Theoretical analysis of the firing pattern of a neuron with stationary N-shaped current voltage characteristic of its dendritic membrane

To confirm the hypothesis of the N-shaped current-voltage characteristic curve of slow ionic currents of the dendritic membrane the role of processes taking place on that membrane in organization of the firing pattern of the nerve cells was examined. On a mathematical model dependence of discharge frequency on strength of depolarizing current can be divided into two ranges. The second range of sharply increased steepness of the curve of discharge frequency versus current can be explained by transitions of the distal parts of the dendrites from resting potential to persistent depolarization. The possibility of hysteresis of the frequency-current curve is postulated and the spontaneous discharge of neurons as an off-response to strong depolarization is explained.     

Application of the Goldman-Hodgkin-Katz current equation to membrane current-voltage data

A new approach for the analysis of current-voltage (IV) data is presented and applied to a variety of published data collected from various systems. Our analysis of published results shows that our method of analysis can account for the observed IV data. The calculated permeability coefficients are in reasonable agreement with those calculated from ion fluxes. In those cases where two ions are assumed to carry the current, the ratios of the calculated permeability coefficients are in agreement with those ratios determined from the Goldman-Hodgkin-Katz voltage equation. In most cases, the entire IV curve can be accounted for by using our method of analysis. In several examples, only a portion of the IV curve is in agreement with the predictions. We attribute the failure to account for the IV data to reflect the failure of one or more of the assumptions used by the GHK current equation. In other cases, assuming that an additional ion carries the current, the treatment can account for the IV data. However, the identity of the extra ion cannot be established from these published data without additional studies (e.g., ionic replacement studies).     

Experimental demonstration of relations between the action potential and the stationary current-voltage characteristic of the ranvier-node

Summary At the Ranvier-Node a stationary current-voltage-characteristic containing a differential negative resistance can be measured, if there is a sufficient number of stationary conducted ions such as K·, Rb· or, in the presence ofveratridine, Na·, Li·, NH₄·, C(NH₂)₃· in the outer solution. The membrane has two different positive conductivities in two voltage regions. The negative resistance is formed by the continous change-over between these two conductivities in a voltage-region of constant width and position (transition region). Actionpotentials can be triggered only at such nodes which show a real negative resistance and only by such stimulating pulses which extend into the negative resistance range. This paper deals with one of the experiments which shows the necessity of these conditions.

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Zusammenfassung Am Ranvierschen Schnürring ist eine Strom-Spannungs-Charakteristik mit einem differentiellen negativen Widerstand stationär meßbar, wenn in ausreichender Menge solche Ladungsträger in der äußeren Lösung vorhanden sind, für die die Membran stationär leitfähig ist und die daher das Membranpotential bestimmen können, wie z. B. K·, (bzw. Rb) oder, bei Anwesenheit vonVeratridin, auch Na· [bzw. Lr·, NH₄·, C(NH₂)₃·]. Der negative Widerstand entsteht dadurch, daß die Membran in zwei Spannungsbereichen zwei verschieden große positive Leitfähigkeiten besitzt, die in einem Spannungsbereich von konstanter Lage und Breite (Übergangsbereich) stetig ineinander übergehen. Es sind nur an solchen Schnürringen Aktionspotentiale anslösbar, die diesen reellen negativen Widerstand tatsächlich besitzen und nur dann, wenn er durch den Reiz angesteuert wird. In der vorliegenden Arbeit wird eines der Experimente beschrieben, die die Notwendigkeit dieser Bedingungen veranschaulichen.

     

Effect of natural convection on the current-voltage characteristic of a DC discharge in neon at intermediate pressures

The parameters of the positive column of a glow discharge in neon are calculated with allowance for the induced hydrodynamic motion. It is shown that natural convection in the pressure range of ∼0.1 atm significantly affects the profiles of the parameters of the positive column and its current-voltage characteristic. The convection arising at large deposited energies improves heat removal, due to which the temperature in the central region of the discharge becomes lower than that calculated from the heat conduction equation. As a result, the current-voltage characteristic is shifted. With allowance for convection, the current-voltage characteristic changes at currents much lower than the critical current at which a transition into the constricted state is observed. This change is uniquely related to the Rayleigh number in the discharge. Thus, a simplified analysis of thermal conduction and diffusion, even with detailed account of kinetic processes occurring in the positive column, does not allow one to accurately calculate the current-voltage characteristic and other discharge parameters at intermediate gas pressures.     

Change of current-voltage characteristics of amphotericin B ion channels accompanying its incorporation into the membrane

Non-linearity of amphotericin B current-voltage characteristics is determined by means of the third harmonic generated in the membrane. A change of the sign of non-linearity is revealed during incorporation of antibiotic molecules into a membrane, i. e. the incorporation is not a simple increase of the number of similar ionic channels in the membrane.     

Interaction of variable bacterial outer membrane lipoproteins with brain endothelium

Background

Previously we reported that the variable outer membrane lipoprotein Vsp1 from the relapsing fever spirochete Borrelia turicatae disseminates from blood to brain better than the closely related Vsp2 [1]. Here we studied the interaction between Vsp1 and Vsp2 with brain endothelium in more detail.

Methodology/Principal Findings

We compared Vsp1 to Vsp2 using human brain microvascular endothelial cell (HBMEC) association assays with aminoacid radiolabeled Vsp-expressing clones of recombinant Borrelia burgdorferi and lanthanide-labeled purified lipidated Vsp1 (LVsp1) and Vsp2 (LVsp2) and inoculations of the lanthanide-labeled proteins into mice. The results showed that heterologous expression of LVsp1 or LVsp2 in B. burgdorferi increased its association with HBMEC to a similar degree. Purified lanthanide-labeled lipidated Vsp1 (LVsp1) and LVsp2 by themselves were capable of associating with HBMEC. The association of LVsp1 with brain endothelium was time-dependent, saturable, and required the lipidation. The association of Vsp1 with HBMEC was inhibited by incubation at lower temperature or with excess unlabeled LVsp1 or LVsp2 but not with excess rVsp1 or mouse albumin or an anti Vsp1 monoclonal antibody. The association of LVsp2 with HBMEC and its movement from blood to brain parenchyma significantly increased in the presence of LVsp1.

Conclusions/Significance

Variable bacterial outer membrane lipoproteins interact with brain endothelium differently; the lipidation and variable features at the protein dome region are key modulators of this interaction.     

Modeling the role of lateral membrane diffusion in AMPA receptor trafficking along a spiny dendrite

AMPA receptor trafficking in dendritic spines is emerging as a major postsynaptic mechanism for the expression of plasticity at glutamatergic synapses. AMPA receptors within a spine are in a continuous state of flux, being exchanged with local intracellular pools via exo/endocytosis and with the surrounding dendrite via lateral membrane diffusion. This suggests that one cannot treat a single spine in isolation. Here we present a model of AMPA receptor trafficking between multiple dendritic spines distributed along the surface of a dendrite. Receptors undergo lateral diffusion within the dendritic membrane, with each spine acting as a spatially localized trap where receptors can bind to scaffolding proteins or be internalized through endocytosis. Exocytosis of receptors occurs either at the soma or at sites local to dendritic spines via constitutive recycling from intracellular pools. We derive a reaction–diffusion equation for receptor trafficking that takes into account these various processes. Solutions of this equation allow us to calculate the distribution of synaptic receptor numbers across the population of spines, and hence determine how lateral diffusion contributes to the strength of a synapse. A number of specific results follow from our modeling and analysis. (1) Lateral membrane diffusion alone is insufficient as a mechanism for delivering AMPA receptors from the soma to distal dendrites. (2) A source of surface receptors at the soma tends to generate an exponential-like distribution of receptors along the dendrite, which has implications for synaptic democracy. (3) Diffusion mediates a heterosynaptic interaction between spines so that local changes in the constitutive recycling of AMPA receptors induce nonlocal changes in synaptic strength. On the other hand, structural changes in a spine following long term potentiation or depression have a purely local effect on synaptic strength. (4) A global change in the rates of AMPA receptor exo/endocytosis is unlikely to be the sole mechanism for homeostatic synaptic scaling. (5) The dynamics of AMPA receptor trafficking occurs on multiple timescales and varies according to spatial location along the dendrite. Understanding such dynamics is important when interpreting data from inactivation experiments that are used to infer the rate of relaxation to steady-state.     

Enhanced negative slope of the readiness potential preceding a target force production task

Readiness potentials (RPs) preceding a trigger pulling movement were recorded in 9 right-handed male subjects. We investigated two tasks, non-purposive and purposive movement tasks. In this study we defined simple trigger pull as non-purposive, and target force production by pulling the trigger as purposive. In the non-purposive task, the subjects were instructed to pull the trigger at their own pace and at an easily-exerted force level. After two sessions in the non-purposive movement task, the subjects were submitted to the purposive movement task, and were requested to pull the trigger in an attempt to produce target force, the range of which was decided individually on the basis of mean force level in the second session of the non-purposive movement task. The RP preceding the purposive movement was larger than that preceding the non-purposive movement. In addition, enhancement of the RP was specific to the negative slope (NS′). Since neither peak force nor time to peak force of the movement differed in the two tasks, it was concluded that the increased NS′ was due to a psychological change associated with execution of the purposive movement.     

A study of the current-voltage relationships of electrogenetic active and passive membrane elements in riccia fluitans

Potassium- and proton-dependent membrane potential, conductance, and current-voltage characteristics (I–V curves) have been measured on rhizoid cells of the liverwort Riccia fluitans. The potential difference (E_m) measured with microelectrodes across plasmalemma and tonoplast is depolarized to the potassium-sensitive diffusion potential (E_D) in the presence of 1 mM NaCN, 1 mM NaN₃, or at temperatures below 6°C. Whereas the temperature change from 25°C to 5°C decreases the membrane conductance (g_m) from 0.71 to 0.43 S ? m^?2, 1 mM NaCN increases g_m by about 25%. The membrane displays potassium-controlled rectification which gradually disappears at temperatures below 5°C. The potassium pathway can be described by an equivalent circuit of a diode and an ohmic resistor in parallel. In the potential interval of E_D ± 100 mV the measured I-V curves roughly fit the theoretical curves obtained from a modified diode equation. ⁸⁶Rb⁺(K⁺)-influx is voltage sensitive: In the presence of 1 mM NaCN, ⁸⁶Rb⁺-influx follows a hyperbolic function corresponding to a low conductance at low [K⁺]_o and high conductance at high [K⁺]_o. On the contrary ⁸⁶Rb⁺-influx is linear with [K⁺]_o when pump activity is normal. It is believed that there are two K⁺-transport pathways in the Riccia membrane, one of which is assigned to the low conductance (0.2 S · m^?2), the other to a temperature-dependent facilitated diffusion system with a higher conductance (7.7 S · m^?2). The electrogenic pump essentially acts as a current source and consumes about 39% of the cellular ATP-turnover. In the presence of 30 μM CCCP the saturation current of 0.1 A · m^?2 is doubled to about 0.2 A · m^?2, and the electromotive force of ?360 mV switches to ?250 mV. It is suggested that this may be due to a change in stoichiometry from one to two transported charges per ATP hydrolyzed.     

The characteristic region of arenicin-1 involved with a bacterial membrane targeting mechanism

The antimicrobial peptide arenicin-1 consists of two antiparallel β-sheets linked by a hydrophilic β-turn. To determine the role of a specific region found in a particular β-sheet structure of the peptide for antibacterial activity, two analogs with N-terminal deletions (RW) and substitutions of Arg to Ala in the β-turn region were designed. In the minimum inhibitory concentration (MIC) test, the antibacterial activities of the analogs were reduced for both Gram-positive and Gram-negative bacteria, when compared to arenicin-1. The influence of the decrease in hydrophobicity on the antibacterial activity was confirmed by a hemolytic assay. Through flow cytometric analysis using propidium iodide (PI) and a 1,6-diphenyl-1,3,5-hexatriene (DPH) assay, it was confirmed that the analogs decreased the degree of plasma membrane permeability compared to arenicin-1. In particular, analog 2 showed a lower permeability in Gram-negative bacteria than in Gram-positive bacteria. The results indicate that a reduction in the net charge weakened the electrostatic interactions between the peptides and the negatively charged membranes. In liposomes, which mimic bacterial membranes, due to a reduced binding affinity to the membranes, the analogs could not deeply penetrate into the hydrocarbon region and induce enough fluorescein isothiocyanate-dextran (FD) leakage compared to that of arenicin-1. It is thought that the Arg residue in the hydrophilic β-turn region is more important to antibacterial activity than the Arg residue in the N-terminal region. This study suggests that the Arg and Trp residues in the N-terminal region and the Arg residue in the β-turn region of arenicin-1 play a key role in antibacterial activity.     

黄土高原阴/阳坡向林草土壤水分随退耕年限的变化特征

研究地点位于半干旱的黄土高原区,在坡向导致的土壤水分差异的基础上,分析该区域撂荒草地和人工林地土壤水分随退耕年限的变化特征,进而以自然草地为参照,分析不同坡向人工林地土壤水分亏缺程度。结果表明:总体上,阴坡土壤水分显著高于阳坡,撂荒草地、自然草地和林地土壤水分在阴/阳坡之间的差异分别为:3.1%、2.6%、1.5%;可见,人工林地降低了由坡向导致的土壤水分的差异。在阴/阳坡上,撂荒草地土壤水分随退耕年限增加皆呈显著增加趋势,并且,总体上,土壤水分的增加程度随年限增加而增大,尤其在深层的土壤水分。而林地土壤水分在阴坡和阳坡皆呈显著降低的趋势;通过对比阴/阳坡不同土层土壤水分随退耕年限变化趋势,阳坡人工林地上层土壤水分(0—1m和1—2m)随年限增加降低程度有所减少,然而,较深层(2—3m和3—4m)土壤水分在后期降低程度更大,而阴坡土壤水分随年限增加的降低程度呈现与阳坡相反的趋势;人工刺槐林地导致的土壤水分亏缺程度(以自然草地土壤水分为参考)随着年限增加呈增加趋势,且随深度增加呈增加趋势,总体上,阳坡人工林地除0—1m土层的土壤水分亏缺程度高于阴坡,其余土层平均土壤水分亏缺程度在前、中、后期皆低于阴坡。     

A membrane preparation that contains proteins characteristic of the rough endoplasmic reticulum

We describe a procedure for disassembling rat liver rough microsomes, which allows the purification of the rough endoplasmic reticulum (ER) membrane. Membrane-bound ribosomes and adsorbed proteins are first detached by washing rough microsomes with 5 mM Na-pyrophosphate. In a second step, the vesicle membrane is opened by digitonin, with concomitant release of the luminal content. The purification is monitored at each step by electron microscopy, and by assaying chemical constituents (protein, phospholipid, RNA) and marker enzymes for the main subcellular organelles. The final membrane preparation is representative of the ER, since it contains 24.1% of the liver glucose 6-phosphatase with a relative specific activity of 14.2. Contaminants represent less than 5% of its protein content. SDS-polyacrylamide gel electrophoresis, followed by immunoblot analysis, reveals that the ribophorins I and II, two established markers of the rough (d) domain are still present in the final membrane preparation. It also contains the docking protein (or signal recognition particle receptor) and protein disulfide isomerase, and has conserved the functional capacity to remove co- and post-translationally the signal peptide of pre-secretory proteins. The membrane preparation is suitable for studies on the polypeptide composition of the d domain.     

Localization and quantitation of proteins characteristic of the complexed membrane of Bacillus subtilis

We prepared antibodies to four proteins (molecular weights, 68,000, 64,000, 45,000, and 31,000) that are characteristic of the complexed (ribosome-bearing) fraction of the membrane of Bacillus subtilis and found that these proteins are immunologically distinct. Quantitation by immunoprecipitation confirmed that the ribosome-free membrane fraction contains much lower concentrations of these four proteins than the complexed-membrane fraction. The 64-kilodalton protein appeared to be attached more loosely than the other proteins, since it was more readily extracted from the membrane. In addition, this protein was also present in the cytosol in an even greater amount than in the membrane. The 68-, 64-, and 31-kilodalton proteins are present in cells in stoichiometrically equivalent amounts.     

Calcium-potassium selectivity: kinetic analysis of current-voltage relationships of the open, slowly activating channel in the vacuolar membrane of Vicia faba guard-cells

Single-channel current-voltage (IV ) relationships of the open, slowly activating vacuolar (SV) channel of Vicia faba L. were recorded in solutions with different activities of Ca²⁺ and K⁺, and have been analyzed for Ca²⁺/K⁺ selectivity. Two models with one binding site have been examined. A rigid-pore model with a main binding site between two energy barriers (nine free parameters) provides fair fits. Slightly better fits are obtained with an alternative, dynamic-pore model, where the selectivity filter is located between two Mitchellian ion wells of the cytoplasmic and luminal pore sections, and where the selectivity filter alternates the orientation of the binding site between the two faces of the pore (ten free parameters). Using sets of IV-relationships with only Ca²⁺ or only K⁺ as transportable substrates, both models consistently predict open-channel IV-relationships in the presence of both substrates. Fits of both models to the entire ensemble of␣data yield very similar flux-voltage characteristics for␣Ca²⁺ and for K⁺ in experimental conditions, and consistently predict such flux-voltage characteristics over physiologically relevant ranges of voltage and substrate concentrations. In a very general sense, physiological Ca⁺ fluxes through the open SV channel are predominantly inward and about 50 times smaller than K⁺ fluxes. The ions Cl⁻, OH⁻, and H⁺, do not pass the SV channel at significant rates. Kinetic details of the SV channel with respect to binding and passage of Ca²⁺ and K⁺ are discussed on the basis of the consistent results of the reaction-kinetic analysis of the experimental data by the two models. Received: 14 July 1997 / Accepted: 26 September 1997     

Properties of extracellular monosynaptic potential of a single afferent in the light of the theory of dendrites with N-shaped volt-ampere characteristics

In the frog tectum mass extracellular monosynaptic PSP of the set of synapses of one individual afferent--the quantum of EEG--was registered. Using the electrical threshold stimulation of the retina we noticed a large pair facilitation. The radial decline of the facilitated quantum of EEG was measured in order to check the conclusions of the dendritic theory which postulates the N-shaped current-voltage characteristic of the membrane. Therefore, we synchronously derived conditional and test quanta of EEG in the centre and 40-60 microns peripherally of terminal axonal arborization. In a half of the experiments the test quantum of EEG twice as large as the conditional one radially declined 25% less. The half-width and rise-time of the test quantum of EEG were longer as compared with the conditional one, especially in the peripheric derivation, the difference being about 1 ms. The totality of our results agrees with the concept of electrically excitable inward current in non-synaptic membrane of the apical dendrites in the tectum. The current is predicted by the theory of the N-shaped current-voltage characteristic of dendrites.