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R T Mathias

Publications and source records attributed to R T Mathias.

54 records · Page 3Linked to original sources
PubMed1985

Epithelial water transport in a balanced gradient system.

The relationship between epithelial fluid transport, standing osmotic gradients, and standing hydrostatic pressure gradients has been investigated using a perturbation expansion of the governing equations. The assumptions used in the expansion are: (a) the volume of lateral intercellular space per unit volume of epithelium is small; (b) the membrane osmotic permeability is much larger than the solute permeability. We find that the rate of fluid reabsorption is set by the rate of active solute transport across lateral membranes. The fluid that crosses the lateral membranes and enters the intercellular cleft is driven longitudinally by small gradients in hydrostatic pressure. The small hydrostatic pressure in the intercellular space is capable of causing significant transmembrane fluid movement, however, the transmembrane effect is countered by the presence of a small standing osmotic gradient. Longitudinal hydrostatic and osmotic gradients balance such that their combined effect on transmembrane fluid flow is zero, whereas longitudinal flow is driven by the hydrostatic gradient. Because of this balance, standing gradients within intercellular clefts are effectively uncoupled from the rate of fluid reabsorption, which is driven by small, localized osmotic gradients within the cells. Water enters the cells across apical membranes and leaves across the lateral intercellular membranes. Fluid that enters the intercellular clefts can, in principle, exit either the basal end or be secreted from the apical end through tight junctions. Fluid flow through tight junctions is shown to depend on a dimensionless parameter, which scales the resistance to solute flow of the entire cleft relative to that of the junction. Estimates of the value of this parameter suggest that an electrically leaky epithelium may be effectively a tight epithelium in regard to fluid flow.

Animals↗
PubMed1985

Electro-osmosis and the reabsorption of fluid in renal proximal tubules.

The lateral intercellular spaces (LIS) are believed to be the final common pathway for fluid reabsorption from the renal proximal tubule. We postulate that electrogenic sodium pumps in the lateral membranes produce an electrical potential within the LIS, that the lateral membranes bear a net negative charge, and that fluid moves parallel to these membranes because of Helmholtz-type electro-osmosis, the field-induced movement of fluid adjacent to a charged surface. Our theoretical analysis indicates that the sodium pumps produce a longitudinal electric field of the order of 1 V/cm in the LIS. Our experimental measurements demonstrate that the electrophoretic mobility of rat renal basolateral membrane vesicles is 1 micron/s per V/cm, which is also the electro-osmotic fluid velocity in the LIS produced by a unit electric field. Thus, the fluid velocity in the LIS due to electro-osmosis should be of the order of 1 micron/s, which is sufficient to account for the observed reabsorption of fluid from renal proximal tubules. Several experimentally testable predictions emerge from our model. First, the pressure in the LIS need not increase when fluid is transported. Thus, the LIS of mammalian proximal tubules need not swell during fluid transport, a prediction consistent with the observations of Burg and Grantham (1971, Membranes and Ion Transport, pp. 49-77). Second, the reabsorption of fluid is predicted to cease when the lumen is clamped to a negative voltage. Our analysis predicts that a voltage of -15 mV will cause fluid to be secreted into the Necturus proximal tubule, a prediction consistent with the observations of Spring and Paganelli (1972, J. Gen. Physiol., 60:181).

Animals↗
PubMed1985

Transport properties of the lens.

Many studies have shown that the lens is a multicellular syncytial tissue whose electrophysiological properties are the integrated result of membrane transport, low-resistance gap junctions interconnecting the cells, and the restricted extracellular space between cells. There are at least three structurally distinct populations of cells within the lens, and the membrane transport properties of each cell type appear to differ. Indeed, there may be subcellular specialization of membrane transport properties in the surface epithelial cells. We review the physical structure of the lens, its electrical structure, and our present knowledge of the membrane transport properties of the different cell types. Our recent work has focused on radially circulating fluxes generated by the spatial localization of membrane transport in surface cell membranes versus inner fiber cell membranes. We review this work and present some simplified models of the results with some discussion of physiological implications.

Animals↗
PubMed1985

Steady state voltages in the frog lens.

Electro-chemical steady state in the lens depends on the transport properties of its various constituent cells. These transport properties, at a minimum, include the active transport of Na/K and the passive leak of Na, K and Cl through membrane channels. The work of Kinsey and Reddy (1), first localized active Na/K transport to the anterior surface cell membranes. In this paper, we estimate that the pump current density is 2 to 4 mu amp/cm2 of surface membrane, by measuring the change in intracellular voltage when the lens is exposed to 100 microM ouabain. Our impedance data suggest the passive leak of K is mostly across the membranes of surface cells, but whether these are anterior or posterior cells is not yet known. Membranes of the fiber cells throughout the volume of the lens appear to have channels that are selective for Na and Cl but few K channels. A simple model of electro-chemical steady state is derived to relate localized transport properties to the resting voltages in the lens. The above described localization of properties predicts radially circulating currents at steady state and spatial gradients in the intracellular and extracellular voltages. These predictions are compared to our measurements of steady state voltages and we find good agreement.

Animals↗
PubMed1983

Electrical properties of sheep Purkinje strands. Electrical and chemical potentials in the clefts.

The impedence of sheep Purkinje strands, measured to 3-5 kHz, is interpreted with circuit models based on morphology. The strand is described as a one-dimensional electrical cable. Clefts between myocytes of the strand allow radial current to flow in parallel with current across the outer membrane. A lumped model of the clefts, in which all the cleft membrane is in series with 100 omega-cm2, fits only below 20 Hz. Two distributed models, pie and disk, fit at all frequencies with somewhat different (31%) luminal resistivities, but with similar membrane parameters. Series resistance representing the endothelial sheath is small. Simulations of voltage clamp experiments include measured linear parameters and nonlinear membrane channels, as well as radial variation of cleft concentration, membrane flux, voltage, and current. Cleft potential is drastically nonuniform when sodium current flows. Cleft potential is reasonably uniform when calcium and potassium currents flow, but the calcium and potassium concentrations change markedly, enough to turn off the calcium current, even if the calcium channel did not inactivate. We conclude that physiological current flows produce significant nonuniformities in electrochemical potentials in the clefts of this cardiac preparation.

Animals↗
PubMed1983

Effect of tortuous extracellular pathways on resistance measurements.

There are many instances in which we are limited to measuring macroscopic quantities such as a bulk flow or an average field. In biology, wer are frequently interested in using such macroscopic measurements, for example, the total current from a tissue, to determine the microscopic properties of the cells or tubules of the tissue. The microstructure of the tissue will generally increase the resistance to flow over what would be measured in an unstructured medium. This paper derives a fairly general expression for the relationship between effective resistance to macroscopic flow and the specific resistance of the medium conducting the microscopic flow. This expression, called a tortuosity factor, is defined entirely in terms of measurable morphometric and geometric parameters of the tissue.

Animals↗
PubMed1981

Linear electrical properties of passive and active currents in spherical heart cell clusters.

Impedance studies were performed on small spherical clusters of embryonic chick heart cells grown in tissue culture. Each syncytial cluster was impaled with two microelectrodes; one injected low amplitude stochastic current and the other recorded the resulting perturbation of intracellular potential. The current and potential records were digitized, decomposed into their sinusoidal components, and the frequency domain impedance of the cluster was determined. The impedance data were compared with a theory for current flow in a spherical syncytium and values were derived for parameters describing the membranes and intercellular clefts of the tissue. The clusters were spontaneously active but usually became temporarily quiescent when impaled with two electrodes. The potential stabilized at a value close to -30 mV. At this depolarized potential, active slow currents, presumably present in the cardiac action potential, contributed noticeably to the linear impedance, producing a resonant peak in the magnitude of the impedance at a frequency of 1-3 Hz. The linearized impedance functions for these currents were characterized in the presence and absence of tetrodotoxin (TTX) and D-600. TTX had no noticeable effect on the impedance but D-600 essentially abolished the active currents. Although the ionic basis of these currents is not known, frequency domain analysis appears to be a viable technique for studying slow currents in heart muscle.

Animals↗
PubMed1981

The lens as a nonuniform spherical syncytium.

The effective intracellular resistivity Ri of the ocular lens is a measure of the coupling between cells. Since degradation of coupling may accompany cataracts, measurements of Ri are of considerable interest. Experimental results show that the lens is a nonuniform syncytium in which Ri is much higher in the nuclear region than in the cortex. A theory describing the lens as a radially nonuniform spherical syncytium is proposed, solved, and described as a simple equivalent circuit. The impedance of the lens is measured with new circuitry which permits the accurate application and measurement of current and voltage over a wide bandwidth without arbitrary compensation of unstable capacitances. The fit of the nonuniform theory to experimental data is satisfactory and the parameters determined are consistent with theoretical assumptions. In the outer region (cortex) of the lens Ri = 2.4 k omega-cm, probably as a consequence of differences in coupling and cytoplasmic resistivity. The radial resistivity of the cortex is some five times the circumferential resistivity, demonstrating a marked anisotropy in the preparation, probably reflecting the anisotropy in the orientation of lens fibers and distribution of gap junctions. Current can flow in the circumferential direction without crossing from fiber to fiber; current can flow in the radial direction only by crossing from fiber to fiber.

Animals↗
PubMed1980

Electrical models of excitation-contraction coupling and charge movement in skeletal muscle.

The consequences of ionic current flow from the T system to the sarcoplasmic reticulum (SR) of skeletal muscle are examined. The Appendix analyzes a simple model in which the conductance gx, linking T system and SR, is in series with a parallel resistor and capacitor having fixed values. The conductance gx is supposed to increase rapidly with depolarization and to decrease slowly with repolarization. Nonlinear transient currents computed from this model have some of the properties of gating currents produced by intramembrane charge movement. In particular, the integral of the transient current upon depolarization approximates that upon repolarization. Thus, equality of nonlinear charge movement can occur without intramembrane charge movement. A more complicated model is used in the text to fit the structure of skeletal muscle and other properties of its charge movement. Rectification is introduced into gx and the membrane conductance of the terminal cisternae to give asymmetry in the time-course of the transient currents and saturation in the curve relating charge movement to depolarization, respectively. The more complex model fits experimental data quite well if the longitudinal tubules of the sarcoplasmic reticulum are isolated from the terminal cisternae by a substantial resistance and if calcium release from the terminal cisternae is, for the most part, electrically silent. Specific experimental tests of the model are proposed, and the implications for excitation-contraction coupling are discussed.

Action Potentials↗
PubMed1980

Structural analysis of electrical properties of cells and tissues.

Most cells and tissues have electrical properties relevant to their natural function. Most cells and tissues have rather complex structure, consisting of folding and invaginating membranes and specialized connections and organelles. The localization of electrical properties is particularly important, since each of the complex structures must be expected to have a specific role in the electrical function of the tissue. The structural analysis of electrical properties consists then in the measurements of the electrical properties of the individual components of the tissue or cell. The structural analysis proceeds by a qualitative analysis of the topology of the preparation, followed by quantitative measurements of the morphometric parameters, the surface, and volume of the relevant structures. A theoretical analysis is performed to determine the electrical properties expected from such a structure. Measurements of natural and induced electrical properties are then made. Comparison of the observed electrical properties with those predicted allows determination of the properties of individual components of the tissue. In this manner the role of individual membrane systems in the function of both skeletal muscle and the lens of the eye has been determined.

Cell Membrane Permeability↗
PubMed1979

Electrical properties of spherical syncytia.

Syncytial tissues consist of many cells whose intracellular spaces are electrically coupled one to another. Such tissues typically include narrow, tortuous extracellular space and often have specialized membranes at their outer surface. We derive differential equations to describe the potentials induced when a sinusoidal or steady current is applied to the intracellular space with a microelectrode. We derive solutions for spherical preparations with isotropic properties or with a particular anisotropy in effective extracellular and intracellular resistivities. Solutions are presented in an approximate form with a simple physical interpretation. The leading term in the intracellular potential describes an "isopotential" cell in which there is no spatial variation of intracellular potential. The leading term in the extracellular potential, and thus the potential across the inner membranes, varies with radial position, even at zero frequency. The next term of the potentials describes the direct effects of the point source of current and, for the parameters given here, acts as a series resistance producing a large local potential drop essentially independent of frequency. A lumped equivalent circuit describes the "low frequency" behavior of the syncytium, and a distributed circuit gives a reasonably accurate general description. Graphs of the spatial variation and frequency dependence of intracellular, extracellular, and transmembrane potential are given, the response to sinusoidal currents is used to calculate numerically the response to a step function of current.

Cytoplasm↗
PubMed1979

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 . cm(2) but large capacitance of 10 muF/cm(2), 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 . cm(2), and low specific capacitance, 0.8 muF/cm(2). 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.

Animals↗
PubMed1979

Intracellular localization of markers within injected or cut frog muscle fibers.

Many experimental procedures require drastic alterations of muscle fibers, such as cutting the fiber or injecting molecular probes through microelectrodes. We report the ultrastructure of similarly altered muscle fibers and the intracellular distribution of injected horseradish peroxidase (HRP). Cut fibers appear structurally normal at distances greater than 500 microM from the cut end, however, the structure deteriorates nearer to the cut. HRP diffuses longitudinally about 2,000 micrometer from the cut end and the concentration is uniform over the fiber's cross section. If HRP is introduced intracellularly either by pressure injection or through a nick in the sarcolemma, it distributes in a C-shaped annulus extending approximately 2,000 micrometer longitudinally and 1-20 micrometer radially. The ultrastructure of injected or nicked fibers appears normal. The HRP freely entered the junctional gap between T-system and sarcoplasmic reticulum (SR) but was excluded from either structure. Occasionally, a light pillar could be seen between T-system and SR; the space of these pillars suggest they are the central area of the "feet" appearing light against the dark marker.

Animals↗
PubMed1979

The extracellular compartments of frog skeletal muscle.

1. Detailed studies of solute efflux from frog sartorius muscle and single muscle fibres were carried out in order to characterize a 'special region' (Harris, 1963) in the extracellular space of muscle and determine whether this 'special region' is the sarcoplasmic reticulum. 2. The efflux of radioactive Na, Cl, glusose, 3-O-methylglucose, xylose, glycine, leucine, cycloleucine, Rb, K, inulin (mol. wt. 5000) and dextran (mol. wt. 17,000) from previously loaded muscles was studied. In all cases except dextran the curve had three components, a rapid (A) component which could be equated with efflux from the extracellular space proper, a slow (C) component representing cellular solute and an intermediate (B) component. The distribution space for the B component was 8% of muscle volume in summer frogs and 12% in winter frogs and appeared to be equal for all compounds studied. We tested the hypothesis that the B component originated from the sarcoplasmic reticulum. 3. The C component was missing from the dextran curves. Both dextran and inulin entered the compartment of origin of the B component (compartment B) to the same extent as small molecules. 4. For all compounds studies, the efflux rate constant for the A component could be predicted from the diffusion coefficient. For the B component the efflux rate constant was 6--10 times slower than that for the A component but was still proportional to the diffusion coefficient for the solute in question. 5. When Na and sucrose efflux from single fibres was followed, a B component was usually observed. The average distribution space for this component was small, averaging 1.5% of fibre volume. There was no difference between the average efflux rate constants for Na and sucrose. 6. In an appendix, the constraints placed on the properties of a hypothetical channel between the sarcoplasmic reticulum and the T-system by the linear electrical parameters of frog skeletal muscle are derived. It is shown that the conductance of such a channel must be less than 0.06 x 10(-3) mohs/cm2 of fibre membrane. 7. The conductance between compartment B and the extracellular space can be calculated from the efflux rate constants for Na, K and Cl. The value obtained was 5 x 10(-3) mhos/cm2 of fibre membrane or 100 times the limiting value for the conductance of the T-SR junction. 8. The finding that there is a B component in the efflux curves for large molecular weight substances like inulin and dextran and the small size of the B component in efflux curves from single muscle fibres indicate that the 'speical region' of the extra-cellular space of frog muscle is not the sarcoplasmic reticulum. This conclusion is confirmed by a calculation of the conductance between the B compartment and the extracellular space. The value obtained is incompatible with predicted electrical properteis of the SR-T-tubule junction...

Animals↗
PubMed1978

An analysis of the electrical properties of a skeletal muscle fiber containing a helicoidal T system.

The linear electrical properties of skeletal muscle fibers have been analyzed using lumped circuit analogues of helicoidal T system. The geometry of a helicoid is assumed to produce two electrical effects, modeled separately. One model is motivated by the pitch or tilt of the T system, which forces the current flowing in the lumen of the tubules to have a longitudinal projection. The second model is motivated by the longitudinal continuity of a helicoid, which forms a structure similar to a cable within the fiber. The pitch or tilting of the T system plane modified the longitudinal resistance of the fiber, making it slightly frequency dependent; however, the magnitude of the change was less than 0.1%. The longitudinal connections between T system networks had a more complicated effect; the magnitude of the correction was again less than 0.1%. The conclusion from this analysis is that a helicoidal T system, whose pitch is constrained by the sarcomere spacing, will not affect electrical signals recorded intracellularly in intact fibers.

Electric Conductivity↗
PubMed1977

Electrical properties of frog skeletal muscle fibers interpreted with a mesh model of the tubular system.

This paper presents the construction, derivation, and test of a mesh model for the electrical properties of the transverse tubular system (T-system) in skeletal muscle. We model the irregular system of tubules as a random network of miniature transmission lines, using differential equations to describe the potential between the nodes and difference equations to describe the potential at the nodes. The solution to the equations can be accurately represented in several approximate forms with simple physical and graphical interpretations. All the parameters of the solution are specified by impedance and morphometric measurements. The effect of wide circumferential spacing between T-system openings is analyzed and the resulting restricted mesh model is shown to be approximated by a mesh with an access resistance. The continuous limit of the mesh model is shown to have the same form as the disk model of the T-system, but with a different expression for the tortuosity factor. The physical meaning of the tortuosity factor is examined, and a short derivation of the disk model is presented that gives results identical to the continuous limit of the mesh model. Both the mesh and restricted mesh models are compared with experimental data on the impedance of muscle fibers of the frog sartorius. The derived value for the resistivity of the lumen of the tubules is not too different from that of the bathing solution, the difference probably arising from the sensitivity of this value to errors in the morphometric measurements.

Animals↗