find that they are essentially unaffected by changes in the cationic species. This finding implies that the structure making/breaking properties of various cations do not exert a significant influence on bulk-phase ET reactions. We evaluate the role of ion pairing in these specific cation effects and find, unsurprisingly, that model redox anions that are more highly charged tend to pair more effectively with spectator cations than their monovalent counterparts. We demonstrate that this ion pairing significantly affects local electrostatic fluctuations for the anionic redox species and thus conclude that ion pairing is one of the likely sources of rate-dependent cation effects in aqueous ET reactions.

The SARS-CoV-2 nucleocapsid protein is dynamic, disordered, and phase separates with RNA

The SARS-CoV-2 nucleocapsid (N) protein is an abundant RNA binding protein critical for viral genome packaging, yet the molecular details that underlie this process are poorly understood. Here we combine single-molecule spectroscopy with all-atom simulations to uncover the molecular details that contribute to N protein function. N protein contains three dynamic disordered regions that house putative transiently-helical binding motifs. The two folded domains interact minimally such that full-length N protein is a flexible and multivalent RNA binding protein. N protein also undergoes liquid-liquid phase separation when mixed with RNA, and polymer theory predicts that the same multivalent interactions that drive phase separation also engender RNA compaction. We offer a simple symmetry-breaking model that provides a plausible route through which single-genome condensation preferentially occurs over phase separation, suggesting that phase separation offers a convenient macroscopic readout of a key nanoscopic interaction.

Connecting Coil-to-Globule Transitions to Full Phase Diagrams for Intrinsically Disordered Proteins

Phase separation is thought to underlie spatial and temporal organization that is required for controlling biochemical reactions in cells. Multivalence of interaction motifs, also known as stickers, is a defining feature of proteins that drive phase separation. Intrinsically disordered proteins with stickers uniformly distributed along the linear sequence can serve as scaffold molecules that drive phase separation. The sequence-intrinsic contributions of disordered proteins to phase separation can be discerned by computing or measuring sequence-specific phase diagrams. These help to delineate the combinations of protein concentration and a suitable control parameter, such as temperature, that support phase separation. Here, we present an approach that combines detailed simulations with a numerical adaptation of an analytical Gaussian cluster theory to enable the calculation of sequence-specific phase diagrams. Our approach leverages the known equivalence between the driving forces for single-chain collapse in dilute solutions and the driving forces for phase separation in concentrated solutions. We demonstrate the application of the theory-aided computations through calculation of phase diagrams for a set of archetypal intrinsically disordered low-complexity domains. We also leverage theories to compute sequence-specific percolation lines and thereby provide a thermodynamic framework for hardening transitions that have been observed for many biomolecular condensates.

Information theoretic measures for quantifying sequence-ensemble relationships of intrinsically disordered proteins

Intrinsically disordered proteins (IDPs) contribute to a multitude of functions. De novo design of IDPs should open the door to modulating functions and phenotypes controlled by these systems. Recent design efforts have focused on compositional biases and specific sequence patterns as the design features. Analysis of the impact of these designs on sequence-function relationships indicates that individual sequence/compositional parameters are insufficient for describing sequence-function relationships in IDPs. To remedy this problem, we have developed information theoretic measures for sequence–ensemble relationships (SERs) of IDPs. These measures rely on prior availability of statistically robust conformational ensembles derived from all atom simulations. We show that the measures we have developed are useful for comparing sequence-ensemble relationships even when sequence is poorly conserved. Based on our results, we propose that de novo designs of IDPs, guided by knowledge of their SERs, should provide improved insights into their sequence–ensemble–function relationships.

Dielectric constant and density of aqueous alkali halide solutions by molecular dynamics: A force field assessment

The concentration dependence of the dielectric constant and the density of 11 aqueous alkali halide solutions (LiCl, NaCl, KCl, RbCl, CsCl, LiI, NaI, KI, CsI, KF, and CsF) is investigated by molecular simulation. Predictions using eight non-polarizable ion force fields combined with the TIP4P/ε water model are compared to experimental data. The influence of the water model and the temperature on the results for the NaCl brine are also addressed. The TIP4P/ε water model improves the accuracy of dielectric constant predictions compared to the SPC/E water model. The solution density is predicted well by most ion models. Almost all ion force fields qualitatively capture the decline of the dielectric constant with the increase of concentration for all solutions and with the increase of temperature for NaCl brine. However, the sampled dielectric constant is mostly in poor quantitative agreement with experimental data. These results are related to the microscopic solution structure, ion pairing, and ultimately the force field parameters. Ion force fields with excessive contact ion pairing and precipitation below the experimental solubility limit generally yield higher dielectric constant values. An adequate reproduction of the experimental solubility limit should therefore be a prerequisite for further investigations of the dielectric constant of aqueous electrolyte solutions by molecular simulation.

Investigating the ferric ion binding site of magnetite biomineralisation protein Mms6

The biomineralization protein Mms6 has been shown to be a major player in the formation of magnetic nanoparticles both within the magnetosomes of magnetotactic bacteria and as an additive in synthetic magnetite precipitation assays. Previous studies have highlighted the ferric iron binding capability of the protein and this activity is thought to be crucial to its mineralizing properties. To understand how this protein binds ferric ions we have prepared a series of single amino acid substitutions within the C-terminal binding region of Mms6 and have used a ferric binding assay to probe the binding site at the level of individual residues which has pinpointed the key residues of E44, E50 and R55 involved in Mms6 ferric binding. No aspartic residues bound ferric ions. A nanoplasmonic sensing experiment was used to investigate the unstable EER44, 50,55AAA triple mutant in comparison to native Mms6. This suggests a difference in interaction with iron ions between the two and potential changes to the surface precipitation of iron oxide when the pH is increased. All-atom simulations suggest that disruptive mutations do not fundamentally alter the conformational preferences of the ferric binding region. Instead, disruption of these residues appears to impede a sequence-specific motif in the C-terminus critical to ferric ion binding.

Dielectric Decrement for Aqueous NaCl Solutions: Effect of Ionic Charge Scaling in Nonpolarizable Water Force Fields

We investigate the dielectric constant and the dielectric decrement of aqueous NaCl solutions by means of molecular dynamic simulations. We thereby compare the performance of four different force fields and focus on disentangling the origin of the dielectric decrement and the influence of scaled ionic charges, as often used in nonpolarizable force fields to account for the missing dynamic polarizability in the shielding of electrostatic ion interactions. Three of the force fields showed excessive contact ion pair formation, which correlates with a reduced dielectric decrement. In spite of the fact that the scaling of charges only weakly influenced the average polarization of water molecules around an ion, the rescaling of ionic charges did influence the dielectric decrement, and a close-to-linear relation of the slope of the dielectric constant as a function of concentration with the ionic charge was found.

A force field of Li+, Na+, K+, Mg2+, Ca2+, Cl-, and SO4 2- in aqueous solution based on the TIP4P/2005 water model and scaled charges for the ions

In this work, a force field for several ions in water is proposed. In particular, we consider the cations Li⁺, Na⁺, K⁺, Mg²⁺, and Ca²⁺ and the anions Cl^- and SO₄ ^2-. These ions were selected as they appear in the composition of seawater, and they are also found in biological systems. The force field proposed (denoted as Madrid-2019) is nonpolarizable, and both water molecules and sulfate anions are rigid. For water, we use the TIP4P/2005 model. The main idea behind this work is to further explore the possibility of using scaled charges for describing ionic solutions. Monovalent and divalent ions are modeled using charges of 0.85 and 1.7, respectively (in electron units). The model allows a very accurate description of the densities of the solutions up to high concentrations. It also gives good predictions of viscosities up to 3 m concentrations. Calculated structural properties are also in reasonable agreement with the experiment. We have checked that no crystallization occurred in the simulations at concentrations similar to the solubility limit. A test for ternary mixtures shows that the force field provides excellent performance at an affordable computer cost. In summary, the use of scaled charges, which could be regarded as an effective and simple way of accounting for polarization (at least to a certain extend), improves the overall description of ionic systems in water. However, for purely ionic systems, scaled charges will not adequately describe neither the solid nor the melt.

q-Canonical Monte Carlo Sampling for Modeling the Linkage between Charge Regulation and Conformational Equilibria of Peptides

The overall charge content and the patterning of charged residues have a profound impact on the conformational ensembles adopted by intrinsically disordered proteins. These parameters can be altered by charge regulation, which refers to the effects of post-translational modifications, pH-dependent changes to charge, and conformational fluctuations that modify the pKa values of ionizable residues. Although atomistic simulations have played a prominent role in uncovering the major sequence-ensemble relationships of IDPs, most simulations assume fixed charge states for ionizable residues. This may lead to erroneous estimates for conformational equilibria if they are linked to charge regulation. Here, we report the development of a new method we term q-canonical Monte Carlo sampling for modeling the linkage between charge regulation and conformational equilibria. The method, which is designed to be interoperable with the ABSINTH implicit solvation model, operates as follows: For a protein sequence with n ionizable residues, we start with all 2n charge microstates and use a criterion based on model compound pKa values to prune down to a subset of thermodynamically relevant charge microstates. This subset is then grouped into mesostates, where all microstates that belong to a mesostate have the same net charge. Conformational distributions, drawn from a canonical ensemble, are generated for each of the charge microstates that make up a mesostate using a method we designate as proton walk sampling. This method combines Metropolis Monte Carlo sampling in conformational space with an auxiliary Markov process that enables interconversions between charge microstates along a mesostate. Proton walk sampling helps identify the most likely charge microstate per mesostate. We then use thermodynamic integration aided by the multistate Bennett acceptance ratio method to estimate the free energies for converting between mesostates. These free energies are then combined with the per-microstate weights along each mesostate to estimate standard state free energies and pH-dependent free energies for all thermodynamically relevant charge microstates. The results provide quantitative estimates of the probabilities and preferred conformations associated with every thermodynamically accessible charge microstate. We showcase the application of q-canonical sampling using two model systems. The results establish the soundness of the method and the importance of charge regulation in systems characterized by conformational heterogeneity.

Improvements to the ABSINTH Force Field for Proteins Based on Experimentally Derived Amino Acid Specific Backbone Conformational Statistics

We present an improved version of the ABSINTH implicit solvation model and force field paradigm (termed ABSINTH-C) by incorporating a grid-based term that bootstraps against experimentally derived and computationally optimized conformational statistics for blocked amino acids. These statistics provide high-resolution descriptions of the intrinsic backbone dihedral angle preferences for all 20 amino acids. The original ABSINTH model generates Ramachandran plots that are too shallow in terms of the basin structures and too permissive in terms of dihedral angle preferences. We bootstrap against the reference optimized landscapes and incorporate CMAP-like residue-specific terms that help us reproduce the intrinsic dihedral angle preferences of individual amino acids. These corrections that lead to ABSINTH-C are achieved by balancing the incorporation of the new residue-specific terms with the accuracies inherent to the original ABSINTH model. We demonstrate the robustness of ABSINTH-C through a series of examples to highlight the preservation of accuracies as well as examples that demonstrate the improvements. Our efforts show how the recent experimentally derived and computationally optimized coil-library landscapes can be used as a touchstone for quantifying errors and making improvements to molecular mechanics force fields.

The influence of polarizability and charge transfer on specific ion effects in the dynamics of aqueous salt solutions

The diffusion rates for water molecules in salt solutions depend on the identity of the ions, as well as their concentration. Among the alkali metal ions, cesium and potassium increase and sodium strongly decreases the diffusion constant of water. The origin of the difference can be understood by examining the simulation results using different potential models. In this work, aqueous solutions of salts are simulated with a variety of models. Commonly used non-polarizable models, which otherwise reproduce many experimental properties, do not capture the trend in the diffusion constant, while models which include polarization and/or charge transfer interactions do. For the non-polarizable models, the diffusion constant decreases too strongly with salt concentration. The changes in the water diffusion constant with increasing salt concentration match the diffusion constant of the ion. The ion diffusion constant is dependent on the residence time for water in the ion solvation shell. The non-polarizable models over-estimate the residence time, relative to the translational diffusion constant and so tend to under-estimate the ion and water diffusion constants.

Control of transcriptional activity by design of charge patterning in the intrinsically disordered RAM region of the Notch receptor

Intrinsically disordered regions (IDRs) play important roles in proteins that regulate gene expression. A prominent example is the intracellular domain of the Notch receptor (NICD), which regulates the transcription of Notch-responsive genes. The NICD sequence includes an intrinsically disordered RAM region and a conserved ankyrin (ANK) domain. The 111-residue RAM region mediates bivalent interactions of NICD with the transcription factor CSL. Although the sequence of RAM is poorly conserved, the linear patterning of oppositely charged residues shows minimal variation. The conformational properties of polyampholytic IDRs are governed as much by linear charge patterning as by overall charge content. Here, we used sequence design to assess how changing the charge patterning within RAM affects its conformational properties, the affinity of NICD to CSL, and Notch transcriptional activity. Increased segregation of oppositely charged residues leads to linear decreases in the global dimensions of RAM and decreases the affinity of a construct including a C-terminal ANK domain (RAMANK) for CSL. Increasing charge segregation from WT RAM sharply decreases transcriptional activation for all permutants. Activation also decreases for some, but not all, permutants with low charge segregation, although there is considerable variation. Our results suggest that the RAM linker is more than a passive tether, contributing local and/or long-range sequence features that modulate interactions within NICD and with downstream components of the Notch pathway. We propose that sequence features within IDRs have evolved to ensure an optimal balance of sequence-encoded conformational properties, interaction strengths, and cellular activities.

Metal Ion Modeling Using Classical Mechanics

Metal ions play significant roles in numerous fields including chemistry, geochemistry, biochemistry, and materials science. With computational tools increasingly becoming important in chemical research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aqueous, and solid phases. Herein, we review both quantum and classical modeling strategies for metal ion-containing systems that have been developed over the past few decades. This Review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond-based models. Quantum mechanical studies of metal ion-containing systems at the semiempirical, ab initio, and density functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion-containing systems.

Sequence Determinants of the Conformational Properties of an Intrinsically Disordered Protein Prior to and upon Multisite Phosphorylation

Many cell signaling events are coordinated by intrinsically disordered protein regions (IDRs) that undergo multisite Serine/Threonine phosphorylation. The conformational properties of these IDRs prior to and following multisite phosphorylation are directly relevant to understanding their functions. Here, we present results from biophysical studies and molecular simulations that quantify the conformational properties of an 81-residue IDR from the S. cerevisiae transcription factor Ash1. We show that the unphosphorylated Ash1 IDR adopts coil-like conformations that are expanded and well-solvated. This result contradicts inferences regarding global compaction that are derived from heuristics based on amino acid compositions for IDRs with low proline contents. Upon phosphorylation at ten distinct sites, the global conformational properties of pAsh1 are indistinguishable from those of unphosphorylated Ash1. This insensitivity derives from compensatory changes to the pattern of local and long-range intrachain contacts. We show that the conformational properties of Ash1 and pAsh1 can be explained in terms of the linear sequence patterning of proline and charged residues vis-à-vis all other residues. The sequence features of the Ash1 IDR are shared by many other IDRs that undergo multisite phosphorylation. Accordingly, we propose that our findings might be generalizable to other IDRs involved in cell signaling.

Energetics, Thermodynamics, and Hydrogen Bonding Diversity in Ammonium Halide Clusters

Contributions from different intermolecular and interionic forces, as well as variations in bond energies, produce size-dependent variations in the structures of acid-base molecular clusters. In this work the structures and interaction energetics of cluster particles with the nominal formulas (NH₄X)_n, X = (F, Cl, Br) are predicted using either "mag-walking" sawtooth simulated annealing Monte Carlo calculations or model building, followed by M06-2X or RI-MP2 geometry optimization and single-point energy calculations. Whereas the n = 1 clusters all exhibit a single hydrogen bond, small (NH₄F)_n particles (n = 2-5) exhibit three distinct types of hydrogen bonds as a function of size (traditional, ion-pair and proton-shared). However, (NH₄Br)_n and (NH₄Cl)_n particles (n = 2-13) all solely exhibit ion-pair hydrogen bonding, with even values of n exhibiting pronounced relative stability. The computed differential interaction energy of the bromide and chloride systems is generally near the bulk limit of the difference in their accepted lattice energies, despite the fact that their structures do not resemble the bulk crystal structures. Nanoparticle growth reactions are predicted to be thermodynamically spontaneous under standard conditions, with significant size and system dependencies. This work is designed to further our understanding of the nature of hydrogen bonding and other intermolecular forces, particularly within ionic nanocrystallites, as well as the thermodynamics of cluster formation.

Pairwise-additive force fields for selected aqueous monovalent ions from adaptive force matching

Simple non-polarizable potentials were developed for Na(+), K(+), Cl(-), and Br(-) using the adaptive force matching (AFM) method with ab initio MP2 method as reference. Our MP2-AFM force field predicts the solvation free energies of the four salts formed by the ions with an error of no more than 5%. Other properties such as the ion-water radial distribution functions, first solvation shell water tilt angle distributions, ion diffusion constants, concentration dependent diffusion constant of water, and concentration dependent surface tension of the solutions were calculated with this potential. Very good agreement was achieved for these properties. In particular, the diffusion constants of the ions are within 6% of experimental measurements. The model predicts bromide to be enriched at the interface in the 1.6M KBr solution but predicts the ion to be repelled for the surface at lower concentration.

Super-Maxwellian helium evaporation from pure and salty water

Helium atoms evaporate from pure water and salty solutions in super-Maxwellian speed distributions, as observed experimentally and modeled theoretically. The experiments are performed by monitoring the velocities of dissolved He atoms that evaporate from microjets of pure water at 252 K and 4-8.5 molal LiCl and LiBr at 232-252 K. The average He atom energies exceed the flux-weighted Maxwell-Boltzmann average of 2RT by 30% for pure water and 70% for 8.5m LiBr. Classical molecular dynamics simulations closely reproduce the observed speed distributions and provide microscopic insight into the forces that eject the He atoms from solution. Comparisons of the density profile and He kinetic energies across the water-vacuum interface indicate that the He atoms are accelerated by He-water collisions within the top 1-2 layers of the liquid. We also find that the average He atom kinetic energy scales with the free energy of solvation of this sparingly soluble gas. This free-energy difference reflects the steeply decreasing potential of mean force on the He atoms in the interfacial region, whose gradient is the repulsive force that tends to expel the atoms. The accompanying sharp decrease in water density suppresses the He-water collisions that would otherwise maintain a Maxwell-Boltzmann distribution, allowing the He atom to escape at high energies. Helium is especially affected by this reduction in collisions because its weak interactions make energy transfer inefficient.

Structural Ensembles of Intrinsically Disordered Proteins Depend Strongly on Force Field: A Comparison to Experiment

Intrinsically disordered proteins (IDPs) are notoriously challenging to study both experimentally and computationally. The structure of IDPs cannot be described by a single conformation but must instead be described as an ensemble of interconverting conformations. Atomistic simulations are increasingly used to obtain such IDP conformational ensembles. Here, we have compared the IDP ensembles generated by eight all-atom empirical force fields against primary small-angle X-ray scattering (SAXS) and NMR data. Ensembles obtained with different force fields exhibit marked differences in chain dimensions, hydrogen bonding, and secondary structure content. These differences are unexpectedly large: changing the force field is found to have a stronger effect on secondary structure content than changing the entire peptide sequence. The CHARMM 22* ensemble performs best in this force field comparison: it has the lowest error in chemical shifts and J-couplings and agrees well with the SAXS data. A high population of left-handed α-helix is present in the CHARMM 36 ensemble, which is inconsistent with measured scalar couplings. To eliminate inadequate sampling as a reason for differences between force fields, extensive simulations were carried out (0.964 ms in total); the remaining small sampling uncertainty is shown to be much smaller than the observed differences. Our findings highlight how IDPs, with their rugged energy landscapes, are highly sensitive test systems that are capable of revealing force field deficiencies and, therefore, contributing to force field development.

Small molecule solvation changes due to the presence of salt are governed by the cost of solvent cavity formation and dispersion

We are interested in the free energies of transferring nonpolar solutes into aqueous NaCl solutions with salt concentrations upwards of 2 M, the Hofmeister regime. We use the semi-explicit assembly (SEA) computational model to represent these electrolyte solutions. We find good agreement with experiments (Setschenow coefficients) on 43 nonpolar and polar solutes and with TIP3P explicit-solvent simulations. Besides being much faster than explicit solvent calculations, SEA is more accurate than the PB models we tested, successfully capturing even subtle salt effects in both the polar and nonpolar components of solvation. We find that the salt effects are mainly due to changes in the cost of forming nonpolar cavities in aqueous NaCl solutions, and not mainly due to solute-ion electrostatic interactions.

Accounting for Electronic Polarization Effects in Aqueous Sodium Chloride via Molecular Dynamics Aided by Neutron Scattering

Modeled ions, described by nonpolarizable force fields, can suffer from unphysical ion pairing and clustering in aqueous solutions well below their solubility limit. The electronic continuum correction takes electronic polarization effects of the solvent into account in an effective way by scaling the charges on the ions, resulting in a much better description of the ionic behavior. Here, we present parameters for the sodium ion consistent with this effective polarizability approach and in agreement with experimental data from neutron scattering, which could be used for simulations of complex aqueous systems where polarization effects are important.

Revised Parameters for the AMOEBA Polarizable Atomic Multipole Water Model

A set of improved parameters for the AMOEBA polarizable atomic multipole water model is developed. An automated procedure, ForceBalance, is used to adjust model parameters to enforce agreement with ab initio-derived results for water clusters and experimental data for a variety of liquid phase properties across a broad temperature range. The values reported here for the new AMOEBA14 water model represent a substantial improvement over the previous AMOEBA03 model. The AMOEBA14 model accurately predicts the temperature of maximum density and qualitatively matches the experimental density curve across temperatures from 249 to 373 K. Excellent agreement is observed for the AMOEBA14 model in comparison to experimental properties as a function of temperature, including the second virial coefficient, enthalpy of vaporization, isothermal compressibility, thermal expansion coefficient, and dielectric constant. The viscosity, self-diffusion constant, and surface tension are also well reproduced. In comparison to high-level ab initio results for clusters of 2-20 water molecules, the AMOEBA14 model yields results similar to AMOEBA03 and the direct polarization iAMOEBA models. With advances in computing power, calibration data, and optimization techniques, we recommend the use of the AMOEBA14 water model for future studies employing a polarizable water model.

Intrinsically disordered C-terminal tails of E. coli single-stranded DNA binding protein regulate cooperative binding to single-stranded DNA

The homotetrameric Escherichia coli single-stranded DNA binding protein (SSB) plays a central role in DNA replication, repair and recombination. E. coli SSB can bind to long single-stranded DNA (ssDNA) in multiple binding modes using all four subunits [(SSB)65 mode] or only two subunits [(SSB)35 binding mode], with the binding mode preference regulated by salt concentration and SSB binding density. These binding modes display very different ssDNA binding properties with the (SSB)35 mode displaying highly cooperative binding to ssDNA. SSB tetramers also bind an array of partner proteins, recruiting them to their sites of action. This is achieved through interactions with the last 9 amino acids (acidic tip) of the intrinsically disordered linkers (IDLs) within the four C-terminal tails connected to the ssDNA binding domains. Here, we show that the amino acid composition and length of the IDL affects the ssDNA binding mode preferences of SSB protein. Surprisingly, the number of IDLs and the lengths of individual IDLs together with the acidic tip contribute to highly cooperative binding in the (SSB)35 binding mode. Hydrodynamic studies and atomistic simulations suggest that the E. coli SSB IDLs show a preference for forming an ensemble of globular conformations, whereas the IDL from Plasmodium falciparum SSB forms an ensemble of more extended random coils. The more globular conformations correlate with cooperative binding.