Interaction of phospholipids (Lysophosphatidylethanolamines) with water and sodium cation

We have performed detailed ab initio SCF calculations on the intermolecular interaction energies for one Na⁺ ion and one water molecule with two molecular fragments, one exemplifying a phospholipid (PL) head (PLHD) and the other, a phospholipid tail (PLTL). A 6-12-1 atom-atom pair potential for the interaction of a Na⁺ ion and water with a lysophosphatidyl-ethanolamine (LPEA) was derived from these results by a fitting procedure. This fitted potential was used to obtain isoenergy maps that provide energy profiles of the Na⁺ ion and the water around the phospholipids. The interaction of the Na⁺ ion with PL, as well as the interaction of water with the PL, can be visualized from these maps, which, as expected, show regions of hydrophilicity and hydrophobicity for the water and indicate a very strong binding site for the Na⁺ ion on the phosphate. It appears to be a stationary site that would limit the Na⁺ ion mobility. This binding site is located near the double-bonded oxygen atom of the phosphate group; its binding energy for Na⁺ is 67 kcal/mol. On the other hand the NH⁺ group of PLHD ahows strong electrostatic repulsion of Na⁺ while interacting with water with a binding energy of 13 kcal/mol. This potential energy well region for water is separated from another of similar depth near the phosphate by a barrier and both regions are expected to act as binding sites for water.     

Statistical energy potential: reduced representation of Dehouck–Gilis–Rooman function by selecting against decoy datasets

Statistical effective energy function (SEEF) is derived from the statistical analysis of the database of known protein structures. Dehouck-Gilis-Rooman (DGR) group has recently created a new generation of SEEF in which the additivity of the energy terms was manifested by decomposing the total folding free energy into a sum of lower order terms. We have tried to optimize the potential function based on their work. By using decoy datasets as screening filter, and through modification of algorithms in calculation of accessible surface area and residue-residue interaction cutoff, four new combinations of the energy terms were found to be comparable to DGR potential in performance test. Most importantly, the term number was reduced from the original 30 terms to only 5 in our results, thereby substantially decreasing the computation time while the performance was not sacrificed. Our results further proved the additivity and manipulability of the DGR original energy function, and our new combination of the energy could be used in prediction of protein structures.     

A semi-microscopic Monte Carlo study of permeation energetics in a gramicidin-like channel: the origin of cation selectivity.

The influence of a gramicidin-like channel former on ion free energy barriers is studied using Monte Carlo simulation. The model explicitly describes the ion, the water dipoles, and the peptide carbonyls; the remaining degrees of freedom, bulk electrolyte, non-polar lipid and peptide regions, and electronic (high frequency) permittivity, are treated in continuum terms. Contributions of the channel waters and peptide COs are studied both separately and collectively. We found that if constrained to their original orientations, the COs substantially increase the cationic permeation free energy; with or without water present, CO reorientation is crucial for ion-CO interaction to lower cation free energy barriers; the translocation free energy profiles for potassium-, rubidium-, and cesium-like cations exhibit no broad barriers; the lipid-bound peptide interacts more effectively with anions than cations; anionic translocation free energy profiles exhibit well defined maxima. Using experimental data to estimate transfer free energies of ions and water from bulk electrolyte to a non-polar dielectric (continuum lipid), we found reasonable ion permeation profiles; cations bind and permeate, whereas anions cannot enter the channel. Cation selectivity arises because, for ions of the same size and charge, anions bind hydration water more strongly.     

The membrane dipole potential in a total membrane potential model. Applications to hydrophobic ion interactions with membranes.

The total potential energy profile for hydrophobic ion interactions with lipid bilayers can be written as the sum of four terms: the electrical Born, image and dipole contributions, and a neutral energy term. We introduce a specific model for the membrane dipole potential, treating it as a two-dimensional array of point dipoles located near each membrane-water interface. Together with specific theoretical models for the other energy terms, a total potential profile is developed that successfully describes the complete set of thermodynamic parameters for binding and translocation for the two hydrophobic ion structural analogues, tetraphenylphosphonium (TPP+) and tetraphenylboron (TPB-). A reasonable fit to the data is possible if the dipole potential energy has a magnitude of 5.5 + 0.5 kcal/mol (240 + 20 mV), positive inside, and if the neutral energy contribution for TPP+ and TPB- is -7.0 + 1.0 kcal/mol. These results may also have important implications for small ion interactions with membranes and the energetics of charged groups in membrane proteins.     

Concerted kinetic folding of a multidomain ribozyme with a disrupted loop-receptor interaction

The free energy landscape for the folding of large, multidomain RNAs is rugged, and kinetically trapped, misfolded intermediates are a hallmark of RNA folding reactions. Here, we examine the role of a native loop-receptor interaction in determining the ruggedness of the energy landscape for folding of the Tetrahymena ribozyme. We demonstrate a progressive smoothing of the energy landscape for ribozyme folding as the strength of the loop-receptor interaction is reduced. Remarkably, with the most severe mutation, global folding is more rapid than for the wild-type ribozyme and proceeds in a concerted fashion without the accumulation of long-lived kinetic intermediates. The results demonstrate that a complex interplay between native tertiary interactions, divalent ion concentration, and non-native secondary structure determines the ruggedness of the energy landscape. Furthermore, the results suggest that kinetic folding transitions involving large regions of highly structured RNAs can proceed in a concerted fashion, in the absence of significant stable, preorganized tertiary structure.     

Irradiation Spillover Effect in Photo-Assisted Ion Batteries: Overcoming Size Limits for Solar Utilization

Photo-assisted ion batteries demonstrate remarkable potential for portable and decentralized solar energy utilization, due to their profound capacity enhancement under irradiation accompanied by promoted discharge voltages. However, ion batteries in practice are highly compact with limited surface area for irradiation. Overcoming the size limit for irradiation is a challenge. Herein, an irradiation spillover effect in photo-assisted ion batteries is demonstrated, that is the impact of irradiation on the battery is not restrained within the irradiated area but can spillover the whole electrode. This phenomenon is a consequence of the light-induced potential difference between irradiated and unirradiated regions, leading to selective ion insertion. Irradiated regions favored H⁺ insertion due to light-induced proton-coupled electron transfer, while unirradiated regions preferred Zn²⁺ insertion. Consequently, the capacity enhancement remains unaffected by halving the irradiated area. This study overcomes the irradiation size limit for photo-assisted ion batteries and encourages highly integrated photo-assisted ion batteries for practice application.     

(In)validity of the constant field and constant currents assumptions in theories of ion transport.

Constant electric fields and constant ion currents are often considered in theories of ion transport. Therefore, it is important to understand the validity of these helpful concepts. The constant field assumption requires that the charge density of permeant ions and flexible polar groups is virtually voltage independent. We present analytic relations that indicate the conditions under which the constant field approximation applies. Barrier models are frequently fitted to experimental current-voltage curves to describe ion transport. These models are based on three fundamental characteristics: a constant electric field, negligible concerted motions of ions inside the channel (an ion can enter only an empty site), and concentration-independent energy profiles. An analysis of those fundamental assumptions of barrier models shows that those approximations require large barriers because the electrostatic interaction is strong and has a long range. In the constant currents assumption, the current of each permeating ion species is considered to be constant throughout the channel; thus ion pairing is explicitly ignored. In inhomogeneous steady-state systems, the association rate constant determines the strength of ion pairing. Among permeable ions, however, the ion association rate constants are not small, according to modern diffusion-limited reaction rate theories. A mathematical formulation of a constant currents condition indicates that ion pairing very likely has an effect but does not dominate ion transport.     

Liquid–vapour interface varying the softness and range of the interaction potential

Molecular dynamics simulations in a canonical ensemble were carried out for simple fluids. The inter-particles interaction law is described by the Morse function plus a repulsive term. This kind of combination allows to tune the repulsive term of the interaction function by fitting the range of the attractive well and vice versa. As a relevant result, we show that for an inhomogeneous system the particle softness affects the vapour pressure, the surface tension and also the equilibrium densities of a simple fluid. Lower numerical values for these same properties were obtained by using a more repulsive interaction potential. The differences among these same interfacial properties are bigger when the range of the attractive interaction is longer. The surface tension written in terms of the corresponding critical parameters, such as scaled surface tension, was plotted for different softness degrees. And from this comparison, a unique master curve was not found.     

Electrostatic calculations for an ion channel. I. Energy and potential profiles and interactions between ions

The electrostatic energy profile of one, two, or three ions in an aqueous channel through a lipid membrane is calculated. It is shown that the previous solution to this problem (based on the assumption that the channel is infinitely long) significantly overestimates the electrostatic energy barrier. For example, for a 3-A radius pore, the energy is 16 kT for the infinite channel and 6.7 kT for an ion in the center of a channel 25 A long. The energy as a function of the position of the ion is also determined. With this energy profile, the rate of crossing the membrane (using the Nernst-Planck equation) was estimated and found to be compatible with the maximum conductance observed for the gramicidin A channel. The total electrostatic energy (as a function of position) required to place two or three ions in the channel is also calculated. The electrostatic interaction is small for two ions at opposite ends of the channel and large for any positioning of the three ions. Finally, the gradient through the channel of an applied potential is calculated. The solution to these problems is based on solving an equivalent problem in which an appropriate surface charge is placed on the boundary between the lipid and aqueous regions. The magnitude of the surface charge is obtained from the numerical solution for a system of coupled integral equations.     

Model for the conformational analysis of hydrated peptides. Effect of hydration on the conformational stability of the terminally blocked residues of the 20 naturally occurring amino acids

The effects of hydration are included in empirical conformational energy computations on oligopeptides by means of a modified hydration-shell model. Free energy terms are introduced to account for “specific hydration” due to water–solute hydrogen bonding and for “nonspecific hydration” describing the interaction of the solute with water molecules in a first-neighbor shell. The dielectric constant has been doubled (over the value used for calculations in the absence of water) to take into account the presence of solvent. Computations were carried out for the N-acetyl-N′-methylamides of the 20 naturally occurring amino acids. Conformational energy maps are compared with similar maps calculated in the absence of hydration. Minimum-energy conformations are located and compared with the corresponding minima for unhydrated peptides in terms of ordering with respect to potential energy, the dihedral angles at the minima, and the presence of intramolecular hydrogen bonds. The Boltzmann factors for various conformational regions are altered significantly on hydration in some cases. These changes can be explained in terms of differences in the hydration free energy terms for various conformations.     

An optimized potential function for the calculation of nucleic acid interaction energies I. Base stacking

An optimized potential function for base-stacking interaction is constructed. Stacking energies between the complementary pairs of a dimer are calculated as a function of the rotational angle and separation distance. Using several different sets of atomic charges, the electrostatic component in the monopole-monopole approximation (MMA) is compared to the more refined segmented multipole–multipole representation (SMMA); the general features of the stacking minima are found to be correctly reproduced with IEHT or CNDO atomic charges. The electrostatic component is observed to control the location of stacking minima. The MMA, in general, is not a reliable approximation of the SMMA in regions away from minima; however, the MMA is reliable in predicting the location and nature of stacking minima. The attractive part of the Lennard-Jones 6–12 potential is compared to and parameterized against the expression for the second-order interaction terms composed of multipole-bond polarizability for the polarization energy and transition-dipole bond polarizabilities for approximation of the dispersion energy. The repulsive part of the Lennard-Jones potential is compared to a Kitaygorodski-type repulsive function; changing the exponent from its usual value of 12 to 11.7 gives significantly better agreement with the more refined repulsive function. Stacking minima calculated with the optimized potential method are compared with various perturbation-type treatments. The optimized potential method yields results that compare as well with melting data as do any of the more recent and expensive perturbation methods.     

Electrostatic interaction between two charged spherical molecules

An explicit analytic expression is obtained for the electrostatic energy of the interaction between two ion-impenetrable space-charged hard spheres as a model for spherical molecules in an electrolyte solution on the basis of the linearized Poisson-Boltzmann equation. An explicit expression for the potential distribution in a 3D-space is also found. The polarization effects due to the mutual influence between the spheres are taken into account. The analysis is done by assuming different dielectric permittivities of the respective spheres and of the solution as well. It is shown that the correction terms in the expression for the total energy of interaction arising from the polarization effects always correspond to forces of attraction between the spheres. The contribution of these terms to the total energy of interaction depends on the distance between the two spheres and the dielectric permittivities of the spheres and the solution as well as on the electrolyte concentration in the solution. A numerical simulation of the potential field topography is carried out at several values of the Debye-Hückel parameter. It is shown that the polarization effect can produce significant changes in the potential distribution in the case of strong interacting spheres.     

Effective pore radius of the gramicidin channel. Electrostatic energies of ions calculated by a three-dielectric model.

Electrostatic calculation of the gramicidin channel is performed on the basis of a three-dielectric model in which the peptide backbone of the channel is added as a third dielectric region to the conventional two-dielectric channel model (whose pore radius is often referred to as the effective pore radius reff). A basic principle for calculating electrostatic fields in three-dielectric models is introduced. It is shown that the gramicidin channel has no unique value of reff. The reff with respect to the "self-image energy" (i.e., the image energy in the presence of a single ion) is 2.6-2.7 A, slightly depending upon the position of the ion (the least-square value over the whole length of the pore is 2.6 A). In contrast, the reff with respect to the electric potential due to an ion (and hence the reff with respect to the interaction energy between two ions) is dependent upon the distance s of separation; it ranges from 2.6 to greater than 5 A, increasing with an increase in s. However, for the purpose of rough estimation, the reff with respect to the self-image energy can also be used in calculating the electric potential and the interaction energy, because the error introduced by this approximation is an overestimation of the order of 30% at most. It is also shown that the apparent dielectric constant for the interaction between two charges depends markedly upon the positions of the charges. In the course of this study, the dielectric constant and polarizability of the peptide backbone in the beta-sheet structure is estimated to be 10 and 8.22 A3.     

Effect of ionic polarizability on electrodiffusion in lipid bilayer membranes.

Ion-carrier complexes and organic ions of similar size and shape have mobilities in lipid bilayer membranes which span several orders of magnitude. In this communication, an examination is made of the hypothesis that the basis for this unusually wide range of ionic mobilities is the potential energy barrier arising from image forces which selectively act on ions according to their polarizability. Using Poisson's equation to evaluate the electrostatic interaction between an ion and its surroundings, the potential energy barrier to ion transport due to image effects is computed, with the result that the potential energy barrier height depends strongly on ionic polarizability. Theoretical membrane potential energy profile calculations are used in conjunction with Nernst-Planck electrodiffusion equation to analyze the available mobility data for several ion-carrier complexes and lipid-soluble ions in lipid bilayer membranes. The variation among the mobilities of different ions is shown to be in agreement with theoretical predictions based on ionic polarizability and size. Furthermore, the important influence exerted by image forces on ion transport in lipid bilayer membranes compared to the frictional effect of membrane viscosity is established by contrasting available data on the activation energy of ionic conductivity with that for membrane fluidity.     

The interaction of gamma-aminobutiric acid with hydrated Ca2+ and Mg2+. A pseudopotential ab initio study

As a continuation of a previous work we consider the interaction of Mg2+ and Ca2+ with a neurotransmitter, gamma-aminobutiric acid (GABA). The purpose is twofold, to determine if there is a direct interaction of Ca2+ with the amino acid, which could have some biological relevance, and to find out if such a hypothesis can account for the different role of Ca2+ and Mg2+ on the amino acid's release. We performed ab initio pseudopotential studies of the GABA-ion complex in the presence of the first hydration shell around the interaction's region. We calculated the interaction energy of the hydrated complex by means of a many-body expansion up to three-body terms. We found out that the three-body terms in systems involving the divalent ion have a considerable value and seems to be of a different character for Mg2+ and Ca2+. We found out that the three-body terms are responsible for the observed difference between the coordination properties of Mg2+ and Ca2+ and can lead to a difference in the aminoacid interaction with each ion. The hypothesis of a gamma-aminobutiric acid-Ca2+ complex, that facilitates the aminoacid release has been substantiated. The reasons for the different effect of Ca2+ and Mg2+ has been envisaged but not clearly established.     

Pair Potentials from ab initio Calculations for use in MD Simulations of Molten Alkali Carbonates

Ab initio calculations at the Hartree-Fock SCF level have been carried out to determine the pair interaction between the alkali ions and the carbonate ion. A distinction has been made between terms in the metal ion - carbonate ion interaction which have different physical origins, such as static coulomb interaction, short-range repulsion and electronic polarization. The additivity of the pair interaction is investigated in 3-body calculations. It is shown that for these 3-body systems pairwise addition of 2-body interactions from which polarization effects have been omitted is superior to pairwise addition of the full Hartree-Fock interactions. A model potential based on these modified interactions has been constructed. Results of MD simulations show that both structural and dynamical properties are well described by these pair potentials.     

Possible role of long-range interactions in the proton transfer of model DNA systems

The possible role of the long-range interactions has been examined within the semiempirical approach for model doubly stranded DNA systems involving the screw symmetry operation. The interaction energy terms seem to be sensitive to the sequence of base pairs. The essential influence of long-range corrections to the proton transfer potential was found resulting in a remarkably more unsymmetrical energy curve. Only in the case of the singlet excited (n, pi*) electronic state of the A...T base pair, more symmetrical potential is predicted. It is concluded that highly polar sugar-phosphate species are of significant importance for the interaction energy components as well as for related proton transfer processes.     

Dynamics of cell deposition on surfaces.

The rate of deposition of particles onto a surface, in the presence of London, double-layer, and gravitational forces, is calculated in terms of the energy of interaction between cell and surface by assuming that Brownian motion over a potential energy barrier is the rate-determining step of the process.     

Resonance microwave volume plasma source

A conceptual design of a microwave gas-discharge plasma source is described. The possibility is considered of creating conditions under which microwave energy in the plasma resonance region would be efficiently converted into the energy of thermal and accelerated (fast) electrons. Results are presented from interferometric and probe measurements of the plasma density in a coaxial microwave plasmatron, as well as the data from probe measurements of the plasma potential and electron temperature. The dynamics of plasma radiation was recorded using a streak camera and a collimated photomultiplier. The experimental results indicate that, at relatively low pressures of the working gas, the nonlinear interaction between the microwave field and the inhomogeneous plasma in the resonance region of the plasmatron substantially affects the parameters of the ionized gas in the reactor volume.