Statistical problems related to excitation threshold and reset value of membrane potentials

Die vorliegende Arbeit ist motiviert durch biologische Fragestellungen bezüglich des Verhaltens von Membranpotentialen in Neuronen. Ein vielfach betrachtetes Modell für spikende Neuronen ist das Folgende. Zwischen den Spikes verhält sich das Membranpotential wie ein Diffusionsprozess X der durch die SDGL dX_t= beta(X_t) dt+ sigma(X_t) dB_t gegeben ist, wobei (B_t) eine Standard-Brown'sche Bewegung bezeichnet. Spikes erklärt man wie folgt. Sobald das Potential X eine gewisse Exzitationsschwelle S überschreitet entsteht ein Spike. Danach wird das Potential wieder auf einen bestimmten Wert x_0 zurückgesetzt. In Anwendungen ist es manchmal möglich, einen Diffusionsprozess X zwischen den Spikes zu beobachten und die Koeffizienten der SDGL beta() und sigma() zu schätzen. Dennoch ist es nötig, die Schwellen x_0 und S zu bestimmen um das Modell festzulegen. Eine Möglichkeit, dieses Problem anzugehen, ist x_0 und S als Parameter eines statistischen Modells aufzufassen und diese zu schätzen. In der vorliegenden Arbeit werden vier verschiedene Fälle diskutiert, in denen wir jeweils annehmen, dass das Membranpotential X zwischen den Spikes eine Brown'sche Bewegung mit Drift, eine geometrische Brown'sche Bewegung, ein Ornstein-Uhlenbeck Prozess oder ein Cox-Ingersoll-Ross Prozess ist. Darüber hinaus beobachten wir die Zeiten zwischen aufeinander folgenden Spikes, die wir als iid Treffzeiten der Schwelle S von X gestartet in x_0 auffassen. Die ersten beiden Fälle ähneln sich sehr und man kann jeweils den Maximum-Likelihood-Schätzer explizit angeben. Darüber hinaus wird, unter Verwendung der LAN-Theorie, die Optimalität dieser Schätzer gezeigt. In den Fällen OU- und CIR-Prozess wählen wir eine Minimum-Distanz-Methode, die auf dem Vergleich von empirischer und wahrer Laplace-Transformation bezüglich einer Hilbertraumnorm beruht. Wir werden beweisen, dass alle Schätzer stark konsistent und asymptotisch normalverteilt sind. Im letzten Kapitel werden wir die Effizienz der Minimum-Distanz-Schätzer anhand simulierter Daten überprüfen. Ferner, werden Anwendungen auf reale Datensätze und deren Resultate ausführlich diskutiert.

Separate neuronal and glial Na+,K+-ATPase isoforms regulate glucose utilization in response to membrane depolarization and elevated extracellular potassium.

The role of cell type-specific Na+,K+-ATPase isozymes in function-related glucose metabolism was studied using differentiated rat brain cell aggregate cultures. In mixed neuron-glia cultures, glucose utilization, determined by measuring the rate of radiolabeled 2-deoxyglucose accumulation, was markedly stimulated by the voltage-dependent sodium channel agonist veratridine (0.75 micromol/L), as well as by glutamate (100 micromol/L) and the ionotropic glutamate receptor agonist N-methyl-D-aspartate (NMDA) (10 micromol/L). Significant stimulation also was elicited by elevated extracellular potassium (12 mmol/L KCl), which was even more pronounced at 30 mmol/L KCl. In neuron-enriched cultures, a similar stimulation of glucose utilization was obtained with veratridine, specific ionotropic glutamate receptor agonists, and 30 mmol/L but not 12 mmol/L KCl. The effects of veratridine, glutamate, and NMDA were blocked by specific antagonists (tetrodotoxin, CNQX, or MK801, respectively). Low concentrations of ouabain (10(-6) mol/L) prevented stimulation by the depolarizing agents but reduced only partially the response to 12 mmol/L KCl. Together with previous data showing cell type-specific expression of Na+,K+-ATPase subunit isoforms in these cultures, the current results support the view that distinct isoforms of Na+,K+-ATPase regulate glucose utilization in neurons in response to membrane depolarization, and in glial cells in response to elevated extracellular potassium.

Influence of fixed electric charges on potential profile across the squid axon membrane

The potential profile for a model of squid axon membrane has been determined for two physiological states: resting and action states. The non-linear Poisson-Boltzmann equation has been solved by considering the volumetric charge densities due to charges dissolved in an electrolytic solution and fixed on both glycocalyx and cytoplasmatic proteins. Results showing the features of the potential profile along the outer electrolytic region are similar for both resting and action states. However, the potential fall along glycocalyx at action state is lower than at resting. A small variation in the Na+ concentration drastically affects the surface membrane potentials and vice versa. We conclude that effects on the potential profile due to surface lipidic bilayer charge and contiguous electric double layers are more relevant than those provoked by fixed charges distributed along the cell cytoplasm. (c) 2007 Elsevier B.V. All rights reserved.

Effect of manganese supplementation on the membrane integrity and the mitochondrial potential of the sperm of grazing Nelore bulls

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Excitatory synaptic inputs to pyramidal neurons of the lateral amygdala

Whole-cell patch clamp recordings were made from pyramidal neurons in the rat lateral amygdala (LA). Synaptic currents were evoked by stimulating in either the external capsule (ec), internal capsule (ic) or basolateral nucleus (BLA). Stimulation of either the ic, ec or BLA evoked a glutamatergic excitatory synaptic current (EPSC) which was mediated by both non-NMDA and NMDA (N-methyl-D-aspartic acid) receptors, The ratio of the amplitude of the NMDA receptor-mediated component measured at +40 mV to the amplitude of the alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) component measured at -60 mV was similar regardless of whether EPSCs were evoked in the ec, ic or BLA. At resting membrane potentials, excitatory synaptic potentials evoked from either the ec or putative thalamic inputs were unaffected by application of the NMDA receptor antagonist APV. Spontaneous glutamatergic currents had two components to their decay phase. The slow component was selectively blocked by the NMDA receptor antagonist D-APV, indicating that AMPA and NMDA receptors are colocalized in spiny neurons. We conclude that pyramidal cells of the LA receive convergent inputs from the cortex, thalamus and basal nuclei. At all inputs, both AMPA/kainate and NMDA-type receptors are active and colocalized in the postsynaptic density.

Rectification of the olfactory cyclic nucleotide-gated channel by intracellular polyamines

Polyamine-induced inward rectification of cyclic nucleotide-gated channels was studied in inside-out patches from rat olfactory neurons. The polyamines, spermine, spermidine and putrescine, induced an 'instantaneous' voltage-dependent inhibition with K-d values at 0 mV of 39, 121 mu M and 2.7 mM, respectively. Hill coefficients for inhibition were significantly < 1, suggesting an allosteric inhibitory mechanism. The Woodhull model for voltage-dependent block predicted that all 3 polyamines bound to a site 1/3 of the electrical distance through the membrane from the internal side. Instantaneous inhibition was relieved at positive potentials, implying significant polyamine permeation. Spermine also induced exponential current relaxations to a 'steady-state' impermeant level. This inhibition was also mediated by a binding site 1/3 of the electrical distance through the pore, but with a K-d of 2.6 mM. Spermine inhibition was explained by postulating two spermine binding sites at a similar depth. Occupation of the first site occurs rapidly and with high affinity, but once a spermine molecule has bound, it inhibits spermine occupation of the second binding site via electrostatic repulsion. This repulsion is overcome at higher membrane potentials, but results in a lower apparent binding affinity for the second spermine molecule. The on-rate constant for the second spermine binding saturated at a low rate (similar to 200 sec(-1) at +120 mV), providing further evidence for an allosteric mechanism. Polyamine-induced inward rectification was significant at physiological concentrations.

Ca2+-activated K+ channels in rat otic ganglion cells: Role of Ca2+ entry via Ca2+ channels and nicotinic receptors

1. Intracellular recordings were made from neurones in the rat otic ganglion in vitro in order to investigate their morphological, physiological and synaptic properties. We took advantage of the simple structure of these cells to test for a possible role of calcium influx via nicotinic acetylcholine receptors during synaptic transmission. 2. Cells filled with biocytin comprised a homogeneous population with ovoid somata and sparse dendritic trees. Neurones had resting membrane potentials of -53 +/- 0.7 mV (n = 69), input resistances of 112 + 7 M Omega, and membrane time constants of 14 +/- 0.9 ms (n = 60). Upon depolarization, all cells fired overshooting action potentials which mere followed by an apamin-sensitive after-hyperpolarization (AHP). In response to a prolonged current injection, all neurones fired tonically. 3. The repolarization phase of action potentials had a calcium component which was mediated by N-type calcium channels. Application of omega-conotoxin abolished both the repolarizing hump and the after-hgrperpolarization suggesting that calcium influx via N-type channels activates SK-type calcium-activated potassium channels which underlie the AHP. 4. The majority (70%) of neurones received innervation from a single preganglionic fibre which generated a suprathreshold excitatory postsynaptic potential mediated by nicotinic acetylcholine receptors. The other 30% of neurones also had one or more subthreshold nicotinic inputs. 5. Calcium influx via synaptic nicotinic receptors contributed to the AHP current, indicating that this calcium has access to the calcium-activated potassium channels and therefore plays a role in regulating cell excitability.

T-type Ca2+ channels, SK2 channels and SERCAs gate sleep-related oscillations in thalamic dendrites.

T-type Ca2+ channels (T channels) underlie rhythmic burst discharges during neuronal oscillations that are typical during sleep. However, the Ca2+-dependent effectors that are selectively regulated by T currents remain unknown. We found that, in dendrites of nucleus reticularis thalami (nRt), intracellular Ca2+ concentration increases were dominated by Ca2+ influx through T channels and shaped rhythmic bursting via competition between Ca2+-dependent small-conductance (SK)-type K+ channels and Ca2+ uptake pumps. Oscillatory bursting was initiated via selective activation of dendritically located SK2 channels, whereas Ca2+ sequestration by sarco/endoplasmic reticulum Ca2+-ATPases (SERCAs) and cumulative T channel inactivation dampened oscillations. Sk2-/- (also known as Kcnn2) mice lacked cellular oscillations, showed a greater than threefold reduction in low-frequency rhythms in the electroencephalogram of non-rapid-eye-movement sleep and had disrupted sleep. Thus, the interplay of T channels, SK2 channels and SERCAs in nRt dendrites comprises a specialized Ca2+ signaling triad to regulate oscillatory dynamics related to sleep.

The fourth transmembrane segment of the Na,K-ATPase alpha subunit: a systematic mutagenesis study.

The Na,K-ATPase is a major ion-motive ATPase of the P-type family responsible for many aspects of cellular homeostasis. To determine the structure of the pathway for cations across the transmembrane portion of the Na,K-ATPase, we mutated 24 residues of the fourth transmembrane segment into cysteine and studied their function and accessibility by exposure to the sulfhydryl reagent 2-aminoethyl-methanethiosulfonate. Accessibility was also examined after treatment with palytoxin, which transforms the Na,K-pump into a cation channel. Of the 24 tested cysteine mutants, seven had no or a much reduced transport function. In particular cysteine mutants of the highly conserved "PEG" motif had a strongly reduced activity. However, most of the non-functional mutants could still be transformed by palytoxin as well as all of the functional mutants. Accessibility, determined as a 2-aminoethyl-methanethiosulfonate-induced reduction of the transport activity or as inhibition of the membrane conductance after palytoxin treatment, was observed for the following positions: Phe(323), Ile(322), Gly(326), Ala(330), Pro(333), Glu(334), and Gly(335). In accordance with a structural model of the Na,K-ATPase obtained by homology modeling with the two published structures of sarcoplasmic and endoplasmic reticulum calcium ATPase (Protein Data Bank codes 1EUL and 1IWO), the results suggest the presence of a cation pathway along the side of the fourth transmembrane segment that faces the space between transmembrane segments 5 and 6. The phenylalanine residue in position 323 has a critical position at the outer mouth of the cation pathway. The residues thought to form the cation binding site II ((333)PEGL) are also part of the accessible wall of the cation pathway opened by palytoxin through the Na,K-pump.

Discharge properties of single neurons in the dorsal nucleus of the lateral lemniscus of the rat.

The aim of the present study was to characterize the discharge properties of single neurons in the dorsal nucleus of the lateral lemniscus (DNLL) of the rat. In the absence of acoustic stimulation, two types of spontaneous discharge patterns were observed: units tended to fire in a bursting or in a nonbursting mode. The distribution of units in the DNLL based on spontaneous firing rate followed a rostrocaudal gradient: units with high spontaneous rates were most commonly located in the rostral part of the DNLL, whereas in the caudal part units had lower spontaneous discharge rates. The most common response pattern of DNLL units to 200 ms binaural noise bursts contained a prominent onset response followed by a lower but steady-state response and an inhibitory response in the early-off period. Thresholds of response to noise bursts were on average higher for DNLL units than for units recorded in the inferior colliculus under the same experimental conditions. The DNLL units were arranged according to a mediolateral sensitivity gradient with the lowest threshold units in the most lateral part of the nucleus. In the rat, as in other mammals, the most common DNLL binaural input type was an excitatory response to contralateral ear stimulation and inhibitory response to ipsilateral ear stimulation (EI type). Pure tone bursts were in general a more effective stimulus compared to noise bursts. Best frequency (BF) was established for 97 DNLL units and plotted according to their spatial location. The DNLL exhibits a loose tonotopic organization, where there is a concentric pattern with high BF units located in the most dorsal and ventral parts of the DNLL and lower BF units in the middle part of the nucleus.

A numerical solver for a nonlinear Fokker-Planck equation representation of neuronal network dynamics

To describe the collective behavior of large ensembles of neurons in neuronal network, a kinetic theory description was developed in [13, 12], where a macroscopic representation of the network dynamics was directly derived from the microscopic dynamics of individual neurons, which are modeled by conductance-based, linear, integrate-and-fire point neurons. A diffusion approximation then led to a nonlinear Fokker-Planck equation for the probability density function of neuronal membrane potentials and synaptic conductances. In this work, we propose a deterministic numerical scheme for a Fokker-Planck model of an excitatory-only network. Our numerical solver allows us to obtain the time evolution of probability distribution functions, and thus, the evolution of all possible macroscopic quantities that are given by suitable moments of the probability density function. We show that this deterministic scheme is capable of capturing the bistability of stationary states observed in Monte Carlo simulations. Moreover, the transient behavior of the firing rates computed from the Fokker-Planck equation is analyzed in this bistable situation, where a bifurcation scenario, of asynchronous convergence towards stationary states, periodic synchronous solutions or damped oscillatory convergence towards stationary states, can be uncovered by increasing the strength of the excitatory coupling. Finally, the computation of moments of the probability distribution allows us to validate the applicability of a moment closure assumption used in [13] to further simplify the kinetic theory.

Structural and functional interaction sites between Na,K-ATPase and FXYD proteins.

Several members of the FXYD protein family are tissue-specific regulators of Na,K-ATPase that produce distinct effects on its apparent K(+) and Na(+) affinity. Little is known about the interaction sites between the Na,K-ATPase alpha subunit and FXYD proteins that mediate the efficient association and/or the functional effects of FXYD proteins. In this study, we have analyzed the role of the transmembrane segment TM9 of the Na,K-ATPase alpha subunit in the structural and functional interaction with FXYD2, FXYD4, and FXYD7. Mutational analysis combined with expression in Xenopus oocytes reveals that Phe(956), Glu(960), Leu(964), and Phe(967) in TM9 of the Na,K-ATPase alpha subunit represent one face interacting with the three FXYD proteins. Leu(964) and Phe(967) contribute to the efficient association of FXYD proteins with the Na,K-ATPase alpha subunit, whereas Phe(956) and Glu(960) are essential for the transmission of the functional effect of FXYD proteins on the apparent K(+) affinity of Na,K-ATPase. The relative contribution of Phe(956) and Glu(960) to the K(+) effect differs for different FXYD proteins, probably reflecting the intrinsic differences of FXYD proteins on the apparent K(+) affinity of Na,K-ATPase. In contrast to the effect on the apparent K(+) affinity, Phe(956) and Glu(960) are not involved in the effect of FXYD2 and FXYD4 on the apparent Na(+) affinity of Na,K-ATPase. The mutational analysis is in good agreement with a docking model of the Na,K-ATPase/FXYD7 complex, which also predicts the importance of Phe(956), Glu(960), Leu(964), and Phe(967) in subunit interaction. In conclusion, by using mutational analysis and modeling, we show that TM9 of the Na,K-ATPase alpha subunit exposes one face of the helix that interacts with FXYD proteins and contributes to the stable interaction with FXYD proteins, as well as mediating the effect of FXYD proteins on the apparent K(+) affinity of Na,K-ATPase.

The fou2 mutation in the major vacuolar cation channel TPC1 confers tolerance to inhibitory luminal calcium.

The SV channel encoded by the TPC1 gene represents a Ca(2+)- and voltage-dependent vacuolar cation channel. Point mutation D454N within TPC1, named fou2 for fatty acid oxygenation upregulated 2, results in increased synthesis of the stress hormone jasmonate. As wounding causes Ca2+ signals and cytosolic Ca2+ is required for SV channel function, we here studied the Ca(2+)-dependent properties of this major vacuolar cation channel with Arabidopsis thaliana mesophyll vacuoles. In patch clamp measurements, wild-type and fou2 SV channels did not exhibit differences in cytosolic Ca2+ sensitivity and Ca2+ impermeability. K+ fluxes through wild-type TPC1 were reduced or even completely faded away when vacuolar Ca2+ reached the 0.1-mm level. The fou2 protein under these conditions, however, remained active. Thus, D454N seems to be part of a luminal Ca2+ recognition site. Thereby the SV channel mutant gains tolerance towards elevated luminal Ca2+. A three-fold higher vacuolar Ca/K ratio in the fou2 mutant relative to wild-type plants seems to indicate that fou2 can accumulate higher levels of vacuolar Ca(2+) before SV channel activity vanishes and K(+) homeostasis is impaired. In response to wounding fou2 plants might thus elicit strong vacuole-derived cytosolic Ca2+ signals resulting in overproduction of jasmonate.

Characterisation of "fou2", a constitutive wound-activated mutant and analysis of the proteome and leaf physiology in the region proximal to wounds in Arabidopsis

Résumé : Les jasmonates (JA), une famille d'hor1none végétale, jouent un rôle central dans la réponse à la blessure, et aux attaques d'insectes et de pathogènes. Les JA sont principalement dérivés d'un acide gras, l'acide linolénique. L'addition par une lipoxygénase d'une molécule d'oxygène à l'acide linolénique initie la synthèse de JA. Cependant les mécanismes régulant l'activation de la biosynthèse de JA ne sont pas encore connus. C'est pour cette raison que dans ce travail, nous avons caractérisé chez Arabidopsis thaliana (l'Arabette des Dames) un mutant fou2 dont l'activité lipoxygénase est plus élevée que celle d'une plante sauvage. Les niveaux de JA sont constitutivement plus élevés et l'activation de la synthèse de JA après blessure est fortement plus induite chez fou2 que chez le type sauvage. En outre, fou2 est plus résistant au pathogène Botrytis cinerea et à la chenille Spodoptera littoralis. Afin de comprendre quel mécanisme chez fou2 génére ce phénotype, nous avons cloné le gène responsable du phénotype de fou2. Le mutant fou2 porte une mutation dans le gène d'un canal à deux pores transportant probablement du potassium, du lumen de la vacuole végétale vers le compartiment cytosolique. L'analyse du protéome de fou2 a permis d'identifier une expression plus élevée de sept protéines régulées par les JA ou le stress. La découverte de l'implication d'un canal dans le phénotype de fou2 renforce l'hypothèse que les flux de cations pourraient être impliqués dans les étapes précoces de la synthèse des JA. Nous avons également étudié le protéome et la physiologie d'une feuille blessée, Pour évaluer les changements d'expression protéique en réponse à la blessure et contrôlés par les JA, nous avons quantifié l'expression de 5937 protéines chez une plante d'Arabidopsis sauvage et chez un mutant incapable de synthétiser des JA. Parmi ces 5937 protéines, nous avons identifié 99 protéines régulées par la blessure chez le type sauvage. Nous avons observé pour 65% des protéines dont l'expression protéique changeait après blessure une bonne corrélation entre la quantité de transcrits et de protéines. Plusieurs enzymes de la voie des chorismates impliquées dans la biosynthèse des acides aminés phénoliques étaient induites par les JA après blessure. Une quantification des acides aminés a montré que les niveaux d'acides aminés phénoliques augmentaient significativement après blessure. La blessure induisait aussi des changements dans l'expression de protéines impliquées dans la réponse au stress et particulièrement au stress oxydatif. Nous avons quantifié l'état réduit et oxydé du glutathion, un tripeptide qui, sous sa forme réduite, est l'antioxydant majeur des cellules. Nous avons trouvé une quantité significativement plus élevée de glutathion oxydé chez le type sauvage blessé que chez la plante aus blessée. Ce résultat suggère que la génération d'un stress oxydatif et la proportion relative de glutathions réduits et oxydés sont contrôlés par les JA après blessure. Abstract : Plants possess a family of potent fatty acid-derived wound-response and developmental regulators: the jasmonates. These compounds are derived from the tri?unsaturated fatty acid a-linolenic-acid (18:3). Addition of an oxygen molecule to 18:3 by 13-lipoxygenases (13-LOX) initiates JA biosynthesis. Actually components regulating the activation of JA biosynthesis are poorly defined. Therefore we characterized in Arabidopsis thaliana the fatty acid Qxygenation upregulated 2 (fou2) mutant, which was previously isolated in a screen for mutants with an enhanced 13-LOX activity. As a consequence of this increased 13-LOX activity, JA levels in fou2 are higher than in wild type (WT) and wounding strongly increased JA biosynthesis compared to WT. fou2 was more resistant to the fungus Botrytis cinerea and the generalist caterpillar Spodaptera littomlis, The fou2 mutant carries a missense mutation in the Two Pore Channel 1 gene (TPCJ), which encodes a vacuolar cation channel transporting probably K* into the cytosol. Patchclamp analysis of fou2 vacuolar membranes showed faster time-dependent conductivity and activation of the mutated channel at lower membrane potentials than wild-type. Proteomic analysis of fou2 leaves identified increased levels of seven biotic stress- and JA- inducible proteins. The discovery of the implication of a channel in the fou2 phenotype strenghtens the hypothesis that cation fluxes might be implicated in early steps of JA synthesis. We further concentrated on the proteome and leaf physiology in the region proximal to wounds in Arabidopsis using the WT and the aos JA-biosynthesis deficient mutant in order to find JA- induced proteins changes. We used two successive proteomic methods to assess protein changes in response to wounding Arabidopsis leaves, two dimensional electrophoresis (2DE) and linear trap quadrupole ion-trap mass spectrometry. In total 5937 proteins were quantified. We identified 99 wound-regulated proteins in the WT. Most these proteins were also wound-regulated at the transcript level showing a good correlation between transcript and protein abundance. We identified several wound-regulated enzymes involved in amino acid biosynthesis and confirmed this result by amino acid quantification. Proteins involved in stress reponses were upregulated, particularly in redox species regulation. We found a significantly higher quantity of oxidized glutathione in wounded WT relative to wounded aos leaves. This result suggests that levels of reduced glutathione are controlled by JA after wounding.

Neuronal in vitro models for the estimation of acute systemic toxicity.

The objective of the EU funded integrated project "ACuteTox" is to develop a strategy in which general cytotoxicity, together with organ-specific endpoints and biokinetic features, are taken into consideration in the in vitro prediction of oral acute systemic toxicity. With regard to the nervous system, the effects of 23 reference chemicals were tested with approximately 50 endpoints, using a neuronal cell line, primary neuronal cell cultures, brain slices and aggregated brain cell cultures. Comparison of the in vitro neurotoxicity data with general cytotoxicity data generated in a non-neuronal cell line and with in vivo data such as acute human lethal blood concentration, revealed that GABA(A) receptor function, acetylcholine esterase activity, cell membrane potential, glucose uptake, total RNA expression and altered gene expression of NF-H, GFAP, MBP, HSP32 and caspase-3 were the best endpoints to use for further testing with 36 additional chemicals. The results of the second analysis showed that no single neuronal endpoint could give a perfect improvement in the in vitro-in vivo correlation, indicating that several specific endpoints need to be analysed and combined with biokinetic data to obtain the best correlation with in vivo acute toxicity.