Membrane Potentials and Ion Permeability in a Cation Exchange Membrane

The nonequilibrium electrical potentials across an artificial membrane bathed by solutions of a single salt have been measured and calculated using the Goldman-Hodgkin-Katz equation and the irreversible thermodynamic equation. The latter equation predicts the observed potential differences over a 2500-fold concentration range, while application of a modified Goldman-Hodgkin-Katz equation leads to difficulties.     

An Analysis of the Surface Fixed-Charge Theory of the Squid Giant Axon Membrane

The observed shift in threshold potential, after perfusion of the squid giant axon with solutions of low ionic strength, can be predicted by assuming a fixed negative charge on the inside of the membrane. The constant field equation, together with the double-layer potential due to this charge, has been used to determine the change in resting potential during perfusion with solutions of low ionic strength. Neither the modified constant field equation nor Planck's diffusion equation can successfully predict the observed shift in resting potential. It is suggested that a positive charge distribution exists about the sodium channel on the outside of the membrane. The double-layer potential due to this positive charge, together with the independence principle, has been used to predict the relationship between sodium current and membrane potential when the ionic strength and sodium activity of the external solution are decreased. These predictions have been compared with the available experimental observations.     

Passive Membrane Potentials: A Generalization of the Theory of Electrotonus

The theory of electrotonus, which has been well developed for small cylinders, is extended: the fundamental potential equations for a membrane of arbitrary shape are derived, and solutions are found for cylindrical and spherical geometries. If two purely conductive media are separated by a resistance-capacitance membrane, then Laplace's equation describes the potential in either medium, and two boundary equations relate the transmembrane potential to applied currents and to currents flowing into the membrane from each medium. The core conductor model, on which most previous work on cylindrical electrotonus has been based, gives rise to a one dimensional diffusion equation, the cable equation, for the transmembrane potential in a small cylinder. Under the assumptions of the core conductor model the more general equations developed here are shown to reduce to the cable equation. The two theories agree well in predicting the transmembrane potential in a small cylinder owing to an applied current step, and the extracellular potential for this cylinder is estimated numerically from the general theory. A detailed proof is given for the isopotentiality of a spherical soma membrane.     

鼎湖山人工松林生态系统蒸散力及计算方法的比较

Based on the consecutive measurement (1995-1997) of meteorology and microclimate of artificial Pinus forest in Mount Dinghu, we calculated the potential evapotranspiration by using four different methods to discuss the method which is fit for forest ecosystem. The results are given as follows.1) In terms of the enviromental conditions of forest ecosystem, we redefined some parameters in Penman equation and used it to calculate the potential evapotranspiration of artificial Pinus forest ecosystem in Mount Dinghu.Preliminary result is that Penman equation is worth spreading for calculating the potential evapotranspiration of forest ecosystem,compared with several other methods.2) The annual average potential evapotranspiration of the artificial Pinus forest in Mount Dinghu is 937.55mm,according to Penman equation. It is 50% of the rainfall in the corresponding period. The highest mean monthly potential evapotranspiration is July and the lowest mean monthly potential evapotranspiration is January. This is completely consistent with the variations of temperature.     

Two-dimensional Fourier representation used in the bioelectric forward problem.

The objective of this paper is the application of two-dimensional discrete Fourier transformation for solving the integral equation of the bioelectric forward problem. Therefore, the potential, the source term, and the integral equation kernel are assumed to be sampled at evenly spaced intervals. Thus the continuous functions of the problem domain can be expressed by their two-dimensional discrete Fourier transform in the spatial frequency domain. The method is applied to compute the surface potential generated by an eccentric dipole in a homogeneous spherical conducting medium. The integral equation for the potential is solved in the spatial frequency domain and the value of the potential at the sampling points is obtained from inverse Fourier transformation. The solution of the presented method is compared to both, an analytic solution and a solution gained from applying the boundary element method. Isoparametric quadrilateral boundary elements are used for modeling the spherical volume conductor in the boundary element solution, while in the two-dimensional Fourier transformation method the volume conductor is represented by a parametric boundary surface approximation.     

The correction factors for sucrose gap measurements and their practical applications.

The distribution of extracellular and intracellular potential in the sucrose gap apparatus, previously established for a single fiber using the cable equations for a core conductor model (Jirounek and Straub, Biophys. J., 11:1, 1971), is obtained for a multifiber preparation. The exact equation is derived relating the true membrane potential change to the measured potential differences across the sucrose gap, the junction potentials between sucrose and physiological solution, the membrane potential in the sucrose region, and the electrical parameters of the preparation in each region of the sucrose gap. The extracellular potential distribution has been measured using a modified sucrose gap apparatus for the frog sciatic nerve and the rabbit vagus nerve. The results indicate a hyperpolarization of the preparations in the sucrose region, of 60--75 mV. The hyperpolarization is independent of the presence of junction potentials. The calculation of the correction terms in the equation relating the actual to the measured potential change is illustrated for the case of complete depolarization by KC1 on one side of the sucrose gap. The correction terms in the equation are given for various experimental conditions, and a number of nomographic charts are presented, by means of which the correction factors can be rapidly evaluated.     

High CO2 levels reduce ethylene production in kiwifruit

We examined the roles of turgor potential and osmotic adjustment in plant growth by comparing the growth of spring wheat ( Triticum aestivum cv. Siete cerrors) and sudangrass ( Sorghum vulgare var. Piper) seedlings in response to soil water and temperature stresses. The rates of leaf area expansion, leaf water potential and osmotic potential were measured at combinations of 5 soil water potentials ranging from −0.03 to −0.25 MPa and 6 soil temperatures ranging from 14 to 36°C. Spring wheat exhibited little osmotic adjustment while sudangrass exhibited a high degree of osmotic adjustment. However, the rate of leaf area growth for sudangrass was more sensitive to water stress than that of spring wheat. These results were used to evaluate the relationship between growth and turgor potential. The modified Arrhenius equation based on thermodynamic considerations of the growth process was evaluated. This equation obtains growth rate as a function of activation energy, enthalpy difference between active and inactive states of enzymes, base growth rate and optimum temperature. Analyses indicate that the modified Arrhenius equation is consistent with the Lockhart equation with a metabolically controlled cell wall extensibility.     

Dimensional anlaysis and the equations of electrophoresis

A set of characteristic parameters is given for electrophoresis accompanied by diffusion, followed by a method of simplification of the transport equation. The concept of electrophoretic similarity is introduced in connection with the presentation of solutions and the final section contains some dimensional considerations of the potential equation.     

Nonlinear cable equations for axons. I. Computations and experiments with internal current injection

Steady-state potential and current distributions resulting from internal injection of current in the squid giant axon have been measured experimentally and also computed from nonlinear membrane cable equation models by numerical methods, using the Hodgkin-Huxley equations to give the membrane current density. The solutions obtained by this method satisfactorily reproduce experimental measurements of the steady-state distribution of membrane potential. Computations of the input current-voltage characteristic for a nonlinear cable were in excellent agreement with measurements on axons. Our results demonstrate the power of Cole's equation to extract the nonlinear membrane characteristics simply from measurement of the input resistance.     

Dependence of cellular potential on ionic concentrations. Data supporting a modification of the constant field equation.

The resting potential in the squid axon has been measured at various concentrations of Cl, K, Na, and Ca ions. The results of these measurements are compared with the Goldman-Hodgkin-Katz (GHK) equation and a modified constant field equation. This modified equation was derived by including currents carried by divalent ions and the effects of the unstirred layer and the periaxonal space. It is shown that, although the GHK equation can fit the V vs. [K]o data well, it has difficulty explaining the observed dependence of V on [Na]o when the axon is bathed in K-free artificial sea water. The use of the modified constant field equation removes this difficulty.     

Transmembrane electrical potential of excitable membranes: a pore analysis influence of surface charges and surface dipoles

A treatment is proposed in order to establish the general expression of the zero-current transmembrane potential of excitable membranes. The membrane model considered here is that of a hydrocarbon layer which is impermeable to ions and which represents the lipid bilayer matrix. In this matrix are incorporated ionic channels. The ion transport process through the channels is described by the absolute-rate theory applied to pores which are seen as chains of potential energy maxima and minima. Only one of the energy barriers corresponds to the gate step, and it is strongly dependent on the transmembrane potential. The kinetic equation is related to the zero current, to electrostatic boundary conditions and to the Gouy-Chapman equation for the aqueous diffuse layer.     

Potassium current activated by depolarization of dissociated neurons from adult guinea pig hippocampus

Currents were generated by depolarizing pulses in voltage-clamped, dissociated neurons from the CA1 region of adult guinea pig hippocampus in solutions containing 1 microm tetrodotoxin. When the extracellular potassium concentration was 100 mM, the currents reversed at -8.1 +/- 1.6 mV (n = 5), close to the calculated potassium equilibrium potential of -7 mV. The currents were depressed by 30 mM tetraethylammonium in the extracellular solution but were unaffected by 4-aminopyridine at concentrations of 0.5 or 1 mM. It was concluded that the currents were depolarization-activated potassium currents. Instantaneous current-voltage curves were nonlinear but could be fitted by a Goldman-Hodgkin-Katz equation with PNa/PK = 0.04. Conductance-voltage curves could be described by a Boltzmann-type equation: the average maximum conductance was 65.2 +/- 15.7 nS (n = 9) and the potential at which gK was half-maximal was -4.8 +/- 3.9 mV (mean +/- 1 SEM, n = 10). The relationship between the null potential and the extracellular potassium concentration was nonlinear and could be fitted by a Goldman-Hodgkin-Katz equation with PNa/PK = 0.04. The rising phase of potassium currents and the decay of tail currents could be fitted with exponentials with single time constants that varied with membrane potential. Potassium currents inactivated to a steady level with a time constant of approximately 450 ms that did not vary with potential. The currents were depressed by substituting cobalt or cadmium for extracellular calcium but similar effects were not obtained by substituting magnesium for calcium.     

The Gibbs-Duhem equation in membrane transport

It is argued that the Gibbs-Duhem equation alone cannot be used for deriving conclusions about the pressure gradient in membrane permeation. Statements regarding spatial variation of pressure in conjunction with chemical potential gradients of the components can legitimately be drawn from an equation that results from a combination of the G-D equation and the mechanical equilibrium equation. The derived equation has been applied here for explaining the mechanics of osmosis. In a further application, the frictional model has been improved here because the driving force also includes the membrane-solute potential interaction, thus allowing the solute partition coefficient to appear in the calculations naturally. By recognizing that because of the membrane-solution interaction, external forces of both potential and frictional character are present, the dissipation function is shown to depend explicitly on the centre-of-mass velocity. Thus the reference velocity for diffusive fluxes cannot be chosen arbitrarily, making Prigogine's theorem invalid in this approach to describing membrane permeation.     

Slow Changes of Potassium Permeability in the Squid Giant Axon

A slow potassium inactivation i.e. decrease of conductance when the inside of the membrane is made more positive with respect to the outside, has been observed for the squid axon. The conductance-potential curve is sigmoid shaped, and the ratio between maximum and minimum potassium conductance is at least 3. The time constant for the change of potassium conductance with potential is independent of the concentration of potassium in the external solution, but dependent upon potential and temperature. At 9 degrees C and at the normal sea water resting potential, the time constant is 11 sec. For lower temperature or more depolarizing potentials, the time constant is greater. The inactivation can be described by modifying the Hodgkin-Huxley equation for potassium current, using one additional parameter. The modified equation is similar in form to the Hodgkin-Huxley equation for sodium current, suggesting that the mechanism for the passive transport of potassium through the axon membrane is similar to that for sodium.     

Nonlinear modelling of the propagation of action potentials]

The role of nerve fibre membrane inductance in the action potential spreading was studied. We received a nonlinear differential equation for the action potential. This equation has soliton solutions. On the basis of the suggested model the numeral calculation results were given in our paper.     

Bound state solutions of Schrödinger equation with modified Mobius square potential (MMSP) and its thermodynamic properties

We solved the Schrödinger equation with the modified Mobius square potential model using the modified factorization method. Within the framework of the Greene–Aldrich approximation for the centrifugal term and using a suitable transformation scheme, we obtained the energy eigenvalues equation and the corresponding eigenfunction in terms of the hypergeometric function. Using the resulting eigenvalues equation, we calculated the vibrational partition function and other relevant thermodynamic properties. We also showed that the modified Mobius square potential can be reduced to the Hua potential model using appropriate potential constant values.     

Inconsistent sodium current records derived on Ranvier nodes with a commercially available potential clamp device according to Nonner

We tried to reproduce some basic implications of the Hodgkin-Huxley-Frankenhaeuser formalism by measuring sodium currents in single myelinated nerve fibres with a commercially available version of the potential clamp device according to Nonner. The following contradictory observations were made: 1. The potential dependence of the time to peak sodium currents showed a discontinuity around the sodium equilibrium potential. 2. Defining the sodium permeability PNa by the constant field equation and fitting the peak PNa-voltage relation by a sigmoid function we obtained unbelievable high values of PNa at rest. 3. Testing PNa as calculated by the constant field equation by so-called "sodium tail current" experiments we obtained instantaneous changes of PNa. Summing up, neither the kinetics of sodium currents nor the constant field concept as tested with the equipment used seem to agree satisfactorily with the standard data of sodium currents in Ranvier nodes.     

GABA responses in rat dentate granule neurons are mediated by chloride

The dendrites of granule cells in hippocampal slices responded to gamma-aminobutyric acid (GABA) with a depolarization. The response was blocked by picrotoxin in a noncompetitive manner. Reductions in the extracellular chloride ion concentration changed the reversal potential of the response by an amount predicted from the Nernst equation for chloride ion. Chloride-dependent hyperpolarizing responses were sometimes also found in the cell body of the granule cells. Since the reversal potential followed that predicted from the Nernst equation for chloride, we conclude that the response was mediated by chloride ions alone with no contribution from other ions. This has not previously been shown for the depolarizing response to GABA in central neurons.     

Chloride action potentials and currents in embryonic skeletal muscle of the chick

Chloride-dependent action potentials were elicited from embryonic skeletal muscle fibers of the chick during the last week of in ovo development. The duration of the action potentials was extremely long (greater than 8 sec). The action potentials were reversibly blocked by the stilbene derivative, SITS, a specific blocker of chloride permeability. Using patch clamp pipettes, in which the intracellular chloride concentration was controlled and with other types of ion channels blocked, the membrane potential at the peak of the action potential closely coincided with the chloride equilibrium potential calculated from the Nernst equation. These data indicate that activation of a chloride-selective conductance underlies the long duration action potential. The occurrence of the chloride-dependent action potential was found to increase during embryonic development. The percentage of fibers that displayed the action potential increased from approximately 20% at embryonic day 13 to approximately 70% at hatching. Chloride-dependent action potentials were not found in adult fibers. The voltage and time-dependent currents underlying the action potential were recorded under voltage clamp using the whole-cell version of the patch pipette technique. The reversal potential of the currents was found to shift with the chloride concentration gradient in a manner predicted by the Nernst equation, and the currents were blocked by SITS. These data indicate that chloride ions were the charge carriers. The conductance was activated by depolarization and exhibited very slow activation and deactivation kinetics.