Membrane Characteristics of the Canine Papillary Muscle Fiber

Passive and active responses to intracellular and extracellular stimulation were studied in the canine papillary muscle. The electrotonic potential produced by extracellular polarization with the partition chamber method fitted the time course and the spatial decay expected from the cable theory (the time constant, 3.3 msec; the space constant, 1.2 mm). Contrariwise, spatial decay of the electrotonic potentials produced by intracellular polarization was very short and did not fit the decay curve expected for a simple cable, although only a small difference of time course in the electrotonic potentials produced by intracellular and extracellular polarizations was observed. A similar time course might result from the fact that when current flow results from intracellular polarization, the input resistance is less dependent on the membrane resistance. The foot of the propagated action potential rose exponentially with a time constant of 1.1 msec and a conduction velocity of 0.68 m/sec. The membrane capacity was calculated from the time constant of the foot potential and the conduction velocity to be 0.76 µF/cm². The responses of the papillary muscle membrane to intracellular stimulation differed from those to extracellular stimulation applied with the partition method in the following ways: higher threshold potential, shorter latency for the active response, linearity of the current-voltage relationship, and no reduction in the membrane resistance at the crest of the action potential during current flow.     

Extracellular and intracellular components of the impedance of neural tissue

Electric phenomena in brain tissue can be measured using extracellular potentials, such as the local field potential, or the electro-encephalogram. The interpretation of these signals depends on the electric structure and properties of extracellular media, but the measurements of these electric properties are still debated. Some measurements point to a model in which the extracellular medium is purely resistive, and thus parameters such as electric conductivity and permittivity should be independent of frequency. Other measurements point to a pronounced frequency dependence of these parameters, with scaling laws that are consistent with capacitive or diffusive effects. However, these experiments correspond to different preparations, and it is unclear how to correctly compare them. Here, we provide for the first time, impedance measurements (in the 1–10 kHz frequency range) using the same setup in various preparations, from primary cell cultures to acute brain slices, and a comparison with similar measurements performed in artificial cerebrospinal fluid with no biological material. The measurements show that when the current flows across a cell membrane, the frequency dependence of the macroscopic impedance between intracellular and extracellular electrodes is significant, and cannot be captured by a model with resistive media. Fitting a mean-field model to the data shows that this frequency dependence could be explained by the ionic diffusion mainly associated with Debye layers surrounding the membranes. We conclude that neuronal membranes and their ionic environment induce strong deviations to resistivity that should be taken into account to correctly interpret extracellular potentials generated by neurons.     

Action currents, internodal potentials, and extracellular records of myelinated mammalian nerve fibers derived from node potentials.

The potential distribution within the internodal axon of mammalian nerve fibers is derived by applying known node potential waveforms to the ends of an equivalent circuit model of the internode. The complete spatial/temporal profile of action potentials synthesized from the internodal profiles is used to compute the node current waveforn, and the extracellular action potential around fibers captured within a tubular electrode. For amphibia, the results agreed with empirical values. For mammals, the amplitude of the node currents plotted against conduction velocity was fitted by a straight line. The extracellular potential waveform depended on the location of the nodes within the tube. For tubes of length from 2 to 8 internodes, extracellular wave amplitude (mammals) was about one-third of the product of peak node current and tube resistance (center to ends). The extracellular potentials developed by longitudinal and radial currents in an anisotropic medium (fiber bundle) are compared.     

Cartilage electromechanics--I. Electrokinetic transduction and the effects of electrolyte pH and ionic strength

Articular cartilage contains a high fixed charge density under physiological conditions associated primarily with the ionized proteoglycan molecules of the extracellular matrix. Oscillatory compression of cartilage using physiological loads produces electrical potentials that have been shown previously to be the result of an electrokinetic (streaming) transduction mechanism. We have now observed two additional electromechanical phenomena not previously seen in cartilage or other soft tissues: 'streaming current' and 'current-generated stress'. Sinusoidal mechanical compression induced a sinusoidal streaming current density through cartilage disks when the Ag/AgCl electrodes that were used to compress the cartilage were shorted together externally. Conversely, a sinusoidal current density applied to the tissue generated a sinusoidal mechanical stress within the tissue. Both these phenomena were found to be consistent with the same electrokinetic transduction mechanism responsible for the streaming potential. Changes in the measured streaming potential response that resulted from modification of bath ionic strength and pH have provided additional insights into the molecular origins of these transduction processes. Finally, we have now observed streaming potentials in living cartilage maintained in organ culture, as well as in previously frozen tissue.     

Unit membrane parameters of electrically syncytial tissues.

A change in the holding voltage, exposure to channel-blocking agents, and similar interventions will induce changes in the membrane properties of electrically syncytial tissues. The altered membrane characteristics will produce changes in the input resistance (RIN) and the phase angle (phi) of the complex admittance of the whole preparation. Exact geometry-independent formulas are derived that give the intervention-induced changes in the membrane capacitance and conductance in terms of the measured changes in RIN and phi. The formulas automatically account for the effects of extracellular resistance in tissues such as skeletal muscle fibers, cardiac Purkinje fibers, and small cardiac "aggregates." The size, shape, and resistance of the extracellular space may be arbitrary and need not be measured. The surface (invaginated) membranes, which face the bath (extracellular space), are assumed to be characterized by an RC circuit with specific capacity Cme (Cmi) and specific conductivity gme (gmi). It is assumed that the intracellular voltage gradient between the electrodes and the membranes is negligible or reliably calculable. The intervention is assumed to leave the geometry and resistivity of the extracellular space unchanged. Under these circumstances the intervention-induced changes in Cme, Cmi, gme, and gmi are determined exactly in terms of the corresponding changes in RIN and certain frequency domain integrals over phi. The technique is illustrated by synthetic data for RIN and phi generated by the "disk" model of a skeletal muscle fiber in which Cme and Cmi depend upon holding voltage. The corresponding voltage dependence of RIN and phi is successfully "inverted" to expose the underlying voltage dependence of Cme and Cmi. These computations suggest that the formulas for Cme and Cmi will be useful in realistic situations, since they are not too sensitive to experimental error in the data for RIN and phi. This method makes it possible to detect voltage-dependent capacity changes due to unit membrane processes (e.g., charge movement) as long as the intrinsic time constant of that process is very small (e.g., less than 1/30 ms). As a second example I consider a disk model that is exposed to increasing concentrations of a channel-blocking agent. The drug dependence of RIN and phi is used to calculate the drug dependence of the total membrane conductivity (the sum of gme and gmi, weighted by the areas of surface and invaginated membranes, respectively).     

Streaming potentials maps are spatially resolved indicators of amplitude, frequency and ionic strength dependant responses of articular cartilage to load.

Streaming potential distributions were measured on the surface of articular cartilage in uniaxial unconfined compression using a linear array of microelectrodes. Potential profiles were obtained for sinusoidal and ramp/stress-relaxation displacements and exhibited dependencies on radial position, sinusoidal amplitude and frequency, time during stress relaxation, and on ionic strength. The measurements agreed with trends predicted by biphasic and related models. In particular, the absolute potential amplitude was maximal at the disk center, as was the predicted fluid pressure and the potential gradient (the electric field) was seen to be maximal at the disk periphery, as was the predicted fluid velocity. We also observed a similarity between non-linear behavior of streaming potential amplitude and load amplitude with respect to sinusoidal displacement amplitude. Taken together, these results support many of the phenomena concerning relative fluid-solid movement and fluid pressurization predicted by biphasic and related models, and they indicate the general utility of spatially resolved measurements of streaming potentials for the investigation of electromechanical phenomena in tissues. For example, these streaming potential maps could be used to non-destructively diagnose cartilage extracellular matrix composition and function, as well as to quantify spatially and temporally varying physical signals in cartilage that can induce cellular and extracellular biological responses to load.     

Electrical behavior of a skeletal muscle fiber in a volume conductor of finite extent

A model study of the spatial distribution of the extracellular potentials and current densities arising from an active single skeletal muscle fiber in a cylindrical volume conductor of finite radial extent is presented. The paper examines the influence of the radius of the volume conductor,b, on the extracellular potentials and currents at different field points. The equivalent sources with respect to the extracellular potential are investigated as well. The axial source density associated with the primary and secondary sources is calculated using the expressions for the intracellular and extracellular potentials. The density of the secondary sources is a decreasing function of the radius of the conducting medium and approaches zero whenb becomes infinitely big.     

A solution method for the determination of cardiac potential distributions with an alternating current source

A recently presented solution method for the bidomain model (Johnston et al. 2006), which involves the application of direct current for studying electrical potential in a slab of cardiac tissue, is extended here to allow the use of an applied alternating current. The advantage of using AC current, in a four-electrode method for determining cardiac conductivities, is that instead of using 'close' and 'wide' electrode spacings to make potential measurements, increasing the frequency of the AC current redirects a fraction of the current from the extracellular space into the intracellular space. The model is based on the work of Le Guyader et al. (2001), but is able to include the effects of the fibre rotation between the epicardium and the endocardium on the potentials. Also, rather than using a full numerical technique, the solution method uses Fourier series and a simple one dimensional finite difference scheme, which has the advantage of allowing the potentials to be calculated only at points, such as the measuring electrodes, where they are required. The new alternating current model, which includes intracellular capacitance, is used with a particular four-electrode configuration, to show that the potential measured is affected by changes in fibre rotation. This is significant because it indicates that it is necessary to include fibre rotation in models, which are to be used in conjunction with measuring arrays that are more complex than those involving simply surface probes or a single vertical probe.     

Regulation of CFTR chloride channel macroscopic conductance by extracellular bicarbonate

The CFTR contributes to Cl? and HCO?? transport across epithelial cell apical membranes. The extracellular face of CFTR is exposed to varying concentrations of Cl? and HCO?? in epithelial tissues, and there is evidence that CFTR is sensitive to changes in extracellular anion concentrations. Here we present functional evidence that extracellular Cl? and HCO?? regulate anion conduction in open CFTR channels. Using cell-attached and inside-out patch-clamp recordings from constitutively active mutant E1371Q-CFTR channels, we show that voltage-dependent inhibition of CFTR currents in intact cells is significantly stronger when the extracellular solution contains HCO?? than when it contains Cl?. This difference appears to reflect differences in the ability of extracellular HCO?? and Cl? to interact with and repel intracellular blocking anions from the pore. Strong block by endogenous cytosolic anions leading to reduced CFTR channel currents in intact cells occurs at physiologically relevant HCO?? concentrations and membrane potentials and can result in up to ～50% inhibition of current amplitude. We propose that channel block by cytosolic anions is a previously unrecognized, physiologically relevant mechanism of channel regulation that confers on CFTR channels sensitivity to different anions in the extracellular fluid. We further suggest that this anion sensitivity represents a feedback mechanism by which CFTR-dependent anion secretion could be regulated by the composition of the secretions themselves. Implications for the mechanism and regulation of CFTR-dependent secretion in epithelial tissues are discussed.     

Extracellular potentials from single spinal motoneurons

Extracellular action potentials found close to the surface of motoneurons are related to the intracellular spikes. Evidence is cited to support the assumption that the extracellular spikes have the same time course as the membrane current at the site of recording. Simultaneously recorded intracellular and extracellular spikes are compared. Intracellular spikes are transformed, by means of a circuit which is equivalent to the extracellular recording situation, into transients that are like those appearing extracellularly. Evidence is given that the recordings are from the cell bodies of motoneurons. The results show that the membrane at the extracellular recording site does not produce a spike since the time course of the extracellular potentials is determined by the passive properties of the membrane.     

Adaptation in the Visual Cortex: Influence of Membrane Trajectory and Neuronal Firing Pattern on Slow Afterpotentials

The input/output relationship in primary visual cortex neurons is influenced by the history of the preceding activity. To understand the impact that membrane potential trajectory and firing pattern has on the activation of slow conductances in cortical neurons we compared the afterpotentials that followed responses to different stimuli evoking similar numbers of action potentials. In particular, we compared afterpotentials following the intracellular injection of either square or sinusoidal currents lasting 20 seconds. Both stimuli were intracellular surrogates of different neuronal responses to prolonged visual stimulation. Recordings from 99 neurons in slices of visual cortex revealed that for stimuli evoking an equivalent number of spikes, sinusoidal current injection activated a slow afterhyperpolarization of significantly larger amplitude (8.5±3.3 mV) and duration (33±17 s) than that evoked by a square pulse (6.4±3.7 mV, 28±17 s; p<0.05). Spike frequency adaptation had a faster time course and was larger during plateau (square pulse) than during intermittent (sinusoidal) depolarizations. Similar results were obtained in 17 neurons intracellularly recorded from the visual cortex in vivo. The differences in the afterpotentials evoked with both protocols were abolished by removing calcium from the extracellular medium or by application of the L-type calcium channel blocker nifedipine, suggesting that the activation of a calcium-dependent current is at the base of this afterpotential difference. These findings suggest that not only the spikes, but the membrane potential values and firing patterns evoked by a particular stimulation protocol determine the responses to any subsequent incoming input in a time window that spans for tens of seconds to even minutes.     

Active electric properties of cardiac muscle

A model of electrical activity in the heart has been developed that treats the intracellular domain and the extracellular domain as electrical syncytia with anisotropic resistivities (bi-syncytial model). At the microscopic level, propagation is assumed to proceed primarily along the axes of individual cells. Considerations at the macroscopic level relate the transmembrane current to the intracellular and extracellular resistivity and the transmembrane potential. The result is a relationship between instantaneous extracellular potentials and cardiac action potentials.     

Modeling extracellular field potentials and the frequency-filtering properties of extracellular space

Extracellular local field potentials are usually modeled as arising from a set of current sources embedded in a homogeneous extracellular medium. Although this formalism can successfully model several properties of extracellular local field potentials, it does not account for their frequency-dependent attenuation with distance, a property essential to correctly model extracellular spikes. Here we derive expressions for the extracellular potential that include this frequency-dependent attenuation. We first show that, if the extracellular conductivity is nonhomogeneous, there is induction of nonhomogeneous charge densities that may result in a low-pass filter. We next derive a simplified model consisting of a punctual (or spherical) current source with spherically symmetric conductivity/permittivity gradients around the source. We analyze the effect of different radial profiles of conductivity and permittivity on the frequency-filtering behavior of this model. We show that this simple model generally displays low-pass filtering behavior, in which fast electrical events (such as Na(+)-mediated action potentials) attenuate very steeply with distance, whereas slower (K(+)-mediated) events propagate over larger distances in extracellular space, in qualitative agreement with experimental observations. This simple model can be used to obtain frequency-dependent extracellular field potentials without taking into account explicitly the complex folding of extracellular space.     

Electrical properties of rabbit corneal endothelium as determined from impedance measurements.

Alternating- and direct-current electrical characteristics of rabbit corneal endothelium were studied under varying experimental conditions. The measurements were performed by sending a 10-microA current (AC or DC) across the tissue layer. Maximal values of transendothelial potential difference and resistance were 1.3 +/- 0.1 mV and 73 +/- 6 omega . cm2, respectively. The short-circuit current was estimated from the potential and resistance values. Impedance loci were obtained for the frequency range 0.5-100 kHz. A capacitive reactance (C = 0.63 +/- 0.02 microF/cm2) was observed in the 100 Hz-100 kHz range. To relate the impedance data to the electrical parameters of the cell membranes, the voltage-divider ratio was determined by sending square pulse across the tissue and measuring voltage responses across the apical and basal membranes with an intracellular microelectrode. The intracellular potential difference was on the average -61 +/- 1 mV, and the voltage-divider ratio was found to be between 0.33 and 4. Impedance data were fit by a computer to an equivalent circuit representing a "lumped" model, and the agreement between the model and the data was satisfactory. The results are discussed in terms of both the morphological characteristics and properties of the fluid transport mechanism across the preparation.     

Extracellular potentials of a single myelinated nerve fiber in an unbounded volume conductor

The extracellular potentials of a single myelinated nerve fiber in an unbounded volume conductor were studied. The spatial distribution of the transmembrane potential was obtained by integrating the system of partial differential equations characterizing the electric processes in the active myelinated nerve fiber. The spatial distribution of the extracellular potentials at various radial distances in the volume conductor were calculated using the line source model. Up to a certain radial distance (500 m) the discontinuity of the action potential propagation is reflected in the extracellular potentials, while further in the volume conductor the potentials are smooth. The effect of the fiber diameter and the internodal distance on the volume conductor potentials as well as the changes in the magnitude of the extracellular potential (in the time domain) between two adjacent nodes at various radial distances were studied. The radial decline of the peak-to-peak amplitude of the extracellular potential depends on the radial coordinater of the field point and increases with the increase ofr.     

Potential and current distributions in a cylindrical bundle of cardiac tissue.

The intracellular and interstitial potentials associated with each cell or fiber in multicellular preparations carrying a uniformly propagating wave are important for characterizing the electrophysiological behavior of the preparation and in particular, for evaluating the source contributed by each fiber. The aforementioned potentials depend on a number of factors including the conductivities characterizing the intracellular, interstitial, and extracellular domains, the thickness of the tissue, and the distance (depth) of the field point from the surface of the tissue. A model study is presented describing the extracellular and interstitial potential distribution and current flow in a cylindrical bundle of cardiac muscle arising from a planar wavefront. For simplicity, the bundle is considered as a bidomain. Using typical values of conductivity, the results show that the intracellular and interstitial potential of fibers near the center of a very large bundle (greater than 10 mm) may be approximated by the potentials of a single fiber surrounded by a limited extracellular space (a fiber in oil), hence justifying a core-conductor model. For smaller bundles, the peak interstitial potential is less than that predicted by the core-conductor model but still large enough to affect the overall source strength. The magnitude of the source strength is greatest for fibers lying near the center of the bundle and diminishes sharply for fibers within 50 microns of the surface.     

The z-model — A proposal for spatial and temporal modeling of visual threshold perception

By considering only the modulation transfer functions of stationary, uniformly moved, and time modulated sinusoidal gratings it is possible to derive a simple model, the z-model, for the spatio-temporal frequency behaviour of one-dimensional patterns. The transmission function of this model is a band pass function of a single coordinate z, which is a quadratic form of the spatial and temporal frequencies (rotational symmetry with respect to space and time). The model is determined by only three constants. Optionally a time phase which accounts for delay and phase distortion can be added. This model can also be derived from reaction time measurements for switched on sinusoidal gratings. With this model the response of a wide variety of spatio-temporal patterns have been calculated and compared with measured threshold data. For two-dimensional patterns orientational filtering has to be added to the model leading to a further parameter. This model predicts satisfactorily the threshold modulation for a great variety of arbitrary spatio-temporal patterns. However the absolute threshold value for aperiodic transient patterns differs slightly in direction of smaller sensitivity as compared with periodic stationary patterns. This suggests that the peak detection scheme usually used in threshold detection modeling should be replaced by an integrative mechanism.     

Cyclopiazonic acid activates a Ca2+-permeable, nonselective cation conductance in porcine and bovine tracheal smooth muscle.

Capacitative Ca2+ entry has been examined in several tissues and, in some, appears to be mediated by nonselective cation channels collectively referred to as "store-operated" cation channels; however, relatively little is known about the electrophysiological properties of these channels in airway smooth muscle. Consequently we examined the electrophysiological characteristics and changes in intracellular Ca2+ concentration associated with a cyclopiazonic acid (CPA)-evoked current in porcine and bovine airway smooth muscle using patch-clamp and Ca2+-fluorescence techniques. In bovine tracheal myocytes, CPA induced an elevation of intracellular Ca2+ that was dependent on extracellular Ca2+ and was insensitive to nifedipine (an L-type voltage-gated Ca2+ channel inhibitor). Using patch-clamp techniques and conditions that block both K+ and Cl- currents, we found that CPA rapidly activated a membrane conductance (I(CPA)) in porcine and bovine tracheal myocytes that exhibits a linear current-voltage relationship with a reversal potential around 0 mV. Replacement of extracellular Na+ resulted in a marked reduction of I(CPA) at physiological membrane potentials (i.e., -60 mV) that was accompanied by a shift in the reversal potential for I(CPA) toward more negative membrane potentials. In addition, I(CPA) was markedly inhibited by 10 microM Gd3+ and La3+ but was largely insensitive to 1 microM nifedipine. We conclude that CPA induces capacitative Ca2+ entry in porcine and bovine tracheal smooth muscle via a Gd3+- and La3+-sensitive, nonselective cation conductance.     

Dipole interactions in electrofusion. Contributions of membrane potential and effective dipole interaction pressures.

The contributions of pulse-induced dipole-dipole interaction to the total pressure acting normal to the membranes of closely positioned pronase treated human erythrocytes during electrofusion was calculated. The total pressure was modeled as the sum of pressures arising from membrane potential and dipole-dipole attraction opposed by interbilayer repulsion. The dipole-dipole interaction was derived from the experimentally obtained cell polarizability. The threshold electric field amplitude necessary for fusion of pronase-treated human erythrocytes was experimentally obtained at various combinations of pulse duration, frequency, and the conductivity of the external medium. The theoretical values of the critical electric field amplitude compared favorably to the experimentally obtained threshold field amplitudes. Fusion by dc pulses may be primarily attributed to attainment of sufficiently high membrane potentials. However, with decreasing external conductivity and increasing sinusoidal pulse frequency (100 kHz-2.5 MHz), the induced dipole-dipole interactions provide the principal driving force for membrane failure leading to fusion.