Tortuous Cardiac Intercalated Discs Modulate Ephaptic Coupling

Cardiac ephaptic coupling, a mechanism mediated by negative electric potentials occurring in the narrow intercellular clefts of intercalated discs, can influence action potential propagation by modulating the sodium current. Intercalated discs are highly tortuous due to the mingling of plicate and interplicate regions. To investigate the effect of their convoluted structure on ephaptic coupling, we refined our previous model of an intercalated disc and tested predefined folded geometries, which we parametrized by orientation, amplitude and number of folds. Ephaptic interactions (assessed by the minimal cleft potential and amplitude of the sodium currents) were reinforced by concentric folds. With increasing amplitude and number of concentric folds, the cleft potential became more negative during the sodium current transient. This is explained by the larger resistance between the cleft and the bulk extracellular space. In contrast, radial folds attenuated ephaptic interactions and led to a less negative cleft potential due to a decreased net cleft resistance. In conclusion, despite limitations inherent to the simplified geometries and sodium channel distributions investigated as well as simplifications regarding ion concentration changes, these results indicate that the folding pattern of intercalated discs modulates ephaptic coupling

Localization of Na + channel clusters in narrowed perinexi of gap junctions enhances cardiac impulse transmission via ephaptic coupling: a model study

ABSTRACT: It has been proposed that when gap junctional coupling is reduced in cardiac tissue, action potential propagation can be supported via ephaptic coupling, a mechanism mediated by negative electric potentials occurring in narrow intercellular clefts of intercalated discs (IDs). Recent studies showed that sodium (Na(+)) channels form clusters near gap junction plaques in nanodomains called perinexi, where the ID cleft is even narrower. To examine the electrophysiological relevance of Na(+) channel clusters being located in perinexi, we developed a 3D finite element model of two longitudinally abutting cardiomyocytes, with a central Na(+) channel cluster on the ID membranes. When this cluster was located in the perinexus of a closely positioned gap junction plaque, varying perinexal width greatly modulated impulse transmission from one cell to the other, with narrow perinexi potentiating ephaptic coupling. This modulation occurred via the interplay of Na(+) currents, extracellular potentials in the cleft and patterns of current flow within the cleft. In contrast, when the Na(+) channel cluster was located remotely from the gap junction plaque, this modulation by perinexus width largely disappeared. Interestingly, the Na(+) current in the ID membrane of the pre‐junctional cell switched from inward to outward during excitation, thus contributing ions to the activating channels on the post‐junctional ID membrane. In conclusion, these results indicate that the localization of Na(+) channel clusters in the perinexi of gap junction plaques is crucial for ephaptic coupling, which is furthermore greatly modulated by perinexal width. These findings are relevant for a comprehensive understanding of cardiac excitation. KEY POINTS: Ephaptic coupling is a cardiac conduction mechanism involving nanoscale‐level interactions between the sodium (Na(+)) current and the extracellular potential in narrow intercalated disc clefts. When gap junctional coupling is reduced, ephaptic coupling acts in conjunction with the classical cardiac conduction mechanism based on gap junctional current flow. In intercalated discs, Na(+) channels form clusters that are preferentially located in the periphery of gap junction plaques, in nanodomains known as perinexi, but the electrophysiological role of these perinexi has never been examined. In our new 3D finite element model of two cardiac cells abutting each other with their intercalated discs, a Na(+) channel cluster located inside a narrowed perinexus facilitated impulse transmission via ephaptic coupling. Our simulations demonstrate the role of narrowed perinexi as privileged sites for ephaptic coupling in pathological situations when gap junctional coupling is decreased

The spaces O

In [1] Laurent Schwartz introduced the spaces M and ′C of multiplication and convolution operators on temperate distributions. Then in [2] Alexandre Grothendieck used tensor products to prove that both M and ′C are bornological. Our proof of this property is more constructive and based on duality

Active force generation contributes to the complexity of spontaneous activity and to the response to stretch of murine cardiomyocyte cultures.

Monolayer cultures of cardiac cells exhibit spontaneous electrical and contractile activity, as in a natural cardiac pacemaker. Beating variability in these preparations recapitulates the power-law behavior of heart rate variability in vivo. However, the effects of mechano-electrical feedback on beating variability are not yet fully understood. Using stretchable microelectrode arrays, we examined the effects of the contraction uncoupler blebbistatin and the non-specific stretch activated channel blocker streptomycin on beating variability and on stretch-induced changes of beat rate. Without stretch, blebbistatin decreased the spatial complexity of beating variability, while streptomycin had no effects. Both stretch and release transiently increased beat rate; blebbistatin attenuated the increase of beat rate upon stretch, while streptomycin had no effects. Active force generation contributes to the complexity of spatiotemporal patterns of beating variability and to the increase of beat rate upon mechanical deformation. Our study contributes to understanding how mechano-electric feedback influences heart rate variability. Cardiomyocyte cultures exhibit spontaneous electrical and contractile activity, as in a natural cardiac pacemaker. In such preparations, beat rate variability exhibits features similar to those of heart rate variability in vivo. Mechanical deformations and forces feedback on the electrical properties of cardiomyocytes, but it is not fully elucidated how this mechano-electrical interplay affects beating variability in such preparations. Using stretchable microelectrode arrays, we assessed the effects of the myosin inhibitor blebbistatin and the nonselective stretch-activated channel blocker streptomycin on beating variability and on the response of neonatal or foetal murine ventricular cell cultures against deformation. Spontaneous electrical activity was recorded without stretch and upon predefined deformation protocols (5% uniaxial and 2% equibiaxial strain, applied repeatedly for 1 min every 3 min). Without stretch, spontaneous activity originated from the edge of the preparations, and its site of origin switched frequently in a complex manner across the cultures. Blebbistatin did not change mean beat rate, but it decreased the spatial complexity of spontaneous activity. In contrast, streptomycin did not exert any manifest effects. During the deformation protocols, beat rate transiently increased upon stretch, but paradoxically also upon release. Blebbistatin attenuated the response to stretch, while this response was not affected by streptomycin. Therefore, our data support the notion that in a spontaneously firing network of cardiomyocytes, active force generation, rather than stretch-activated channels, is mechanistically involved in the complexity of the spatiotemporal patterns of spontaneous activity and in the stretch-induced acceleration of beating. Abstract figure legend Mechano-electric feedback modulates myocardial electrical function, including pacemaking. By growing monolayer cultures of spontaneously active murine cardiac cells on stretchable microelectrode arrays, we examined whether active contractions influence the spatiotemporal characteristics of beating variability and the effects of stretching on beat rate. Under control conditions (no stretch and no pharmacological agent), the origin of the electrical activity changed frequently. After blocking contractions with blebbistatin, the spatiotemporal pattern of electrical activity became less variable and less complex. Under control conditions (no pharmacological agent), stretching (and also releasing) the cardiomyocyte monolayers transiently increased beat rate. Blebbistatin attenuated the acceleration of beating upon stretch. In contrast, streptomycin had no detectable effects. Thus, active force generation is involved in determining beating variability in spontaneously active cardiac tissue. Possible mechanisms may include cellular processes that sense contraction and chemical messengers. Our study contributes to understanding how mechano-electric feedback influences heart rate variability. This article is protected by copyright. All rights reserved

Continuity of multiplication of distributors

In a reference book for distributions [1], it is shown that the multiplication (u,f)↦uf on C∞×′, as well as on M×′, is hypocontinuous. We show here that in both cases it is discontinuous

Tail Removal Block Validation: Implementation and Analysis

In this paper a solution for the removal of long tail blocktimes in a proof-of-work blockchain is proposed, implemented and analysed. Results from the mainnet of the Bismuth blockchain demonstrate that the variances in the key variables, difficulty level and blocktime, were approximately halved after the tail removal code was enabled. Low variances in difficulty and blocktimes are desirable for timely execution of transactions in the network as well as reduction of unwanted oscillations in the feedback control problem

A detailed analysis of single-channel Nav 1.5 recordings does not reveal any cooperative gating.

Cardiac voltage-gated sodium (Na+ ) channels (Nav 1.5) are crucial for myocardial electrical excitation. Recent studies based on single-channel recordings have suggested that Na+ channels interact functionally and exhibit coupled gating. However, the analysis of such recordings frequently relies on manual interventions, which can lead to bias. Here, we developed an automated pipeline to de-trend and idealize single-channel currents, and assessed possible functional interactions in cell-attached patch clamp experiments in HEK293 cells expressing human Nav 1.5 channels as well as in adult mouse and rabbit ventricular cardiomyocytes. Our pipeline involved de-trending individual sweeps by linear optimization using a library of predefined functions, followed by digital filtering and baseline offset. Subsequently, the processed sweeps were idealized based on the idea that the ensemble average of the idealized current identified by thresholds between current levels reconstructs at best the ensemble average current from the de-trended sweeps. This reconstruction was achieved by non-linear optimization. To ascertain functional interactions, we examined the distribution of the numbers of open channels at every time point during the activation protocol and compared it to the distribution expected for independent channels. We also examined whether the channels tended to synchronize their openings and closings. However, we did not uncover any solid evidence of such interactions in our recordings. Rather, our results indicate that wild-type Nav 1.5 channels are independent entities or exhibit only very weak functional interactions that are probably irrelevant under physiological conditions. Nevertheless, our unbiased analysis will be important for further studies examining whether auxiliary proteins potentiate functional Na+ channel interactions. KEY POINTS: Nav 1.5 channels are critical for cardiac excitation. They are part of macromolecular interacting complexes, and it was previously suggested that two neighbouring channels may functionally interact and exhibit coupled gating. Manual interventions when processing single-channel recordings can lead to bias and inaccurate data interpretation. We developed an automated pipeline to de-trend and idealize single-channel currents and assessed possible functional interactions between Nav 1.5 channels in HEK293 cells and cardiomyocytes during activation protocols using the cell-attached patch clamp technique. In recordings consisting of up to 1000 sweeps from the same patch, our analysis did not reveal any evidence of functional interactions or coupled gating between wild-type Nav 1.5 channels. Our unbiased analysis may be useful in further studies examining how Na+ channel interactions are affected by mutations and auxiliary proteins

Development of Sensory Neurons in the Absence of NGF/TrkA Signaling In Vivo

The neurotrophin survival dependence of peripheral neurons in vitro is regulated by the proapoptotic BCL-2 homolog BAX. To study peripheral neuron development in the absence of neurotrophin signaling, we have generated mice that are double null for BAX and nerve growth factor (NGF), and BAX and the NGF receptor TrkA. All dorsal root ganglion (DRG) neurons that normally die in the absence of NGF/TrkA signaling survive if BAX is also eliminated. These neurons extend axons through the dorsal roots and collateral branches into the dorsal horn. In contrast, superficial cutaneous innervation is absent. Furthermore, rescued sensory neurons fail to express biochemical markers characteristic of the nociceptive phenotype. These findings establish that NGF/TrkA signaling regulates peripheral target field innervation and is required for the full phenotypic differentiation of sensory neurons