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.

Field theory of reaction-diffusion: Law of mass action with an energetic variational approach.

We extend the energetic variational approach so it can be applied to a chemical reaction system with general mass action kinetics. Our approach starts with an energy-dissipation law. We show that the chemical equilibrium is determined by the choice of the free energy and the dynamics of the chemical reaction is determined by the choice of the dissipation.

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.

Effects of Diffusion Coefficients and Permanent Charge on Reversal Potentials in Ionic Channels.

In this work, the dependence of reversal potentials and zero-current fluxes on diffusion coefficients are examined for ionic flows through membrane channels. The study is conducted for the setup of a simple structure defined by the profile of permanent charges with two mobile ion species, one positively charged (cation) and one negatively charged (anion). Numerical observations are obtained from analytical results established using geometric singular perturbation analysis of classical Poisson-Nernst-Planck models.

Do Bistable Steric Poisson-Nernst-Planck Models Describe Single-Channel Gating?

Experiments measuring currents through single protein channels show unstable currents, a phenomena called the gating of a single channel. Channels switch between an "open" state with a well-defined single amplitude of current and "closed" states with nearly zero current. The existing mean-field theory of ion channels focuses almost solely on the open state.

Poisson-Fermi modeling of ion activities in aqueous single and mixed electrolyte solutions at variable temperature.

The combinatorial explosion of empirical parameters in tens of thousands presents a tremendous challenge for extended Debye-Hückel models to calculate activity coefficients of aqueous mixtures of the most important salts in chemistry. The explosion of parameters originates from the phenomenological extension of the Debye-Hückel theory that does not take steric and correlation effects of ions and water into account. By contrast, the Poisson-Fermi theory developed in recent years treats ions and water molecules as nonuniform hard spheres of any size with interstitial voids and includes ion-water and ion-ion correlations.

Nonlocal Poisson-Fermi model for ionic solvent.

We propose a nonlocal Poisson-Fermi model for ionic solvent that includes ion size effects and polarization correlations among water molecules in the calculation of electrostatic potential. It includes the previous Poisson-Fermi models as special cases, and its solution is the convolution of a solution of the corresponding nonlocal Poisson dielectric model with a Yukawa-like kernel function. The Fermi distribution is shown to be a set of optimal ionic concentration functions in the sense of minimizing an electrostatic potential free energy.

Poisson-Fermi Modeling of the Ion Exchange Mechanism of the Sodium/Calcium Exchanger.

The ion exchange mechanism of the sodium/calcium exchanger (NCX) crystallized by Liao et al. in 2012 is studied using the Poisson-Fermi theory developed by Liu and Eisenberg in 2014. A cycle of binding and unbinding is proposed to account for the Na(+)/Ca(2+) exchange function of the NCX molecule.

Numerical methods for a Poisson-Nernst-Planck-Fermi model of biological ion channels.

Numerical methods are proposed for an advanced Poisson-Nernst-Planck-Fermi (PNPF) model for studying ion transport through biological ion channels. PNPF contains many more correlations than most models and simulations of channels, because it includes water and calculates dielectric properties consistently as outputs. This model accounts for the steric effect of ions and water molecules with different sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of polarized water molecules in an inhomogeneous aqueous electrolyte.

Poisson-Nernst-Planck-Fermi theory for modeling biological ion channels.

A Poisson-Nernst-Planck-Fermi (PNPF) theory is developed for studying ionic transport through biological ion channels. Our goal is to deal with the finite size of particle using a Fermi like distribution without calculating the forces between the particles, because they are both expensive and tricky to compute. We include the steric effect of ions and water molecules with nonuniform sizes and interstitial voids, the correlation effect of crowded ions with different valences, and the screening effect of water molecules in an inhomogeneous aqueous electrolyte.

Analytical models of calcium binding in a calcium channel.

The anomalous mole fraction effect of L-type calcium channels is analyzed using a Fermi like distribution with the experimental data of Almers and McCleskey [J. Physiol. 353, 585 (1984)] and the atomic resolution model of Lipkind and Fozzard [Biochemistry 40, 6786 (2001)] of the selectivity filter of the channel.

Ion permeation in the NanC porin from Escherichia coli: free energy calculations along pathways identified by coarse-grain simulations.

Using the X-ray structure of a recently discovered bacterial protein, the N-acetylneuraminic acid-inducible channel (NanC), we investigate computationally K(+) and Cl(-) ions' permeation. We identify ion permeation pathways that are likely to be populated using coarse-grain Monte Carlo simulations. Next, we use these pathways as reaction coordinates for umbrella sampling-based free energy simulations.

Correlated ions in a calcium channel model: a Poisson-Fermi theory.

We derive a continuum model, called the Poisson-Fermi equation, of biological calcium channels (of cardiac muscle, for example) designed to deal with crowded systems in which ionic species and side chains nearly fill space. The model is evaluated in three dimensions. It includes steric and correlation effects and is derived from classical hard-sphere lattice models of configurational entropy of finite size ions and solvent molecules.

Ionic interactions in biological and physical systems: a variational treatment.

Chemistry is about chemical reactions. Chemistry is about electrons changing their configurations as atoms and molecules react. Chemistry has for more than a century studied reactions as if they occurred in ideal conditions of infinitely dilute solutions.

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.

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.

PNP equations with steric effects: a model of ion flow through channels.

The flow of current through an ionic channel is studied using the energetic variational approach of Liu applied to the primitive (implicit solvent) model of ionic solutions. This approach allows the derivation of self-consistent (Euler-Lagrange) equations to describe the flow of spheres through channels. The partial differential equations derived involve the global interactions of the spheres and are replaced here with a local approximation that we call steric PNP (Poisson-Nernst-Planck) (Lin, T.

Ionizable side chains at catalytic active sites of enzymes.

Catalytic active sites of enzymes of known structure can be well defined by a modern program of computational geometry. The CASTp program was used to define and measure the volume of the catalytic active sites of 573 enzymes in the Catalytic Site Atlas database. The active sites are identified as catalytic because the amino acids they contain are known to participate in the chemical reaction catalyzed by the enzyme.

Single-channel measurements of an N-acetylneuraminic acid-inducible outer membrane channel in Escherichia coli.

NanC is an Escherichia coli outer membrane protein involved in sialic acid (Neu5Ac, i.e., N-acetylneuraminic acid) uptake.

A method for treating the passage of a charged hard sphere ion as it passes through a sharp dielectric boundary.

In the implicit solvent models of electrolytes (such as the primitive model (PM)), the ions are modeled as point charges in the centers of spheres (hard spheres in the case of the PM). The surfaces of the spheres are not polarizable which makes these models appropriate to use in computer simulations of electrolyte systems where these ions do not leave their host dielectrics. The same assumption makes them inappropriate in simulations where these ions cross dielectric boundaries because the interaction energy of the point charge with the polarization charge induced on the dielectric boundary diverges.

Selectivity sequences in a model calcium channel: role of electrostatic field strength.

The energetics that give rise to selectivity sequences of ionic binding selectivity of Li(+), Na(+), K(+), Rb(+), and Cs(+) in a model of a calcium channel are considered. This work generalizes Eisenman's classic treatment (Biophys J 2(Suppl. 2):259, 1962) by including multiple, mobile binding site oxygens that coordinate many permeating ions (all modeled as charged, hard spheres).

Analyzing the components of the free-energy landscape in a calcium selective ion channel by Widom's particle insertion method.

The selectivity filter of the L-type calcium channel works as a Ca(2+) binding site with a very large affinity for Ca(2+) versus Na(+). Ca(2+) replaces half of the Na(+) ions in the filter even when these ions are present in 1 μM and 30 mM concentrations in the bath, respectively. The energetics of this strong selectivity is analyzed in this paper.