Ionic Interactions Are Everywhere

Statistical Thermodynamic Description of Self-Assembly of Large Inclusions in Biological Membranes

Recent studies revealed anomalous underscreening in concentrated electrolytes, and we suggest that the underscreened electrostatic forces between membrane proteins play a significant role in the process of self-assembly. In this work, we assumed that the underscreened electrostatic forces compete with the thermodynamic Casimir forces induced by concentration fluctuations in the lipid bilayer, and developed a simplified model for a binary mixture of oppositely charged membrane proteins with different preference to liquid-ordered and liquid-disordered domains in the membrane. In the model, like macromolecules interact with short-range Casimir attraction and long-range electrostatic repulsion, and the cross-interaction is of the opposite sign. We determine energetically favored patterns in a system in equilibrium with a bulk reservoir of the macromolecules. Different patterns consisting of clusters and stripes of the two components and of vacancies are energetically favorable for different values of the chemical potentials. Effects of thermal flutuations at low temperature are studied using Monte Carlo simulations in grand canonical and canonical ensembles. For fixed numbers of the macromolecules, a single two-component cluster with a regular pattern coexists with dispersed small one-component clusters, and the number of small clusters depends on the ratio of the numbers of the molecules of the two components. Our results show that the pattern formation is controlled by the shape of the interactions, the density of the proteins, and the proportion of the components.

Structures and bonding characteristics of KCl(H2O)n clusters with n = 1-10 based on density functional theory

Aqueous inorganic salt solutions play a prominent role in both physiological and chemical experiments, and significant attention has been directed toward understanding the mechanisms underlying salt dissolution. In our effort to elucidate the hydration process of potassium chloride, we employed a comprehensive genetic algorithm to explore the structures of KCl(H2O)n (n = 1-10). A series of stable structures were identified by high-level ab initio optimization and single-point energy calculations with a zero-point energy correction. An analysis of the probability distribution of KCl(H2O)1-10 revealed that clusters with high probability at low temperatures exhibit reduced probabilities at higher temperatures, while others become more prevalent. When n = 1-9, the contact ion pair configurations or partially dissociated structures dominate in the system, and the probability distribution plot shows that the proportion of the solvent-separated ion pair (SSIP) structures of KCl(H2O)n is very small, while the SSIP configuration in KCl(H2O)10 becomes a stable structure with increasing temperature. The results from natural bond orbital analysis reveal a stronger interaction between chloride ions and water molecules. These findings provide valuable insights for a more comprehensive understanding of the intricacies of potassium chloride dissolution in water.

Microstructural modification of papaya tissue during calcium diffusion: Effects on macrostructure level

The microstructural changes in papaya tissue during calcium diffusion, the effect on drying kinetics and texture parameters were investigated. Calcium pretreatment was applied to papaya samples for 3 h, at a solution concentration of 1.5 g Ca(OH)2/100 mL H2O, and a solution temperature of 25 °C; subsequently, the samples were convectively dried at 70 °C, air flow of 1.5 m/s, and a relative humidity of 5 ± 2%. Calcium content was determined using the Inductively Coupled Plasma-Optical Emission Spectrometry (ICP-OES) technique, the microstructure of the samples was analyzed by High-Resolution Scanning Electron Microscopy (HR-SEM), and the elementary analysis was performed by Energy-Dispersive X-ray Spectroscopy (EDS). Effective diffusivity of calcium (DefCa) and moisture (Defw) were calculated during pretreatment and drying, respectively and texture parameters were determined by double compression using a texturometer. The transport mechanism determined during calcium pretreatment was diffusion with a DefCa = 3.10 × 10-10 m2/s. Also, branched calcium microstructures in the cell walls of tissue were observed due to the calcium effect, it was supported by elemental analysis, which showed an increase of calcium in section restructured compared to non-restructured. During drying, Defw = 1.86 × 10-9 m2/s was higher in pretreated compared to non-pretreated samples with Defw = 1.17 × 10-9 m2/s, indicating a higher drying rate and moisture loss. The texture values changed significantly (α ≤ 0.05) due to calcium pretreatment and drying; the calcium microstructures caused higher cohesiveness, springiness, gumminess, and chewiness. Calcium modifies the microstructure and composition of papaya tissue; therefore, drying kinetics and texture parameters depend on this modification.

Theoretical Investigation of the Structures and Energetics of (MX)-Ethanol Complexes in the Gas Phase

The structures and energy of alkali halide salt (MX) complexes with ethanol have been investigated in this work. The core of this study is to explore the effect of ion size on the interactions between solvent and solute. LiF and KBr as monovalent salts with different sizes of inion and cation have been chosen to explore this difference in addition to various physical properties. Three complexes of each LiF and KBr with ethanol taking the formula MX(CH3CH2OH)n (n=1-3), were studied. Ab-initio calculations have been performed to optimize the chemical structures of these complexes and explore the possible structures, isomers, and their corresponding IR spectra using Density functional theory (DFT/ B3LYP). 6-311G** were chosen as basis sets for these calculations. The geometry evaluations, energy searches, vibrational frequency calculations, and each complex's binding energy were also theoretically extracted in this study. The minimum energy structures were calculated, and different isomers were found. The presence of Ionic hydrogen bonds (IHBs) was observed and proposed to be the main binding between the MX salt and ethanol. Also, the infrared vibrational bands in the OH stretching region were recorded for the minimum structures, and the determined red-shift was at about 400 cm-1. In addition, the binding energy calculations found a gradual rise in the BE value with every additional ethanol molecule added to MX salt.

Setting Boundaries for Statistical Mechanics

Statistical mechanics has grown without bounds in space. Statistical mechanics of noninteracting point particles in an unbounded perfect gas is widely used to describe liquids like concentrated salt solutions of life and electrochemical technology, including batteries. Liquids are filled with interacting molecules. A perfect gas is a poor model of a liquid. Statistical mechanics without spatial bounds is impossible as well as imperfect, if molecules interact as charged particles, as nearly all atoms do. The behavior of charged particles is not defined until boundary structures and values are defined because charges are governed by Maxwell's partial differential equations. Partial differential equations require boundary structures and conditions. Boundary conditions cannot be defined uniquely 'at infinity' because the limiting process that defines 'infinity' includes such a wide variety of structures and behaviors, from elongated ellipses to circles, from light waves that never decay, to dipolar fields that decay steeply, to Coulomb fields that hardly decay at all. Boundaries and boundary conditions needed to describe matter are not prominent in classical statistical mechanics. Statistical mechanics of bounded systems is described in the EnVarA system of variational mechanics developed by Chun Liu, more than anyone else. EnVarA treatment does not yet include Maxwell equations.

Absence of anomalous underscreening in highly concentrated aqueous electrolytes confined between smooth silica surfaces

Recent surface forces apparatus experiments that measured the forces between two mica surfaces and a series of subsequent theoretical studies suggest the occurrence of universal underscreening in highly concentrated electrolyte solutions. We performed a set of systematic Atomic Force Spectroscopy measurements for aqueous salt solutions in a concentration range from 1 mM to 5 M using chloride salts of various alkali metals as well as mixed concentrated salt solutions (involving both mono- and divalent cations and anions), that mimic concentrated brines typically encountered in geological formations. Experiments were carried out using flat substrates and submicrometer-sized colloidal probes made of smooth oxidized silicon immersed in salt solutions at pH values of 6 and 9 and temperatures of 25 °C and 45 °C. While strong repulsive forces were observed for the smallest tip-sample separations, none of the conditions explored displayed any indication of anomalous long range electrostatic forces as reported for mica surfaces. Instead, forces are universally dominated by attractive van der Waals interactions at tip-sample separations of ≈2 nm and beyond for salt concentrations of 1 M and higher. Complementary calculations based on classical density functional theory for the primitive model support these experimental observations and display a consistent decrease in screening length with increasing ion concentration.

Electrodiffusion Phenomena in Neuroscience and the Nernst–Planck–Poisson Equations

This work is aimed to give an electrochemical insight into the ionic transport phenomena in the cellular environment of organized brain tissue. The Nernst–Planck–Poisson (NPP) model is presented, and its applications in the description of electrodiffusion phenomena relevant in nanoscale neurophysiology are reviewed. These phenomena include: the signal propagation in neurons, the liquid junction potential in extracellular space, electrochemical transport in ion channels, the electrical potential distortions invisible to patch-clamp technique, and calcium transport through mitochondrial membrane. The limitations, as well as the extensions of the NPP model that allow us to overcome these limitations, are also discussed.

Molecular Mean-Field Theory of Ionic Solutions: A Poisson-Nernst-Planck-Bikerman Model

We have developed a molecular mean-field theory—fourth-order Poisson–Nernst–Planck–Bikerman theory—for modeling ionic and water flows in biological ion channels by treating ions and water molecules of any volume and shape with interstitial voids, polarization of water, and ion-ion and ion-water correlations. The theory can also be used to study thermodynamic and electrokinetic properties of electrolyte solutions in batteries, fuel cells, nanopores, porous media including cement, geothermal brines, the oceanic system, etc. The theory can compute electric and steric energies from all atoms in a protein and all ions and water molecules in a channel pore while keeping electrolyte solutions in the extra- and intracellular baths as a continuum dielectric medium with complex properties that mimic experimental data. The theory has been verified with experiments and molecular dynamics data from the gramicidin A channel, L-type calcium channel, potassium channel, and sodium/calcium exchanger with real structures from the Protein Data Bank. It was also verified with the experimental or Monte Carlo data of electric double-layer differential capacitance and ion activities in aqueous electrolyte solutions. We give an in-depth review of the literature about the most novel properties of the theory, namely Fermi distributions of water and ions as classical particles with excluded volumes and dynamic correlations that depend on salt concentration, composition, temperature, pressure, far-field boundary conditions etc. in a complex and complicated way as reported in a wide range of experiments. The dynamic correlations are self-consistent output functions from a fourth-order differential operator that describes ion-ion and ion-water correlations, the dielectric response (permittivity) of ionic solutions, and the polarization of water molecules with a single correlation length parameter.

Relative dielectric constants and selectivity ratios in open ionic channels

We investigate the effects of the relative dielectric coefficient on ionic flows in open ion channels, using mathematical analysis of reasonably general Poisson-Nernst-Planck type models that can include the finite sizes of ions. The value of the relative dielectric coefficient is of course a crucial parameter for ionic behavior in general. Using the powerful theory of singularly perturbed problems in applied mathematics, we show that some properties of open channels are quite insensitive to variation in the relative dielectric coefficient, thereby explaining such effects seen unexpectedly in simulations. The ratio between the total number of one ion species and that of another ion species, and the ratio between the flux of one ion species and that of another ion species do not depend significantly on the relative dielectric coefficient.

Dynamics of Current, Charge and Mass

Electricity plays a special role in our lives and life. The dynamics of electrons allow light to flow through a vacuum. The equations of electron dynamics are nearly exact and apply from nuclear particles to stars. These Maxwell equations include a special term, the displacement current (of a vacuum). The displacement current allows electrical signals to propagate through space. Displacement current guarantees that current is exactly conserved from inside atoms to between stars, as long as current is defined as the entire source of the curl of the magnetic field, as Maxwell did.We show that the Bohm formulation of quantum mechanics allows the easy definition of the total current, and its conservation, without the dificulties implicit in the orthodox quantum theory. The orthodox theory neglects the reality of magnitudes, like the currents, during times that they are not being explicitly measured.We show how conservation of current can be derived without mention of the polarization or dielectric properties of matter. We point out that displacement current is handled correctly in electrical engineering by ‘stray capacitances’, although it is rarely discussed explicitly. Matter does not behave as physicists of the 1800’s thought it did. They could only measure on a time scale of seconds and tried to explain dielectric properties and polarization with a single dielectric constant, a real positive number independent of everything. Matter and thus charge moves in enormously complicated ways that cannot be described by a single dielectric constant,when studied on time scales important today for electronic technology and molecular biology. When classical theories could not explain complex charge movements, constants in equations were allowed to vary in solutions of those equations, in a way not justified by mathematics, with predictable consequences. Life occurs in ionic solutions where charge is moved by forces not mentioned or described in the Maxwell equations, like convection and diffusion. These movements and forces produce crucial currents that cannot be described as classical conduction or classical polarization. Derivations of conservation of current involve oversimplified treatments of dielectrics and polarization in nearly every textbook. Because real dielectrics do not behave in that simple way-not even approximately-classical derivations of conservation of current are often distrusted or even ignored. We show that current is conserved inside atoms. We show that current is conserved exactly in any material no matter how complex are the properties of dielectric, polarization, or conduction currents. Electricity has a special role because conservation of current is a universal law.Most models of chemical reactions do not conserve current and need to be changed to do so. On the macroscopic scale of life, conservation of current necessarily links far spread boundaries to each other, correlating inputs and outputs, and thereby creating devices.We suspect that correlations created by displacement current link all scales and allow atoms to control the machines and organisms of life. Conservation of current has a special role in our lives and life, as well as in physics. We believe models, simulations, and computations should conserve current on all scales, as accurately as possible, because physics conserves current that way. We believe models will be much more successful if they conserve current at every level of resolution, the way physics does.We surely need successful models as we try to control macroscopic functions by atomic interventions, in technology, life, and medicine. Maxwell’s displacement current lets us see stars. We hope it will help us see how atoms control life.

Strong Relationships in Acid-Base Chemistry - Modeling Protons Based on Predictable Concentrations of Strong Ions, Total Weak Acid Concentrations, and pCO2

Understanding acid-base regulation is often reduced to pigeonholing clinical states into categories of disorders based on arterial blood sampling. An earlier ambition to quantitatively explain disorders by measuring production and elimination of acid has not become standard clinical practice. Seeking back to classical physical chemistry we propose that in any compartment, the requirement of electroneutrality leads to a strong relationship between charged moieties. This relationship is derived in the form of a general equation stating charge balance, making it possible to calculate [H+] and pH based on all other charged moieties. Therefore, to validate this construct we investigated a large number of blood samples from intensive care patients, where both data and pathology is plentiful, by comparing the measured pH to the modeled pH. We were able to predict both the mean pattern and the individual fluctuation in pH based on all other measured charges with a correlation of approximately 90% in individual patient series. However, there was a shift in pH so that fitted pH in general is overestimated (95% confidence interval -0.072-0.210) and we examine some explanations for this shift. Having confirmed the relationship between charged species we then examine some of the classical and recent literature concerning the importance of charge balance. We conclude that focusing on the charges which are predictable such as strong ions and total concentrations of weak acids leads to new insights with important implications for medicine and physiology. Importantly this construct should pave the way for quantitative acid-base models looking into the underlying mechanisms of disorders rather than just classifying them.

Energetics of discrete selectivity bands and mutation-induced transitions in the calcium-sodium ion channels family

We use Brownian dynamics (BD) simulations to study the ionic conduction and valence selectivity of a generic electrostatic model of a biological ion channel as functions of the fixed charge Q(f) at its selectivity filter. We are thus able to reconcile the discrete calcium conduction bands recently revealed in our BD simulations, M0 (Q(f)=1e), M1 (3e), M2 (5e), with a set of sodium conduction bands L0 (0.5e), L1 (1.5e), thereby obtaining a completed pattern of conduction and selectivity bands vs Q(f) for the sodium-calcium channels family. An increase of Q(f) leads to an increase of calcium selectivity: L0 (sodium-selective, nonblocking channel) → M0 (nonselective channel) → L1 (sodium-selective channel with divalent block) → M1 (calcium-selective channel exhibiting the anomalous mole fraction effect). We create a consistent identification scheme where the L0 band is putatively identified with the eukaryotic sodium channel The scheme created is able to account for the experimentally observed mutation-induced transformations between nonselective channels, sodium-selective channels, and calcium-selective channels, which we interpret as transitions between different rows of the identification table. By considering the potential energy changes during permeation, we show explicitly that the multi-ion conduction bands of calcium and sodium channels arise as the result of resonant barrierless conduction. The pattern of periodic conduction bands is explained on the basis of sequential neutralization taking account of self-energy, as Q(f)(z,i)=ze(1/2+i), where i is the order of the band and z is the valence of the ion. Our results confirm the crucial influence of electrostatic interactions on conduction and on the Ca(2+)/Na(+) valence selectivity of calcium and sodium ion channels. The model and results could be also applicable to biomimetic nanopores with charged walls.

Interacting ions in biophysics: real is not ideal

Ions in water are important throughout biology, from molecules to organs. Classically, ions in water were treated as ideal noninteracting particles in a perfect gas. Excess free energy of each ion was zero. Mathematics was not available to deal consistently with flows, or interactions with other ions or boundaries. Nonclassical approaches are needed because ions in biological conditions flow and interact. The concentration gradient of one ion can drive the flow of another, even in a bulk solution. A variational multiscale approach is needed to deal with interactions and flow. The recently developed energetic variational approach to dissipative systems allows mathematically consistent treatment of the bio-ions Na(+), K(+), Ca(2+), and Cl(-) as they interact and flow. Interactions produce large excess free energy that dominate the properties of the high concentration of ions in and near protein active sites, ion channels, and nucleic acids: the number density of ions is often >10 M. Ions in such crowded quarters interact strongly with each other as well as with the surrounding protein. Nonideal behavior found in many experiments has classically been ascribed to allosteric interactions mediated by the protein and its conformation changes. The ion-ion interactions present in crowded solutions-independent of conformation changes of the protein-are likely to change the interpretation of many allosteric phenomena. Computation of all atoms is a popular alternative to the multiscale approach. Such computations involve formidable challenges. Biological systems exist on very different scales from atomic motion. Biological systems exist in ionic mixtures (like extracellular and intracellular solutions), and usually involve flow and trace concentrations of messenger ions (e.g., 10(-7) M Ca(2+)). Energetic variational methods can deal with these characteristic properties of biological systems as we await the maturation and calibration of all-atom simulations of ionic mixtures and divalents.