Kinetic Theory Model for Ion Movement through Biological Membranes: II. Interionic Selectivity

The equation presented in the previous paper for steady-state membrane ionic current as a function of externally applied electric field strength is numerically analyzed to determine the influence of ionic and membrane molecule parameters on current densities. The model displays selectivity between different ions. A selectivity coefficient S_i, defined as the ratio of current carried by an ionic species i at a given field strength to the current carried by a reference species at the same field strength, has the following properties: (a) S_i is a function of electric field strength except for ion-membrane molecule interactions yielding velocity independent collision frequencies; (b) for ion-membrane molecule interactions characterized by a collision frequency that is a decreasing (increasing) function of increasing ionic velocity, ions whose S_i > 1 (<1) at zero field strength will show maxima (minima) (minima[maxima]) in their S_i vs. electric field strength curves.     

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.     

Determinants of time-dependent membrane conductance. The nonrole of classical ion-membrane molecule interactions

We have examined the steady-state and time-dependent electrical properties of a model membrane system. The model assumes that the directed velocity and energy of ions moving through the membrane are determined by the applied electric field, ionic diffusion forces, and central elastic collisions between ions and membrane molecules. A simple analysis of the steady-state electrical properties of the model yields results identical with ones obtained previously using a more complex analysis procedure. The time-dependent conductance changes of the model in response to a step change in electric field strength when there is solution symmetry display three qualitative patterns dependent on the nature of the ion-membrane molecule interaction. One of the patterns of conductance change is quite similar to that observed in the sodium conductance system of a number of excitable tissues: an initial conductance rise to a maximum (activation) followed by a decay to a final steady-state value (inactivation). However, the correspondence between the time-dependent model behavior and known experimental behavior of excitable systems is only qualitative. We conclude that the classical ion-membrane molecule interactions we consider are not involved in determining time-dependent conductance processes in the excitable systems for which comparison is possible.     

Net Electric Charge on Photopigment Molecules and Frog Retinal Receptor Disk Membrane Structure

The photopigment molecules in frog retinal receptor disk membranes protude some 50-65% of their molecular diameter (~42 A) into the aqueous surface layer of the disk membrane, depending on whether the photopigment is bleached, while the remainder is embedded in the lipid core of the membrane. In order to determine whether the presumably polar groups covering this surface protruding into the aqueous phase possessed net electric charge, we collected X-ray diffraction data from the photopigment molecules in wet pellets of oriented disk membranes as a function of the pH and ionic strength of the sedimentation medium. The Fourier analysis applied to this data provided average nearest neighbor separations for the photopigment molecules for their planar arrangement in the disk membranes. Changes in the average separation of photopigment molecule nearest neighbors as a function of pH, ionic strength, and photopigment bleaching indicated that photopigment molecules possess negative net electric charge, that this net electric charge occurs in the aqueous surface layer of the disk membrane, and that this net charge is reduced on photopigment bleaching. This polar portion of the photopigment molecule may thereby determine the location of the photopigment molecules relative to the lipid core and other photopigment molecules in the disk membrane. In addition, the orientation (dichroism) of the photopigment relative to an axis normal to the plane of the disk membrane and the bleaching-dependent “sinking” of the photopigment molecule into the lipid core of the disk membrane may be accounted for.     

Ionic permeability of K, Na, and Cl in potassium-depolarized nerve. Dependency on pH, cooperative effects, and action of tetrodotoxin.

The passive ionic membrane conductances (gj) and permeabilities (Pj) of K, Na, and Cl of crayfish (Procambarus clarkii) medial giant axons were determined in the potassium-depolarized axon and compared with that of the resting axon. Passive ionic conductances and permeabilities were found to be potassium dependent with a major conductance transition occurring around an external K concentration of 12-15 mM (Vm = -60 to -65 mV). The results showed that K, Na, and Cl conductances increased by 6.2, 6.9, and 27-fold, respectively, when external K was elevated from 5.4 to 40 mM. Permeability measurements indicated that K changed minimally with K depolarization while Na and Cl underwent an order increase in permeability. In the resting axon (K0 = 5.4 mM, pH = 7.0) PK = 1.33 X 10(-5), PCl = 1.99 X 10(-6), PNa = 1.92 X 10(-8) while in elevated potassium (K0 = 40 mM, pH 7.0), PK = 1.9 X 10(-5), PCl = 1.2 X 10(-5), and PNa = 2.7 X 10(-7) cm/s. When membrane potential is reduced to 40 mV by changes in internal ions, the conductance changes are initially small. This suggests that resting channel conductances depend also on ion environments seen by each membrane surface in addition to membrane potential. In elevated potassium, K, Na, and Cl conductances and permeabilities were measured from pH 3.8 to 11 in 0.2 pH increments. Here a cooperative transition in membrane conductance or permeability occurs when pH is altered through the imidazole pK (approximately pH 6.3) region. This cooperative conductance transition involves changes in Na and Cl but not K permeabilities. A Hill coefficient n of near 4 was found for the cooperative conductance transition of both the Na and Cl ionic channel which could be interpreted as resulting from 4 protein molecules forming each of the Na and Cl ionic channels. Tetrodotoxin reduces the Hill coefficient n to near 2 for the Na channel but does not affect the Cl channel. In the resting or depolarized axon, crosslinking membrane amino groups with DIDS reduces Cl and Na permeability. Following potassium depolarization, buried amino groups appear to be uncovered. The data here suggest that potassium depolarization produces a membrane conformation change in these ionic permeability regulatory components. A model is proposed where membrane protein, which forms the membrane ionic channels, is oriented with an accessible amino terminal group on the axon exterior. In this model the ionizable groups on protein and phospholipid have varied associations with the different ionic channel access sites for K, Na, and Cl, and these groups exert considerable control over ion permeation through their surface potentials.     

Effects of physostigmine on the voltage dependent ionic conductances of skeletal muscle fibres

The voltage dependent ionic conductances were studied by analysing the phase plane trajectories of action potentials evoked by electrical stimulation of the sartorius muscles of the frog (Rana esculenta). The delayed outward potassium current was measured also under voltage clamp conditions on muscle fibres of either the frog (Rana esculenta) or Xenopus laevis. On analysing the effect of physostigmine decreasing the peak amplitude, the rate of both the rising and falling phases of the action potentials, it was revealed that the alkaloid at a concentration of 1 mmol/l reduced significantly both the delayed potassium conductance and the outward ionic current values during the action potentials. The inhibition of sodium conductance and inward ionic current was less expressed. The maximum value of delayed potassium conductance measured under voltage clamp conditions was decreased by 1 mmol/l physostigmine. The time constant determined from the development of delayed potassium conductance was increased at a given membrane potential. The voltage vs. n relationship describing the membrane potential dependence of the delayed rectifier was not influenced by physostigmine. It has been concluded that physostigmine changes the time course of the action potentials by decreasing the value of both voltage dependent ionic conductances and by slowing down their kinetics. It is discussed that results obtained from the phase plane analysis of complex pharmacological effects can only be accepted with some restrictions.     

Effects of the dipolar form of phloretin on potassium conductance in squid giant axons.

The effects of phloretin on membrane ionic conductances have been studied in the giant axon of the squid, Loligo pealei. Phloretin reversibly suppresses the potassium and sodium conductances and modifies their dependence on membrane potential (Em). Its effects on the potassium conductance (GK) are much greater than on the sodium conductance; no effects on sodium inactivation are observed. Internal perfusion of phloretin produces both greater shifts in GK(Em) and greater reductions maximum GK than does external perfusion; the effect of simultaneous internal and external perfusion is little greater than that of internal perfusion alone. Lowering the internal pH, which favors the presence of the neutral species of weakly acidic phloretin (pKa 7.4), potentiates the actions of internally perfused phloretin. Other organic cations with dipole moments similar to phloretin's have little effect on either potassium or sodium conductances in squid axons. These results can be explained by either of two mechanisms; on postulates a phloretin "receptor" near the voltage sensor component of the potassium channel which is accessible to drug molecules applied at either the outer or inner membrane surface and is much more sensitive to the neutral than the negatively charged form of the drug. The other mechanism proposes that neutral phloretin molecules are dispersed in an ordered array in the membrane interior, producing a diffuse dipole field which modifies potassium channel gating. Different experimental results support these two mechanisms, and neither hypothesis can be disproven.     

A hydrodynamic theory of ion conductance through Ohmic pores

A method of calculating the size of membrane pores lacking strong ionic selectivity is presented. By treating the flow of ions through a small channel as a hydrodynamic phenomenon, the electrical conductance becomes a function of the ratio of ion radius to channel radius. Thus when both the channel conductance and the ion size are known, the radius of the channel may be estimated. The method gives good agreement among radii predicted from conductances of four different alkali cations in alamethicin pores.     

A model for understanding membrane potential using springs

In this report, I present a simple model using springs to conceptualize the relationship between ionic conductances across a cellular membrane and their effect on membrane potential. The equation describing the relationships linking membrane potential, ionic equilibrium potential, and ionic conductance is of similar form to that describing the force generated by a spring as a function of its displacement. The spring analogy is especially useful in helping students to conceptualize the effects of multiple conductances on membrane potential.     

Taurine: a preventive agent of the acute ethanol depletive action on the isolated human amniotic membrane

Summary The preventive effect of taurine towards the acute ethanol reduction action was studied on the ionic transfer through the isolated human amniotic membrane. Taurine increased 3 components of the ionic transfer expressed by the conductance measurements (Na⁺ and K⁺ paracellular conductances through the intercellular spaces and coupling cell factor between 2 adjacent epithelial cells, expressed by a voltage ratio). These components were decreased by ethanol. Electrophysiological studies (conductance and voltage measurements) indicated that the addition of taurine (0.1–1 mM) before ethanol (0.4 g/l) hindered the decrease action of ethanol on the Na⁺ and K⁺ paracellular conductances and on the coupling cell factor. These data indicated a common target between taurine and ethanol: the membraneous phospholipids, particularly the distribution of the external fixed charges. The preventive action of taurineversus ethanol, on the human amniotic membrane, was exerted on the polar groups of phospholipids, hindering the incorporation of ethanol molecules.     

Biological effects of oscillating electric fields: Role of voltage-sensitive ion channels

An alternating component of potential across the membrane of an excitable cell may change the membrane conductance by interacting with the voltagesensing charged groups of the protein macromolecules that form voltage-sensitive ion channels. Because the probability that a voltage sensor is in a given state is a highly nonlinear function of the applied electric field, the average occupancy of a particular state will change in an oscillating electric field of sufficient magnitude. This “rectification” at the level of the voltage sensors could result in conformational changes (gating) that would modify channel conductance. A simplified two-state model is examined where the relaxation time of the voltage sensor is assumed to be considerably faster than the fastest changes of ionic conductance. Significant changes in the occupancy of voltage sensor states in response to an applied oscillating electric field are predicted by the model.     

Urinary proteases degrade epithelial sodium channels

Summary The mammalian urinary bladder epithelium accommodates volume changes by the insertion and withdrawal of cytoplasmic vesicles. Both apical membrane (which is entirely composed of fused vesicles) and the cytoplasmic vesicles contain three types of ionic conductances, one amiloride sensitive, an-other a cation-selective conductance and the third a cation conductance which seems to partition between the apical membrane and the mucosal solution. The transport properties of the apical membrane (which has been exposed to urine in vivo) differ from the cytoplasmic vesicles by possessing a lower density of amiloride-sensitive channels and a variable level of leak conductance. It was previously shown that glandular kallikrein was able to hydrolyze epithelial sodium channels into the leak conductance and that this leak conductance was further degraded into a channel which partitioned between the apical membrane and the mucosal solution. This report investigates whether kallikrein is the only urinary constituent capable of altering the apical membrane ionic permeability or whether other proteases or ionic conditions also irreversible modify apical membrane permeability.Alterations of mucosal pH, urea concentrations, calcium concentrations or osmolarity did not irreversible affect the apical membrane ionic conductances. However, urokinase and plasmin (both serine proteases found in mammalian urine) were found to cause an irreversible loss of amiloride-sensitive current, a variable change in the leak current as well as the appearance of a third conductance which was unstable in the apical membrane and appears to partition between the apical membrane and the mucosal solution. Amiloride protects the amiloride-sensitive conductance from hydrolysis but does not protect the leak pathway. Neither channel is protected by sodium. Fluctuation analysis demonstrated that the loss of amiloride-sensitive current was due to a decrease in the sodium-channel density and not a change in the single-channel current. Assuming a simple model of sequential degradation, estimates of single-channel currents and conductances for both the leak channel and unstable leak channel are determined.     

On the voltage-dependent action of tetrodotoxin.

The use of the maximum rate-of-rise of the action potential (Vmax) as a measure of the sodium conductance in excitable membranes is invalid. In the case of membrane action potentials, Vmax depends on the total ionic current across the membrane; drugs or conditions that alter the potassium or leak conductances will also affect Vmax. Likewise, long-term depolarization of the membrane lessens the fraction of total ionic current that passes through the sodium channels by increasing potassium conductance and inactivating the sodium conductance, and thereby reduces the effect of Vmax of drugs that specifically block sodium channels. The resultant artifact, an apparent voltage-dependent potency of such drugs, is theoretically simulated for the effects of tetrodotoxin on the Hodgkin-Huxley squid axon.     

The representation of membrane admittance.

An integral representation for the membrane admittance in terms of its known current response to a voltage step function is presented. It is demonstrated that the frequency-dependent terms in the contribution to the membrane admittance by the ion-selective conductance of the nerve membrane are proportional to the static conductances. The additional information contained in the real and imaginary parts of the membrane admittance should allow the parameters of the ion conductance to be determined. Eventually, these measurements should also give information about the electric dipole displacement currents of the conductance systems themselves, and about the metabolically supported active ion transport currents that maintain the ion concentration gradients.     

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

We 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.     

Inactivation of monazomycin-induced voltage-dependent conductance in thin lipid membranes. II. Inactivation produced by monazomycin transport through the membrane

At sufficiently large conductances, the voltage-dependent conductance induced in thin lipid membranes by monazomycin undergoes inactivation. This is a consequence of depletion of monazomycin from the membrane solution interface, as monazomycin crosses the membrane to the opposite (trans) side from which it was added. The flux of monazomycin is directly proportional to the monazomycin-induced conductance; at a given conductance it is independent of monazomycin concentration. We conclude that when monazomycin channels break up, some or all of the molecules making up a channel are deposited on the trans side. We present a model for the monazomycin channel: approximately five molecules, each spanning the membrane with its NH3+ on the trans side and an uncharged hydrophilic (probably sugar) group anchored to the cis side, form an aqueous channel lined by--OH groups. The voltage dependence arises from the flipping by the electrical field of molecules lying parallel to the cis surface into the "spanned state;" the subsequent aggregation of these molecules into channels is, to a first approximation, voltage independent. The channel breakup that deposits monomers on the trans side involves the collapsing of the channel in such a way that the uncharged hydrophilic groups remain in contact with the water in the channel as they close the channel from behind. We also discuss the possibility that inactivation of sodium channels in nerve involves the movement from one side of the membrane to the other of the molecules (or molecule) forming the channel.     

Mobility of adsorbed proteins: a Brownian dynamics study

We simulate the adsorption of lysozyme on a solid surface, using Brownian dynamics simulations. A protein molecule is represented as a uniformly charged sphere and interacts with other molecules through screened Coulombic and double-layer forces. The simulation starts from an empty surface and attempts are made to introduce additional proteins at a fixed time interval that is inversely proportional to the bulk protein concentration. We examine the effect of ionic strength and bulk protein concentration on the adsorption kinetics over a range of surface coverages. The structure of the adsorbed layer is examined through snapshots of the configurations and quantitatively with the radial distribution function. We extract the surface diffusion coefficient from the mean square displacement. At high ionic strengths the Coulombic interaction is effectively shielded, leading to increased surface coverage. This effect is quantified with an effective particle radius. Clustering of the adsorbed molecules is promoted by high ionic strength and low bulk concentrations. We find that lateral protein mobility decreases with increasing surface coverage. The observed trends are consistent with previous theoretical and experimental studies.     

Electrical Activation of Na/K Pumps Can Increase Ionic Concentration Gradient and Membrane Resting Potential

It has been previously demonstrated by our group that our specifically designed synchronization modulation electric field can dynamically entrain the Na/K ATPase molecules, effectively accelerating the pumping action of these molecules. The ATPase molecules are first synchronized by the field, and subsequently their pumping rates are gradually modulated in a stepwise pattern to progressively higher and higher levels. Here, we present results obtained on application of the field to intact twitch skeletal muscle fibers. The ionic concentration gradient across the cell membrane was monitored, with the membrane potential extrapolated using a slow fluorescent probe with a confocal microimaging technique. The applied synchronization-modulation electric field is able to slowly but consistently increase the ionic concentration gradient across the membrane and, hence, hyperpolarize the membrane potential. All of these results were fully eliminated if ouabain was applied to the bathing solution, indicating a correlation with the action of the Na/K pump molecules. These results in combination with our previous results into the entrainment of the pump molecules show that the synchronization-modulation electric field-induced activation of the Na/K pump functions can effectively increase the ionic concentration gradient and the membrane potential.     

Asymmetric electrostatic effects on the gating of rat brain sodium channels in planar lipid membranes.

The effects of ionic strength (10-1,000 mM) on the gating of batrachotoxin-activated rat brain sodium channels were studied in neutral and in negatively charged lipid bilayers. In neutral bilayers, increasing the ionic strength of the extracellular solution, shifted the voltage dependence of the open probability (gating curve) of the sodium channel to more positive membrane potentials. On the other hand, increasing the intracellular ionic strength shifted the gating curve to more negative membrane potentials. Ionic strength shifted the voltage dependence of both opening and closing rate constants of the channel in analogous ways to its effects on gating curves. The voltage sensitivities of the rate constants were not affected by ionic strength. The effects of ionic strength on the gating of sodium channels reconstituted in negatively charged bilayers were qualitatively the same as in neutral bilayers. However, important quantitative differences were noticed: in low ionic strength conditions (10-150 mM), the presence of negative charges on the membrane surface induced an extra voltage shift on the gating curve of sodium channels in relation to neutral bilayers. It is concluded that: (a) asymmetric negative surface charge densities in the extracellular (1e-/533A2) and intracellular (1e-/1,231A2) sides of the sodium channel could explain the voltage shifts caused by ionic strength on the gating curve of the channel in neutral bilayers. These surface charges create negative electric fields in both the extracellular and intracellular sides of the channel. Said electric fields interfere with gating charge movements that occur during the opening and closing of sodium channels; (b) the voltage shifts caused by ionic strength on the gating curve of sodium channels can be accounted by voltage shifts in both the opening and closing rate constants; (c) net negative surface charges on the channel's molecule do not affect the intrinsic gating properties of sodium channels but are essential in determining the relative position of the channel's gating curve; (d) provided the ionic strength is below 150 mM, the gating machinery of the sodium channel molecule is able to sense the electric field created by surface changes on the lipid membrane. I propose that during the opening and closing of sodium channels, the gating charges involved in this process are asymmetrically displaced in relation to the plane of the bilayer. Simple electrostatic calculations suggest that gating charge movements are influenced by membrane electrostatic potentials at distances of 48 and 28 A away from the plane of the membrane in the extracellular sides of the channel, respectively.     

Direct ion channel gating: A new function for intracellular messengers

1. There is widespread belief that intracellular messengers [e.g., Ca2+, cyclic AMP, cyclic GMP, inositol-1,4,5-triphosphate (IP3)] assert their actions primarily through activation of protein kinases. 2. In studies of excitable cells protein kinase activation has been shown to alter membrane ionic conductance, presumably through phosphorylation of ion channels (see Levitan, 1985). However, recent reports from several laboratories indicate that intracellular messengers can also affect membrane ionic conductances directly without invoking protein kinase activation. 3. In this article we examine those examples of direct activation of ionic conductances by intracellular messengers which are supported by single-channel studies of isolated membrane patches. The list of cell types displaying this kind of response is growing and includes cells of neuronal as well as nonneuronal origin.