Ion specific correlations in bulk and at biointerfaces

Counterion Release from Macroion Assemblies of Planar Geometry

Macroions such as nanoparticles, polyelectrolytes, ionic gels, and amphiphiles can form condensed, often self-assembled, phases that are embedded in a solvent region. The condensed phase contains not only the partially or fully immobile charges of their macroions but also corresponding counterions that are mobile and thus free to migrate out of their confinement into the solvent region where they benefit from high translational entropy. Based on the nonlinear Poisson-Boltzmann model for monovalent ions, we quantify the corresponding fraction of released counterions for a planar slab geometry of the macroion phase. Slab thickness, extension of the solvent phase, fixed background charge density provided by the macroions, and dielectric constants inside slab and solvent combine into three dimensionless parameters that the fraction of released counterions depends on. We calculate that fraction and analyze the limits of a thin macroion phase, a large solvent phase, and linearized theory, where simple analytic results become available. Of particular interest is the presence of a single-planar interface that separates a bulk macroion phase from an extended solvent region. We calculate the apparent surface charge density that emerges due to the released counterions. Our model yields a comprehensive description of counterion partitioning between a planar macroion phase and a solvent region on the level of mean-field electrostatics in the absence of added salt ions.

Anions and Cations Affect Amino Acid Dissociation Equilibria via Distinct Mechanisms

Salts reduce the pKa of weak acids by a mechanism sensitive to ion identity and concentration via charge screening of the deprotonated state. In this study, we utilize constant pH molecular dynamics simulations to understand the molecular mechanism behind the salt-dependent dissociation of aspartic acid (Asp). We calculate the pKa of Asp in the presence of a monovalent salt and investigate Hofmeister ion effects by systematically varying the ionic radii. We observe that increasing the anion size leads to a monotonic decrease in Asp pKa. Conversely, the cation size affects the pKa nonmonotonically, interpretable in the context of the law of matching water affinity. The net effect of salt on Asp acidity is governed by an interplay of solvation and competing ion interactions. The proposed mechanism is rather general and can be applicable to several problems in Hofmeister ion chemistry, such as pH effects on protein stability and soft matter interfaces.

Multivalent ions and biomolecules: Attempting a comprehensive perspective

Ions are ubiquitous in nature. They play a key role for many biological processes on the molecular scale, from molecular interactions, to mechanical properties, to folding, to self-organisation and assembly, to reaction equilibria, to signalling, to energy and material transport, to recognition etc. Going beyond monovalent ions to multivalent ions, the effects of the ions are frequently not only stronger (due to the obviously higher charge), but qualitatively different. A typical example is the process of binding of multivalent ions, such as Ca2+ , to a macromolecule and the consequences of this ion binding such as compaction, collapse, potential charge inversion and precipitation of the macromolecule. Here we review these effects and phenomena induced by multivalent ions for biological (macro)molecules, from the "atomistic/molecular" local picture of (potentially specific) interactions to the more global picture of phase behaviour including, e. g., crystallisation, phase separation, oligomerisation etc. Rather than attempting an encyclopedic list of systems, we rather aim for an embracing discussion using typical case studies. We try to cover predominantly three main classes: proteins, nucleic acids, and amphiphilic molecules including interface effects. We do not cover in detail, but make some comparisons to, ion channels, colloidal systems, and synthetic polymers. While there are obvious differences in the behaviour of, and the relevance of multivalent ions for, the three main classes of systems, we also point out analogies. Our attempt of a comprehensive discussion is guided by the idea that there are not only important differences and specific phenomena with regard to the effects of multivalent ions on the main systems, but also important similarities. We hope to bridge physico-chemical mechanisms, concepts of soft matter, and biological observations and connect the different communities further.

Hydration of monovalent and divalent cations near a cathode surface

Hydration of monovalent (Li⁺, Na⁺, K⁺, and Cs⁺) and divalent (Mg²⁺, Ca²⁺, Sr²⁺, and Ba²⁺) cations on a cathode surface was studied by a classical molecular dynamics simulation. The potential of mean force (PMF) for each cation species was calculated as a function of the distance from the cathode surface, and the potential barriers for dehydrating the first and second hydration shells near the cathode surface were estimated. The positions of the minimum of the PMF closest to the cathode surface were found to be in the order Li⁺ < Na⁺ < Mg²⁺ < Ca²⁺ < Sr²⁺ < Ba²⁺ < K⁺ < Cs⁺. It was found that Li⁺, Mg²⁺, Ca²⁺, Sr²⁺, and Ba²⁺ ions are most likely doubly hydrated when they are adsorbed on the cathode surface without an applied voltage, whereas Na⁺, K⁺, and Cs⁺ ions are most likely singly hydrated at room temperature. On the other hand, when a voltage of 1 V was applied to the electrodes, all the cation species that we studied appeared most likely to be singly hydrated on the cathode surface. The depths of the potential well closest to the cathode surface under an applied voltage of 1 V were found to be in the order Ba²⁺ < Sr²⁺ < Ca²⁺ < Mg²⁺ for the divalent cations and Li⁺ < Na⁺ < K⁺ < Cs⁺ for the monovalent cations in the set of models that we used. These orders coincide with the Hofmeister series from the kosmotropic to the chaotropic.

Salt Effects on Protein Folding Thermodynamics

Salts differ in their ability to stabilize protein conformations, thereby affecting the thermodynamics and kinetics of protein folding. We developed a coarse-grained protein model that can predict salt-induced changes in protein properties by using the transfer free-energy data of various chemical groups from water to salt solutions. Using this model and molecular dynamics simulations, we probed the effect of seven different salts on the folding thermodynamics of the DNA binding domain of lac repressor protein ( lac-DBD) and N-terminal domain of ribosomal protein (NTL9). We show that a salt can act as a protein stabilizing or destabilizing agent depending on the protein sequence and folded state topology. The computed thermodynamic properties, especially the m values for various salts, which reveal the relative ability of a salt to stabilize the protein folded state, are in quantitative agreement with the experimentally measured values. The computations show that the degree of protein compaction in the denatured ensemble strongly depends on the salt identity, and for the same variation in salt concentration, the compaction in the protein dimensions varies from ∼4% to ∼30% depending on the salt. The transition-state ensemble (TSE) of lac-DBD is homogeneous and polarized, while the TSE of NTL9 is heterogeneous and diffusive. Salts induce subtle structural changes in the TSE that are in agreement with Hammond's postulate. The barrier to protein folding tends to disappear in the presence of moderate concentrations (∼3-4 m) of strongly stabilizing salts.

Hydration and dehydration of monovalent cations near an electrode surface

The mechanism of hydration and dehydration of monovalent ions, Li⁺, Na⁺, K⁺, and Cs⁺, in a dilute solution near an electrode surface was studied by molecular dynamics simulations. The potentials of mean force for these ions were calculated as a function of the distance from the electrode surface and the potential barriers for dehydrating the first and the second hydration shell near the electrode surface and were estimated for each ion species. It was found that the mechanism of hydration for Li⁺ is distinct from those for Na⁺, K⁺, and Cs⁺. Penetration of ions into the first layer of water molecules on the electrode surface is unlikely to occur for the case of Li⁺, while that would occur with certain probabilities for the case of Na⁺, K⁺, or Cs⁺, whether or not voltage is applied to the electrode. Li⁺ ions would be adsorbed on the electrode surface in a doubly hydrated form with a significant probability, while Na⁺, K⁺, and Cs⁺ ions would be adsorbed most likely in a singly hydrated form. Furthermore, the theory of ionic radii, which has been successfully used in the analysis of bulk solutions, was applied to the electrode/electrolyte interface. It was found that the theory of ionic radii is also useful in explaining the structural behaviors of ions near an electrode surface. The distance between an ion and the layers of water molecules on the electrode surface showed almost linear dependence on the radius of the ion, as predicted by the theory of ionic radii. Analysis of the deviation from the linearity showed that Li⁺ ions are most likely adsorbed in the first layer of water molecules on the electrode surface, while Na⁺, K⁺, and Cs⁺ ions are adsorbed on the second layer of water molecules. These analyses indicate that Li⁺ is a structure maker, while Na⁺, K⁺, and Cs⁺ are structure breakers, which is consistent with the widely accepted idea in explaining the behaviors of the bulk solutions.

Ca2+ -Cl- Association in Water Revisited: the Role of Cation Hydration

We investigate the dissociation of a Ca²⁺ -Cl^- pair in water using classical molecular dynamics simulations with a polarizable interaction potential, parameterized from ab initio calculations. By computing the potential of mean force as a function not only of the interionic distance but also of the coordination numbers by water molecules, we show that it is necessary to use a collective variable describing the cation hydration in order to capture the dissociation mechanism. In the contact ion pair, the Ca²⁺ cation has a first coordination sphere containing 5 or 6 water molecules. The minimum free-energy path for dissociation involves a two-step process: First one or two additional water molecules enter the cation coordination shell, increasing the coordination number up to 7 with an almost fixed interionic distance. Then the dissociation of the ionic pair occurs at this fixed coordination number.

Beyond the Hofmeister Series: Ion-Specific Effects on Proteins and Their Biological Functions

Ions differ in their ability to salt out proteins from solution as expressed in the lyotropic or Hofmeister series of cations and anions. Since its first formulation in 1888, this series has been invoked in a plethora of effects, going beyond the original salting out/salting in idea to include enzyme activities and the crystallization of proteins, as well as to processes not involving proteins like ion exchange, the surface tension of electrolytes, or bubble coalescence. Although it has been clear that the Hofmeister series is intimately connected to ion hydration in homogeneous and heterogeneous environments and to ion pairing, its molecular origin has not been fully understood. This situation could have been summarized as follows: Many chemists used the Hofmeister series as a mantra to put a label on ion-specific behavior in various environments, rather than to reach a molecular level understanding and, consequently, an ability to predict a particular effect of a given salt ion on proteins in solutions. In this Feature Article we show that the cationic and anionic Hofmeister series can now be rationalized primarily in terms of specific interactions of salt ions with the backbone and charged side chain groups at the protein surface in solution. At the same time, we demonstrate the limitations of separating Hofmeister effects into independent cationic and anionic contributions due to the electroneutrality condition, as well as specific ion pairing, leading to interactions of ions of opposite polarity. Finally, we outline the route beyond Hofmeister chemistry in the direction of understanding specific roles of ions in various biological functionalities, where generic Hofmeister-type interactions can be complemented or even overruled by particular steric arrangements in various ion binding sites.

Exploring LacI-DNA dynamics by multiscale simulations using the SIRAH force field

The lac repressor protein (LacI) together with its target regulatory sequence are a common model for studying DNA looping and its implications on transcriptional control in bacteria. Owing to the molecular size of this system, standard all-atom (AA) simulations are prohibitive for achieving relevant biological time scales. As an alternative, multiscale models, which combine AA descriptions at particular regions with coarse-grained (CG) representations of the remaining components, were used to address this computational challenge while preserving the relevant details of the system. In this work, we implement a new multiscale approach based on the SIRAH force field to gain deeper insights into the dynamics of the LacI-DNA system. Our methodology allows for a dual resolution treatment of the solute and solvent, explicitly representing the protein, DNA, and solvent environment without compromising the AA region. Starting from the P1 loop configuration in an undertwisted conformation, we were able to observe the transition to the more stable overtwisted state. Additionally, a detailed characterization of the conformational space sampled by the DNA loop was done. In agreement with experimental and theoretical evidence, we observed the transient formation of kinks at the loop, which were stabilized by the presence of counterions at the minor groove. We also show that the loop's intrinsic flexibility can account for reported FRET measurements and bent conformations required to bind the CAP transcription factor.

Ionic Interactions Are Everywhere

Ionic solutions are dominated by interactions because they must be electrically neutral, but classical theory assumes no interactions. Biological solutions are rather like seawater, concentrated enough so that the diameter of ions also produces important interactions. In my view, the theory of complex fluids is needed to deal with the interacting reality of biological solutions.

Radial distribution functions of non-additive hard sphere mixtures via Percus' test particle route

Using fundamental density functional theory we calculate the partial radial distribution functions, g(ij)(r), of a binary non-additive hard sphere mixture using either Percus' test particle approach or inversion of the analytic structure factor obtained via the Ornstein-Zernike route. We find good agreement between the theoretical results and Monte Carlo simulation data for both positive and moderate negative non-additivities. We investigate the asymptotic, [Formula: see text], decay of the g(ij)(r) and show that this agrees with the analytic analysis of the contributions to the partial structure factors in the plane of complex wavevectors. We find the test particle density profiles to be free of unphysical artefacts, contrary to earlier reports.

First-order layering and critical wetting transitions in nonadditive hard-sphere mixtures

Using fundamental-measure density functional theory we investigate entropic wetting in an asymmetric binary mixture of hard spheres with positive nonadditivity. We consider a general planar hard wall, where preferential adsorption is induced by a difference in closest approach of the different species and the wall. Close to bulk fluid-fluid coexistence, the phase rich in the minority component adsorbs either through a series of first-order layering transitions, where an increasing number of liquid layers adsorbs sequentially, or via a critical wetting transition, where a thick film grows continuously.

Ion-specific weak adsorption of salts and water/octanol transfer free energy of a model amphiphilic hexapeptide

An amphiphilic hexapeptide has been used as a model to quantify how specific ion effects induced by addition of four salts tune the hydrophilic/hydrophobic balance and induce temperature-dependant coacervate formation from aqueous solution. The hexapeptide chosen is present as a dimer with low transfer energy from water to octanol. Taking sodium chloride as the reference state in the Hofmeister scale, we identify water activity effects and therefore measure the free energy of transfer from water to octanol and separately the free energy associated to the adsorption of chaotropic ions or the desorption of kosmotropic ions for the same amphiphilic peptide. These effects have the same order of magnitude: therefore, both energies of solvation as well as transfer into octanol strongly depend on the nature of the electrolytes used to formulate any buffer. Model peptides could be used on separation processes based on criteria linked to "Hofmeister" but different from volume and valency.