Simulated pressure changes in LacI suggest a link between hydration and functional conformational changes.

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.

Directing Intrinsic Chirality in Gold Nanoclusters: Preferential Formation of Stable Enantiopure Clusters in High Yield and Experimentally Unveiling the "Super" Chirality of Au144.

Chiral gold nanoclusters offer significant potential for exploring chirality at a fundamental level and for exploiting their applications in sensing and catalysis. However, their widespread use is impeded by low yields in synthesis, tedious separation procedures of their enantiomeric forms, and limited thermal stability. In this study, we investigated the direct synthesis of enantiopure chiral nanoclusters using the chiral ligand 2-MeBuSH in the fabrication of Au25, Au38, and Au144 nanoclusters. Notably, this approach leads to the unexpected formation of intrinsically chiral clusters with high yields for chiral Au38 and Au144 nanoclusters. Experimental evaluation of chiral activity by circular dichroism (CD) spectroscopy corroborates previous theoretical calculations, highlighting the stronger CD signal exhibited by Au144 compared to Au38 or Au25. Furthermore, the formation of a single enantiomeric form is experimentally confirmed by comparing it with intrinsically chiral Au38(2-PET)24 (2-PET: 2-phenylethanethiol) and is supported theoretically for both Au38 and Au144. Moreover, the prepared chiral clusters show stability against diastereoisomerization, up to temperatures of 80 °C. Thus, our findings not only demonstrate the selective preparation of enantiopure, intrinsically chiral, and highly stable thiolate-protected Au nanoclusters through careful ligand design but also support the predicted "super" chirality in the Au144 cluster, encompassing hierarchical chirality in ligands, staple configuration, and core structure.

Kirkwood-Buff-Derived Force Field for Peptides and Proteins: Philosophy and Development of KBFF20.

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 ß percentages for small peptides. This, the first of two articles, describes in detail the philosophy and development behind KBFF20.

Kirkwood-Buff-Derived Force Field for Peptides and Proteins: Applications of 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 ß-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.

Gas or Liquid? The Supercritical Behavior of Pure Fluids.

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 system, 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.

Classical harmonic model for the behavior of pure fluids at the critical point.

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.

Experimental Investigation of Triplet Correlation Approximations for Fluid Water.

Triplet correlations play a central role in our understanding of fluids and their properties. Of particular interest is the relationship between the pair and triplet correlations. Here we use a combination of Fluctuation Solution Theory and experimental pair radial distribution functions to investigate the accuracy of the Kirkwood Superposition Approximation (KSA), as given by integrals over the relevant pair and triplet correlation functions, at a series of state points for pure water using only experimental quantities. The KSA performs poorly, in agreement with a variety of other studies. Several additional approximate relationships between the pair and triplet correlations in fluids are also investigated and generally provide good agreement for the fluid thermodynamics for regions of the phase diagram where the compressibility is small. A simple power law relationship between the pair and triplet fluctuations is particularly successful for state points displaying low to moderately high compressibilities.

Simulated pressure denaturation thermodynamics of ubiquitin.

Simulations of protein thermodynamics are generally difficult to perform and provide limited information. It is desirable to increase the degree of detail provided by simulation and thereby the potential insight into the thermodynamic properties of proteins. In this study, we outline how to analyze simulation trajectories to decompose conformation-specific, parameter free, thermodynamically defined protein volumes into residue-based contributions. The total volumes are obtained using established methods from Fluctuation Solution Theory, while the volume decomposition is new and is performed using a simple proximity method. Native and fully extended ubiquitin are used as the test conformations. Changes in the protein volumes are then followed as a function of pressure, allowing for conformation-specific protein compressibility values to also be obtained. Residue volume and compressibility values indicate significant contributions to protein denaturation thermodynamics from nonpolar and coil residues, together with a general negative compressibility exhibited by acidic residues.

To Polarize or Not to Polarize? Charge-on-Spring versus KBFF Models for Water and Methanol Bulk and Vapor-Liquid Interfacial Mixtures.

Simulations of water and methanol mixtures using polarizable force fields (FFs) for methanol (COS/M and CPC) and water (COS/G2) were performed and compared to experiment and also to a nonpolarizable methanol (KBFF) model with SPC/E water in an effort to quantify the importance of explicit electronic polarization effects in bulk liquid mixtures and vapor-liquid interfaces. The bulk liquid mixture properties studied included the center of mass radial distribution functions, Kirkwood-Buff integrals (KBIs), volumetric properties, isothermal compressibility, enthalpy of mixing, dielectric constant, and diffusion coefficients. The vapor-liquid interface properties investigated included the relative surface probability distributions, surface tension, excess surface adsorption, preferred surface molecule orientations, and the surface dipole. None of the three FFs tested here was clearly superior for all of the properties examined. All the force fields typically reproduced the correct trends with composition for both the bulk and interfacial system properties; the differences between the force fields were primarily quantitative. The overall results suggest that the polarizable FFs are not, at the present stage of development, inherently better able to reproduce the studied bulk and interfacial properties-despite the added degree of explicit transferability that is, by definition, built into the polarizable models. Indeed, the specific parametrization of the FF appears to be just as important as the class of FF.

Particle and Energy Pair and Triplet Correlations in Liquids and Liquid Mixtures from Experiment and Simulation.

Recent advances in fluctuation solution theory (FST) have provided access to information concerning triplet fluctuations and integrals, in addition to the established pair fluctuations and integrals, for liquids and liquid mixtures using both experimental and simulation data. Here, FST is used to investigate pair and triplet correlations for (i) pure water as provided by experiment and simulation using both polarizable and nonpolarizable water models, (ii) liquid mixtures of methanol and water as provided by experiment and simulation, and (iii) native and denatured states of proteins as provided by simulation. The last application is particularly powerful, as it provides exact equations for the volume, enthalpy, compressibility, thermal expansion, and heat capacity of a single protein form provided by a single simulation. In addition, a discussion of the quality of the integrals obtained from experiment and simulation is provided. The results clearly illustrate that FST can be a powerful tool for the analysis and interpretation of both experimental and simulation data in complex liquid mixtures, including biomolecular systems, and that current simulation protocols can provide reliable values for the pair and triplet correlations and integrals.

Experimental triplet and quadruplet fluctuation densities and spatial distribution function integrals for liquid mixtures.

Kirkwood-Buff or Fluctuation Solution Theory can be used to provide experimental pair fluctuations, and/or integrals over the pair distribution functions, from experimental thermodynamic data on liquid mixtures. Here, this type of approach is used to provide triplet and quadruplet fluctuations, and the corresponding integrals over the triplet and quadruplet distribution functions, in a purely thermodynamic manner that avoids the use of structure factors. The approach is then applied to binary mixtures of water + methanol and benzene + methanol over the full composition range under ambient conditions. The observed correlations between the different species vary significantly with composition. The magnitude of the fluctuations and integrals appears to increase as the number of the most polar molecule involved in the fluctuation or integral also increases. A simple physical picture of the fluctuations is provided to help rationalize some of these variations.

Experimental triplet and quadruplet fluctuation densities and spatial distribution function integrals for pure liquids.

Fluctuation solution theory has provided an alternative view of many liquid mixture properties in terms of particle number fluctuations. The particle number fluctuations can also be related to integrals of the corresponding two body distribution functions between molecular pairs in order to provide a more physical picture of solution behavior and molecule affinities. Here, we extend this type of approach to provide expressions for higher order triplet and quadruplet fluctuations, and thereby integrals over the corresponding distribution functions, all of which can be obtained from available experimental thermodynamic data. The fluctuations and integrals are then determined using the International Association for the Properties of Water and Steam Formulation 1995 (IAPWS-95) equation of state for the liquid phase of pure water. The results indicate small, but significant, deviations from a Gaussian distribution for the molecules in this system. The pressure and temperature dependence of the fluctuations and integrals, as well as the limiting behavior as one approaches both the triple point and the critical point, are also examined.

Infinitely dilute partial molar properties of proteins from computer simulation.

A detailed understanding of temperature and pressure effects on an infinitely dilute protein's conformational equilibrium requires knowledge of the corresponding infinitely dilute partial molar properties. Established molecular dynamics methodologies generally have not provided a way to calculate these properties without either a loss of thermodynamic rigor, the introduction of nonunique parameters, or a loss of information about which solute conformations specifically contributed to the output values. Here we implement a simple method that is thermodynamically rigorous and possesses none of the above disadvantages, and we report on the method's feasibility and computational demands. We calculate infinitely dilute partial molar properties for two proteins and attempt to distinguish the thermodynamic differences between a native and a denatured conformation of a designed miniprotein. We conclude that simple ensemble average properties can be calculated with very reasonable amounts of computational power. In contrast, properties corresponding to fluctuating quantities are computationally demanding to calculate precisely, although they can be obtained more easily by following the temperature and/or pressure dependence of the corresponding ensemble averages.

Flexible connection of the N-terminal domain in ClpB modulates substrate binding and the aggregate reactivation efficiency.

ClpB reactivates aggregated proteins in cooperation with DnaK/J. The ClpB monomer contains two nucleotide-binding domains (D1, D2), a coiled-coil domain, and an N-terminal domain attached to D1 with a 17-residue-long unstructured linker containing a Gly-Gly motif. The ClpB-mediated protein disaggregation is linked to translocation of substrates through the central channel in the hexameric ClpB, but the events preceding the translocation are poorly understood. The N-terminal domains form a ring surrounding the entrance to the channel and contribute to the aggregate binding. It was suggested that the N-terminal domain's mobility that is maintained by the unstructured linker might control the efficiency of aggregate reactivation. We produced seven variants of ClpB with modified sequence of the N-terminal linker. To increase the linker's conformational flexibility, we inserted up to four Gly next to the GG motif. To decrease the linker's flexibility, we deleted the GG motif and converted it into GP and PP. We found that none of the linker modifications inhibited the basal ClpB ATPase activity or its capability to form oligomers. However, the modified linker ClpB variants showed lower reactivation rates for aggregated glucose-6-phosphate dehydrogenase and firefly luciferase and a lower aggregate-binding efficiency than wt ClpB. We conclude that the linker does not merely connect the N-terminal domain, but it supports the chaperone activity of ClpB by contributing to the efficiency of aggregate binding and disaggregation. Moreover, our results suggest that selective pressure on the linker sequence may be crucial for maintaining the optimal efficiency of aggregate reactivation by ClpB.

A Kirkwood-Buff force field for the aromatic amino acids.

In a continuation of our efforts to develop a united atom non-polarizable protein force field based upon the solution theory of Kirkwood and Buff i.e., the Kirkwood-Buff Force Field (KBFF) approach, we present KBFF models for the side chains of phenylalanine, tyrosine, tryptophan, and histidine, including both tautomers of neutral histidine and doubly-protonated histidine. The force fields were specifically designed to reproduce the thermodynamic properties of mixtures over the full composition range in an attempt to provide an improved description of intermolecular interactions. The models were developed by careful parameterization of the solution phase partial charges to reproduce the experimental Kirkwood-Buff integrals for mixtures of solutes representative of the amino acid sidechains in solution. The KBFF parameters and simulated thermodynamic and structural properties are presented for the following eleven binary mixtures: benzene + methanol, benzene + toluene, toluene + methanol, toluene + phenol, toluene + p-cresol, pyrrole + methanol, indole + methanol, pyridine + methanol, pyridine + water, histidine + water, and histidine hydrochloride + water. It is argued that the present approach and models provide a reasonable description of intermolecular interactions which ensures that the required balance between solute-solute, solute-solvent, and solvent-solvent distributions is obtained.

Local fluctuations in solution mixtures.

An extension of the traditional Kirkwood-Buff (KB) theory of solutions is outlined which provides additional fluctuating quantities that can be used to characterize and probe the behavior of solution mixtures. Particle-energy and energy-energy fluctuations for local regions of any multicomponent solution are expressed in terms of experimentally obtainable quantities, thereby supplementing the usual particle-particle fluctuations provided by the established KB inversion approach. The expressions are then used to analyze experimental data for pure water over a range of temperatures and pressures, a variety of pure liquids, and three binary solution mixtures - methanol and water, benzene and methanol, and aqueous sodium chloride. In addition to providing information on local properties of solutions it is argued that the particle-energy and energy-energy fluctuations can also be used to test and refine solute and solvent force fields for use in computer simulation studies.

Kirkwood-Buff integrals for ideal solutions.

The Kirkwood-Buff (KB) theory of solutions is a rigorous theory of solution mixtures which relates the molecular distributions between the solution components to the thermodynamic properties of the mixture. Ideal solutions represent a useful reference for understanding the properties of real solutions. Here, we derive expressions for the KB integrals, the central components of KB theory, in ideal solutions of any number of components corresponding to the three main concentration scales. The results are illustrated by use of molecular dynamics simulations for two binary solutions mixtures, benzene with toluene, and methanethiol with dimethylsulfide, which closely approach ideal behavior, and a binary mixture of benzene and methanol which is nonideal. Simulations of a quaternary mixture containing benzene, toluene, methanethiol, and dimethylsulfide suggest this system displays ideal behavior and that ideal behavior is not limited to mixtures containing a small number of components.

Developing Force Fields from the Microscopic Structure of Solutions.

We have been developing force fields designed for the eventual simulation of peptides and proteins using the Kirkwood-Buff (KB) theory of solutions as a guide. KB theory provides exact information on the relative distributions for each species present in solution. This information can also be obtained from computer simulations. Hence, one can use KB theory to help test and modify the parameters commonly used in biomolecular studies. A series of small molecule force fields representative of the fragments found in peptides and proteins have been developed. Since this approach is guided by the KB theory, our results provide a reasonable balance in the interactions between self-association of solutes and solute solvation. Here, we present our progress to date. In addition, our investigations have provided a wealth of data concerning the properties of solution mixtures, which is also summarized. Specific examples of the properties of aromatic (benzene, phenol, p-cresol) and sulfur compounds (methanethiol, dimethylsulfide, dimethyldisulfide) and their mixtures with methanol or toluene are provided as an illustration of this kind of approach.