THE GOLDMAN CONSTANT FIELD ASSUMPTION - SIGNIFICANCE AND APPLICABILITY CONDITIONS
Ionic transport phenomena in simple, porous membranes can be approximately represented by the Nernst-Planck flux equations and Poisson's equation. In order to solve this set of equations for each particular case, the Goldman constant field assumption is one of the most widely used. In the present paper the significance and the applicability conditions of the above hypothesis is critically examined. and the particular situations where it is exact are shown. These conditions are later verified by solving numerically the electrodiffusion equations. The analysis carried out shows that some of the earlier studies based on asymptotic expansions and numerical solutions should be partially revised.
IONIC TRANSPORT ACROSS POROUS CHARGED MEMBRANES AND THE GOLDMAN CONSTANT FIELD ASSUMPTION
Starting from a simple theoretical model based on Nernst-Planck flux equations and the Donnan equilibrium relationship, the ionic transport across a porous, charged membrane is analysed and conditions are given which make exact the so-called “constant field assumption”. The validity of the reported results is later verified in the case of a well-known problem: the ionic transport across a cation-exchange membrane under bi-ionic conditions.
Electrical Pumping of Potassium Ions Against an External Concentration Gradient in a Biological Ion Channel
We show experimentally and theoretically that significant currents can be obtained with a biological ion channel, the OmpF porin of Escherichia coli, using zero-average potentials as driving forces. The channel rectifying properties can be used to pump potassium ions against an external concentration gradient under asymmetric pH conditions. The results are discussed in terms of the ionic selectivity and rectification ratio of the channel. The physical concepts involved may be applied to separation processes with synthetic nanopores and to bioelectrical phenomena. (C) 2013 AIP Publishing LLC.
A pH-tunable nanofluidic diode: electrochemical rectification in a reconstituted single ion channel.
We report pH-dependent electrochemical rectification in a protein ion channel (the bacterial porin OmpF) reconstituted on a planar phospholipid membrane. The measurements performed at single-channel level show that the electric current is controlled by the protein fixed charge and it can be tuned by adjusting the local pH. Under highly asymmetric pH conditions, the channel behaves like a liquid diode. Unlike other nanofluidic devices that display also asymmetric conductance, here the microscopic charge distribution of the system can be explored by using the available high-resolution (2.4 A) channel crystallographic structure. Continuum electrostatics calculations confirm the hypothesized bi…
Validity of the electroneutrality and goldman constant-field assumptions in describing the diffusion potential for ternary electrolyte systems in simple, porous membranes
Abstract Three numerical algorithms capable of simulating transport processes through simple, porous membranes in the steady state have been employed in order to study the change in the diffusion potential with the membrane thickness and the ionic concentrations for the ternary systems NaClHClH20 and CaCI2NaC1H 2 O. The first simulation procedure uses Poisson's equation, the two others replace this equation by the electroneutrality and Goldman constant-field approximations respectively. From the results presented here, conditions for the applicability of the electroneutrality and constantfield assumption to ternary electrolyte systems are given.
Gibbs' Dividing Surface between a Fixed-Charge Membrane and an Electrolyte Solution. Application to Electrokinetic Phenomena in Charged Pores
The Gibbs model for the boundary between two phases consists of replacing the finite interfacial region, where the properties of the system change gradually, by a dividing surface which acts as a third phase of zero volume in which some magnitudes change abruptly. This thermodynamic concept was recently applied to a planar interface between a fixed charge membrane and an electrolyte solution.1 The continuous decrease of counterions with the distance from the charged surface is replaced by a step function, so that the diffuse double layer is ideally represented by a charged region depleted of all co-ions. Here the cylindrical geometry is analyzed, and the planar case is revisited by proposin…
Double layer potential and degree of dissociation in charged lipid monolayers
Abstract One of the contributions to the surface potential in charged phospholipid monolayers at air–water interfaces is the double layer potential. In this note several misconceptions found in the literature concerning the relationship between the double layer potential and the degree of dissociation of the lipid polar headgroups are critically analyzed. The deviations of the double layer potential measurements from the Gouy–Chapman theory observed by several authors are explained by taking into account the dependence of the degree of dissociation with concentration, area per lipid molecule and pH.
Thermodynamics of electrokinetic processes—I. Formulations
Abstract The phenomenological equations of electrokinetic processes are studied according to five different formulations. Transformation matrices with Haase's formulation are given. A study of the measurable character of fluxes, forces and phenomenological coefficients in those formulations is also made. The extrinsic character, if so, of the formulations is examined and a general definition of formulations established only for binary solutions is given. Finally, a review of the literature is included, aiming to clarify the possible misunderstandings arising from the application of these five formulations.
Synthetic nanopores with fixed charges: An electrodiffusion model for ionic transport
Synthetic nanopores with fixed charges exhibit ionic equilibrium and transport properties that resemble those displayed by biological ion channels. We present an electrodiffusion model based on the Nernst-Planck flux equations, which allows for a qualitative description of the steady state ionic transport through a nanopore when the membrane fixed charges and all mobile carriers (including the water ions) are properly taken into account. In particular, we study the current-voltage curve, the electrical conductance, the reversal potential (a measure of the nanopore ionic selectivity), as well as the flux inhibition by protons and divalent cations in the nanopore. The model clearly shows how …
Entropy–enthalpy compensation at the single protein level: pH sensing in the bacterial channel OmpF
The pH sensing mechanism of the OmpF channel operates via ligand modification: increasing acidity induces the replacement of cations with protons in critical binding sites decreasing the channel conductance. Aside from the change in enthalpy associated with the binding, there is also a change in the microscopic arrangements of ligands, receptors and the surrounding solvent. We show that the pH-modulation of the single channel conduction involves small free energy changes because large enthalpic and entropic contributions change in opposite ways, demonstrating an approximate enthalpy–entropy compensation for different salts and concentrations. We wish to acknowledge the support from the Span…
A finite-difference method for numerical solution of the steady-state nernst—planck equations with non-zero convection and electric current density
Abstract A computer algorithm has been developed for digital simulation of ionic transport through membranes obeying the Nernst—Planck and Poisson equations. The method of computation is quite general and allows the treatment of steady-state electrodiffusion equations for multiionic environments, the ionic species having arbitrary valences and mobilities, when convection and electric current are involved. The procedure provides a great flexibility in the choice of suitable boundary conditions and avoids numerical instabilities which are so frequent in numerical methods. Numerical results for concentration and electric potential gradient profiles are presented in the particular case of the t…