Competition between beta-subunits of cardiac L-type calcium channels

Cardiac L-type Ca (CaV1.2) channels are composed of a pore forming CaV1.2-α1 subunit and auxiliary β- and α2δ-subunits. β-subunits are important not only for surface expression of the channel pore but also for modulation of channel gating properties. Different β-subunits differentially modulate channel activity (Hullin et al., PLOSone, 2007) and thus L-type Ca2+ channel gating is altered when β-subunit expression pattern is changed. In human heart failure increased activity of single ventricular L-type Ca2+-channels is associated with an increased expression of β2-subunits. Interestingly, induction of β2-subunit over-expression in hearts of transgenic mice resembled this heart failure phenotype of hyperactive single L-type Ca2+-channel channels (Beetz et al., Cardiovasc Res. 2009). We hypothesised that competition of less stimulating β-subunits (e.g. β1) with β-subunits causing strong channel stimulation (e.g. β2) might be a means to treat dysfunctional L-type Ca2+-channel activity. To test this hypothesis, we performed whole-cell and single-channel measurements employing recombinant CaV1.2 channels expressed in HEK293 cells together with both β- and β1a2b-subunits. Whole-cell analysis revealed no differences of maximum L-type Ca2+-current densities [pA/pF] with coexpression of either β1a-subunits (-52±3.8), β2b-subunits (-61.5±6.6) or the mixtures of β- and β1a2b-subunits with the plasmid transfection ratio of 2:1 (-60.2±1.6) and 1:1 (-56.7±2.6) respectively. However, steady state inactivation kinetics differed between particular β-subunit and the relative amount of β-subunit presence in the mixtures (β1a1a-subunit (-41.1±1.0), β2b-subunits (-35.1±1.1), mixture 2:1 (-40.3±1.5), and mixture 1:1 (-38.4±2.0); [mV]; p<0.05, students t-test). Using a novel single-channel analysis, switching of gating between β1-like and β2-like modes was monitored on a minute time-scale when both β-subunits were co-expressed in the same cells, but the larger amount of β1a-subunits is required for the effective switching of gating. Our results indicate a model of mutually exclusive binding and effective competition between several β-subunits suggesting that hyperactive channel gating mediated e.g. by β2-subunits can be normalized by β1-subunits. Therefore, competitive replacement between different L-type Ca2+-channel β-subunits might serve as a novel therapeutic strategy for e.g. heart failure.

Statistical mechanics in the extended Gaussian ensemble

The extended Gaussian ensemble (EGE) is introduced as a generalization of the canonical ensemble. This ensemble is a further extension of the Gaussian ensemble introduced by Hetherington [J. Low Temp. Phys. 66, 145 (1987)]. The statistical mechanical formalism is derived both from the analysis of the system attached to a finite reservoir and from the maximum statistical entropy principle. The probability of each microstate depends on two parameters ß and ¿ which allow one to fix, independently, the mean energy of the system and the energy fluctuations, respectively. We establish the Legendre transform structure for the generalized thermodynamic potential and propose a stability criterion. We also compare the EGE probability distribution with the q-exponential distribution. As an example, an application to a system with few independent spins is presented.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

Regulation of Nav1.7 and Nav1.8 voltage-gated sodium channels by Nedd4-2 and β-subunits and its implication in neuropathic pain

In mammals, the presence of excitable cells in muscles, heart and nervous system is crucial and allows fast conduction of numerous biological information over long distances through the generation of action potentials (AP). Voltage-gated sodium channels (Navs) are key players in the generation and propagation of AP as they are responsible for the rising phase of the AP. Navs are heteromeric proteins composed of a large pore-forming a-subunit (Nav) and smaller ß-auxiliary subunits. There are ten genes encoding for Navl.l to Nav1.9 and NaX channels, each possessing its own specific biophysical properties. The excitable cells express differential combinations of Navs isoforms, generating a distinct electrophysiological signature. Noteworthy, only when anchored at the membrane are Navs functional and are participating in sodium conductance. In addition to the intrinsic properties of Navs, numerous regulatory proteins influence the sodium current. Some proteins will enhance stabilization of membrane Navs while others will favour internalization. Maintaining equilibrium between the two is of crucial importance for controlling cellular excitability. The E3 ubiquitin ligase Nedd4-2 is a well-characterized enzyme that negatively regulates the turnover of many membrane proteins including Navs. On the other hand, ß-subunits are known since long to stabilize Navs membrane anchoring. Peripheral neuropathic pain is a disabling condition resulting from nerve injury. It is characterized by the dysregulation of Navs expressed in dorsal root ganglion (DRG) sensory neurons as highlighted in different animal models of neuropathic pain. Among Navs, Nav1.7 and Nav1.8 are abundantly and specifically expressed in DRG sensory neurons and have been recurrently incriminated in nociception and neuropathic pain development. Using the spared nerve injury (SNI) experimental model of neuropathic pain in mice, I observed a specific reduction of Nedd4-2 in DRG sensory neurons. This decrease subsequently led to an upregulation of Nav1.7 and Nav1.8 protein and current, in the axon and the DRG neurons, respectively, and was sufficient to generate neuropathic pain-associated hyperexcitability. Knocking out Nedd4-2 specifically in nociceptive neurons led to the same increase of Nav1.7 and Nav1.8 concomitantly with an increased thermal sensitivity in mice. Conversely, rescuing Nedd4-2 downregulation using viral vector transfer attenuated neuropathic pain mechanical hypersensitivity. This study demonstrates the significant role of Nedd4-2 in regulating cellular excitability in vivo and its involvement in neuropathic pain development. The role of ß-subunits in neuropathic pain was already demonstrated in our research group. Because of their stabilization role, the increase of ßl, ß2 and ß3 subunits in DRGs after SNI led to increased Navs anchored at the membrane. Here, I report a novel mechanism of regulation of a-subunits by ß- subunits in vitro; ßl and ß3-subunits modulate the glycosylation pattern of Nav1.7, which might account for stabilization of its membrane expression. This opens new perspectives for investigation Navs state of glycosylation in ß-subunits dependent diseases, such as in neuropathic pain. - Chez les mammifères, la présence de cellules excitables dans les muscles, le coeur et le système nerveux est cruciale; elle permet la conduction rapide de nombreuses informations sur de longues distances grâce à la génération de potentiels d'action (PA). Les canaux sodiques voltage-dépendants (Navs) sont des participants importants dans la génération et la propagation des PA car ils sont responsables de la phase initiale de dépolarisation du PA. Les Navs sont des protéines hétéromériques composées d'une grande sous-unité a (formant le pore du canal) et de petites sous-unités ß accompagnatrices. Il existe dix gènes qui codent pour les canaux sodiques, du Nav 1.1 au Nav 1.9 ainsi que NaX, chacun possédant des propriétés biophysiques spécifiques. Les cellules excitables expriment différentes combinaisons des différents isoformes de Navs, qui engendrent une signature électrophysiologique distincte. Les Navs ne sont fonctionnels et ne participent à la conductibilité du Na+, que s'ils sont ancrés à la membrane plasmique. En plus des propriétés intrinsèques des Navs, de nombreuses protéines régulatrices influencent également le courant sodique. Certaines protéines vont favoriser l'ancrage et la stabilisation des Navs exprimés à la membrane, alors que d'autres vont plutôt favoriser leur internalisation. Maintenir l'équilibre des deux processus est crucial pour contrôler l'excitabilité cellulaire. Dans ce contexte, Nedd4-2, de la famille des E3 ubiquitin ligase, est une enzyme bien caractérisée qui régule l'internalisation de nombreuses protéines, notamment celle des Navs. Inversement, les sous-unités ß sont connues depuis longtemps pour stabiliser l'ancrage des Navs à la membrane. La douleur neuropathique périphérique est une condition débilitante résultant d'une atteinte à un nerf. Elle est caractérisée par la dérégulation des Navs exprimés dans les neurones sensoriels du ganglion spinal (DRG). Ceci a été démontré à de multiples occasions dans divers modèles animaux de douleur neuropathique. Parmi les Navs, Nav1.7 et Nav1.8 sont abondamment et spécifiquement exprimés dans les neurones sensoriels des DRG et ont été impliqués de façon récurrente dans le développement de la douleur neuropathique. En utilisant le modèle animal de douleur neuropathique d'épargne du nerf sural (spared nerve injury, SNI) chez la souris, j'ai observé une réduction spécifique des Nedd4-2 dans les neurones sensoriels du DRG. Cette diminution avait pour conséquence l'augmentation de l'expression des protéines et des courants de Nav 1.7 et Nav 1.8, respectivement dans l'axone et les neurones du DRG, et était donc suffisante pour créer l'hyperexcitabilité associée à la douleur neuropathique. L'invalidation pour le gène codant pour Nedd4-2 dans une lignée de souris génétiquement modifiées a conduit à de similaires augmentations de Nav1.7 et Nav1.8, parallèlement à une augmentation à la sensibilité thermique. A l'opposé, rétablir une expression normale de Nedd4-2 en utilisant un vecteur viral a eu pour effet de contrecarrer le développement de l'hypersensibilité mécanique lié à ce modèle de douleur neuropathique. Cette étude démontre le rôle important de Nedd4-2 dans la régulation de l'excitabilité cellulaire in vivo et son implication dans le développement des douleurs neuropathiques. Le rôle des sous-unités ß dans les douleurs neuropathiques a déjà été démontré dans notre groupe de recherche. A cause de leur rôle stabilisateur, l'augmentation des sous-unités ßl, ß2 et ß3 dans les DRG après SNI, conduit à une augmentation des Navs ancrés à la membrane. Dans mon travail de thèse, j'ai observé un nouveau mécanisme de régulation des sous-unités a par les sous-unités ß in vitro. Les sous-unités ßl et ß3 régulent l'état de glycosylation du canal Nav1.7, et stabilisent son expression membranaire. Ceci ouvre de nouvelles perspectives dans l'investigation de l'état de glycosylation des Navs dans des maladies impliquant les sous-unités ß, notamment les douleurs neuropathiques.

Bistability driven by Gaussian colored noise: First-passage times

Herein we present a calculation of the mean first-passage time for a bistable one-dimensional system driven by Gaussian colored noise of strength D and correlation time ¿c. We obtain quantitative agreement with experimental analog-computer simulations of this system. We disagree with some of the conclusions reached by previous investigators. In particular, we demonstrate that all available approximations that lead to a state-dependent diffusion coefficient lead to the same result for small D¿c.

Exact solution to the mean exit time problem for free inertial processes driven by Gaussian white noise

We obtain the exact analytical expression, up to a quadrature, for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise from a region (0,L) in space. We obtain a completely explicit expression for T(x,0) and discuss the dependence of T(x,v) as a function of the size L of the region. We develop a new method that may be used to solve other exit time problems.

Fractal dimension for Gaussian colored processes

The exact analytical expression for the Hausdorff dimension of free processes driven by Gaussian noise in n-dimensional space is obtained. The fractal dimension solely depends on the time behavior of the arbitrary correlation function of the noise, ranging from DX=1 for Orstein-Uhlenbeck input noise to any real number greater than 1 for fractional Brownian motions.

Free inertial processes driven by Gaussian noise: Probability distributions, anomalous diffusion and fractal behavior

We study the motion of an unbound particle under the influence of a random force modeled as Gaussian colored noise with an arbitrary correlation function. We derive exact equations for the joint and marginal probability density functions and find the associated solutions. We analyze in detail anomalous diffusion behaviors along with the fractal structure of the trajectories of the particle and explore possible connections between dynamical exponents of the variance and the fractal dimension of the trajectories.

Exact solution to the exit-time problem for an undamped free particle driven by Gaussian white noise

In a recent paper [Phys. Rev. Lett. 75, 189 (1995)] we have presented the exact analytical expression for the mean exit time, T(x,v), of a free inertial process driven by Gaussian white noise out of a region (0,L) in space. In this paper we give a detailed account of the method employed and present results on asymptotic properties and averages of T(x,v).

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Three-dimensional aspects of fluid flows in channels. I. Meniscus and thin film regimes

We study the forced displacement of a fluid-fluid interface in a three-dimensional channel formed by two parallel solid plates. Using a lattice-Boltzmann method, we study situations in which a slip velocity arises from diffusion effects near the contact line. The difference between the slip and channel velocities determines whether the interface advances as a meniscus or a thin film of fluid is left adhered to the plates. We find that this effect is controlled by the capillary and Péclet numbers. We estimate the crossover from a meniscus to a thin film and find good agreement with numerical results. The penetration regime is examined in the steady state. We find that the occupation fraction of the advancing finger relative to the channel thickness is controlled by the capillary number and the viscosity contrast between the fluids. For high viscosity contrast, lattice-Boltzmann results agree with previous results. For zero viscosity contrast, we observe remarkably narrow fingers. The shape of the finger is found to be universal.

ROLES OF ACID-SENSING ION CHANNELS (ASICS) IN PERIPHERAL NEUROPEPTIDE SECRETION AND PAIN

Acid-sensing ion channels (ASICs) are non-voltage-gated sodium channels activated by an extracellular acidification. They are widely expressed in neurons of the central and peripheral nervous system. ASICs have a role in learning, the expression of fear, in neuronal death after cerebral ischemia, and in pain sensation. Tissue damage leads to the release of inflammatory mediators. There is a subpopulation of sensory neurons which are able to release the neuropeptides calcitonin gene-related peptide (CGRP) and substance P (SP). Neurogenic inflammation refers to the process whereby peripheral release of the neuropeptides CGRP and SP induces vasodilation and extravasation of plasma proteins, respectively. Our laboratory has previously shown that calcium-permeable homomeric ASIC1a channels are present in a majority of CGRP- or SP-expressing small diameter sensory neurons. In the first part of my thesis, we tested the hypothesis that a local acidification can produce an ASIC-mediated calcium-dependant neuropeptide secretion. We have first verified the co-expression of ASICs and CGRP/SP using immunochemistry and in-situ hybridization on dissociated rat dorsal root ganglion (DRG) neurons. We found that most CGRP/SP-positive neurons also expressed ASIC1a and ASIC3 subunits. Calcium imaging experiments with Fura-2 dye showed that an extracellular acidification can induce an increase of intracellular Ca2+ concentration, which is essential for secretion. This increase of intracellular Ca2+ concentration is, at least in some cells, ASIC-dependent, as it can be prevented by amiloride, an ASIC antagonist, and by Psalmotoxin (PcTx1), a specific ASIC1a antagonist. We identified a sub-population of neurons whose acid-induced Ca2+ entry was completely abolished by amiloride, an amiloride-resistant population which does not express ASICs, but rather another acid-sensing channel, possibly transient receptor potential vanilloïde 1 (TRPV1), and a population expressing both H+-gated channel types. Voltage-gated calcium channels (Cavs) may also mediate Ca2+ entry. Co-application of the Cavs inhibitors (ω-conotoxin MVIIC, Mibefradil and Nifedipine) reduced the Ca2+ increase in neurons expressing ASICs during an acidification to pH 6. This indicates that ASICs can depolarise the neuron and activate Cavs. Homomeric ASIC1a are Ca2+-permeable and allow a direct entry of Ca2+ into the cell; other ASICs mediate an indirect entry of Ca2+ by inducing a membrane depolarisation that activates Cavs. We showed with a secretion assay that CGRP secretion can be induced by extracellular acidification in cultured rat DRG neurons. Amiloride and PcTx1 were not able to inhibit the secretion at acidic pH, but BCTC, a TRPV1 inhibitor was able to decrease the secretion induced by an extracellular acidification in our in vitro secretion assay. In conclusion, these results show that in DRG neurons a mild extracellular acidification can induce a calcium-dependent neuropeptide secretion. Even if our data show that ASICs can mediate an increase of intracellular Ca2+ concentration, this appears not to be sufficient to trigger neuropeptide secretion. TRPV1, a calcium channel whose activation induces a sustained current - in contrary of ASICs - played in our experimental conditions a predominant role in neurosecretion. In the second part of my thesis, we focused on the role of ASICs in neuropathic pain. We used the spared nerve injury (SNI) model which consists in a nerve injury that induces symptoms of neuropathic pain such as mechanical allodynia. We have previously shown that the SNI model modifies ASIC currents in dissociated rat DRG neurons. We hypothesized that ASICs could play a role in the development of mechanical allodynia. The SNI model was performed on ASIC1a, -2, and -3 knock-out mice and wild type littermates. We measured mechanical allodynia on these mice with calibrated von Frey filaments. There were no differences between the wild-type and the ASIC1, or ASIC2 knockout mice. ASIC3 null mice were less sensitive than wild type mice at 21 day after SNI, indicating a role for ASIC3. Finally, to investigate other possible roles of ASICs in the perception of the environment, we measured the baseline heat responses. We used two different models; the tail flick model and the hot plate model. ASIC1a null mice showed increased thermal allodynia behaviour in the hot plate test at three different temperatures (49, 52, 55°C) compared to their wild type littermates. On the contrary, ASIC2 null mice showed reduced thermal allodynia behaviour in the hot plate test compared to their wild type littermates at the three same temperatures. We conclude that ASIC1a and ASIC2 in mice can play a role in temperature sensing. It is currently not understood how ASICs are involved in temperature sensing and what the reason for the opposed effects in the two knockout models is.

Modulation of the c-Jun N-terminal kinase activity in the embryonic heart in response to anoxia-reoxygenation: involvement of the Ca2+ and mitoKATP channels.

Whether the response of the fetal heart to ischemia-reperfusion is associated with activation of the c-Jun N-terminal kinase (JNK) pathway is not known. In contrast, involvement of the sarcolemmal L-type Ca2+ channel (LCC) and the mitochondrial KATP (mitoKATP) channel has been established. This work aimed at investigating the profile of JNK activity during anoxia-reoxygenation and its modulation by LCC and mitoK(ATP) channel. Hearts isolated from 4-day-old chick embryos were submitted to anoxia (30 min) and reoxygenation (60 min). Using the kinase assay method, the profile of JNK activity in the ventricle was determined every 10 min throughout anoxia-reoxygenation. Effects on JNK activity of the LCC blocker verapamil (10 nM), the mitoK(ATP) channel opener diazoxide (50 microM) and the blocker 5-hydroxydecanoate (5-HD, 500 microM), the mitochondrial Ca2+ uniporter (MCU) inhibitor Ru360 (10 microM), and the antioxidant N-(2-mercaptopropionyl) glycine (MPG, 1 mM) were determined. In untreated hearts, JNK activity was increased by 40% during anoxia and peaked fivefold relative to basal level after 30-40 min reoxygenation. This peak value was reduced by half by diazoxide and was tripled by 5-HD. Furthermore, the 5-HD-mediated stimulation of JNK activity during reoxygenation was abolished by diazoxide, verapamil or Ru360. MPG had no effect on JNK activity, whatever the conditions. None of the tested pharmacological agents altered JNK activity under basal normoxic conditions. Thus, in the embryonic heart, JNK activity exhibits a characteristic pattern during anoxia and reoxygenation and the respective open-state of LCC, MCU and mitoKATP channel can be a major determinant of JNK activity in a ROS-independent manner.