A Special Perturbation Method in Orbital Dynamics

Bead models are used in dynamical simulation of tethers. These models discretize a cable using beads distributed along its length. The time evolution is obtained nu- merically. Typically the number of particles ranges between 5 and 50, depending on the required accuracy. Sometimes the simulation is extended over long periods (several years). The complex interactions between the cable and its spatial environment require to optimize the propagators —both in runtime and precisión that constitute the central core of the process. The special perturbation method treated on this article conjugates simpleness of computer implementation, speediness and precision, and is capable to propagate the orbit of whichever material particle. The paper describes the evolution of some orbital elements, which are constants in a non-perturbed problem, but which evolve in the time scale imposed by the perturbation. It can be used with any kind of orbit and it is free of sin- gularities related to small inclination and/or small eccentricity. The use of Euler parameters makes it robust.

Low Work-Function Thermionic Emission and Orbital-Motion-Limited Ion Collection at Bare-Tether Cathodic Contact

Una amarra electrodinámica (electrodynamic tether) opera sobre principios electromagnéticos intercambiando momento con la magnetosfera planetaria e interactuando con su ionosfera. Es un subsistema pasivo fiable para desorbitar etapas de cohetes agotadas y satélites al final de su misión, mitigando el crecimiento de la basura espacial. Una amarra sin aislamiento captura electrones del plasma ambiente a lo largo de su segmento polarizado positivamente, el cual puede alcanzar varios kilómetros de longitud, mientras que emite electrones de vuelta al plasma mediante un contactor de plasma activo de baja impedancia en su extremo catódico, tal como un cátodo hueco (hollow cathode). En ausencia de un contactor catódico activo, la corriente que circula por una amarra desnuda en órbita es nula en ambos extremos de la amarra y se dice que ésta está flotando eléctricamente. Para emisión termoiónica despreciable y captura de corriente en condiciones limitadas por movimiento orbital (orbital-motion-limited, OML), el cociente entre las longitudes de los segmentos anódico y catódico es muy pequeño debido a la disparidad de masas entre iones y electrones. Tal modo de operación resulta en una corriente media y fuerza de Lorentz bajas en la amarra, la cual es poco eficiente como dispositivo para desorbitar. El electride C12A7 : e−, que podría presentar una función de trabajo (work function) tan baja como W = 0.6 eV y un comportamiento estable a temperaturas relativamente altas, ha sido propuesto como recubrimiento para amarras desnudas. La emisión termoiónica a lo largo de un segmento así recubierto y bajo el calentamiento de la operación espacial, puede ser más eficiente que la captura iónica. En el modo más simple de fuerza de frenado, podría eliminar la necesidad de un contactor catódico activo y su correspondientes requisitos de alimentación de gas y subsistema de potencia, lo que resultaría en un sistema real de amarra “sin combustible”. Con este recubrimiento de bajo W, cada segmento elemental del segmento catódico de una amarra desnuda de kilómetros de longitud emitiría corriente como si fuese parte de una sonda cilíndrica, caliente y uniformemente polarizada al potencial local de la amarra. La operación es similar a la de una sonda de Langmuir 2D tanto en los segmentos catódico como anódico. Sin embargo, en presencia de emisión, los electrones emitidos resultan en carga espacial (space charge) negativa, la cual reduce el campo eléctrico que los acelera hacia fuera, o incluso puede desacelerarlos y hacerlos volver a la sonda. Se forma una doble vainas (double sheath) estable con electrones emitidos desde la sonda e iones provenientes del plasma ambiente. La densidad de corriente termoiónica, variando a lo largo del segmento catódico, podría seguir dos leyes distintas bajo diferentes condiciones: (i) la ley de corriente limitada por la carga espacial (space-charge-limited, SCL) o (ii) la ley de Richardson-Dushman (RDS). Se presenta un estudio preliminar sobre la corriente SCL frente a una sonda emisora usando la teoría de vainas (sheath) formada por la captura iónica en condiciones OML, y la corriente electrónica SCL entre los electrodos cilíndricos según Langmuir. El modelo, que incluye efectos óhmicos y el efecto de transición de emisión SCL a emisión RDS, proporciona los perfiles de corriente y potencial a lo largo de la longitud completa de la amarra. El análisis muestra que en el modo más simple de fuerza de frenado, bajo condiciones orbitales y de amarras típicas, la emisión termoiónica proporciona un contacto catódico eficiente y resulta en una sección catódica pequeña. En el análisis anterior, tanto la transición de emisión SCL a RD como la propia ley de emisión SCL consiste en un modelo muy simplificado. Por ello, a continuación se ha estudiado con detalle la solución de vaina estacionaria de una sonda con emisión termoiónica polarizada negativamente respecto a un plasma isotrópico, no colisional y sin campo magnético. La existencia de posibles partículas atrapadas ha sido ignorada y el estudio incluye tanto un estudio semi-analítico mediante técnica asintóticas como soluciones numéricas completas del problema. Bajo las tres condiciones (i) alto potencial, (ii) R = Rmax para la validez de la captura iónica OML, y (iii) potencial monotónico, se desarrolla un análisis asintótico auto-consistente para la estructura de plasma compleja que contiene las tres especies de cargas (electrones e iones del plasma, electrones emitidos), y cuatro regiones espaciales distintas, utilizando teorías de movimiento orbital y modelos cinéticos de las especies. Aunque los electrones emitidos presentan carga espacial despreciable muy lejos de la sonda, su efecto no se puede despreciar en el análisis global de la estructura de la vaina y de dos capas finas entre la vaina y la región cuasi-neutra. El análisis proporciona las condiciones paramétricas para que la corriente sea SCL. También muestra que la emisión termoiónica aumenta el radio máximo de la sonda para operar dentro del régimen OML y que la emisión de electrones es mucho más eficiente que la captura iónica para el segmento catódico de la amarra. En el código numérico, los movimientos orbitales de las tres especies son modelados para potenciales tanto monotónico como no-monotónico, y sonda de radio R arbitrario (dentro o más allá del régimen de OML para la captura iónica). Aprovechando la existencia de dos invariante, el sistema de ecuaciones Poisson-Vlasov se escribe como una ecuación integro-diferencial, la cual se discretiza mediante un método de diferencias finitas. El sistema de ecuaciones algebraicas no lineal resultante se ha resuelto de con un método Newton-Raphson paralelizado. Los resultados, comparados satisfactoriamente con el análisis analítico, proporcionan la emisión de corriente y la estructura del plasma y del potencial electrostático. ABSTRACT An electrodynamic tether operates on electromagnetic principles and exchanges momentum through the planetary magnetosphere, by continuously interacting with the ionosphere. It is a reliable passive subsystem to deorbit spent rocket stages and satellites at its end of mission, mitigating the growth of orbital debris. A tether left bare of insulation collects electrons by its own uninsulated and positively biased segment with kilometer range, while electrons are emitted by a low-impedance active device at the cathodic end, such as a hollow cathode, to emit the full electron current. In the absence of an active cathodic device, the current flowing along an orbiting bare tether vanishes at both ends and the tether is said to be electrically floating. For negligible thermionic emission and orbital-motion-limited (OML) collection throughout the entire tether (electron/ion collection at anodic/cathodic segment, respectively), the anodic-to-cathodic length ratio is very small due to ions being much heavier, which results in low average current and Lorentz drag. The electride C12A7 : e−, which might present a possible work function as low as W = 0.6 eV and moderately high temperature stability, has been proposed as coating for floating bare tethers. Thermionic emission along a thus coated cathodic segment, under heating in space operation, can be more efficient than ion collection and, in the simplest drag mode, may eliminate the need for an active cathodic device and its corresponding gas-feed requirements and power subsystem, which would result in a truly “propellant-less” tether system. With this low-W coating, each elemental segment on the cathodic segment of a kilometers-long floating bare-tether would emit current as if it were part of a hot cylindrical probe uniformly polarized at the local tether bias, under 2D probe conditions that are also applied to the anodic-segment analysis. In the presence of emission, emitted electrons result in negative space charge, which decreases the electric field that accelerates them outwards, or even reverses it, decelerating electrons near the emitting probe. A double sheath would be established with electrons being emitted from the probe and ions coming from the ambient plasma. The thermionic current density, varying along the cathodic segment, might follow two distinct laws under different con ditions: i) space-charge-limited (SCL) emission or ii) full Richardson-Dushman (RDS) emission. A preliminary study on the SCL current in front of an emissive probe is presented using the orbital-motion-limited (OML) ion-collection sheath and Langmuir’s SCL electron current between cylindrical electrodes. A detailed calculation of current and bias profiles along the entire tether length is carried out with ohmic effects considered and the transition from SCL to full RDS emission is included. Analysis shows that in the simplest drag mode, under typical orbital and tether conditions, thermionic emission provides efficient cathodic contact and leads to a short cathodic section. In the previous analysis, both the transition between SCL and RDS emission and the current law for SCL condition have used a very simple model. To continue, considering an isotropic, unmagnetized, colissionless plasma and a stationary sheath, the probe-plasma contact is studied in detail for a negatively biased probe with thermionic emission. The possible trapped particles are ignored and this study includes both semianalytical solutions using asymptotic analysis and complete numerical solutions. Under conditions of i) high bias, ii) R = Rmax for ion OML collection validity, and iii) monotonic potential, a self-consistent asymptotic analysis is carried out for the complex plasma structure involving all three charge species (plasma electrons and ions, and emitted electrons) and four distinct spatial regions using orbital motion theories and kinetic modeling of the species. Although emitted electrons present negligible space charge far away from the probe, their effect cannot be neglected in the global analysis for the sheath structure and two thin layers in between the sheath and the quasineutral region. The parametric conditions for the current to be space-chargelimited are obtained. It is found that thermionic emission increases the range of probe radius for OML validity and is greatly more effective than ion collection for cathodic contact of tethers. In the numerical code, the orbital motions of all three species are modeled for both monotonic and non-monotonic potential, and for any probe radius R (within or beyond OML regime for ion collection). Taking advantage of two constants of motion (energy and angular momentum), the Poisson-Vlasov equation is described by an integro differential equation, which is discretized using finite difference method. The non-linear algebraic equations are solved using a parallel implementation of the Newton-Raphson method. The results, which show good agreement with the analytical results, provide the results for thermionic current, the sheath structure, and the electrostatic potential.

Low work-function thermionic emission and orbital-motion-limited ion collection at bare-tether cathodic contact

With a thin coating of low-work-function material, thermionic emission in the cathodic segment of bare tethers might be much greater than orbital-motion-limited (OML) ion collection current. The space charge of the emitted electrons decreases the electric field that accelerates them outwards, and could even reverse it for high enough emission, producing a potential hollow. In this work, at the conditions of high bias and relatively low emission that make the potential monotonic, an asymptotic analysis is carried out, extending the OML ion-collection analysis to investigate the probe response due to electrons emitted by the negatively biased cylindrical probe. At given emission, the space charge effect from emitted electrons increases with decreasing magnitude of negative probe bias. Although emitted electrons present negligible space charge far away from the probe, their effect cannot be neglected in the global analysis for the sheath structure and two thin layers in between sheath and the quasineutral region. The space-charge-limited condition is located. It is found that thermionic emission increases the range of probe radius for OML validity and is greatly more effective than ion collection for cathodic contact of tethers.

R-type Ca2+ currents evoke transmitter release at a rat central synapse

Voltage-dependent Ca2+ currents evoke synaptic transmitter release. Of six types of Ca2+ channels, L-, N-, P-, Q-, R-, and T-type, only N- and P/Q-type channels have been pharmacologically identified to mediate action-potential-evoked transmitter release in the mammalian central nervous system. We tested whether Ca2+ channels other than N- and P/Q-type control transmitter release in a calyx-type synapse of the rat medial nucleus of the trapezoid body. Simultaneous recordings of presynaptic Ca2+ influx and the excitatory postsynaptic current evoked by a single action potential were made at single synapses. The R-type channel, a high-voltage-activated Ca2+ channel resistant to L-, N-, and P/Q-type channel blockers, contributed 26% of the total Ca2+ influx during a presynaptic action potential. This Ca2+ current evoked transmitter release sufficiently large to initiate an action potential in the postsynaptic neuron. The R-type current controlled release with a lower efficacy than other types of Ca2+ currents. Activation of metabotropic glutamate receptors and γ-aminobutyric acid type B receptors inhibited the R-type current. Because a significant fraction of presynaptic Ca2+ channels remains unidentified in many other central synapses, the R-type current also could contribute to evoked transmitter release in these synapses.

Antisense oligonucleotides against α1E reduce R-type calcium currents in cerebellar granule cells

Many neurons of the central nervous system display multiple high voltage-activated Ca2+ currents, pharmacologically classified as L-, N-, P-, Q-, and R-type. Of these current types, the R-type is the least understood. The leading candidate for the molecular correlate of R-type currents in cerebellar granule cells is the α1E subunit, which yields Ca2+ currents very similar to the R-type when expressed in heterologous systems. As a complementary approach, we tested whether antisense oligonucleotides against α1E could decrease the expression of R-type current in rat cerebellar granule neurons in culture. Cells were supplemented with either antisense or sense oligonucleotides and whole-cell patch clamp recordings were obtained after 6–8 days in vitro. Incubation with α1E antisense oligonucleotide caused a 52.5% decrease in the peak R-type current density, from −10 ± 0.6 picoamperes/picofarad (pA/pF) (n = 6) in the untreated controls to −4.8 ± 0.8 pA/pF (n = 11) (P < 0.01). In contrast, no significant changes in the current expression were seen in sense oligonucleotide-treated cells (−11.3 ± 3.2 pA/pF). The specificity of the α1E antisense oligonucleotides was supported by the lack of change in estimates of the P/Q current amplitude. Furthermore, antisense and sense oligonucleotides against α1A did not affect R-type current expression (−11.5 ± 1.7 and −11.7 ± 1.7 pA/pF, respectively), whereas the α1A antisense oligonucleotide significantly reduced whole cell currents under conditions in which P/Q current is dominant. Our results support the hypothesis that members of the E class of α1 subunits support the high voltage-activated R-type current in cerebellar granule cells.

Activation and inhibition of K-ATP currents by guanine nucleotides is mediated by different channel subunits

The ATP-sensitive potassium channel (K-ATP channel) plays a key role in insulin secretion from pancreatic β-cells. It is closed by glucose metabolism, which stimulates secretion, and opened by the drug diazoxide, which inhibits insulin release. Metabolic regulation is mediated by changes in ATP and MgADP concentration, which inhibit and potentiate channel activity, respectively. The β-cell K-ATP channel consists of a pore-forming subunit, Kir6.2, and a regulatory subunit, SUR1. The site at which ATP mediates channel inhibition lies on Kir6.2, while the potentiatory action of MgADP involves the nucleotide-binding domains of SUR1. K-ATP channels are also activated by MgGTP and MgGDP. Furthermore, both nucleotides support the stimulatory actions of diazoxide. It is not known, however, whether guanine nucleotides mediate their effects by direct interaction with one or more of the K-ATP channel subunits or indirectly via a GTP-binding protein. We used a truncated form of Kir6.2, which expresses independently of SUR1, to show that GTP blocks K-ATP currents by interaction with Kir6.2 and that the potentiatory effects of GTP are endowed by SUR1. We also showed that mutation of the lysine residue in the Walker A motif of either the first (K719A) or second (K1384M) nucleotide-binding domain of SUR1 abolished both the potentiatory effects of GTP and GDP on K-ATP currents and their ability to support stimulation by diazoxide. This argues that the stimulatory effects of guanine nucleotides require the presence of both Walker A lysines.

Defective γ-aminobutyric acid type B receptor-activated inwardly rectifying K+ currents in cerebellar granule cells isolated from weaver and Girk2 null mutant mice

Stimulation of inhibitory neurotransmitter receptors, such as γ-aminobutyric acid type B (GABAB) receptors, activates G protein-gated inwardly rectifying K+ channels (GIRK) which, in turn, influence membrane excitability. Seizure activity has been reported in a Girk2 null mutant mouse lacking GIRK2 channels but showing normal cerebellar development as well as in the weaver mouse, which has mutated GIRK2 channels and shows abnormal development. To understand how the function of GIRK2 channels differs in these two mutant mice, we compared the G protein-activated inwardly rectifying K+ currents in cerebellar granule cells isolated from Girk2 null mutant and weaver mutant mice with those from wild-type mice. Activation of GABAB receptors in wild-type granule cells induced an inwardly rectifying K+ current, which was sensitive to pertussis toxin and inhibited by external Ba2+ ions. The amplitude of the GABAB receptor-activated current was severely attenuated in granule cells isolated from both weaver and Girk2 null mutant mice. By contrast, the G protein-gated inwardly rectifying current and possibly the agonist-independent basal current appeared to be less selective for K+ ions in weaver but not Girk2 null mutant granule cells. Our results support the hypothesis that a nonselective current leads to the weaver phenotype. The loss of GABAB receptor-activated GIRK current appears coincident with the absence of GIRK2 channel protein and the reduction of GIRK1 channel protein in the Girk2 null mutant mouse, suggesting that GABAB receptors couple to heteromultimers composed of GIRK1 and GIRK2 channel subunits.

Ca2+-induced rebound potentiation of γ-aminobutyric acid-mediated currents requires activation of Ca2+/calmodulin-dependent kinase II

In cerebellar Purkinje neurons, γ-aminobutyric acid (GABA)-mediated inhibitory synaptic transmission undergoes a long-lasting “rebound potentiation” after the activation of excitatory climbing fiber inputs. Rebound potentiation is triggered by the climbing-fiber-induced transient elevation of intracellular Ca2+ concentration and is expressed as a long-lasting increase of postsynaptic GABAA receptor sensitivity. Herein we show that inhibitors of the Ca2+/calmodulin-dependent protein kinase II (CaM-KII) signal transduction pathway effectively block the induction of rebound potentiation. These inhibitors have no effect on the once established rebound potentiation, on voltage-gated Ca2+ channel currents, or on the basal inhibitory transmission itself. Futhermore, a protein phosphatase inhibitor and the intracellularly applied CaM-KII markedly enhanced GABA-mediated currents in Purkinje neurons. Our results demonstrate that CaM-KII activation and the following phosphorylation are key steps for rebound potentiation.

Ablation of P/Q-type Ca2+ channel currents, altered synaptic transmission, and progressive ataxia in mice lacking the α1A-subunit

The Ca2+ channel α1A-subunit is a voltage-gated, pore-forming membrane protein positioned at the intersection of two important lines of research: one exploring the diversity of Ca2+ channels and their physiological roles, and the other pursuing mechanisms of ataxia, dystonia, epilepsy, and migraine. α1A-Subunits are thought to support both P- and Q-type Ca2+ channel currents, but the most direct test, a null mutant, has not been described, nor is it known which changes in neurotransmission might arise from elimination of the predominant Ca2+ delivery system at excitatory nerve terminals. We generated α1A-deficient mice (α1A−/−) and found that they developed a rapidly progressive neurological deficit with specific characteristics of ataxia and dystonia before dying ≈3–4 weeks after birth. P-type currents in Purkinje neurons and P- and Q-type currents in cerebellar granule cells were eliminated completely whereas other Ca2+ channel types, including those involved in triggering transmitter release, also underwent concomitant changes in density. Synaptic transmission in α1A−/− hippocampal slices persisted despite the lack of P/Q-type channels but showed enhanced reliance on N-type and R-type Ca2+ entry. The α1A−/− mice provide a starting point for unraveling neuropathological mechanisms of human diseases generated by mutations in α1A.

Glutamate transporter currents in Bergmann glial cells follow the time course of extrasynaptic glutamate

Glutamate transporters in the central nervous system are expressed in both neurons and glia, they mediate high affinity, electrogenic uptake of glutamate, and they are associated with an anion conductance that is stoichiometrically uncoupled from glutamate flux. Although a complete cycle of transport may require 50–100 ms, previous studies suggest that transporters can alter synaptic currents on a much faster time scale. We find that application of l-glutamate to outside-out patches from cerebellar Bergmann glia activates anion-potentiated glutamate transporter currents that activate in <1 ms, suggesting an efficient mechanism for the capture of extrasynaptic glutamate. Stimulation in the granule cell layer in cerebellar slices elicits all or none α-amino-3-hydroxy-5-methyl-4-isoxazolepropionate receptor and glutamate transporter currents in Bergmann glia that have a rapid onset, suggesting that glutamate released from climbing fiber terminals escapes synaptic clefts and reaches glial membranes shortly after release. Comparison of the concentration dependence of both α-amino-3-hydroxy-5-methyl-4-isoxazolepropionate receptor and glutamate transporter kinetics in patches with the time course of climbing fiber-evoked responses indicates that the glutamate transient at Bergmann glial membranes reaches a lower concentration than attained in the synaptic cleft and remains elevated in the extrasynaptic space for many milliseconds.

Nitric oxide-related species inhibit evoked neurotransmission but enhance spontaneous miniature synaptic currents in central neuronal cultures

Nitric oxide (NO·) does not react significantly with thiol groups under physiological conditions, whereas a variety of endogenous NO donor molecules facilitate rapid transfer to thiol of nitrosonium ion (NO+, with one less electron than NO·). Here, nitrosonium donors are shown to decrease the efficacy of evoked neurotransmission while increasing the frequency of spontaneous miniature excitatory postsynaptic currents (mEPSCs). In contrast, pure NO· donors have little effect (displaying at most only a slight increase) on the amplitude of evoked EPSCs and frequency of spontaneous mEPSCs in our preparations. These findings may help explain heretofore paradoxical observations that the NO moiety can either increase, decrease, or have no net effect on synaptic activity in various preparations.

Stretch-activated single K+ channels account for whole-cell currents elicited by swelling

Functionally significant stretch-activated ion channels have been clearly identified in excitable cells. Although single-channel studies suggest their expression in other cell types, their activity in the whole-cell configuration has not been shown. This discrepancy makes their physiological significance doubtful and suggests that their mechanical activation is artifactual. Possible roles for these molecules in nonexcitable cells are acute cell-volume regulation and, in epithelial cells, the complex adjustment of ion fluxes across individual cell membranes when the rate of transepithelial transport changes. We report the results of experiments on isolated epithelial cells expressing in the basolateral membrane stretch-activated K+ channels demonstrable by the cell-attached patch-clamp technique. In these cells, reversible whole-cell currents were elicited by both isosmotic and hyposmotic cell swelling. Cation selectivity and block by inorganic agents were the same for single-channel and whole-cell currents, indicating that the same entity underlies single-channel and whole-cell currents and that the single-channel events are not artifactual. In these cells, when the rate of apical-membrane NaCl entry increases, the cell Na+ content and volume also increase, stimulating the Na+,K+-ATPase at the basolateral membrane, i.e., both Na+ extrusion and K+ uptake increase. We speculate that, under these conditions, the parallel activation of basolateral K+ channels (by the swelling) elevates conductive K+ loss, tending to maintain the cell K+ content constant (“pump-leak parallelism”). This study describes a physiologically relevant stretch-activated channel, at both the single-channel and whole-cell levels, in a nonneural cell type.

β subunits influence the biophysical and pharmacological differences between P- and Q-type calcium currents expressed in a mammalian cell line

Human epithelial kidney cells (HEK) were prepared to coexpress α1A, α2δ with different β calcium channel subunits and green fluorescence protein. To compare the calcium currents observed in these cells with the native neuronal currents, electrophysiological and pharmacological tools were used conjointly. Whole-cell current recordings of human epithelial kidney α1A-transfected cells showed small inactivating currents in 80 mM Ba2+ that were relatively insensitive to calcium blockers. Coexpression of α1A, βIb, and α2δ produced a robust inactivating current detected in 10 mM Ba2+, reversibly blockable with low concentration of ω-agatoxin IVA (ω-Aga IVA) or synthetic funnel-web spider toxin (sFTX). Barium currents were also supported by α1A, β2a, α2δ subunits, which demonstrated the slowest inactivation and were relatively insensitive to ω-Aga IVA and sFTX. Coexpression of β3 with the same combination as above produced inactivating currents also insensitive to low concentration of ω-Aga IVA and sFTX. These data indicate that the combination α1A, βIb, α2δ best resembles P-type channels given the rate of inactivation and the high sensitivity to ω-Aga IVA and sFTX. More importantly, the specificity of the channel blocker is highly influenced by the β subunit associated with the α1A subunit.