Electrodiffusion Model Research Articles

An electro-diffusion model for computing membrane potentials and ionic concentrations in branching dendrites, spines and axons

The Nernst-Planck equation for electrodiffusion was applied to axons, dendrites and spines. For thick processes (1 μm) the results of computer simulation agreed accurately with the cable model for passive conduction and for propagating action potentials. For thin processes (0.1 μm) and spines, however, the cable model may fail during transient events such as synaptic potentials. First, ionic concentrations can rapidly change in small compartments, altering ionic equilibrium potentials and the driving forces for movement of ions across the membrane. Second, longitudinal diffusion may dominate over electrical forces when ionic concentration gradients become large. We compare predictions of the cable model and the electro-diffusion model for excitatory postsynaptic potentials on spines and show that there are significant discrepancies for large conductance changes. The electro-diffusion model also predicts that inhibition on small structures such as spines and thin processes is ineffective. We suggest a modified cable model that gives better agreement with the electro-diffusion model.

A proposed physical explanation of the activation of sodium channels

Abstract A physical mechanism for activation of excitable Na channels is proposed, based on an electrodiffusion model with the assumption of constant dielectric permittivity replaced with a dielectric equation of state descriptive of ferroelectric behavior. The model postulates a ferroelectric channel unit within the glycoprotein Na channel to be in a ferroelectric state in a membrane at resting potential as a result of field-induced elevation of the transition temperature. A threshold depolarization initiates a first-order transition to a paraelectric state. A screening layer of permeant cations is drawn across the membrane by the negative bound charge at the phase boundary. This hypothesis is consistent with experimental observations of current-voltage hysteresis, voltage-dependent birefringence, single-channel currents, “gating” currents, heat and cold block of excitability, electromechanical and thermoelectric responses, and nonlinear ion conduction, and in quantitative agreement with the estimated magnitude of the surface charge of the channel.

Ion permeation through single channels activated by acetylcholine in denervated toad sartorius skeletal muscle fibers: Effects of alkali cations

The gigaohm seal technique was used to study ion permeation through acetylcholine-activated channels in cell-attached patches of the extrajunctional membrane of chronically denervated, enzyme-treated cells from the sartorius muscle of the toad Bufo marinus. The most frequently occurring channel type (greater than 95% of channel openings), provisionally classified as 'extrajunctional,' had a chord conductance of approximately 25 pS under normal conditions (-70 mV, 11 degrees C, Normal Toad Ringer's). The less frequently observed channel type (less than 5% of channel openings), classified as a 'junctional' type, had a conductance of 35 pS under the same conditions, and a similar null potential. In many patches, a small percentage (usually less than 2%) of openings of the extrajunctional channel displayed a lower conductance state. The shape of the I-V curves obtained for the extrajunctional channel depended on the predominant extracellular cation. For Cs and K, the I-V curves were essentially linear over the voltage range +50 to -150 mV across the patch, suggesting that the potential independent component of the energy profile within the channel was symmetrical. For Li, the I-V curve was very nonlinear, displaying a significant sublinearity at hyperpolarized potentials. Both an electrodiffusion and a symmetrical uniform four-barrier, three-site rate-theory model provided reasonable fits to the data, whereas symmetrical two-barrier, single-site rate-theory models did not. For the alkali cations examined, the relative permeability sequence was PCs greater than PK greater than PNa greater than PLi--a "proportional" selectivity sequence. This was different from the single channel conductance sequence which was found to be gamma K greater than gamma Cs greater than gamma Na greater than gamma Li implying that ions do not move independently through the channel. The relative binding constant sequence for the channel sites was found to be a "polarizability" sequence, i.e., KLi greater than KCs greater than KNa greater than KK. There was an inverse relationship between the relative binding constant and the relative mobility for the cations examined. Under conditions when the single-channel conductance was relatively high, the conductance at depolarized potentials was lower than that predicted by both electrodiffusion and rate theory models, suggesting that there was a rate-limiting access step for ions, from the intracellular compartment into the channel.

Chemical kinetics in isotachophoresis : Effects of non-instantaneously reversible complexing equilibria on the stability of zones

A theoretical description is given of kinetic effects in cationic isotachophoretic systems where anionic complexes are formed with the counter ion. The theory is based on a model of electrodiffusion across the isotachophoretic boundary. It shows, in agreement with experiment, that the slow dissociation of an anionic complex results (i) in the formation of a time-dependent tail where the loss of the cation is proportional to the square root of the electric field intensity and (ii) in zone bleeding (when the complex is kinetically inert), where the zone leaves behind a trace with a constant concentration of the complex.

Contribution of electrodiffusion to the dynamics of electrically stimulated changes in mechanical properties of collagen membranes.

AbstractWe have studied the kinetics of oscillatory tensile forces in collagen membranes. These forces were generated by sinusoidal electric fields applied across the membrane. Both the magnitude and phase of the measured force changed with frequency over a three‐decade range. The membrane‐separated electrolyte baths had different ionic strength but identical non‐isoelectric pH. Changes in intramembrane ionic strength due to the electric field were calculated over the same frequency range via an electrodiffusion model that was generalized to include convection and electrokinetic coupling. A comparison of the experimental and theoretical phases and amplitudes versus frequency suggests that electrodiffusion is the dominant rate‐limiting process in this electromechanochemical transduction. These results are relevant to electrostatic interactions in connective tissues and to membrane‐based filtration devices in which membrane permeability may be actively varied and controlled by an applied electric field.

Anomalous permeabilities of the egg cell membrane of a starfish in K+-Tl+ mixtures.

The electrical properties of "inward" rectifying egg cell membranes of the starfish mediastera aequalis have been studied in the presence of K(+)-Tl(+) mixtures. When the ratio of the external concentrations of these ions is changed while their sum is kept constant, both the conductance and the zero-current membrane potential go through a minimum, showing clear discrepancies from theoretical results based on conventional electrodiffusion models (E.g., Goldman's equation). By contrast, when the ration of the two concentrations is fixed and their sum varied, the potential follows an ideal Nernst slope, consistent with Goldman's equation. The membrane conductance which, according to previous studies on similar membranes, is to be viewed as a function of the displacement of the membrane potential from its resting value deltaV, shows marked differences between the cases in which K(+) or Tl(+) are the predominant ions: when K(+) is the predominant permeant ion in solution, the addition of small amounts of Tl(+) inhibits the current, while corresponding blocking effects of K(+) on the current are not observed when Tl(+) is the predominant permeant ion. Also, the time course of the conductance during voltage clamp is different in the two cases, being much faster in Tl(+) than in K(+) solution for comparable values of deltaV. Most of the above features are accounted for by a model in which it is assumed that the ionic channels have external binding sites for cations and that their permeability properties depend on the species of the cation bound (K(+)or Tl(+) in the present experiments).

A Molecular Cybernetic Model of Active Membrane Behavior

The observation of Cole and Curtis [3] concerning the impedance variation contemporary with the action potential still challenges the ingenuity of research workers in the field [18]. The electro-diffusion models are inadequate to describe the properties of conducting membranes [2] and the more recent attempts to describe the permeability changes in terms of ion exchangers [1, 16] fail to take into account basic biochemical data.

Simple model of ion transport through alamethicin channels in lipid membranes

The electrical characteristics of wide membrane channels such as those induced in lipid membranes by alamethicin have been analyzed using an electrodiffusion model. The channel is considered to be a water filled cylinder in which the potential energy barrier is a result of the difference in polarization energy of the ion environment when the ion is located inside as compared to outside of the channel. In addition, an electric field related to the channel structure is assumed. It is shown that without postulating any specific chemical ion-channel interaction one can reproduce experimental membrane potentials for NaCl, KCl, and CaCl 2 concentration gradients with a single set of channel parameters. The calculations also yield experimental J-V characteristics of discrete conduction states. In addition, a simple mechanism of interchannel coupling based on the above model is discussed. The model suggests a unifying approach to the problem of the origin of interionic selectivity of membrane channels induced by polyene antibiotics.

The Independence Principle: A Reconsideration

The electrodiffusion model presented in the previous paper, which specifically excludes ion-ion interactions, is analyzed for the ratio of one-way fluxes (flux ratio) as a function of the ionic driving force across the membrane. Significant deviations from the behavior expected on the basis of the Ussing relation are found. These are sufficient to explain the "nonindependent" ion movement noted in some biological flux ratio data. One-way fluxes are dependent on the ionic concentration on both sides of the membrane. The coupling of these fluxes to ionic concentrations comes from the dependence of ionic mobility and the diffusion coefficient on the equilibrium potential. It is concluded that nonindependent behavior in experimental data is not sufficient to implicate ion-ion interaction as the source of the discrepancy.

Kinetic Theory Model for Ion Movement through Biological Membranes: III. Steady-State Electrical Properties with Solution Asymmetry

An electrodiffusion model for plasma membrane ion transport, which takes into account the influence of high electric field strengths and ion-membrane molecule interactions, is presented and analyzed. A generalized Nernst-Planck equation for steady-state situations is derived which has electric field-dependent mobility and diffusion coefficients. Under the assumption of a constant electric field within the membrane, this equation is integrated to give a more general form of the Goldman equation. Based on this equation numerical computations of ionic chord conductance as a function of applied electric field strength were carried out for several permeant ion concentration ratios. The model is capable of yielding significantly larger rectification ratios than is the Goldman equation. Further, high field asymptotes to the current vs. electric field strength curve do not generally intersect at the origin.