The resistance of the septum of the medium giant axon of the earthworm

It is generally thought that nexuses constitute low-resistance pathways between cell interiors in epithelial, neural, muscular, and even connective tissues. However, there are no reliable estimates of the specific resistance of a nexus. The reason for this is that in most cases the surfaces of nexuses between cells are geometrically complex and therefore it has been very hard to accurately estimate nexal areas. However, the septa of the median giant axon have a relatively simple shape. Moreover, in this preparation, it is possible to make a measuring current flow parallel to the axon axis so that from the voltage difference appearing between intracellular electrodes during current flow, the specific septal membrane resistance could be calculated. The average specific nexal resistance obtained was 5.9 ω cm(2) if one assumes that 100 percent of the septum is nexus. The steady state I-V curve for the septum is linear (+/- 10 mV). Placement of electrodes was validated by septa even though the septa were found to be permeable to fluorescein and TEA. Exposure of the axon to hypertonic saline impedes the movement of fluorescein across the septa. By analogy with other tissues it is concluded that hypertonic solutions disrupt nexuses.

A mathematical model was derived which predicts the steady- state transmembrane potential vs. distance from a point source of intracellular current. When the specific nexal membrane resistance is 5.9 ω cm(2), the prediction closely approximates the fall of transmembrane potential vs. distance in an ordinary infinite cable. This is commensurate with the electrophysiological behavior of this multicellular “axon.”

     

Cable correction of membrane currents recorded from root hairs of Arabidopsis thaliana L.

Membrane currents were recorded under voltage clamp from roothairs of Arabidopsis thaliana L. using the two-electrode method.Concurrent measurements of membrane voltage distal to the pointof current injection were also carried out to assess the extentof current dissipation along the root hair axis. Estimates ofthe characteristic cable length,     

An efficient algorithm for cable theory,applied to blowfly photoreceptor cells and LMC's

A both simple and efficient algorithm is presented that yields the voltages and currents in an arbitrary cable structure. The algorithm consists of the following steps: 1. The cable structure is divided into homogeneous cable segments; 2. Each cable segment is considered as a two-port, and replaced by an equivalent circuit consisting of discrete elements; 3. The resulting equivalent scheme of the whole cable structure is solved with an algorithm for ladder networks (or, if the structure is not tree-like, with a network analysis program), which yields the input and output voltages and currents of each cable segment; and if required 4. The voltage and current distribution in each segment is determined from the input and output voltages and currents. The algorithm is applied to blowfly photoreceptor cells that are electrically coupled, and to blowfly Large Monopolar Cells. For LMC's it is shown that the loads at the input and output sides of the axon determine whether unidirectional or bidirectional signal transmission occurs.     

The rising phase of the miniature endplate current at the frog neuromuscular junction

(1) The rising phase of minature endplate currets was recorded at the frog's neuromuscular junction using both the two electrode voltage clamp and a single external electrode, or Strickholm, voltage clamp. (2) The $\text{Q}$(10) of the miniature endplate current rising phase was 2.3 in a variety of solutions selected to alter presynaptic behavior. (3) Increasing the solution's viscosity by an amount sufficient to slow the diffusion coefficient of acetylcholine by a third has no effect on the duration of the rising or the decay phase. This solution does seem to further slow the miniature endplate current decay phase, but not the rising phase, after inhibition of the acetylcholinesterase. (4) As the membrane potential is made more positive, the miniature endplate current rising phase is prolonged, with an $\text{e-}\text{fold}$ slowing per 170 mV change. (5) It is concluded that neither presynaptic nor subsynaptic events determine the rising phase of miniature endplate currents at the frog neuromuscular junction. Rather, the limiting step occurs within the membrane and is most likely a change in the binding constant of the receptor for the acetylcholine molecule.     

The distribution of membrane current in nerve with longitudinal linearly increasing applied current

The distribution of membrane current in three models of nerve, when a longitudinal, linearly increasing current is applied, is derived. For the simple core conductor model it is shown that, if the region over which such a current is applied is large compared to the space constant of the model, the membrane current in the mid-portion of the region is a constant, independent of the distance, the time following the application of the current, and the impedance of the membrane. The effect of nonlinear membrane electrical properties is discussed. It is further shown that these conclusions apply equally to the case in which the simple model is surrounded by another concentric sheath (the double cable model). In this case the impedance of the sheath does not influence the membrane current in the mid-polar region. Finally, it is shown that the form of the solution for the saltatory model, for this type of applied current, is identical with that for the simple model.     

Mixture Models for Distance Sampling Detection Functions

We present a new class of models for the detection function in distance sampling surveys of wildlife populations, based on finite mixtures of simple parametric key functions such as the half-normal. The models share many of the features of the widely-used “key function plus series adjustment” (K+A) formulation: they are flexible, produce plausible shapes with a small number of parameters, allow incorporation of covariates in addition to distance and can be fitted using maximum likelihood. One important advantage over the K+A approach is that the mixtures are automatically monotonic non-increasing and non-negative, so constrained optimization is not required to ensure distance sampling assumptions are honoured. We compare the mixture formulation to the K+A approach using simulations to evaluate its applicability in a wide set of challenging situations. We also re-analyze four previously problematic real-world case studies. We find mixtures outperform K+A methods in many cases, particularly spiked line transect data (i.e., where detectability drops rapidly at small distances) and larger sample sizes. We recommend that current standard model selection methods for distance sampling detection functions are extended to include mixture models in the candidate set.     

Theoretical analysis of the amplification of synaptic potentials by small clusters of persistent sodium channels in dendrites

We extend on the work developed by R.R. Poznanski and J. Bell from a linearized somatic persistent sodium current source to a non-linear representation of the dendritic Na(+)P current source associated with a small number of persistent sodium channels. The main objective is to investigate the modulation in the amplification of excitatory postsynaptic potentials (EPSPs) in dendrites studded with persistent sodium channels. The relation between membrane potential (V) and persistent sodium current density (I(NaP)) is approximated heuristically with a sigmoidal function and the resultant cable equation is solved analytically using a regular perturbation expansion and Green's function techniques. The transient simulated (non-evoked) response is found as a result of current injection in the form of synaptically induced voltage change located at a distance from the recording site in a cable with a uniform distribution of ion channel densities per unit length of cable (the so-called 'hot-spots') and with the conductance of each hot-spot (i.e., number of channels per hot-spot) assumed to be a constant. The results show an amplification in the observed EPSPs to be compatible with the experimentally derived estimates, and in addition a saturation in the amplification is observed indicating an optimum number of ionic channels.     

Subthreshold oscillatory responses of the Hodgkin-Huxley cable model for the squid giant axon

The classical cable equation, in which membrane conductance is considered constant, is modified by including the linearized effect of membrane potential on sodium and potassium ionic currents, as formulated in the Hodgkin-Huxley equations for the squid giant axon. The resulting partial differential equation is solved by numerical inversion of the Laplace transform of the voltage response to current and voltage inputs. The voltage response is computed for voltage step, current step, and current pulse inputs, and the effect of temperature on the response to a current step input is also calculated.The validity of the linearized approximation is examined by comparing the linearized response to a current step input with the solution of the nonlinear partial differential cable equation for various subthreshold current step inputs.All the computed responses for the squid giant axon show oscillatory behavior and depart significantly from what is predicted on the basis of the classical cable equation. The linearization procedure, coupled with numerical inversion of the Laplace transform, proves to be a convenient approach which predicts at least qualitatively the subthreshold behavior of the nonlinear system.     

Parameter Estimation Methods for Single Neuron Models

With the advancement in computer technology, it has become possible to fit complex models to neuronal data. In this work, we test how two methods can estimate parameters of simple neuron models (passive soma) to more complex ones (neuron with one dendritic cylinder and two active conductances). The first method uses classical voltage traces resulting from current pulses injection (time domain), while the second uses measures of the neuron's response to sinusoidal stimuli (frequency domain). Both methods estimate correctly the parameters in all cases studied. However, the time-domain method is slower and more prone to estimation errors in the cable parameters than the frequency-domain method. Because with noisy data the goodness of fit does not distinguish between different solutions, we suggest that running the estimation procedure a large number of times might help find a good solution and can provide information about the interactions between parameters. Also, because the formulation used for the model's response in the frequency domain is analytical, one can derive a local sensitivity analysis for each parameter. This analysis indicates how well a parameter is likely to be estimated and helps choose an optimal stimulation protocol. Finally, the tests suggest a strategy for fitting single-cell models using the two methods examined.     

Axon voltage-clamp simulations. II. Double sucrose-gap method.

This is the second in a series of four papers on the simulation of the voltage clamp of cylindrical excitable cells. In this paper we evaluate the double sucrose-gap voltage-clamp technique for the squid and lobster giant axons. Using the Crank-Nicolson method of solution of the cable equations and differential equations representing the voltage clamp circuit we studied the effect of length of the sucrose gap "node" on the voltage profile along an excitable cell during a simulated voltage clamp. The voltage gradients along the region of the cell within the node produce "notches" in the current recording as well as changes in the magnitude of the sodium and potassium current for a given voltage step. Our results show that good voltage clamp control requires node lengths less than one-half the axon diameter.     

χ Recombination Activity in Phage λ Decays as a Function of Genetic Distance

In Escherichia coli, χ is a recombination hotspot that stimulates RecBCD-dependent exchange at and to one side of itself. χ activity is highest at χ and decreases with distance from χ. The decrease in χ activity may be a simple property of the physical distance over which χ can stimulate recombination. Alternatively, the decay in χ activity with distance may reflect the high likelihood that χ-stimulated recombination occurs in a single χ-proximal act, to the exclusion of additional χ-stimulated exchanges more distal to χ. To test the models, we determined if χ activity decreases as a function of physical distance (i.e., DNA base pairs) or genetic distance (homologous DNA base pairs). Our results indicate that χ activity decays as a function of genetic distance. In addition, we found that the sbcB gene product (exonuclease I, a 3' -> 5' ssDNA exonuclease) modulates the distance over which χ can act. In contrast, the recJ gene product (a 5' -> 3' ssDNA exonuclease) does not alter the decay of χ activity.     

Measurement of GABA-evoked conductance changes of lobster muscle fibres by a three-microelectrode voltage clamp technique

The effective membrane conductance and capacity of lobster muscle fibres was measured by a three-intracellular-microelectrode voltage clamp technique. Conductance values agreed well with those determined under current clamp, by means of the 'short' cable equations. Reversible increases in conductance evoked by gamma-aminobutyric acid (GABA) were reflected by differences (delta V) in electrotonic potential amplitude recorded at the centre, and midway between the centre and fibre end respectively. GABA dose--conductance curves derived from cable theory or from delta V measurements were virtually identical. The effective capacity (ceff), determined from the area beneath the 'on' delta V capacity transient, yielded values of the membrane time constant consistently lower than those obtained by the graphical method of E. Stefani & A.B. Steinbach (J. Physiol., London. 203, 383-401 (1969)); one possible explanation for this discrepancy is discussed. In the presence of GABA, the effective capacity was reduced in a dose-related manner. The results were interpreted in terms of an equivalent circuit in which surface membrane was arranged in parallel with cleft-tubular membrane of finite conductance, charged through an access resistance. GABA was though to be decreasing ceff by selectively increasing the conductance of the cleft-tubular membranes.     

Determination by capillary zone electrophoresis of berenil, phenamidine, diampron and dibromopropamidine in serum and urine

A quick, simple and reliable analysis method has been developed in order to determine berenil, phenamidine, diampron and dibromopropamidine by capillary zone electrophoresis in samples of serum and urine. In order to define the operation parameters in CZE, we have carried out a study on how the apparent electrophoretic mobility (μ_app) varies when pH, buffer concentration, voltage and temperature are modified. Ohm’s law plot has been studied, too. With the data obtained from this study we have determined the optimum work conditions, which are: citrate buffer 25 mM, pH=3.70, 14 kV, 30°C, wavelength of the UV detector: 200 nm, capillary tube: 570 mm×75 μm. Under these conditions, all the products appear in times between: 7.6 min phenamidine and 8.8 min dibromopropamidine, limits of detection being: berenil: 0.50, phenamidine: 0.25, diampron: 0.40 and dibromopropamidine: 0.80 μg ml⁻¹. We have carried out a recovery study with three kinds of extraction cartridges: Sep-pak C-18 plus, Sep-pak C-8 plus and Oasis HBL for each one of the products in blood and urine.     

Pulse Dipolar ESR of Doubly Labeled Mini TAR DNA and Its Annealing to Mini TAR RNA

Pulse dipolar electron-spin resonance in the form of double electron electron resonance was applied to strategically placed, site-specifically attached pairs of nitroxide spin labels to monitor changes in the mini TAR DNA stem-loop structure brought on by the HIV-1 nucleocapsid protein NCp7. The biophysical structural evidence was at Ångstrom-level resolution under solution conditions not amenable to crystallography or NMR. In the absence of complementary TAR RNA, double labels located in both the upper and the lower stem of mini TAR DNA showed in the presence of NCp7 a broadened distance distribution between the points of attachment, and there was evidence for several conformers. Next, when equimolar amounts of mini TAR DNA and complementary mini TAR RNA were present, NCp7 enhanced the annealing of their stem-loop structures to form duplex DNA-RNA. When duplex TAR DNA-TAR RNA formed, double labels initially located 27.5 Å apart at the 3′- and 5′-termini of the 27-base mini TAR DNA relocated to opposite ends of a 27 bp RNA-DNA duplex with 76.5 Å between labels, a distance which was consistent with the distance between the two labels in a thermally annealed 27-bp TAR DNA-TAR RNA duplex. Different sets of double labels initially located 26–27 Å apart in the mini TAR DNA upper stem, appropriately altered their interlabel distance to ∼35 Å when a 27 bp TAR DNA-TAR RNA duplex formed, where the formation was caused either through NCp7-induced annealing or by thermal annealing. In summary, clear structural evidence was obtained for the fraying and destabilization brought on by NCp7 in its biochemical function as an annealing agent and for the detailed structural change from stem-loop to duplex RNA-DNA when complementary RNA was present.     

Idiosyncratic Gating of HERG-like K+ Channels in Microglia

A simple kinetic model is presented to explain the gating of a HERG-like voltage-gated K⁺ conductance described in the accompanying paper (Zhou, W., F.S. Cayabyab, P.S. Pennefather, L.C. Schlichter, and T.E. DeCoursey. 1998. J. Gen. Physiol. 111:781–794). The model proposes two kinetically distinct closing pathways, a rapid one favored by depolarization (deactivation) and a slow one favored by hyperpolarization (inactivation). The overlap of these two processes leads to a window current between −50 and +20 mV with a peak at −36 mV of ∼12% maximal conductance. The near absence of depolarization-activated outward current in microglia, compared with HERG channels expressed in oocytes or cardiac myocytes, can be explained if activation is shifted negatively in microglia. As seen with experimental data, availability predicted by the model was more steeply voltage dependent, and the midpoint more positive when determined by making the holding potential progressively more positive at intervals of 20 s (starting at −120 mV), rather than progressively more negative (starting at 40 mV). In the model, this hysteresis was generated by postulating slow and ultra-slow components of inactivation. The ultra-slow component takes minutes to equilibrate at −40 mV but is steeply voltage dependent, leading to protocol-dependent modulation of the HERG-like current. The data suggest that “deactivation” and “inactivation” are coupled through the open state. This is particularly evident in isotonic Cs⁺, where a delayed and transient outward current develops on depolarization with a decay time constant more voltage dependent and slower than the deactivation process observed at the same potential after a brief hyperpolarization.     

Permeability of iodide in multilamellar liposomes modeled by two compartments and a reservoir

A previously published rate law for the diffusion of iodide from multilamellar egg phosphatidylcholine liposomes (Schullery, S.E. (1975) Chem. Phys. Lipids 49–58) is fitted to the relatively simple mathematical model of two compartments in series with a reservoir. All of the inner liposome compartments are assumed to behave as effectively one compartment in series with the liposome's outermost compartment. Based on this model, reasonable values are calculated for the fraction of the total solution trapped by liposomes which is in the outermost liposome compartment, 17%, and the permeability coefficient of iodide against isotonic, mixed iodide-chloride solution, $\text{2 · 10}{}^{\mathrm{?9}}\text{cm/s}$.     

An Electrical Inspection of the Subsurface Cisternae of the Outer Hair Cell

The cylindrical outer hair cell (OHC) of Corti’s organ drives cochlear amplification by a voltage-dependent activation of the molecular motor, prestin (SLC26a5), in the cell’s lateral membrane. The voltage-dependent nature of this process leads to the troublesome observation that the membrane resistor-capacitor filter could limit high-frequency acoustic activation of the motor. Based on cable theory, the unique 30 nm width compartment (the extracisternal space, ECS) formed between the cell’s lateral membrane and adjacent subsurface cisternae (SSC) could further limit the influence of receptor currents on lateral membrane voltage. Here, we use dual perforated/whole-cell and loose patch clamp on isolated OHCs to sequentially record currents resulting from excitation at apical, middle, and basal loose patch sites before and after perforated patch rupture. We find that timing of currents is fast and uniform before whole-cell pipette washout, suggesting little voltage attenuation along the length of the lateral membrane. Prior treatment with salicylate, a disrupter of the SSC, confirms the influence of the SSC on current spread. Finally, a cable model of the OHC, which can match our data, indicates that the SSC poses a minimal barrier to current flow across it, thereby facilitating rapid delivery of voltage excitation to the prestin-embedded lateral membrane.     

Predicting spike timing of neocortical pyramidal neurons by simple threshold models

Neurons generate spikes reliably with millisecond precision if driven by a fluctuating current—is it then possible to predict the spike timing knowing the input? We determined parameters of an adapting threshold model using data recorded in vitro from 24 layer 5 pyramidal neurons from rat somatosensory cortex, stimulated intracellularly by a fluctuating current simulating synaptic bombardment in vivo. The model generates output spikes whenever the membrane voltage (a filtered version of the input current) reaches a dynamic threshold. We find that for input currents with large fluctuation amplitude, up to 75% of the spike times can be predicted with a precision of ±2 ms. Some of the intrinsic neuronal unreliability can be accounted for by a noisy threshold mechanism. Our results suggest that, under random current injection into the soma, (i) neuronal behavior in the subthreshold regime can be well approximated by a simple linear filter; and (ii) most of the nonlinearities are captured by a simple threshold process.     

Random currents through nerve membranes

The linear cable equation with uniform Poisson or white noise input current is employed as a model for the voltage across the membrane of a onedimensional nerve cylinder, which may sometimes represent the dendritic tree of a nerve cell. From the Green's function representation of the solutions, the mean, variance and covariance of the voltage are found. At large times, the voltage becomes asymptotically wide-sense stationary and we find the spectral density functions for various cable lengths and boundary conditions. For large frequencies the voltage exhibits “1/f ^3/2 noise”. Using the Fourier series representation of the voltage we study the moments of the firing times for the diffusion model with numerical techniques, employing a simplified threshold criterion. We also simulate the solution of the stochastic cable equation by two different methods in order to estimate the moments and density of the firing time.