Synchronization of pacemaker cell firing by weak ELF fields: simulation by a circuit model.

Entrainment of output action potentials from repetitively firing pacemaker cells, brought about by regularly spaced excitatory or inhibitory postsynaptic inputs, is a well-known phenomenon. Synchronization of neural firing patterns by extremely low frequency (ELF) external electric fields has also been observed. Whereas current densities of approximately 10 A-m(-2) are required for direct excitation of otherwise quiescent neural tissue, much lower peak current densities (approximately 10[-2] A-m2) have been reported to entrain spontaneously firing molluscan pacemaker cells. We have developed a neural spike generator circuit model that simulates repetitive spike generation by a space clamped patch (area approximately 10[-7] m2) of excitable membrane subjected to depolarizing current. Picoampere (pA) range variation of DC depolarizing current causes a corresponding smooth variation of neural spike frequency, producing a physiologically realistic stimulus-response (S-R) characteristic. When lower pA range 60 Hz AC current is superposed upon the DC depolarizing current, smooth variation of the S-R characteristic is distorted by subharmonic locking of the spike generator at 30, 20, 15, 12, 10 Hz, and higher order subharmonic frequencies. Although the additional superposition of a physiologically realistic level of "white" current noise, covering the bandwidth 4-200 Hz, suffices to obscure higher order subharmonic locking, locking at 30, 20, and 15 Hz is still clearly evident in the presence of noise. Subharmonic locking is observed at an root mean square AC simulated tissue current density of approximately 10(-5) A-m(-2).

A three state model for alamethicin conductance in bilayer membranes.

Alamethicin is an antibiotic which produces voltage gated channels in lipid bilayer membranes. Recently completed studies of the pressure dependence of alamethicin conductance have shown that its onset following application of a suprathreshold voltage step at a pressure of 100 MPa (1000 atm) is markedly slowed relative to that observed at ambient pressure. Furthermore, the time course of the onset of conductance becomes distinctly sigmoidal at elevated pressure, a condition which is not evident at atmospheric pressure. The decay of alamethicin conductance upon removal of suprathreshold applied voltage is also slowed by application of hydrostatic pressure, but it follows a single exponential time course at all pressures. In addition, kinetic parameters characterizing the onset and decay of conductance show distinctly different pressure dependences. These observations cannot be explained by a two state model in which alamethicin moves reversibly between nonconducting and conducting states. Therefore we re-examine critically a hypothesis made by previous workers, namely that alamethicin, in monomeric or aggregate form, moves upon application of suprathreshold voltage first from a nonconducting surface state to a nonconducting preassembly or precursor state, and then finally into a conducting state. Parameters of this three state model are related to a geometric factor which measures the degree of sigmoidal conductance response and which can be evaluated directly from experimental data. An alternative aggregation-type analysis, equivalent to that applied by Hodgkin & Huxley to the potassium conductance in squid axon, is also considered in the context of this same geometric factor. The possibility of distinguishing between these analyses on the basis of experimental data is discussed.

Pressure effects on mechanisms of charge transport across bilayer membranes.

Ion transport across diphytanoylphosphatidylcholine/decane bilayer membranes was measured as a function of hydrostatic pressure over the range 0.1-100 MPa (1-1000 atm). Carrier-mediated K+ conductance decreased with increasing pressure, yielding positive activation volumes of 45 A3 per complex for valinomycin mediated transport, and 74 A3 per complex in the case of nonactin. Comparison with the known pressure dependence of the viscosity of bulk alkane liquids supports the view that the rate limiting step for carrier-mediated transport is the translocation of the carrier-cation complex across an essentially fluid hydrocarbon membrane core. The parameters characterizing transient conductance by the hydrophobic anions, dipicrylaminate and tetraphenylborate, by contrast, were found to be insensitive to pressure over the range available. This was also the case for the steady-state conductance observed at elevated concentrations of both tetraphenylborate and the hydrophobic cation, tetraphenylarsonium. The quasi-stationary conductance observed at elevated concentrations of dipicrylaminate did, however, decrease significantly with increasing pressure, indicating a positive activation volume of 20 A3 per ion. Alternative explanations of this more complex response of hydrophobic ions to pressure are considered. Ancillary measurements of specific membrane capacitance revealed an increase of about 10% with an increase of pressure to 100 MPa, yielding an estimated membrane compressibility on the order of 10(-9) m2 X N-1, comparable to that of bulk liquid hydrocarbons.

Chemical and solvent effects on the interaction of tetraphenylborate with lipid bilayer membranes.

Alkali metal salts of tetraphenylboron dissociate in aqueous solution to yield the hydrophobic anion, BPh-4, which is strongly adsorbed at the surfaces of lipid bilayer membranes. Upon application of a transmembrane voltage pulse these anions cross the membrane without appreciable desorption, thereby exhibiting a transient electrical conductance. The relaxation time of this transient is governed by the height of the central potential barrier which the anions must surmount in crossing the membrane. Because of discrete charge effects, the barrier height and hence the observed relaxation time increase markedly with increasing surface density of adsorbed BPh-4. Since adsorbed BPh-4 are in partition equilibrium with the same species dissolved in the aqueous phase, measurement of the relaxation time for BPh-4 membrane conductance can be used to assay the aqueous-phase concentration of the hydrophobic anion. In this way we have observed the precipitation of KBPh4 in water, obtaining a solubility concentration product of 1.0 X 10(-7) mol2 X dm-6 for the precipitation reaction at 25 degrees C. This result is larger by a factor of two than the most directly comparable published values from other sources. In additional experiments we have reduced the polarity of the aqueous phases bathing the membrane by adding varying amount of ethylene glycol to the water. Using the same conductance relaxation assay, we have determined that partitioning of BPh-4 into the membrane/solution interfaces is lessened as the polarity of the bathing solutions is reduced. This result is attributed to a lowering of the chemical potential of the BPh-4 in the less polar medium.

Pressure effects on alamethicin conductance in bilayer membranes.

We report here the first observations of the effects of elevated hydrostatic pressure on the kinetics of bilayer membrane conductance induced by the pore-forming antibiotic, alamethicin. Bacterial phosphatidylethanolamine-squalene bilayer membranes were formed by the apposition of lipid monolayers in a vessel capable of sustaining hydrostatic pressures in the range, 0.1-100 MPa (1-1,000 atm). Principal observations were (a) the lifetimes of discrete conductance states were lengthened with increasing pressure, (b) both the onset and decay of alamethicin conductance accompanying application and removal of supra-threshold voltage pulses were slowed with increasing pressure, (c) the onset of alamethicin conductance at elevated pressure became distinctly sigmoidal, suggesting an electrically silent intermediate state of channel assembly, (d) the magnitudes of the discrete conductance levels observed did not change with pressure, and, (e) the voltage threshold for the onset of alamethicin conductance was not altered by pressure. Apparent activation volumes for both the formation and decay of conducting states were positive and of comparable magnitude, namely, approximately 100 A3/event. Observation d indicates that channel geometry and the kinetics of ion transport through open channels were not affected by pressure in the range employed. The remaining observations indicate that, while the relative positions of free-energy minima characterizing individual conducting states at a given voltage were not modified by pressure, the heights of intervening potential maxima were increased by its application.

The influence of hydrophobic ions and dipolar molecules on the electrostatic barrier in biomembranes.

To calculate the electric field inside a membrane the aqueous phase can be approximated by a conductor since the dielectric constant of water is much larger than that of the membrane. Then, using the method of image charges, ions adsorbed inside the membrane can be considered as dipoles and dipolar molecules adsorbed inside the membrane may similarly be regarded as sets of two similarly oriented dipoles. The microscopic interactions and, therefore, the spatial correlations of the adsorbed species can then be obtained. Together with the Gouy theory for the diffuse double layer these results allow the determination of the adsorbed phase--aqueous phase equilibrium. From the densities and spatial correlations of the adsorbed ions and dipolar species, their influence upon the electrostatic barrier as experienced by an ion translocating the membrane can be calculated. Changes observed in the relaxation time and initial conductance of translocating hydrophobic ions in voltage-pulse experiments on bilayer membranes are predicted using this model of the electrostatic barrier. In addition, an equation giving the surface tension as a function of the (non-ideal) adsorption of hydrophobic ions and dipoles is derived.

Hydrophobic ion probe studies of membrane dipole potentials.

Hydrophobic anions of dipicrylamine and of sodium tetraphenylborate have been employed as probes of interfacial dipole potential variations in lipid bilayer membranes. Systematic variation of dipole potentials has been achieved by introduction of compounds incorporating N+ and B- charge centers. Distribution of hydrophilic and hydrophobic groups relative to these charge centers has been shown to control the orientation in the membrane/solution interface of the electric dipole moment formed by these centers. Thus triphenyl-[4-trimethylphenylammonium] borate orients with the B- center, surrounded by phenyl groups, embedded in the membrane, while the smaller methylated N+ center is directed toward the aqueous phases. This orientation has been confirmed using dipicrylamine probe ions. Results obtained in this system have been interpreted quantitatively using a previously developed model incorporating discrete charge effects. A second class of compounds, tri-n-alkylamine borane (TnAB) complexes having the generic formula (CnH2n+1)3N+B-H3, have also been synthesized for this study, using even-carbon alkyls ranging from ethyl to decyl. Molecular orientation of the complex is with the N+ center and its associated alkyl groups directed into the membranes, while the protonated B- center is directed toward the aqueous phases, as confirmed by use of tetraphenylborate ions as probes.

Autocorrelation analysis of hydrophobic ion current noise in lipid bilayer membranes.

The autocorrelation function of a given process is related to its spectral density by the Wiener-Khintchine theorem, and both expressions contain the same information. We report here a measurement of the current noise produced in a lipid bilayer membrane doped with hydrophobic anions of dipicrylamine. The results are in good agreement both with relaxation measurements on the same membrane and with an analysis of the spectral density of the current noise for this system which has been presented by other workers. Although measurement of the spectral density function is generally more complete for technical reasons, the autocorrelation function provides, for the case studied here, more physical insight into the underlying charge transport mechanism. We find that the measured autocorrelation function is negative at short, but nonzero, times. This is a consequence of the operative conductance mechanism in this case, which cannot carry current continuously in the same direction without compensatory reverse flow.

Evidence for a discrete charge effect within lipid bilayer membranes.

A high amplitude voltage step technique has been used to meausre the surface density of dipicrylamine anions adsorbed at the surfaces of lipid bilayer membranes. Accompanying low amplitude measurements have determined the relaxation time for transient current flow across the membranes, a parameter governed by the height of the central energy barrier which dipicrylamine anions must cross in moving from one membrane surface to the other. Measured relaxation times and surface charge densities have been related by a quasi-continuum model of the discrete charge effect, which predicts that the membrane central barrier height will increase with increasing density of adsorbed surface charge. The experimentally determined relationship is in satisfactory agreement with the predictions of the model. The model does not provide a complete description of the membrane/solution interface, however, because it cannot be applied to the description of previously measured isotherms for the adsorption of dipicrylamine anions onto bilayer membranes surfaces. Possible reasons for this discrepancy are discussed.

Modification of valinomycin-mediated bilayer membrane conductance by 4,5,6,7-tetrachloro-2-methylbenzimidazole.

The compound 4,5,6,7-tetrachloro-2-methylbenzimidazole (TMB), has been found to markedly modify the steady-state valinomycin-mediated conductance of potassium (K+) ions through lipid bilayer membranes. TMB alone does not contribute significantly to membrane conductance, being electrically neutral in solution. In one of two classes of experiments (I), valinomycin is first added to the aqueous phases, then changes of membrane conductance accompanying stepwise addition of TMB to the water are measured. In a second class of experiments (II), valinomycin is added to the membrane-forming solution, followed by TMB additions to the surrounding water. In both cases membrane conductance shows an initial increase with increasing TMB concentration which is more pronounced at lower K+ ion concentration. At TMB concentrations in excess of 10(-5) M, membrane conductance becomes independent of K+ ion concentration, in contrast to the linear dependence observed at TMB concentrations below 10(-7) M. This transition is accompanied by a change of high field current-voltage characteristics from superlinear (or weakly sublinear) to a strongly sublinear form. All of these observations may be correlated by the kinetic model for carrier-mediated transport proposed by Läuger and Stark (Biochim. Biophys. Acta 211:458, 1970) from which it may be concluded that valinomycin-mediated ion transport is limited by back diffusion of the uncomplexed carrier at high TMB concentrations. Experiments of class I reveal a sharp drop of conductance at high (greater than 10(-5) M) TMB concentration, not seen in class II experiments, which is attributed to blocked entry of uncomplexed carrier from the aqueous phases. Valinomycin initially in the membrane is removed by lateral diffusion to the surrounding torus. The time dependence of this removal has been studied in a separate series of experiments, leading to a measured coefficient of lateral diffusion for valinomycin of 5 x 10(-6) cm2/sec at 25 degrees C. This value is about two orders of magnitude larger than the corresponding coefficient for transmembrane carrier diffusion, and provides further evidence for localization of valinomycin in the membrane/solution interfaces.

Blocking of valinomycin-mediated bilayer membrane conductance by substituted benzimidazoles.

Valinomycin selectively transports alkali cations, e.g. potassium ions, across lipid bilayer membranes. The blocking of this carrier-mediated transport by four substituted benzimidazoles has been investigated. The compounds are 4,5,6,7-tetrachloro-2-trifluoromethylbenzimidazole, (TTFB); 4,5,6,7,-tetrachloro-2-methylbenzimidazole, (TMB); 2-trifluoromethylbenzimidazole, (TFB); and 2-methylbenzimidazole, (MBM). Because of its low acidic dissociation constant (pKa = 5.04), the blocking efficiency of TTFB in both neutral and anionic forms in the aqueous phase could be studied. The compounds exhibit the blocking efficiency sequence, TTFB- greater than TTFB0 greater than TMB0 greater than TFB0 greater than MBM0. The corresponding scale of decreasing lipophilicity, as determined by octanol/water partitioning, is TTFB0 greater than TMB0 greater than TTFB- greater than TFB0 greater than MBM0. Comparison of neutral species establishes a positive correlation of blocking efficiency with lipophilicity, with the latter being conferred primarily by chlorination of the benzenoid nucleus. Anionic TTFB, on the other hand, is the most effective blocking agent studied in spite of the fact that its dissociation in the aqueous phase markedly impedes its entry (presumably as a neutral species) into a bulk hydrocarbon phase. This observation suggests that the blocking of valinomycin-mediated bilayer membrane conductance takes place at the membrane/solution interface.

The interaction of hydrophobic ions with lipid bilayer membranes.

Electrical relaxation studies have been made on lecithin bilayer membranes of varying chain length and degree of unsaturation, in the presence of dipicrylamine. Results obtained are generally consistent with a model for the transport of hydrophobic ions previously proposed by Ketterer, Neumcke, and Läuger (J. Membrane Biol. 5:225, 1971). This medel visualizes as three distinct steps the interfacial absorption, translocation, and desorption of ions. Measurements at high electric field yield directly the density of ions absorbed to the membrane-solution interface. Variation of temperature has permitted determination of activation enthalpies for the translocation step which are consistent with the assumption of an electrostatic barrier in the hydrocarbon core of the membrane. The change of enthalpy upon absorption of ions is, however, found to be negligible, the process being driven instead by an increase of entropy. It is suggested that this increase may be due to the destruction, upon absorption, of a highly ordered water structure which surrounds the hydrophic ion in the aqueous phase. Finally, it is shown that a decrease of transient membrane conductance observed at high concentration of hydrophobic ions, previously interpreted in terms of interfacial saturation, must instead by attributed to a more complex effect equivalent to a reduction of membrane fluidity.

The permeability of thin lipid membranes to bromide and bromine.

Thin lipid (optically black) membranes were made from sheep red cell lipids dissolved in n-decane. The flux of Br across these membranes was measured by the use of tracer (82)Br. The unidirectional flux of Br (in 50-100 mM NaBr) was 1-3 x 10(-12) mole/cm(2)sec. This flux is more than 1000 times the flux predicted from the membrane electrical resistance (>10(8) ohm-cm(2)) and the transference number for Br(-) (0.2-0.3), which was estimated from measurements of the zero current potential difference. The Br flux was not affected by changes in the potential difference imposed across the membrane (+/-60 mv) or by the ionic strength of the bathing solutions. However, the addition of a reducing agent, sodium thiosulfate (10(-3)M), to the NaBr solution bathing the membrane caused a 90% reduction in the Br flux. The inhibiting effect of S(2)O(3) (=) suggests that the Br flux is due chiefly to traces of Br(2) in NaBr solutions. As expected, the addition of Br(2) to the NaBr solutions greatly stimulated the Br flux. However, at constant Br(2) concentration, the Br flux was also stimulated by increasing the Br(-) concentration, in spite of the fact that the membrane was virtually impermeable to Br(-). Finally, the Br flux appeared to saturate at high Br(2) concentrations, and the saturation value was roughly proportional to the Br(-) concentration. These results can be explained by a model which assumes that Br crosses the membrane only as Br(2) but that rapid equilibration of Br between Br(2) and Br(-) occurs in the unstirred layers of aqueous solution bathing the two sides of the membrane. A consequence of the model is that Br(-) "facilitates" the diffusion of Br across the unstirred layers.

The electrical conductance of semipermeable membranes III. bipolar flow-symmetric electrolytes.

The first paper of this series presented a general formulation of the problem of stationary ion flow through membranes. The second treated in detail the special case of unipolar flow across membranes separating symmetric electrolytes. In this, the third paper of the series, we deal with another special case, that of bipolar flow between symmetric electrolytes. Here it is assumed that the total current is carried by both positive and negative permeant ions. The restriction to symmetric electrolytes implies that all ions present in the membrane and surrounding solutions have valences of identical absolute magnitude. After extracting from the general development a set of equations appropriate to the special case being considered, we outline a procedure for the numerical solution of the conductance problem for this case. Numerical results, presented as part of a discussion of approximate analytic methods of solution, establish the utility of these methods. A discussion of the significance of this work for membrane studies is presented in conclusion.