Conductive properties of the proximal tubule in Necturus kidney

The electrical properties of the proximal tubule of the in vivo Necturus kidney were investigated by injecting current (as rectangular waves) into the lumen or into the epithelium of single tubules and by studying the resulting changes of transepithelial (VL) and/or cell membrane potential (VC) at various distances from the source. In some experiments paired measurements of VL and VC were performed at two abscissas x and x'. The luminal length constant of about 1,030 micrometer was shown to provide a good estimate of the transepithelial resistance, specific resistance (RTE = 420 omega.cm2) and/or per unit length (rTE = 1.3 x 10(4) omega.cm). The apparent intraepithelial length constant was subject to distortions arising from concomitant current spread in the lumen. The resistances of luminal membrane (rL), basolateral membrane (rB), and shunt pathway (rS) were estimated by two independent methods at 3.5 x 10(4), 1.2 x 10(4), and 1.7 x 10(4) omega.cm, respectively. The corresponding specific resistances were close to 1,200, 600, and 600 omega.cm2. There are two main conclusions of this study. (a) The resistances of cell membranes and shunt pathway are of the same order of magnitude. The figure of the shunt resistance is at variance with the notion that the proximal tubule of Necturus is a leaky epithelium. (b) A rigorous assessment of the conductive properties of concentric cylindrical double cables (such as renal tubules) requires that electrical interactions arising from one cable to another be taken into account. Appropriate equations were developed to deal with this problem.     

Effect of diameter on membrane capacity and conductance of sheep cardiac Purkinje fibers

Membrane electrical properties were measured in sheep cardiac Purkinje fibers, having diameters ranging from 50 to 300 mum. Both membrane capacitance and conductance per unit area of apparent fiber surface varied fourfold over this range. Membrane time constant, and capacitance per unit apparent surface area calculated from the foot of the action potential were independent of fiber diameter, having average values of 18.8 +/- 0.7 ms, and 3.4 +/- 0.25 muF/cm2, respectively (mean +/- SEM). The conduction velocity and time constant of the foot of the action potential also appeared independent of diameter, having values of 3.0 +/- 0.1 m/s and 0.10 +/- 0.007 ms. These findings are consistent with earlier suggestions that in addition to membrane on the surface of the fiber, there exists a large fraction of membrane in continuity with the extracellular space but not directly on the surface of the fiber. Combining the electrical and morphological information, it was possible to predict a passive length constant for the internal membranes of about 100 mum and a time constant for chaning these membranes in a passive 100-mum fiber of 1.7 ms.     

Quantitation of conductance pathways in antral gastric mucosa

The magnitude of cellular and shunt conductance of Necturus gastric antral mucosa was studied by (a) comparing the cellular PD response to transepithelial PD response during changes of ionic activity in the serosal bathing solution and (b) by measurement of current spread within the epithelial sheet. Using constant product KCl changes cellular resistance was 6,788 omegacm2 and shunt resistance was 1,803 omegacm2. Deletion of HCO3- from the serosal solution produced similar but quantitatively smaller changes in PD. Using HCO3- deletion cellular resistance was 7,338 omegacm2 and shunt resistance was 1,973 omegacm2. Measurement of current spead within the mucosa avoids changing ionic gradients yet gave very similar results; cellular resistance was 8,967 omegacm2 and shunt resistance was 2,947 omegacm2. The shunt contribution to transepithelial conductance ranged from 75.2 to 79.0%. Shunt selectivity was assessed using KCl dilution potentials, where mucosal dilution gave a small change in tissue PD compatible with an anion/cation selectivity ratio of 1.16 across the shunt, whereas serosal dilution effect was dominated by a PD change across the serosal membrane of the cell.     

The cylindrical cell with a time-variant membrane resistance. Measuring passive parameters.

The passive electrical properties of a cable can be measured by injecting a step of current at a point and fitting the resulting potentials at several positions along the cable with analytic solutions of the cable equation. An error analysis is presented for this method (which is based on constant membrane resistance) when the membrane resistance is not constant, but increases linearly with time. The increase of rm produces a "creep" in the membrane potential at long times, as observed in cardiac, skeletal, and smooth muscle. The partial differential equation describing the time-varying cable was solved numberically for a step of current and these "data" were fit by standard constant-resistance methods. Comparing the resulting parameter values with the known true values, we suggest that a correction of the standard methods is not satisfactory for resistance changes of the kind observed; instead, the cable equation must be solved again for the particular form of rm(t). The practical implementation of a method by Adrian and Peachey for measuring the membrane capacitance and an approximate method for estimating the rate-of-change of membrane resistance are discussed in appendices.     

土壤-植物系统水分运移过程的阻容电模拟

把土壤-植物系统水分运移作为一维水流运动由阻容电路进行模拟,在于将D arcy-R ichards方程从对单点的描述扩展到对一段流路的描述。由此出发,考虑到水流的非稳态性,某一流路的水阻定义为其水势差与平均流量之比,水容为其贮水量对平均水势的导数。与D arcy-R ichards方程相对应,水阻、时间常数分别为导水度、水分扩散度的倒数,相应地单位化的水阻率、比时间常数分别为导水率、水分扩散率的倒数。把SP系统沿水流通道分为若干部分,每一局部的水阻与其水容相并联,各局部间相串联。在此基础上,文章给出了土壤-植物系统水流模拟通式、总水容与分水容间的关系式、总水阻与分水阻间的关系式及特定条件下叶水势随时间变化的关系式。     

Action potentials initiated by single channels opening in a small neuron (rat olfactory receptor).

Rat olfactory receptor neurons were enzymatically dissociated and studied with the cell-attached configuration of the patch-clamp technique. Biphasic current waveforms induced across the membrane patch by intracellular action potentials were observed in approximately 5% of cells studied. In one cell in particular, current injected by the opening of a single channel initiated an action potential in the remainder of the cell each time the channel opened. A conventional type of electrical model of the cell and patch allowed the accurate modeling of cell excitability. The same model was used to explain the shape of the action potential current waveforms induced across the patch. The analysis indicated that the whole cell resistance (Ro) was approximately 40 G omega and the membrane capacitance (Co) was close to the standard value of 1 microF.cm-2. In addition, the threshold potential change necessary to initiate an action potential (Vth) was approximately 13 mV and a minimum current injection of 1 pA was required to depolarize the cell to spike threshold. When the smaller size of mammalian receptors are taken into account, membrane electrical properties were found to be consistent with those of salamander cells investigated by others using whole-cell recording. The analysis also revealed possible errors in the determination of single-channel conductances and reversal potentials by cell-attached recording from small cells.     

Chronopotentiometric studies of phosphatidylcholine bilayers modified by ergosterol

We have monitored the effect of ergosterol on electrical capacitance and electrical resistance of the phosphatidylcholine bilayer membranes using chronopotentiometry method. The chronopotentiometric characteristic of the bilayers depends on constant-current flow through the membranes. For low current values, no electroporation takes place and the membrane voltage rises exponentially to a constant value described by the Ohm's law. Based on these kinds of chronopotentiometric curves, a method of the membrane capacitance and the membrane resistance calculations is presented.     

Electrophysiological properties of tissue cultured heart cells grown in a linear array.

Embryonic chick heart cells were grown in tissue culture on an oriented substrate (channels cut in an agar coated slide), so that they formed narrow(5-100mu) strands of arbitrary length. The electrical properties of these strands were examined using intracellular microelectrodes. ac and dc cable studies were performed to determine the passive cable parameters. Quantitative histology, using light and electronmicroscopy, permitted calculation of intrinsic capacitances and resistivities. Electrical coupling between polarizing and recording electrodes was ubiquitous, falling off exponentially with distance. It was concluded that individual cells were electrically connected, since coupling was observed at distances greater than 3 mm, and the maximum cell length was estimated to be less that 300 mu. The strands were usually spontaneously active, with phase 4 depolarization (pacemaker potential) occurring almost simultaneously in all cells of a strand. The passive electrical properties determined during phase 4 were: core resistivity (cytoplasm plus cell-to-cell resistance), 245 ohm/cm; membrane capacitance, 1.46 muF/CM2. The membrane resistance increased from 16 to 136 kohm/cm2 during phase 4. The space and time constants showed commensurate changes, from 0.95 to 3.2 mm, and from 29 to 269 msec, respectively. The input resistance also increased, from 1.1 to 3.8 Mohm.     

Improved electrical coupling in uterine smooth muscle is associated with increased numbers of gap junctions at parturition

We have studied some passive electrical properties of uterine smooth muscle to determine whether a change in electrical parameters accompanies gap junction formation at delivery. The length constant of the longitudinal myometrium increased from 2.6 +/- 0.8 mm (X +/- SD) before term to 3.7 +/- 1 mm in tissues from delivering animals. The basis of the change was a 33% decrease in internal resistance and a 46% increase in membrane resistance. Axial current flow in an electrical syncytium such as myometrium is impeded by the cytoplasm of individual cells plus the junctions between cells. Measurement of the longitudinal impedance indicated that the specific resistance of the myoplasmic component was constant at 319 +/- 113 omega . cm before term and 340 +/- 93 omega . cm at delivery. However, a decrease in junctional resistance was apparent from 323 +/- 161 omega . cm to 134 +/- 64 omega . cm at delivery. 1.5-2 d after delivery, the junctional resistance was increased, as was the myoplasmic resistance. Thin-section electron microscopy of some of the same muscle samples showed that gap junctions were present in significantly greater numbers in the delivering tissues. Therefore, our results support the hypothesis that gap junction formation at delivery is associated with improved electrical coupling of uterine smooth muscle.     

Chronopotentiometric Technique as a Method for Electrical Characterization of Bilayer Lipid Membranes

The basic electrical parameters of bilayer lipid membranes are capacitance and resistance. This article describes the application of chronopotentiometry to the research of lipid bilayers. Membranes were made from egg yolk phosphatidylcholine. The chronopotentiometric characteristic of the membranes depends on the current value. For low current values, no electroporation takes place and the voltage rises exponentially to a constant value. Based on these kinds of chronopotentiometric curves, a method of the membrane capacitance and the membrane resistance calculations are presented.     

Analysis of Certain Errors in Squid Axon Voltage Clamp Measurements

Localized membrane current and potential measurements were made on the squid giant axon in voltage clamp experiments. Spatial control of potential was impaired by the use of axial current supplying electrodes with surface resistance greater than 20 ohms for a centimeter length of axon. No region of membrane which was indeed subjected to a potential step showed more than one inward current peak. Other patterns were results of space clamp failure. Membrane current and potential patterns during space clamp failure were approximately reproduced in computations on a model containing two membrane patches obeying the equations of Hodgkin and Huxley. Non-uniformities in the axon or electrodes are not necessary for non-uniform electrical behavior. An extension of the core conductor model which includes the axial wire and external solution has been analyzed. The space constant of electrotonic spread is less than 0.5 mm with a usable electrode. Errors of about 5 per cent are introduced by ignoring the external solution. Resistance between the membrane and the control electrodes reduces the control and a few ohm cm² could lead to serious errors in interpretation.     

The electrical structure of normal liver tissue]

The electrical coupling between cells of mouse liver was investigated in vitro. The membrane potential of liver cells is 15--30 mv immediatly after dissection, and increases to 40--48 mv within 4--7 hours. This level of membrane potential is constant during the next 2--3 hours. The mean input resistance varies within 189+/-9 and 613+/-+25 kohm to be higher in preparations examined in summer than in winter time. The cytoplasm of liver cells is equipotential. The reducing of potential from intracellular source is not exponential. This potential distribution is well approximated by a solution for the two-dimentional model of the liver lamella, when characteristic length is 500 mcm. On the basis of this model the outher membrane resistance and functional membrane resistance were found to be 700-2100 and 1.2 ohm-cm2, resp.     

Electrical Signs of New Membrane Production during Cleavage of Rana pipiens Eggs

Rana pipiens eggs dividing normally in diluted Ringer's solution show an increase in transmembrane potential inside negative, a decrease in resistance, and no change in total surface membrane capacitance at the appearance of a division furrow. Furrows of eggs in solutions with the tonicity of full Ringer develop partially, then regress so that the surface is again spherical. The potential and resistance changes are greater and substantial increases in capacitance occur when furrowing is so inhibited. It is proposed that the electrical changes at division are due to the introduction of new plasma membrane, between the blastomeres, having selective permeability to K and a low resistance compared to the outer spherical membrane. A narrow gap between blastomeres limits current flow through new membrane during normal division. A direct exposure of new membrane to the bathing medium when furrowing is disrupted results in larger changes in potential and resistance and permits the capacitance of new membrane to be detected.     

Mechanisms of conduction slowing during myocardial stretch by ventricular volume loading in the rabbit

Acute ventricular loading by volume inflation reversibly slows epicardial electrical conduction, but the underlying mechanism remains unclear. This study investigated the potential contributions of stretch-activated currents, alterations in resting membrane potential, or changes in intercellular resistance and membrane capacitance. Conduction velocity was assessed using optical mapping of isolated rabbit hearts at end-diastolic pressures of 0 and 30 mmHg. The addition of 50 microM Gd3+ (a stretch-activated channel blocker) to the perfusate had no effect on slowing. The effect of volume loading on conduction velocity was independent of changes in resting membrane potential created by altering the perfusate potassium concentration between 1.5 and 8 mM. Bidomain model analysis of optically recorded membrane potential responses to a unipolar stimulus suggested that the cross-fiber space constant and membrane capacitance both increased with loading (21%, P = 0.006, and 56%, P = 0.004, respectively), and these changes, when implemented in a resistively coupled one-dimensional network model, were consistent with the observed slowing (14%, P = 0.005). In conclusion, conduction slowing during ventricular volume loading is not attributable to stretch-activated currents or altered resting membrane potential, but a reduction of intercellular resistance with a concurrent increase of effective membrane capacitance results in a net slowing of conduction.     

Electrical Properties of Structural Components of the Crystalline Lens

The electrical properties of the crystalline lens of the frog eye are measured with stochastic currents applied with a microelectrode near the center of the preparation and potential recorded just under the surface. The stochastic signals are decomposed by Fourier analysis into sinusoidal components, and the impedance is determined from the ratio of mean cross power to input power. The data are fit by an electrical model that includes two paths for current flow: one through the cytoplasm, gap junctions, and outer membrane; the other through inner membranes and the extracellular space between lens fibers. The electrical properties of the structures of the lens which appear as circuit components in the model are determined by the fit to the data. The resistivity of the extracellular space within the lens is comparable to the resistivity of Ringer. The outer membrane has a normal resistance of 5 kohm · cm² but large capacitance of 10 μF/cm², probably because it represents the properties of several layers of fibers. The inner membranes have properties reminiscent of artificial lipid bilayers: they have high membrane resistance, 2.2 megohm · cm², and low specific capacitance, 0.8 μF/cm². There is so much membrane within the lens, however, that the sum of the current flow across all the inner membranes is comparable to that across the outer surface.     

Electrical Characteristics of Tunicate Heart Cell Membranes and Nexuses

The tubular ascidian heart is composed of a single layer of cells joined together by apical (zonulae occludentes) and spot (maculae occludentes) nexuses. Intercalated discs or desmosomes were not observed in this tissue. Rectangular pulses of current were applied across the opened and flattened myocardium. Assuming that all the transepithelial current flowed through a uniform gap between cells, the resistivity in the gap must be very high compared to that in bulk solution. It is likely, therefore, that the gap width is of the order of an ionic radius or smaller. Assuming that all the transepithelial current flowed through the cells and that the inner and outer membranes had the same resistivity, the membrane resistivity was about 210 ohms cm² and the membrane capacitance was about 1.6 µF per cm². The myocardial cells were found to be in electrical continuity with each other through the nexuses since current could be passed through a strip of myocardium in a sucrose gap. Assuming that the longitudinal resistance of the cytoplasm was negligible, the cell-to-cell resistivity of the nexuses was 0.2 ohm cm². It is concluded that the nexuses provide a low resistance pathway between cells and a transepithelial barrier.     

Effect of hypoxia and fenigidin on the action potential duration and the strength of myocardial contraction in frogs

A 40-minute perfusion of the frog ventricular strip with a hypoxic Ringer solution brings about a decline in action potential duration by 37 plus or minus 10% whereas the contractility is completely suppressed by that time. The time constant of the contractility exponential decline constitutes 8 plus or minus 2 min. the effect of hypoxia is reversible. Complete blockade of the calcium channels by fenigidin (3.5 x 10(-5) M) irreversibly lowers action potential duration by 62 plus or minus 2%. Contraction is completely suppressed on attaining the given level of action potentials. Hypoxia does not virtually affect action potential after the preliminary blockade of the calcium channels by fenigidin. It is suggested that the hypoxic solution mainly blocks the inward current across the calcium channels without affecting the potassium permeability of the sarcolemma. Meanwhile complete suppression of the contractility under hypoxia cannot be accounted for only by the blockade of the calcium channels.     

Frequency domain impedance measurements of erythrocytes. Constant phase angle impedance characteristics and a phase transition.

We report measurements of the electrical impedance of human erythrocytes in the frequency range from 1 Hz to 10 MHz, and for temperatures from 4 to 40 degrees C. In order to achieve high sensitivity in this frequency range, we embedded the cells in the pores of a filter, which constrains the current to pass through the cells in the pores. Based on the geometry of the cells embedded in the filter a circuit model is proposed for the cell-filter saline system. A constant phase angle (CPA) element, i.e., an impedance of the form Z = A/(j omega)alpha, where A is a constant, j = square root of -1, omega is angular frequency, and 0 less than alpha less than 1 has been used to describe the ac response of the interface between the cell surface and the electrolyte solution, i.e., the electrical double layer. The CPA and other elements of the circuit model are determined by a complex nonlinear least squares (CNLS) fit, which simultaneously fits the real and imaginary parts of the experimental data to the circuit model. The specific membrane capacitance is determined to be 0.901 +/- 0.036 microF/cm2, and the specific cytoplasm conductivity to be 0.413 +/- 0.031 S/m at 26 degrees C. The temperature dependence of the cytoplasm conductivity, membrane capacitance, and CPA element has been obtained. The membrane capacitance increases markedly at approximately 37 degrees C, which suggests a phase transition in the cell membrane.     

Effect of polarization of horizontal cells of the pike retina on spread of their electrical potentials

The spread of electrical responses over the layer of horizontal cells of the pike retina was investigated at different levels of their membrane potential varied by application of a steady current. Depolarization of the membrane, accompanied by an increase in its resistance, led to an increase in its time constant and length constant, so that electrical waves spread further over the layer of horizontal cells. The effect of polarization was thus due to the nonlinear membrane properties of the horizontal cells, i.e., to the increase in their resistance on depolarization and its decrease on hyperpolarization. In some cases this nonlinearlity was manifested as a special type of regeneration: the same strength of steady current crossing the membrane of the horizontal cells corresponded to two stable levels of the membrane potential. The role of various factors (changes in resistance of the extrasynaptic and subsynaptic membranes of the horizontal cells, the presynaptic effect of the current) determining the spread of the potentials over the horizontal cells under natural conditions during photic stimulation is discussed.Institute of Problems of Information Transmission, Academy of Sciences of the USSR, Moscow. Translated from Neirofiziologiya, Vol. 4, No. 1, pp- 90–96, January–February, 1972.