The ion atmosphere that develops around a central ion in solution results in neutralization of the central charge together with additional changes in ion distributions that contribute to the thermodynamics of the solution mixture. The nature of these changes is poorly understood beyond the limiting Debye-Hückel behavior, with mixed electrolyte solutions being particularly challenging to study. Recently, we developed a combined Kirkwood-Buff (KB) inversion and electroneutrality based approach for bulk mixed electrolyte solutions that provide the experimentally derived ion-ion KB integrals (KBIs), which quantify the relative affinity between all the possible ion pairs. Here, we use the resulting experimental KBIs to obtain the fractional contributions from all ions to the ion atmosphere of a central ion for two mixed electrolyte solutions and their single and common ion subsystems, namely NaCl + KBr (aq) at 298.15 K and 1 bar and MgCl2 + KBr (aq) at 373.45 K and 1 bar. These quantities are further decomposed into two contributions. One term contributes to the neutralization of the central charge but not to the thermodynamic properties of closed electrolyte solutions, and the other term gives rise to the thermodynamic properties of the electrolyte solution but does not contribute to the neutralization of the central charge. The results suggest that the thermodynamics of these solutions are dominated by the net thermodynamic enrichment of all ions at low concentrations which, for the systems studied here, typically changes to net thermodynamic depletion of all ions at higher total concentrations. For mixed electrolytes, the switch between behaviors passes through an intermediate concentration range where some ions are thermodynamically enriched and others thermodynamically depleted. Furthermore, we illustrate how to study the competition between two different ions in a particular ion atmosphere for the simpler case of the common ion subsystems, and detail how this relates to the solution thermodynamics.

Ion adsorption or exclusion from surfaces plays a major role in many systems and processes. Unfortunately, thermodynamic information characterizing the relative surface adsorption of individual ions is not currently available from approaches based on the Gibbs adsorption isotherm for mixed electrolytes without approximation. Here, we address this issue for electrolyte solutions containing any number of components at any concentration in a single phase in the presence of any type of fixed charged or uncharged surface in the absence of chemisorption or other chemical reactions. This is achieved by reference to local and global electroneutrality requirements between integrals over the surface-ion distributions. The results indicate that the surface-ion distribution integrals can be decomposed into two independent contributions: one that leads to surface charge neutralization, and the other that explains the surface thermodynamics. The resulting surface-ion integral relationships obtained here indicate exactly how the presence of additional electrolytes affects the surface distribution of any target ion of interest. The validity of the resulting relationships is confirmed using classical all atom explicit solvent molecular dynamics simulations. Using these relationships, one can then obtain individual relative surface-ion adsorptions from experimental data. We illustrate how to use the approach to extract more detailed information from experimental data than was previously available for two experimental mixed electrolyte systems involving vacuum electrolyte solution interfaces. The approach is exact and does not require a particular model for the surface region or the use of single ion chemical potentials.

For single electrolytes, it is already well established that the net affinities between salt-salt, salt-solvent, and solvent-solvent can be derived from bulk thermodynamic volumetric and chemical potential composition-derivative data via Kirkwood-Buff integrals (KBIs). In this simplest case, it is also widely known how to reinterpret those component-based KBIs to obtain the species-based KBIs (cation-cation, cation-anion, etc.). However, this process has never been performed for systems with more than one species of cation and/or anion-a severe restriction. Here, we show how to obtain the ion-ion KBIs for bulk mixed electrolyte solutions regardless of the ion concentration, valency, molecular complexity, degree of ion pairing, etc., assuming one has correlating equations for the bulk thermodynamic data and the system is miscible. This is achieved using a combination of Kirkwood-Buff theory and global and local electroneutrality constraints and is illustrated for mixtures of NaCl + KBr (aq) at 298 K and 1 bar and MgCl2 + KBr (aq) at 373 K and 1 bar. The single electrolyte and select common ion subsystems are also studied. A comparison of the experimental KBIs to those obtained from molecular dynamics simulations shows excellent agreement for the ambient NaCl + KBr (aq) system using the KBFF + SPC/E force field.

In proteins, amino acid changes at "rheostat" positions exhibit functional changes that vary with the substitution chosen: some substitutions enhance function, some are like wild-type, some are partially detrimental, while others abolish function. One way that substitutions might exert their complex effects is by altering protein conformational landscapes. To test this, we studied five substitutions of V52 in E. coli LacI, an experimentally-known rheostat position. For each variant, we mapped the accessible conformational landscapes by performing molecular dynamics simulations at ambient conditions and under three perturbations: increased pressure, binding to allosteric ligand "ONPF", and ONPF plus pressure. The simulated DNA binding domain landscapes were compared to published experimentally-measured parameters, and the results suggest that complex combinations of dynamic parameters and/or additional simulations in the presence of DNA are needed to predict DNA binding specificity. For the variants regulatory domains all landscapes displayed boundaries similar to wild-type, but changes within the boundaries were unique. Of these, V52A/ONPF was striking: The regulatory domains for ONPF-bound, wild-type LacI are in an "Open" conformation and, experimentally, ONPF enhances DNA binding. Four variants responded to ONPF like wild-type, but ONPF binding to V52A shifted these domains to a "Closed" conformation that is associated with diminished DNA binding for wild-type LacI. This finding predicted that ONPF's allosteric regulation of V52A would change from "anti-inducer" to "inducer", which we experimentally validated in vivo and in vitro. This supports the hypothesis that substituting rheostat positions can alter function by altering the relative populations on protein conformational landscapes.

Ion atmospheres play a critical role in modulating the interactions between charged components in solutions. However, a detailed description of the nature of ion atmospheres remains elusive. Here, we use Kirkwood-Buff theory, an exact theory of solution mixtures, together with a series of local and bulk electroneutrality constraints to provide relationships between all the net ion-ion distributions in bulk electrolyte mixtures. The validity of the underlying relationships is then confirmed using classical explicit solvent molecular simulations of a range of electrolyte mixtures. Further analysis indicates the ion distributions can be separated into two contributions, one resulting in charge neutralization, for which each ion contributes in proportion to its ionic strength, and the other accounting for all the solution thermodynamics. The relationships hold for atomic and molecular ions of any size and valency regardless of ionic strength, temperature, or pressure, in any solvent system.

Partial molar volumes and compressibilities of four globular native proteins (lysozyme, ribonuclease A, ubiquitin, and α-lactalbumin) were determined from molecular dynamics simulations and the Kirkwood-Buff and Fluctuation Solution theories. Total protein properties were decomposed into individual residue side chain and backbone contributions. By combining the results of constant protonation simulations with those that are largely inaccessible to experiment (e.g., where the motion of protein atoms is greatly reduced or where the net charge on charged side chains is neutralized while retaining bond dipoles), the contributions of volume fluctuations, electrostriction, and changes in hydration to the compressibility were probed. Similarities were found in the properties of the proteins; however, the compressibility change for lysozyme on going from intermediate to low pH was different from the other proteins. The reason for this was revealed through the residue-level decomposition. Solvent exposed carboxylate groups gave a large negative contribution to protein compressibility. At intermediate pH, the overall contribution from acidic residues differed qualitatively for lysozyme as compared to the other three proteins because the lysozyme acidic side chains had more intramolecular polar contacts. Finally, the side chain properties were compared to those obtained from experimental small peptide data modeled using an additive scheme that models unfolded conformation properties.

During protein evolution, some amino acid substitutions modulate protein function ("tuneability"). In most proteins, the tuneable range is wide and can be sampled by a set of protein variants that each contains multiple amino acid substitutions. In other proteins, the full tuneable range can be accessed by a set of variants that each contains a single substitution. Indeed, in some globular proteins, the full tuneable range can be accessed by the set of site-saturating substitutions at an individual "rheostat" position. However, in proteins with intrinsically disordered regions (IDRs), most functional studies-which would also detect tuneability-used multiple substitutions or small deletions. In disordered transcriptional activation domains (ADs), studies with multiple substitutions led to the "acidic exposure" model, which does not anticipate the existence of rheostat positions. In the few studies that did assess effects of single substitutions on AD function, results were mixed: the ADs of two full-length transcription factors did not show tuneability, whereas a fragment of a third AD was tuneable by single substitutions. In this study, we tested tuneability in the AD of full-length human class II transactivator (CIITA). Sequence analyses and experiments showed that CIITA's AD is an IDR. Functional assays of singly-substituted AD variants showed that CIITA's function was highly tuneable, with outcomes not predicted by the acidic exposure model. Four tested positions showed rheostat behavior for transcriptional activation. Thus, tuneability of different IDRs can vary widely. Future studies are needed to illuminate the biophysical features that govern whether an IDR is tuneable by single substitutions.

The functions of many proteins are associated with interconversions among conformational substates. However, these substates can be difficult to measure experimentally, and determining contributions from hydration changes can be especially difficult. Here, we assessed the use of pressure perturbations to sample the substates accessible to the Escherichia coli lactose repressor protein (LacI) in various liganded forms. In the presence of DNA, the regulatory domain of LacI adopts an Open conformation that, in the absence of DNA, changes to a Closed conformation. Increasing the simulation pressure prevented the transition from an Open to a Closed conformation, in a similar manner to the binding of DNA and anti-inducer, ONPF. The results suggest the hydration of specific residues play a significant role in determining the population of different LacI substates and that simulating pressure perturbation could be useful for assessing the role of hydration changes that accompany functionally-relevant amino acid substitutions.

A new classical nonpolarizable force field, KBFF20, for the simulation of peptides and proteins is presented. The force field relies heavily on the use of Kirkwood-Buff theory to provide a comparison of simulated and experimental Kirkwood-Buff integrals for solutes containing the functional groups common in proteins, thus ensuring intermolecular interactions that provide a good balance between the peptide-peptide, peptide-solvent, and solvent-solvent distributions observed in solution mixtures. In this way, it differs significantly from other biomolecular force fields. Further development and testing of the intermolecular potentials are presented here. Subsequently, rotational potentials for the ϕ/ψ and χ dihedral degrees of freedom are obtained by analysis of the Protein Data Bank, followed by small modifications to provide a reasonable balance between simulated and observed α and β percentages for small peptides. This, the first of two articles, describes in detail the philosophy and development behind KBFF20.

Here, we perform structural, thermodynamic, and kinetics tests of the Kirkwood-Buff-derived force field, KBFF20, for peptides and proteins developed in the previous article. The physical/structural tests measure the ability of KBFF20 to capture the experimental J-couplings for small peptides, to keep globular monomeric and oligomeric proteins folded, and to produce the experimentally relevant expanded conformational ensembles of intrinsically disordered proteins. The thermodynamic-based tests probe KBFF20's ability to quantify the preferential interactions of sodium chloride around native β-lactoglobulin and urea around native lysozyme, to reproduce the melting curves for small helix- and sheet-based peptides, and to fold the small proteins Trp-cage and Villin. The kinetics-based tests quantify how well KBFF20 can match the experimental contact formation rates of small, repeat-sequence peptides of variable lengths and the rotational diffusion coefficients of globular proteins. The results suggest that KBFF20 is naturally able to reproduce properties of both folded and disordered proteins, which we attribute to the use of the Kirkwood-Buff theory as the foundation of the force field's development. However, we show that KBFF20 tends to lose some well-defined secondary structural elements and increases the percentage of coil regions, indicating that the perfect balance of all interactions remains elusive. Nevertheless, we argue that KBFF20 is an improvement over recently modified force fields that require ad hoc interventions to prevent the collapse of intrinsically disordered proteins.

Protein function can be progressively fine-tuned by substituting amino acids at “rheostat” positions. For example, at a rheostat position that modulates binding affinity, substitutions exhibit Kd values that span a wide range. Early studies of rheostat positions revealed outcomes that could not be explained by side chain chemical similarities or by evolutionary frequency. In ongoing efforts to catalog the prevalence of rheostat positions, we have identified them in proteins that evolved under different physical constraints: globular soluble, integral membrane, and intrinsically disordered proteins. However, the density of rheostat positions within a protein can vary widely: >40% of E. coli LacI comprises rheostat positions, whereas they have yet to be identified in Z. mobilis pyruvate kinase despite numerous selection strategies. Among these strategies, analyses of sequence alignments can identify sets of positions enriched for rheostat positions, but no single metric definitively identified rheostat positions. In contrast, a subset of “neutral” positions (all substitutions have wild-type function) were identified from combined sequence analyses. In crystallo and in silico structural studies of rheostat substitutions showed only local perturbations and modest effects on protein stability. Additional functional studies revealed new complexities: (1) The rheostat character of each position falls on a continuum between the all-or-none substitution outcomes of “toggle” positions and the mutational insensitivity of neutral positions. (2) Some rheostat positions have complex effects on ligand specificity. (3) “Multiplex” rheostat positions simultaneously modulate multiple functional parameters, such as Kd and allosteric coupling; these show intriguing overlap with positions involved in allosteric regulation. To understand the complex roles of rheostat positions, biophysical studies are key: Indeed, dynamic coupling calculations for rheostat substitutions showed promising correlations with measured functional changes. Results suggest that emergent properties of coupled amino acid networks could produce the complex outcomes observed for rheostat substitutions.

We present a simple model to explain the limiting behavior of many thermodynamic properties of pure classical fluids as one approaches the critical point. The model consists of four main aspects: (i) a focus on the thermodynamic properties as described by Fluctuation Solution Theory (FST); (ii) the removal of all intramolecular energy contributions from the FST expressions; (iii) particle fluctuations (and not the energy fluctuations) dominate the thermodynamics close to the critical point; and (iv) the equipartition theorem applies to the resulting low frequency collective modes of the fluid at the critical point. Using this approach, we predict and compare the thermodynamic results for 121 pure fluids as provided by accurate equations of state. The model explains why some ratios of diverging thermodynamic properties remain finite at the critical point, and reliably predicts the value of these ratios for equations of state that mimic both mean field and Ising system types, suggesting universal behavior.

By definition, the distinction between a gas and a liquid ceases to exist beyond the critical point for pure fluids. Nevertheless, there remains a strong desire to attribute gas-like or liquid-like behavior to fluids corresponding to different parts of the supercritical region, especially as this becomes important for understanding and designing the properties of supercritical fluids. Here, we use a combination of fluctuation solution theory and accurate equation of state data to elucidate an easily accessible dividing line and corresponding transition regime between liquid-like and gas-like behavior in the supercritical region of all pure fluids. Liquid-like behavior in the supercritical region is characterized by a negative skewness in the particle number distribution for an equivalent open indicating that particle deletion is favored for liquids, whereas gas-like behavior is characterized by a positive skewness, indicating that particle insertion is favored for gases. Identical behavior is observed either side of the liquid-vapor line. The possible consequences for the behavior of fluids at the critical point are also discussed.

The activity and function of many macromolecules in cellular environments are coupled with the binding of divalent ions such as calcium or magnesium. In principle, computer simulations can be used to understand the molecular level aspects of how many important macromolecules interact with ions. However, most of the force fields currently available often fail to accurately reproduce the properties of divalent ions in aqueous environments. Here we develop classical non-polarizable force fields for the aqueous alkaline earth metal halides (MX2), where M = Mg2+, Ca2+, Sr2+, Ba2+ and X = Cl-, Br-, I-, which can be used in bimolecular simulations and which are compatible with the Simple Point Charge/Extended (SPC/E) water model. The force field parameters are specifically developed to reproduce the experimental Kirkwood-Buff integrals for aqueous solutions and thereby the experimental activity derivatives, partial molar volumes, and excess coordination numbers. This ensures that a reasonable balance between ion-ion, ion-water, and water-water distributions is obtained. However, this requires a scaling of the cation to water oxygen interaction strength in order to accurately reproduce the integrals. The scaling factors developed for chloride salts are successfully transferable to the bromide and iodide salts. Use of these new models leads to reasonable diffusion constants and dielectric decrements. However, the performance of the models decreases with increasing salt concentration (>4m), and simulations of the pure crystals exhibited unstable behavior.