Antibody association in solution: cluster distributions and mechanisms

Understanding factors that affect the clustering and association of antibodies molecules in solution is critical to their development as therapeutics. For 19 different monoclonal antibody (mAb) solutions, we measured the viscosities, the second virial coefficients, the Kirkwood-Buff integrals, and the cluster distributions of the antibody molecules as functions of protein concentration. Solutions were modeled using the statistical-physics Wertheim liquid-solution theory, representing antibodies as Y-shaped molecular structures of seven beads each. We found that high-viscosity solutions result from more antibody molecules per cluster. Multi-body properties such as viscosity are well predicted experimentally by the 2-body Kirkwood-Buff quantity, G22, but not by the second virial coefficient, B22, and well-predicted theoretically from the Wertheim protein-protein sticking energy. Weakly interacting antibodies are rate-limited by nucleation; strongly interacting ones by propagation. This approach gives a way to relate micro to macro properties of solutions of associating proteins.

Protein Association in Solution: Statistical Mechanical Modeling

Protein molecules associate in solution, often in clusters beyond pairwise, leading to liquid phase separations and high viscosities. It is often impractical to study these multi-protein systems by atomistic computer simulations, particularly in multi-component solvents. Instead, their forces and states can be studied by liquid state statistical mechanics. However, past such approaches, such as the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory, were limited to modeling proteins as spheres, and contained no microscopic structure-property relations. Recently, this limitation has been partly overcome by bringing the powerful Wertheim theory of associating molecules to bear on protein association equilibria. Here, we review these developments.

Biophysical Principles Emerging from Experiments on Protein-Protein Association and Aggregation

Protein-protein association and aggregation are fundamental processes that play critical roles in various biological phenomena, from cellular signaling to disease progression. Understanding the underlying biophysical principles governing these processes is crucial for elucidating their mechanisms and developing strategies for therapeutic intervention. In this review, we provide an overview of recent experimental studies focused on protein-protein association and aggregation. We explore the key biophysical factors that influence these processes, including protein structure, conformational dynamics, and intermolecular interactions. We discuss the effects of environmental conditions such as temperature, pH and related buffer-specific effects, and ionic strength and related ion-specific effects on protein aggregation. The effects of polymer crowders and sugars are also addressed. We list the techniques used to study aggregation. We analyze emerging trends and challenges in the field, including the development of computational models and the integration of multidisciplinary approaches for a comprehensive understanding of protein-protein association and aggregation. Expected final online publication date for the Annual Review of Biophysics, Volume 53 is May 2024. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

The mechanism of self-association of human γ-D crystallin from molecular dynamics simulations

The aggregation of human γ-D crystallin is associated with the age-onset cataract formation. Here, we extensively investigated the self-association mechanism of human γ-D crystallin through molecular dynamics computer simulations. By mutating the protein surface we found that electrostatic interactions between charged amino acids play a crucial role in its self-association. We have confirmed the two-fold role of arginine molecules. If they are located as residues on the protein surface they can initiate protein contacts and contribute to their stickiness with noteworthy hydrophobic interactions through stacking of their methylene groups. But if they are added as free arginine in the protein solution they can also stabilize it, by associating with the protein surface and also with themselves to form effective inter-protein spacers that obstruct protein aggregation.

The Role of Buffers in Wild-Type HEWL Amyloid Fibril Formation Mechanism: A Methodological Approach

The amyloidophilic dyes thioflavin T and Congo red are small, yet powerful, molecules that allow the in vitro and in vivo detection of amyloid fibrils in protein solutions. Even though Congo red and thioflavin T binding assays are widespread techniques for unveiling amyloid fibers and are gradually replacing the more demanding X-ray diffraction method, handling samples containing amyloid fibrils is still challenging and can lead to false-positive/negative results. Here we describe a relatively straightforward procedure of preparing hen egg-white lysozyme amyloid fibrils in different buffer solutions and their detection with thioflavin T and Congo red, supported by an indispensable method for determining the secondary structure of proteins - circular dichroism.

CAT-Site: Predicting Protein Binding Sites Using a Convolutional Neural Network

Identifying binding sites on the protein surface is an important part of computer-assisted drug design processes. Reliable prediction of binding sites not only assists with docking algorithms, but it can also explain the possible side-effects of a potential drug as well as its efficiency. In this work, we propose a novel workflow for predicting possible binding sites of a ligand on a protein surface. We use proteins from the PDBbind and sc-PDB databases, from which we combine available ligand information for similar proteins using all the possible ligands rather than only a special sub-selection to generalize the work of existing research. After performing protein clustering and merging of ligands of similar proteins, we use a three-dimensional convolutional neural network that takes into account the spatial structure of a protein. Lastly, we combine ligandability predictions for points on protein surfaces into joint binding sites. Analysis of our model's performance shows that its achieved sensitivity is 0.829, specificity is 0.98, and F1 score is 0.517, and that for 54% of larger and pharmacologically relevant binding sites, the distance between their real and predicted centers amounts to less than 4 Å.

The influence of excipients on the viscosity of monoclonal antibody solutions

The aggregation propensity of monoclonal antibodies can be modified by adding different cosolutes into the solution. A simple coarse-grained model in the combination with the thermodynamic perturbation theory was used to predict cluster distribution and viscosity of the solutions of IgG4 monoclonal anibody in the presence of L-Arginine Hydrochloride. The data were analysed using binding polynomial to describe the binding of cosolute (Arginine) to the antibody molecule. The results show that by binding to the antibody molecule the cosolute occupies some of the binding sites of the antibody, and in this way reduces the amount of binding sites available to other antibody molecules. The aggregation propensity of the antibody molecules is therefore reduced.

A new fibrillization mechanism of β-lactoglobulin in glycine solutions

Even though amyloid aggregates were discovered many years ago the mechanism of their formation is still a mystery. Because of their connection to many of untreatable neurodegenerative diseases the motivation for finding a common aggregation path is high. We report a new high heat induced fibrillization path of a model protein β-lactoglobulin (BLG) when incubated in glycine instead of water at pH 2. By combining atomic force microscopy (AFM), transmission emission microscopy (TEM), dynamic light scattering (DLS) and circular dichroism (CD) we predict that the basic building blocks of fibrils made in glycine are not peptides, but rather spheroid oligomers of different height that form by stacking of ring-like structures. Spheroid oligomers linearly align to form fibrils by opening up and combining. We suspect that glycine acts as an hydrolysation inhibitor which consequently promotes a different fibrillization path. By combining the known data on fibrillization in water with our experimental conclusions we come up with a new fibrillization scheme for BLG. We show that by changing the fibrillization conditions just by small changes in buffer composition can dramatically change the aggregation pathway and the effect of buffer shouldn't be neglected. Fibrils seen in our study are also gaining more and more attention because of their pore-like structure and a possible cytotoxic mechanism by forming pernicious ion-channels. By preparing them in a simple model system as BLG we opened a new way to study their formation.

Tetrahedrality, hydrogen bonding and the density anomaly of the central force water model. A Monte Carlo study

Monte Carlo computer simulations in the canonical and grand canonical statistical ensemble were used to explore the properties of the central force (CF1) water model. The intramolecular structure of the H₂O molecule is well reproduced by the model. Emphasis was made on hydrogen bonding, and on the tehrahedral, q, and translational, τ, order parameters. An energetic definition of the hydrogen bond gives more consistent results for the average number of hydrogen bonds compared to the one-parameter distance criterion. At 300 K, an average value of 3.8 was obtained. The q and τ metrics were used to elucidate the water-like anomalous behaviour of the CF1 model. The structural anomalies lead to the density anomaly, with a good agreement of the model's density with the experimental ρ(T) trends. The chemical potential-density projection of the model's equation of state was explored. Vapour-liquid coexistence was observed at sufficiently low temperatures.

Effect of Buffer on Protein Stability in Aqueous Solutions: A Simple Protein Aggregation Model

Liquid-liquid phase separation (LLPS) of proteins has recently been associated with the onset of numerous diseases. Despite several studies in this area of protein aggregation, buffer-specific effects always seem to be overlooked. In this study we investigated the influence of buffers on the phase stability of hen egg-white lysozyme (HEWL) and its respective protein-protein interactions by measuring the cloud point temperature, second virial coefficient, and interaction diffusion coefficient of several HEWL-buffer solutions (MOPS, phosphate, HEPES, cacodylate) at pH 7.0. The results indicate that the buffer molecules, depending on their hydration, adsorb on the protein surface, and modulate their electrostatic stability. The obtained information was used to extend the recently developed coarse-grained protein model to incorporate buffer-specific effects. Treated by Wertheim's perturbation theory the model qualitatively correctly predicted the experimentally observed phase separation of all investigated HEWL-buffer solutions, and further allowed us to predict the phase stability of protein formulations even in experimentally unattainable conditions. Since the theory can be straightforwardly extended to include multiple components it presents a useful tool to study protein aggregation in crowded cell-like systems.

Studying the mechanism of phase separation in aqueous solutions of globular proteins via molecular dynamics computer simulations

Proteins are the most abundant biomacromolecules in living cells, where they perform vital roles in virtually every biological process. To maintain their function, proteins need to remain in a stable (native) state. Inter- and intramolecular interactions in aqueous protein solutions govern the fate of proteins, as they can provoke their unfolding or association into aggregates. The initial steps of protein aggregation are difficult to capture experimentally, therefore we used molecular dynamics simulations in this study. We investigated the initial phase of aggregation of two different lysozymes, hen egg-white (HEWL) and T4 WT* lysozyme and also human lens γ-D crystallin by using atomistic simulations. We monitored the phase stability of their aqueous solutions by calculating time-dependent density fluctuations. We found that all proteins remained in their compact form despite aggregation. With an extensive analysis of intermolecular residue-residue interactions we discovered that arginine is of paramount importance in the initial stage of aggregation of HEWL and γ-D crystallin, meanwhile lysine was found to be the most involved amino acid in forming initial contacts between T4 WT* molecules.

The Role of Buffers in Wild-Type HEWL Amyloid Fibril Formation Mechanism

Amyloid fibrils, highly ordered protein aggregates, play an important role in the onset of several neurological disorders. Many studies have assessed amyloid fibril formation under specific solution conditions, but they all lack an important phenomena in biological solutions-buffer specific effects. We have focused on the formation of hen egg-white lysozyme (HEWL) fibrils in aqueous solutions of different buffers in both acidic and basic pH range. By means of UV-Vis spectroscopy, fluorescence measurements and CD spectroscopy, we have managed to show that fibrillization of HEWL is affected by buffer identity (glycine, TRIS, phosphate, KCl-HCl, cacodylate, HEPES, acetate), solution pH, sample incubation (agitated vs. static) and added excipients (NaCl and PEG). HEWL only forms amyloid fibrils at pH = 2.0 under agitated conditions in glycine and KCl-HCl buffers of high enough ionic strength. Phosphate buffer on the other hand stabilizes the HEWL molecules. Similar stabilization effect was achieved by addition of PEG12000 molecules to the solution.

Replica Ornstein-Zernike Theory Applied for Studying the Equilibrium Distribution of Electrolytes across Model Membranes

By means of replica Ornstein-Zernike theory (supplemented in a few cases by Monte Carlo simulations) we examined the distribution of an annealed primitive model +1:-1 electrolyte in a mixture with uncharged hard spheres, or another model +1:-1 or +2:-1 electrolyte inside and outside the quenched vesicles, decorated by a model membrane, and across the membrane phase. We explored the influence of the size and charge of the annealed fluid on the partition equilibrium, as well as the effect of the vesicle size and membrane interaction parameters (repulsive barrier height, attractive depth, and membrane width). A hydrophobic cation, present in the mixture with NaCl, slightly enhanced the concentration of sodium ions inside the model vesicle, compared to pure NaCl solution. The replica theory was in good agreement with computer simulations and as such adequate for studying partitioning of small and hydrophobic ions or hydrophobic solutes across model membranes.

DNA-Polyelectrolyte Complexation Study: The Effect of Polyion Charge Density and Chemical Nature of the Counterions

Complexes of polycations and DNA, also known as polyplexes, have been extensively studied in the past decade, as potential gene delivery systems. Their stability depends strongly on the characteristics of the polycations, as well as the nature of the added salt. We present here a study of the DNA ionene complexation in which we used fluorescence, UV, and CD spectroscopy, combined with molecular dynamics computer simuations, to systematically examine the influence of the polycation charge density, as well as the influence of the nature of the counterion, on the stability of these systems. Ionenes as polycations, depending on their structural characteristics, have previously been found to possess low cytotoxicity, and are therefore particularly interesting as potential gene delivery agents. The results show that the DNA solutions in the presence of the polycation are more stable in the case of very large or very small ionene charge density, suggesting different mechanism of complexation. The computer simulations show that the ionenes with high charge density bind to the minor groove of the DNA molecules, while the ionenes with lower charge density bind to the major groove of the DNA. The nature of the counterions play only a minor role: precipitation of the DNA molecules occurs at slightly lower ionene concentration when fluoride counterion are present, compared to the bromide counterions.

How Water's Properties Are Encoded in Its Molecular Structure and Energies

How are water's material properties encoded within the structure of the water molecule? This is pertinent to understanding Earth's living systems, its materials, its geochemistry and geophysics, and a broad spectrum of its industrial chemistry. Water has distinctive liquid and solid properties: It is highly cohesive. It has volumetric anomalies-water's solid (ice) floats on its liquid; pressure can melt the solid rather than freezing the liquid; heating can shrink the liquid. It has more solid phases than other materials. Its supercooled liquid has divergent thermodynamic response functions. Its glassy state is neither fragile nor strong. Its component ions-hydroxide and protons-diffuse much faster than other ions. Aqueous solvation of ions or oils entails large entropies and heat capacities. We review how these properties are encoded within water's molecular structure and energies, as understood from theories, simulations, and experiments. Like simpler liquids, water molecules are nearly spherical and interact with each other through van der Waals forces. Unlike simpler liquids, water's orientation-dependent hydrogen bonding leads to open tetrahedral cage-like structuring that contributes to its remarkable volumetric and thermal properties.

Modelling the Correlation Between Molecular Electrostatic Potential and pKa on Sets of Carboxylic Acids, Phenols and Anilines

Calculations of molecular electrostatic potential were correlated with experimental pKa values for different sets of acidic molecules (carboxylic acids, phenols, and anilines) to obtain linear relationships of variable quality. A single tri-parameter model function was constructed to describe the pKa dependence on MEP maxima together with two automatically generated molecular descriptors, namely the counts of carboxylic acid and amine functional groups.

Volumetric and calorimetric properties of aqueous ionene solutions

The volumetric (partial and apparent molar volumes) and calorimetric properties (apparent heat capacities) of aqueous cationic polyelectrolyte solutions - ionenes - were studied using the oscillating tube densitometer and differential scanning calorimeter. The polyion's charge density and the counterion properties were considered as variables. The special attention was put to evaluate the contribution of electrostatic and hydrophobic effects to the properties studied. The contribution of the CH₂ group of the polyion's backbone to molar volumes and heat capacities was estimated. Synergistic effect between polyion and counterions was found.

Phase behaviour of a continuous shouldered well model fluid. A grand canonical Monte Carlo study

The phase behavior of the continuous shouldered well model fluid proposed by Franzese [J. Mol. Liq. 136 (2007) 267] was examined using the Monte Carlo computer simulations in the grand canonical ensemble. The essential parts of the vapour-liquid and liquid-liquid coexistence envelopes were obtained. The Widom lines departing from coexistence envelopes were calculated using maxima of the fluctuations of the number of particles as a function of chemical potential along various isotherms. The region embracing anomalies in the properties of the model was located using the approximate criterion that involves the excess pair entropy.. The temperature of maximum density line was built by performing canonical Monte Carlo simulations. Our results are consistent with previous results from molecular dynamics constant pressure-constant temperature simulations and provide wider insight into the phase behavior of the model by using the chemical potential as the external parameter.

Protein aggregation in salt solutions

Protein aggregation is broadly important in diseases and in formulations of biological drugs. Here, we develop a theoretical model for reversible protein-protein aggregation in salt solutions. We treat proteins as hard spheres having square-well-energy binding sites, using Wertheim's thermodynamic perturbation theory. The necessary condition required for such modeling to be realistic is that proteins in solution during the experiment remain in their compact form. Within this limitation our model gives accurate liquid-liquid coexistence curves for lysozyme and γ IIIa-crystallin solutions in respective buffers. It provides good fits to the cloud-point curves of lysozyme in buffer-salt mixtures as a function of the type and concentration of salt. It than predicts full coexistence curves, osmotic compressibilities, and second virial coefficients under such conditions. This treatment may also be relevant to protein crystallization.

Effects of the translational and rotational degrees of freedom on the hydration of simple solutes

Molecular dynamics simulations with separate thermostats for rotational and translational motion were used to study the effect of these degrees of freedom on the structure of water around model solutes. To describe water molecules we used the SPC/E model. The simplest solute studied here, the hydrophobe, was represented as a Lennard-Jones particle. Since direct interaction between the hydrophobe and water molecules has no angular dependence the influence of the increase of the rotational temperature on the solvation of a hydrophobe is only indirect. In the next step the central solute was assumed to be charged with either a positive or a negative charge to mimic an ion in water. Hence, depending on the charge of the ion, the neighboring water molecules assumed different angular distributions. The principal conclusions of this work are: (i) an increase of the translational temperature always decreases the height of the first peak in the solute-water radial distribution function; (ii) an increase of the rotational temperature yields an increase in the first peak in the solute-water radial distribution function for hydrophobes and cations; (iii) in contrast to this, the solvation peak decreases around ions with sufficiently large negative charge; and (iv) an increase of the rotational temperature affects cations in an opposite way to anions. For this reason complex molecules with a small net charge may not be very sensitive to variation of the rotational temperature.

An Investigation of Ion-Pairing of Alkali Metal Halides in Aqueous Solutions Using the Electrical Conductivity and the Monte Carlo Computer Simulation Methods

The ion pairing is, in very dilute aqueous solutions, of rather small importance for solutions' properties, which renders its precise quantification quite a laborious task. Here we studied the ion pairing of alkali halides in water by using the precise electric conductivity measurements in dilute solutions, and in a wide temperature range. The low-concentration chemical model was used to analyze the results, and to estimate the association constant of different alkali halide salts. It has been shown that the association constant is related to the solubility of salts in water and produces a 'volcano relationship', when plotted against the difference between the free energy of hydration of the corresponding individual ions. The computer simulation, using the simple MB+dipole water model, were used to interprete the results, to find a microscopic basis for Collins' law of matching water affinities.

The application of the integral equation theory to study the hydrophobic interaction

The Wertheim's integral equation theory was tested against newly obtained Monte Carlo computer simulations to describe the potential of mean force between two hydrophobic particles. An excellent agreement was obtained between the theoretical and simulation results. Further, the Wertheim's integral equation theory with polymer Percus-Yevick closure qualitatively correctly (with respect to the experimental data) describes the solvation structure under conditions where the simulation results are difficult to obtain with good enough accuracy.

The application of the thermodynamic perturbation theory to study the hydrophobic hydration

The thermodynamic perturbation theory was tested against newly obtained Monte Carlo computer simulations to describe the major features of the hydrophobic effect in a simple 3D-Mercedes-Benz water model: the temperature and hydrophobe size dependence on entropy, enthalpy, and free energy of transfer of a simple hydrophobic solute into water. An excellent agreement was obtained between the theoretical and simulation results. Further, the thermodynamic perturbation theory qualitatively correctly (with respect to the experimental data) describes the solvation thermodynamics under conditions where the simulation results are difficult to obtain with good enough accuracy, e.g., at high pressures.

Thermodynamics of Asymmetric Primitive Model Electrolytes via the Hypernetted Chain Approximation

The accuracy of the activity coefficient expression (Hansen-Vieillefosse-Belloni (HVB) equation), valid within the hypernetted-chain (HNC) approximation, was tested in a wide concentration range against newly obtained grand canonical Monte Carlo data for the size and charge asymmetric primitive model electrolytes. In some cases, uncharged hard sphere component was also present. The HVB expression enables a direct calculation of the excess chemical potential, without invoking the time consuming calculation via the Gibbs-Duhem relation. We found the Ornstein-Zernike (OZ)/HNC results for the mean activity coefficient, as well as for the reduced excess internal energy and osmotic coefficient, to be in good agreement with the machine calculations performed for the same model. The accuracy of the results was found to be dependent on the packing fraction of the solutions. The mean spherical approximation calculations were also used to describe the thermodynamics of these systems and compared with the OZ/HNC and simulation results.

The application of the replica ornstein-zernike methodology for studying ionic membrane equilibria

The applicability of the replica Ornstein-Zernike (ROZ) method, often used to explore the partly quenched systems, for studying ionic equilibria in membrane-like systems was investigated. A simple +1:-1 electrolyte solution was modelled as a primitive model electrolyte on the McMillan-Mayer level of approximation. The particles mimicking membrane were modelled as permeable hard spheres frozen in space in their positions. The ion-membrane potential was chosen to conform as closely as possible to the experimental data. The density profiles of ions near the membrane, as well as adsorption isotherms, were calculated using the ROZ equations complemented by the hypernetted chain (HNC) approximation. The method provides reasonable results in qualitative agreement with experimental observations.

Simple model of hydrophobic hydration

Water is an unusual liquid in its solvation properties. Here, we model the process of transferring a nonpolar solute into water. Our goal was to capture the physical balance between water's hydrogen bonding and van der Waals interactions in a model that is simple enough to be nearly analytical and not heavily computational. We develop a 2-dimensional Mercedes-Benz-like model of water with which we compute the free energy, enthalpy, entropy, and the heat capacity of transfer as a function of temperature, pressure, and solute size. As validation, we find that this model gives the same trends as Monte Carlo simulations of the underlying 2D model and gives qualitative agreement with experiments. The advantages of this model are that it gives simple insights and that computational time is negligible. It may provide a useful starting point for developing more efficient and more realistic 3D models of aqueous solvation.

Receptacle model of salting-in by tetramethylammonium ions

Water is a poor solvent for nonpolar solutes. Water containing ions is an even poorer solvent. According to standard terminology, the tendency of salts to precipitate oils from water is called salting-out. However, interestingly, some salt ions, such as tetramethylammonium (TMA), cause instead the salting-in of hydrophobic solutes. Even more puzzling, there is a systematic dependence on solute size. TMA causes the salting-out of small hydrophobes and the salting-in of larger nonpolar solutes. We study these effects using NPT Monte Carlo simulations of the Mercedes-Benz (MB) + dipole model of water, which was previously shown to account for hydrophobic effects and ion solubilities in water. The present model gives a structural interpretation for the thermodynamics of salting-in. The TMA structure allows deep penetration by a first shell of waters, the dipoles of which interact electrostatically with the ion. This first water shell sets up a second water shell that is shaped to act as a receptacle that binds the nonpolar solute. In this way, a nonpolar solute can actually bind more tightly to the TMA ion than to another hydrophobe, leading to the increased solubility and salting-in. Such structuring may also explain why molecular ions do not follow the same charge density series as atomic ions do.

Interplay of ion-specific and charge-density effects in aqueous solutions of weakly charged ionenes as revealed by electric-transport measurements

In 3,3-ionenes, one quaternary nitrogen is bonded to a chain of three methylene groups on each side, and in 6,9-ionene, it is bonded to a chain of six on one side and nine on the other. We examined how the solution properties of several ionenes changed with increased hydrophobicity of the polyion, depending on the nature of the counterion. We determined the electrical conductivities of aqueous solutions of 3,3-, 4,5-, 6,6-, and 6,9-ionene fluorides and bromides in the range of concentrations from 5 x 10(-3) to 1 x 10(-1) M and for the temperature interval 5-35 degrees C. Over these ranges, the conductivities of the ionenes were found to decrease with increasing concentration and increase with increasing temperature. The conductivity of 3,3-ionene bromide was lower than that of its fluoride analogue throughout the whole range of concentrations, whereas for the 6,9-ionenes, the trend was reversed. For 4,5- and 6,6-ionene, we observed a crossover in the concentration dependence of conductivity. The conductivity data were compared with the predictions of Manning's theory and scaling theory. Separately determined transport-number values were combined with the conductivity data to obtain the fractions of so-called "free" counterions, f. For bromide samples, f increased from 3,3- to 6,9-ionene. In the case of fluoride counterions, the fraction of free counterions was the lowest for 3,3-ionene and, within the experimental uncertainty, approximately constant for the other less charged ionenes.

Modeling Hofmeister Effects

A two dimensional model of water, so-called Mercedes-Benz model, was used to study effects of the size of hydrophobic solute on the insertion thermodynamics in electrolyte solutions. The model was examined by the constant pressure Monte Carlo computer simulation. The results were compared with the experimental data for noble gasses and methane in water and electrolyte solution. The influence of different ions at infinite dilution on the free energy of transfer was explored. Qualitative agreement with the experimental results was obtained. The mechanism of Hofmeister effects was proposed.

Electrolyte exclusion from charged adsorbent: replica Ornstein-Zernike theory and simulations

Structural and thermodynamic properties of the restrictive primitive model +1:-1 electrolyte solution adsorbed in a disordered charged media were studied by means of the Grand Canonical Monte Carlo simulation and the replica Ornstein-Zernike theory. Disordered media (adsorbent, matrix) was represented by a distribution of negatively charged hard spheres frozen in a particular equilibrium distribution. The annealed counterions and co-ions were assumed to be distributed within the nanoporous adsorbent in thermodynamic equilibrium with an external reservoir of the same electrolyte. In accordance with the primitive model of electrolyte solutions, the solvent was treated as a dielectric continuum. The simulations were performed for a set of model parameters, varying the net charge of the matrix (i.e., concentrations of matrix ions) and of annealed electrolyte, in addition to the dielectric constant of the invading solution. The concentration of adsorbed electrolyte was found to be lower than the corresponding concentration of the equilibrium bulk solution. This electrolyte "exclusion" depends strongly on the dielectric constant of the invading solution, as also on concentrations of all components. The most important parameter is the net charge of the matrix. Interestingly, the electrolyte rejection decreases with increasing Bjerrum length for the range of parameters studied here. The latter finding can be ascribed to strong inter-ionic correlation in cases where the Bjerumm length is high enough. To a minor extent, the adsorption also depends on the spacial distribution of fixed charges in adsorbent material. The replica Ornstein-Zernike theory was modified to cater for this model and tested against the computer simulations. For the range of parameters explored in this work, the agreement between the two methods is very good. These calculations were also compared with the results of the classical Donnan theory for electrolyte exclusion.

Modeling Water, the Hydrophobic Effect, and Ion Solvation

Water plays a central role in the structures and properties of biomolecules--proteins, nucleic acids, and membranes--and in their interactions with ligands and drugs. Over the past half century, our understanding of water has been advanced significantly owing to theoretical and computational modeling. However, like the blind men and the elephant, different models describe different aspects of water's behavior. The trend in water modeling has been toward finer-scale properties and increasing structural detail, at increasing computational expense. Recently, our labs and others have moved in the opposite direction, toward simpler physical models, focusing on more global properties-water's thermodynamics, phase diagram, and solvation properties, for example-and toward less computational expense. Simplified models can guide a better understanding of water in ways that complement what we learn from more complex models. One ultimate goal is more tractable models for computer simulations of biomolecules. This review gives a perspective from simple models on how the physical properties of water-as a pure liquid and as a solvent-derive from the geometric and hydrogen bonding properties of water.