The release of drugs from iontophoretic pipettes

A theoretical account is given of the relationship between applied current and release of drug ions from an iontophoretic pipette. The Nernst-Planck equation predicts a non-linear relationship except in the region of large ejecting currents. No finite value of retaining current can completely suppress spontaneous diffusional leakage. These conclusions apply to both conical and cylindrical tip geometries. An expression is derived giving release as a function of pulsed charge applied to a conical pipette. This relation is also non-linear. Dose-response curves constructed using charge as a measure of drug ejection should be interpreted with some caution.     

Membrane transport of electrolyte ions and time-dependent membrane potential

Equations are derived for the transport of a symmetrical electrolyte, consisting of cations and anions of equal valency, through a neutral membrane that separates two solutions of finite volume under quasi-steady-state conditions. The time-dependent membrane potential produced by the flow of ions is taken into account. Deviation of the time course of the solute concentrations from that of neutral solutes is found to be determined by the permeability ratio of cations and anions (when this ratio equals unity, the derived membrane transport equations reduce to those for neutral substances). Simple approximate expressions for the solute concentrations and of the membrane potential as functions of time are proposed, which are in excellent agreement with the exact numerical results.     

Nonlinear generalizations of the Kedem-Katachalsky equations for ionic fluxes

The transport equation of Kedem and Katchalsky for the flux of ions through a membrane is generalized to demonstrate explicitly the role of impermeant ions in determining its mathematical form. Whereas the Kedem-Katchalsky equation is linear in the salt concentrations in the bathing solutions, the more general equation is bilinear (and symmetric) in the ionic concentrations of the permeant species. The Kedem-Katchalsky flux equation is further generalized to include explicitly a term for ion-exchange in systems having more than a single permeant salt. This additional term is also bilinear (and antisymmetric) in the concentrations of the exchanging ionic species. Flux equations are derived for systems having (1) a single mono-monovalent salt, (2) two mono-monovalent salts and (3) an arbitrary number of salts with no restriction upon the valencies of the ionic components. Since it has no effect upon the form of concentration-dependent terms in the flux equations, coupling to volume flow is neglected.     

THE POTENTIOMETRIC ANALYSIS OF MEMBRANE STRUCTURE AND ITS APPLICATION TO LIVING ANIMAL MEMBRANES

1. The electromotive forces which arise, if two electrolyte solutions are separated from each other by a layer of any kind, are discussed. A general equation is derived comprising the known equations for diffusion, partition, and membrane (Donnan) potentials as special cases. 2. A method is proposed to analyse membranes potentiometrically with respect to their cation or anion selectivity, their dissolving power for ions, and their influence on ion mobility (migration velocity). 3. The possibility of analysing a membrane composed of several layers of different permeability is discussed. 4. The investigation of the skin of the belly of Rana temporaria leads to the following results. It is composed of at least four layers of different permeability, one of which is specifically permeable to H ions and is very likely identical with the "basal membrane" situated between the stratum germinativum and the corium. The major part of the resting potential of the skin is located across this membrane and is due to the difference of H⁺ concentrations on both sides of the membrane. 5. Experiments on muscle show that the sarcolemma is specifically permeable to H ions. The injury potential of the muscle is attributed to the difference of H⁺ concentration inside and outside the fibre.     

Strong electrolyte continuum theory solution for equilibrium profiles, diffusion limitation, and conductance in charged ion channels.

The solution for the ion flux through a membrane channel that incorporates the electrolyte nature of the aqueous solution is a difficult theoretical problem that, until now, has not been properly formulated. The difficulty arises from the complicated electrostatic problem presented by a high dielectric aqueous channel piercing a low dielectric lipid membrane. The problem is greatly simplified by assuming that the ratio of the dielectric constant of the water to that of the lipid is infinite. It is shown that this is a good approximation for most channels of biological interest. This assumption allows one to derive simple analytical expressions for the Born image potential and the potential from a fixed charge in the channel, and it leads to a differential equation for the potential from the background electrolyte. This leads to a rigorous solution for the ion flux or the equilibrium potential based on a combination of the Nernst-Planck equation and strong electrolyte theory (i.e., Gouy-Chapman or Debye-Huckel). This approach is illustrated by solving the system of equations for the specific case of a large channel containing fixed negative charges. The following characteristics of this channels are discussed: anion and mono- and divalent cation conductance, saturation of current with increasing concentration, current-voltage relationship, influence of location and valence of fixed charge, and interaction between ions. The qualitative behavior of this channel is similar to that of the acetylcholine receptor channel.     

Electrostatic interactions at charged lipid membranes. Calcium binding

A quantitative study of calcium-ion binding by the negatively-charged phospholipid methylphosphatidic acid is presented. Experimental results are compared with the predictions of the Gouy-Chapman theory, taking into account both the ions bound at the membrane surface and the ions held in the diffuse layer. This theory suffices to explain the titration of the calcium/lipid system, but fails to explain completely the behaviour of the ordered-fluid transition temperature, which shows a splitting that according to electrostatic theory alone should not occur. The dependence of the calcium-lipid binding constant. upon 1: 1 electrolyte concentration is correctly predicted by the theory; the latter however gives equations which can only be solved numerically. A simple, approximate equation is therefore given (in the text, eq. 34) for the prediction of the degree of calcium binding to a negatively-charged lipid membrane.     

The osmotic flow of an electrolyte through a charged porous membrane

A pore model in which the pore wall has a continuous distribution of electrical charge is used to investigate the osmotic flow through a charged permeable membrane separating electrolyte solutions of unequal concentrations. The pore is treated as a long, circular, cylindrical duct. The analysis is based on a continuum formulation in which a dilute electrolyte solution is described by the coupled Nernst-Planck/Poisson creeping flow equations. Account is taken of the significant size of the electrolyte ions (assumed to be rigid spheres) when compared with the diameter of the membrane pores. Analytical solutions for the ion concentrations, hydrostatic pressure and electrostatic potential in the electrolyte solutions are given and an intra-pore flow solution is derived. A mathematical expression for the osmotic reflection coefficient as a function of the solute ion: pore diameter ratio λ and the solute fluxes is obtained. Approximate solutions are quoted which relate the solute fluxes and the solution electrostatic potentials at the membrane surfaces to the bulk solution concentrations, the membrane pore charge and pore geometry. The osmotic reflection coefficient is thus determined as a function of these parameters.     

Electrostatic Potential of B-DNA: Effect of Interionic Correlations

Modified Poisson-Boltzmann (MPB) equations have been numerically solved to study ionic distributions and mean electrostatic potentials around a macromolecule of arbitrarily complex shape and charge distribution. Results for DNA are compared with those obtained by classical Poisson-Boltzmann (PB) calculations. The comparisons were made for 1:1 and 2:1 electrolytes at ionic strengths up to 1 M. It is found that ion-image charge interactions and interionic correlations, which are neglected by the PB equation, have relatively weak effects on the electrostatic potential at charged groups of the DNA. The PB equation predicts errors in the long-range electrostatic part of the free energy that are only ∼1.5 kJ/mol per nucleotide even in the case of an asymmetrical electrolyte. In contrast, the spatial correlations between ions drastically affect the electrostatic potential at significant separations from the macromolecule leading to a clearly predicted effect of charge overneutralization.     

Ionic processes in excitable membranes

The dynamical theory of ionized media is applied to the semi-electrolyte component of an excitable cell membrane, and the adjacent electrolytes. The equations of conservation of charge and momentum for the ions, and Poisson's equation for the electrostatic potential, are applied first to investigate the steady states of the membrane, and then transient effects in the membrane. A dispersion equation is derived, and the characteristic modes of relaxation within the membrane are determined. Among these are oscillating modes whose frequencies and amplitudes are of the correct order of magnitude to explain the observed excitation phenomena.A pair of coupled non-linear equations in the ionic potentials, with action potential solutions, is derived from the time-dependent electrodiffusion equations, and calculations are presented which model the behaviour of the excitable membrane during the voltage clamp. It is not necessary to postulate large changes in the ionic permeabilities in the course of the action potential and the voltage clamp to account for the large transient membrane conductances. It is suggested that the sodium hypothesis be replaced by one which attributes the action potential to non-linear plasma oscillations.     

Real-time detection of Cu2+ sequestration and release by immobilized apo-metallothioneins using SECM combined with SPR

Scanning electrochemical microscopy (SECM) combined with surface plasmon resonance (SPR), SECM-SPR, was applied for real-time detection of the incorporation of Cu(2+) by apo-metallothionein (apo-MT) immobilized on the SPR substrate and release of Cu(2+) from surface-confined metallothionein (MT). Cu(2+) anodically stripped from a Cu-coated SECM Au tip was sequestered by apo-MT upon its diffusion to the SPR substrate, and release of Cu(2+) by MT was accomplished by generating protons via oxidation of hydroquinone at the tip. The high sensitivity of the SPR instrument is capable of following the structural and compositional changes of MT molecules during the metal sequestration and release processes. Due to the enhanced mass transfer rate at the SECM tip, the complication of mass transfer limitation on kinetic measurements, commonly encountered in flow injection SPR, is circumvented. The time-resolved SPR response reveals stepwise changes among three stable MT structures and allows the number of copper ions coordinated in each structure to be determined. The numbers of copper ions incorporated by each MT molecule in the three structures were determined to be 5, 9, and 12. This work expands the SECM-SPR approach to assessments of the dynamics and affinity of binding of small ions to surface-confined proteins and to studies of proteins that do not undergo facile electron transfer reactions.     

Electroviscosity of polyelectrolyte solutions

A theoretical expression for the electroviscous effect in polyelectrolyte solutions, caused by the distortion of counterion-distribution and counterion flow around a polyion under a velocity gradient of solvent flow, was obtained to elucidate the characteristic behaviour of the viscosity of highly charged polyelectrolyte solutions observed at low salt concentration. The derivation of the theory was performed on the basis of the Navier-Stokes-Onsager equation, Poisson equation, and diffusion equations for low molecular ions by the use of a cell model (free-volume model) for a polyion. Energy dissipation was obtained without directly solving these equations. It was found that the derived expression of viscosity explained the experimental results satisfactorily, and that the streaming potential effect caused by the counterion flow played an essential role in the increase in viscosity of polyelectrolyte solutions at finite polymer concentration and low salt concentration ranges.     

A model of propagating calcium-induced calcium release mediated by calcium diffusion

The effect of sudden local fluctuations of the free sarcoplasmic [Ca++]i in cardiac cells on calcium release and calcium uptake by the sarcoplasmic reticulum (SR) was calculated with the aid of a simplified model of SR calcium handling. The model was used to evaluate whether propagation of calcium transients and the range of propagation velocities observed experimentally (0.05-15 mm s(-1)) could be predicted. Calcium fluctuations propagate by virtue of focal calcium release from the SR, diffusion through the cytosol (which is modulated by binding to troponin and calmodulin and sequestration by the SR), and subsequently induce calcium release from adjacent release sites of the SR. The minimal and maximal velocities derived from the simulation were 0.09 and 15 mm s(-1) respectively. The method of solution involved writing the diffusion equation as a difference equation in the spatial coordinates. Thus, coupled ordinary differential equations in time with banded coefficients were generated. The coupled equations were solved using Gear's sixth order predictor-corrector algorithm for stiff equations with reflective boundaries. The most important determinants of the velocity of propagation of the calcium waves were the diastolic [Ca++]i, the rate of rise of the release, and the amount of calcium released from the SR. The results are consistent with the assumptions that calcium loading causes an increase in intracellular calcium and calcium in the SR, and an increase in the amount and rate of calcium released. These two effects combine to increase the propagation velocity at higher levels of calcium loading.     

Ion transfer during electrolyte osmosis through a charged porous membrane

In an earlier investigation (I) concerning the osmotic flow of an electrolyte through a charged porous membrane it was shown that in order to determine the osmotic reflection coefficient for the process a solution of the associated ion transfer equations is required. In I, previously unpublished approximate formulae for the required variables were quoted. The current paper presents the derivation of these solutions. The investigation considers the solution of the one-dimensional form of the coupled Poisson/convection-free Nernst-Planck equations subject to boundary conditions derived in I. Both equations and boundary conditions contain unknown parameters which are evaluated as part of the solution. Exact numerical and approximate analytical solutions are derived for the intrapore electrostatic potential and ion concentrations and for the unknown ion fluxes. Formulae are given for the electric current generated in the process and for the electrolyte factor in the osmotic reflection coefficient.     

Exact continuum solution for a channel that can be occupied by two ions

The classical Nernst-Planck continuum equation is extended to the case where the channel can be occupied simultaneously by two ions. A two-dimensional partial differential equation is derived to describe the steady-state channel. This differential equation is of the form of the generalized Laplace equation, but it has the novel feature that the boundary conditions are periodic. The finite difference solution takes approximately 8 s on a large computer. The equations are solved for the special case of a cylindrical channel with a fixed charge in the center. It is assumed that the forces on the ions result entirely from the sum of the Born image potential, the fixed charge potential, the interaction potential between the two ions, and the applied voltage. Approximate simple analytical expressions are derived for these potential terms, based on the assumption that the electric field perpendicular to the channel wall is zero. The potentials include the contribution from a diffuse charge (Debye-Huckel) reaction field in the bulk solution for the monovalent cation flux was obtained for channels with a radius of 4 A and lengths of 16 and 32 A and a fixed charge valence of -1 and -1.5. For these channels, a significant fraction (up to 90%) of the total resistance is contributed by the bulk solution and results were obtained for the case where the "channel" included 8 A of bulk solution at each channel end. These results for the two-ion channel were compared with the analytical solution for a one-ion channel. The one-ion channel is a fair approximation to the two-ion channel for a fixed charge of -1, underestimating the flux at high concentrations by approximately 30%. However, for a fixed charge of -1.5, the one-ion model is a poor approximation, with the two-ion flux about seven times that of the one-ion model at high concentrations. The absolute conductance and concentration dependence of these channels (with a fixed charge of -1) mimic the behavior of the large conductance K+ channel and the acetylcholine receptor channel.     

A model for the mechanism of tip extension in pollen tubes

Three main mechanisms are proposed to account for the tip growth of pollen tubes. (1) The tip region is supported against the internal osmotic pressure of the cell by a fibrillar network, composed mainly of microfilaments, that is stabilized by calcium ions. Tip extension is promoted by a lowering of the local cytoplasmic calcium ion concentration, through uptake by the mitochondria and/or endoplasmic reticulum, which leads to a weakening of the fibrillar network. (2) Vesicles, derived from dictyosomes in the main body of the tube, fuse with the apical plasma membrane, providing new membrane and further carbohydrate for the wall. The rate of fusion is proportional to the rate of diffusion of calcium ion across the plasma membrane at the tip. (3) The callose lining present in the pollen tube wall, except at the tip, renders the wall impermeable and restricts entry of calcium ions to the apical plasma membrane. This restriction limits the rate of vesicle fusion, and tube growth, to the tip.This model is discussed in the light of previous observations on the growth and structure of pollen tubes under normal and experimental conditions.     

Irreversible thermodynamic analysis of electrophoretic light scattering experiments

A fluctuation theory for electrolyte solutions is developed based on the coupling between the equations of nonequilibrium thermodynamics and the Poisson equation. The resulting fluctuation theory is applied to the analysis of electrophoretic light scattering. It is shown that in a binary electrolyte solution (two ionic species), the Doppler shift is not determined by the electrical mobility of either ion, but depends instead on the rate of change of transference number with salt concentration. In addition the ionic relaxation time is shown to be proportional to the conductivity of the solution.     

Thermoosmosis through charged membranes. theoretical analysis of concentration dependence

A theoretical equation for thermoosmosis through charged membranes in electrolyte solutions is derived from nonequilibrium thermodynamics. The theory shows that the volume flux through the membrane is proportional to the temperature difference across the membrane. The proportionality constant, i.e., the thermoosmotic coefficient is a function of electrolyte concentration. The electrolyte concentration dependence of the thermoosmotic coefficient calculated is compared with our previous experimental results. Agreement between theory and experiments is satisfactory.     

Ecological risk assessment of accidental release of flowback water: A conceptual framework

The aim of the study is to conduct an ecological risk assessment of accidental release of flowback water into freshwater body. Flowback water produced from the hydraulic fracturing process has a complex combination of high concentration of salts, organic compounds and metals. The toxicity of flowback water is assessed and an exposure assessment method for the inorganic constituents of the flowback water is developed. An equation for risk is derived to characterize the risk of the flowback water to the aquatic ecology. A case study is conducted for accidental release of hydraulic fracturing flowback water in Montney unconventional play trend in northern British Columbia. The flowback water quality data for 212 wells, including the concentrations of various salt ions, metal ions, and hydrogen sulfide, is collected for the assessment. The risk quotient is found to be 0.16 (<1), proving no significant risk to the aquatic ecosystem with 90% confidence. However, the overall results of the uncertainty and scenario analysis concludes that the risk to the ecology cannot be completely overlooked. Scenario analysis was done for monthly creek discharge and a relationship between risk quotient and the ratio of spill volume to the creek discharge was derived.     

Effect of pH on the interfacial tension of bilayer lipid membrane formed from phosphatidylcholine or phosphatidylserine

The effect of pH of an electrolyte solution on the interfacial tension of lipid membrane formed from phosphatidylcholine (PC) or phosphatidylserine (PS) was studied. The relationships were well described by an equation presented earlier based on the Gibbs isotherm but only in the proximity of the isoelectric point. Therefore, in this work models have been derived to describe the adsorption of the H(+) and OH(-) ions at lipid surfaces formed from PC or PS, which would reproduce changes in interfacial tension more correctly, particularly in the ranges distant from the isoelectric point. In one model, the surface is continuous with uniformly distributed functional groups constituting the centres of H(+) and OH(-) ion adsorption while in the other the surface is built of lipid molecules, free or with attached H(+) and OH(-) ions. In both models, the contributions of the individual lipid molecule forms to the interfacial tension of the bilayer were assumed to be additive.     

Single‐Particle Performances and Properties of LiFePO4 Nanocrystals for Li‐Ion Batteries

It has been recently reported that the solution diffusion, efficiency porosity, and electrode thickness can dominate the high rate performance in the 3D‐printed and traditional LiMn_0.21Fe_0.79PO₄ electrodes for Li‐ions batteries. Here, the intrinsic properties and performances of the single‐particle (SP) of LiFePO₄ are investigated by developing the SP electrode and creating the SP‐model, which will share deep insight on how to further improve the performance of the electrode and related materials. The SP electrode is generated by fully scattering and distributing LiFePO₄ nanoparticles to contact with the conductive network of carbon nanotube or conductive carbon to demonstrate the sharpest cyclic voltammetry peak and related SP‐model is developed, by which it is found that the interfacial rate constant in aqueous electrolyte is one order of magnitude higher, accounting for the excellent rate performance in aqueous electrolyte for LiFePO₄. For the first time it has been proposed that the insight of pre‐exponential factor of interface kinetic Arrhenius equation is related to desolvation/solvation process. Thus, this much higher interfacial rate constant in aqueous electrolyte shall be attributed to the much larger pre‐exponential factor of interface kinetic Arrhenius equation, because the desolvation process is much easier for Li‐ions jumping from aqueous electrolyte to the Janus solid–liquid interface of LiFePO₄.