Ephaptic Coupling Research Articles

Old cogs, new tricks: A scaffolding role for connexin43 and a junctional role for sodium channels?

Cardiac conduction is the process by which electrical excitation is communicated from cell to cell within the heart, triggering synchronous contraction of the myocardium. The role of conduction defects in precipitating life-threatening arrhythmias in various disease states has spurred scientific interest in the phenomenon. While the understanding of conduction has evolved greatly over the last century, the process has largely been thought to occur via movement of charge between cells via gap junctions. However, it has long been hypothesized that electrical coupling between cardiac myocytes could also occur ephaptically, without direct transfer of ions between cells. This review will focus on recent insights into cardiac myocyte intercalated disk ultrastructure and their implications for conduction research, particularly the ephaptic coupling hypothesis.

Ephaptic Coupling in Cardiac Myocytes

While it is widely believed that conduction in cardiac tissue is regulated by gap junctions, recent experimental evidence suggests that the extracellular space may play a significant role in action potential propagation. Cardiac tissue with low gap junctional coupling still exhibits conduction, with conflicting degrees of slowing that may be due to variations in the extracellular space. Inhomogeneities in the extracellular space caused by the complex cellular structure in cardiac tissue can lead to ephaptic, or field effect, coupling. Here, we present data from simulations of a cylindrical strand of cells in which we see the dramatic effect highly resistant extracellular spaces have on propagation velocity. We find that ephaptic effects occur in all areas of small extracellular spaces and are not restricted to the junctional cleft between cells. This previously unrecognized type of field coupling, which we call lateral coupling, can allow conduction in the absence of gap junctions. We compare our results with the classically used cable theory, demonstrating the quantitative difference in propagation velocity arising from the cellular geometry. Ephaptic effects are shown to be highly dependent upon parameter values, frequently enhancing, but sometimes decreasing propagation speed. Our mathematical analysis incorporates the inhomogeneities in the extracellular microdomains that cannot be directly measured by experimental techniques and will aid in optimizing cardiac treatments that require manipulation of the cellular geometry and understanding heart functionality.

On optimizing therapies, Orai, and ORNs

On optimizing therapies, Orai, and ORNs

Non-synaptic inhibition between grouped neurons in an olfactory circuit

SummaryDiverse sensory organs, including mammalian taste buds and insect chemosensory sensilla, show a striking compartmentalization of receptor cells. However, the functional impact of this organization remains unclear. Here we show that compartmentalized Drosophila olfactory receptor neurons (ORNs) communicate with each other directly. The sustained response of one ORN is inhibited by the transient activation of a neighboring ORN. Mechanistically, such lateral inhibition does not depend on synapses and is likely mediated by ephaptic coupling. Moreover, lateral inhibition in the periphery can modulate olfactory behavior. Together, the results show that integration of olfactory information can occur via lateral interactions between ORNs. Inhibition of a sustained response by a transient response may provide a means of encoding salience. Finally, a CO2-sensitive ORN in the malaria mosquito Anopheles can also be inhibited by excitation of an adjacent ORN, suggesting a broad occurrence of lateral inhibition in insects and possible applications in insect control.

A Novel Role for Ephaptic Coupling in Cardiac Conduction: An Experimental and Modeling Study

Introduction: We demonstrated that edema slows conduction (θ and increases anisotropy (ARθ). Existing mathematical models incorporating only gap junctional (Gj) coupling cannot explain these data. We hypothesized that inhibiting ion channels during edema would unmask ephaptic coupling effects. Methods: θ and ARθ were quantified by optical mapping in Langendorff-perfused guinea pig ventricles. Mannitol (26.1g/l) was perfused to increase VIS. INa, which partially colocalizes with Gj, was inhibited by flecainide (0.5μM). IK1, which exhibits low intercalated disk colocalization with Gj, was inhibited by BaCl2 (10 μM). Conduction was mathematically modeled in a 2D tissue slab with both Gj and ephaptic coupling and appropriate INa and IK1 cellular distributions. Results: During control, longitudinal (θL) and transverse (θT) θ were 51.9±1.0cm/s and 21.2±0.6cm/s respectively; ARθ was 2.5±0.1. Flecainide decreased both θL and θT by 17±2% (n=5, p<0.05 vs. control). BaCl2 increased both θL and θT by 23±2% (n=4, p<0.05 vs. control). Neither altered ARθ (p=ns vs. control). Mannitol decreased θL (16±3%, n=3, p<0.05) and θT (26±2%, n=3, p<0.05) and increased ARθ to 3.0±0.1 (n=3, p<0.05), relative to control. Importantly, flecainide + mannitol decreased θL and θT by 17±2 and 9±2% respectively (p<0.05), raising ARθ to 3.3±0.2 (p<0.05) relative to mannitol alone. BaCl2 + mannitol increased θT (by 15±3%, p<0.05) but not θL relative to mannitol alone, thereby lowering ARθ to 2.6±0.1 (p<0.05). Interestingly, the computer model of edema and ephaptic coupling recapitulated experimental findings where reducing INa decreased θ and increased ARθ while reducing IK1 increased θ and decreased ARθ. Conclusions: INa and IK1 blockade isotropically affected θ by themselves, but preferentially altered θT during edema. This is the first demonstration that altering ionic currents can alter ARθ, and the mechanism may involve ephaptic coupling.

Empirical Study of an Adaptive Multiscale Model for Simulating Cardiac Conduction

We modify and empirically study an adaptive multiscale model for simulating cardiac action potential propagation along a strand of cardiomyocytes. The model involves microscale partial differential equations posed over cells near the action potential upstroke and macroscale partial differential equations posed over the remainder of the tissue. An important advantage of the modified model of this paper is that, unlike our original model, it does not require perfect alignment between myocytes and the macroscale computational grid. We study the effects of gap-junctional coupling, ephaptic coupling, and macroscale grid spacing on the accuracy of the multiscale model. Our simulations reveal that the multiscale method accurately reproduces both the wavespeed and the waveform, including both upstroke and recovery, of fully microscale models. They also reveal that perfect alignment between myocytes and the macroscale grid is not necessary to reproduce the dynamics of a traveling action potential. Further, our simulations suggest that the macroscale grid spacing used in an adaptive multiscale model need not be much finer than the spatial width of an action potential. These results are demonstrated to hold under high, low, and zero gap-junctional coupling regimes.

Ephaptic coupling of cortical neurons

The electrochemical processes that underlie neural function manifest themselves in ceaseless spatiotemporal field fluctuations. However, extracellular fields feed back onto the electric potential across the neuronal membrane via ephaptic coupling, independent of synapses. The extent to which such ephaptic coupling alters the functioning of neurons under physiological conditions remains unclear. To address this question, we stimulated and recorded from rat cortical pyramidal neurons in slices with a 12-electrode setup. We found that extracellular fields induced ephaptically mediated changes in the somatic membrane potential that were less than 0.5 mV under subthreshold conditions. Despite their small size, these fields could strongly entrain action potentials, particularly for slow (<8 Hz) fluctuations of the extracellular field. Finally, we simultaneously measured from up to four patched neurons located proximally to each other. Our findings indicate that endogenous brain activity can causally affect neural function through field effects under physiological conditions.

Modeling electrical activity of myocardial cells incorporating the effects of ephaptic coupling.

Existing models of electrical activity in myocardial tissue are unable to easily capture the effects of ephaptic coupling. Homogenized models do not account for cellular geometry, while detailed spatial models are too complicated to simulate in three dimensions. Here we propose a unique model that accurately captures the geometric effects while being computationally efficient. We use this model to provide an initial study of the effects of changes in extracellular geometry, gap junctional coupling, and sodium ion channel distribution on propagation velocity in a single 1D strand of cells. In agreement with previous studies, we find that ephaptic coupling increases propagation velocity at low gap junctional conductivity while it decreases propagation at higher conductivities. We also find that conduction velocity is relatively insensitive to gap junctional coupling when sodium ion channels are located entirely on the cell ends and cleft space is small. The numerical efficiency of this model, verified by comparison with more detailed simulations, allows a thorough study in parameter variation and shows that cellular structure and geometry has a nontrivial impact on propagation velocity. This model can be relatively easily extended to higher dimensions while maintaining numerical efficiency and incorporating ephaptic effects through modeling of complex, irregular cellular geometry.

Adaptive multiscale model for simulating cardiac conduction

We present a multiscale model and an adaptive numerical scheme for simulating cardiac action potential propagation along a linear strand of heart muscle cells. This model couples macroscale partial differential equations posed over the tissue to microscale equations posed over discrete cellular geometry. The microscopic equations are used only near action potential wave fronts, and the macroscopic equations are used everywhere else. We study the effects of gap-junctional and ephaptic coupling on conduction in the multiscale model and its fully macroscale and fully microscale analogues. Our simulations reveal that the adaptive multiscale model accurately reproduces the action potential wave forms and wave speeds of the fully microscale model. They also demonstrate that, at low gap-junctional conductivities, the accuracy of fully macroscale simulations is sensitive to numerical grid spacing. Moreover, adaptive multiscale simulations capture the effect of ephaptic coupling, whereas fully macroscale simulations do not. We propose two ways of generalizing our multiscale model to higher dimensions, and we argue that such generalizations may be necessary to obtain accurate three-dimensional simulations of cardiac conduction in certain pathophysiological parameter regimes.

Ephaptic coupling of cardiac cells through the junctional electric potential

Cardiac cells are electrically coupled through gap junction channels, which allow ionic current to spread intercellularly from one cell to the next. In addition, it is possible that cardiac cells are coupled through the electric potential in the junctional cleft space between neighboring cells. We develop and analyze a mathematical model of two cells coupled through a common junctional cleft potential. Consistent with more detailed models, we find that the coupling mechanism is highly parameter dependent. Analysis of our model reveals that there are two time scales involved, and the dynamics of the slow subsystem provide new mathematical insight into how the coupling mechanism works. We find that there are two distinct types of propagation failure and we are able to characterize parameter space into regions of propagation success and the two different types of propagation failure.

Traveling Wave Solutions to a Coupled System of Spatially Discrete Nagumo Equations

We consider a coupled system of discrete Nagumo equations and derive traveling wave solutions to this system using McKean's caricature of the cubic. A certain form of this system is used to model ephaptic coupling between pairs of nerve axons. We study the difference $g(c)=a_1-a_2$ between the detuning parameters $a_i$ that is required to make both waves move at the same speed c. Of particular interest is the effect of a coupling parameter $\alpha$ and an "alignment" parameter A on the function g. Numerical investigation indicates that for fixed A, there exists a time delay value $\beta$ that results in $g=0$, and for large enough wave speeds, multiple such $\beta$ values exist. Also, numerical results indicate that the perturbation of $\alpha$ away from zero will yield additional solutions with positive wave speed when $A={1\over 2}$. We employ both analytical and numerical results to demonstrate our claims.

Hierarchical model of the population dynamics of hippocampal dentate granule cells.

A hierarchical modeling approach is used as the basis for a mathematical representation of the population activity of hippocampal dentate granule cells. Using neural field equations, the variation in time and space of dentate granule cell activity is derived from the summed synaptic potential and summed action potential responses of a population of granule cells evoked by monosynaptic excitatory input from entorhinal cortical afferents. In this formulation of the problem, we have considered a two-level hierarchy: the synapses of entorhinal cortical axons define the first level of organization, and dentate granule cells, which include these synapses, define the second, higher level of organization. The model is specified by two state field variables, for membrane potential and for synaptic efficacy, respectively, with both evolving according to different time scales. The two state field variables introduce new parameters, physiological and anatomical, which characterize the dentate from the point of view of neuronal and synaptic populations: (1) a set of geometrical constraints corresponding to the morphological properties of granule cells and anatomical characteristics of entorhinal-dentate connections; and (2) a set of neuronal parameters corresponding to physiological mechanisms. Assuming no interaction between granule cells, i.e., neither ephaptic nor synaptic coupling, the model is shown to be mathematically tractable and allows solution of the field equations leading to the determination of activity. This treatment leads to the definition of two state variables, volume of stimulated synapses and firing time, which describe observed activity. Numerical simulations are used to investigate the populational characterization of the dentate by individual parameters: (1) the relationship between the conditions of stimulation of active perforant path fibers, e.g., stimulating intensity, and activity in the granule cell layer; and (2) the influence of geometry on the generation of activity, i.e., the influence of neuron density and synaptic density-connectivity. As an example application of the model, the granule cell population spike is reconstructed and compared with experimental data.

Ephaptic Interactions in the Mammalian Olfactory System

Ephaptic coupling refers to interactions between neurons mediated by current flow through the extracellular space. Ephaptic interactions between axons are considered negligible, because of the relatively large extracellular space and the layers of myelin that separate most axons. By contrast, olfactory nerve axons are unmyelinated and arranged in tightly packed bundles, features that may enhance ephaptic coupling. We tested the hypothesis that ephaptic interactions occur in the mammalian olfactory nerve with the use of a computational approach. Numerical solutions of models of axon fascicles show that significant ephaptic interactions occur for a range of physiologically relevant parameters. An action potential in a single axon can evoke action potentials in all other axons in the fascicle. Ephaptic interactions can also lead to synchronized firing of independently stimulated axons. Our findings suggest that ephaptic interactions may be significant determinants of the olfactory code and that such interactions may occur in other, similarly organized axonal or dendritic bundles.

Ephaptic coupling of myelinated nerve fibers

Numerical predictions of a simple myelinated nerve fiber model are compared with theoretical results in the continuum and discrete limits, clarifying the nature of the conduction process on an isolated nerve axon. Since myelinated nerve fibers are often arranged in bundles, this model is used to study ephaptic (nonsynaptic) interactions between impulses on parallel fibers, which may play a functional role in neural processing.

Ephaptic coupling of large fibers as a clue to mechanism in chronic neuropathic allodynia following damage to dorsal roots

Ephaptic coupling of large fibers as a clue to mechanism in chronic neuropathic allodynia following damage to dorsal roots

The island of Calleja complex of rat basal forebrain. I. Light and electron microscopic observations.

An analysis of the cells and their processes within the island of Calleja complexes (ICC) was made in light and electron microscopic preparations to determine synaptic relationships within this part of the basal forebrain. The light microscopic preparations showed that the ICC contained two cell types, granule cells and large cells. In electron microscopic preparations, the somata of granule cells were grouped together and were directly apposed to other somata of granule cells. Specialized junctions (4-6 nm wide) that occurred at sites of somal apposition suggested ephaptic coupling of granule cells. The granule cell somata had nuclei that contained clumps of heterochromatin adjacent to smooth nuclear envelopes. The perikaryal cytoplasm of these cells consisted of a relatively thin rim containing few organelles. Spinous dendrites of small diameter were occasionally found in continuity with these cells. Axon terminals rarely formed synapses with the somata of granule cells, but were more frequently found to synapse on their dendrites and dendritic spines. These features for granule cells are similar to those for medium-sized spiny neurons in the neostriatum. The somata of the large cells were found either within the core or along the dorsal margin of the ICC. The large cells had infolded nuclei and an abundant perikaryal cytoplasm that contained many organelles. Large diameter dendrites that tapered down to smaller diameters emanated in many directions from these somata. Axon terminals covered nearly the entire surface of these somata and dendrites where they commonly formed symmetric synaptic junctions. These characteristics of large cells indicate a resemblance to the large cells in the globus pallidus and ventral pallidum. Therefore, the ICC have ultrastructural features found in both the neostriatum and globus pallidus.

EFFECTS EVOKED IN AN AXON BY THE ACTIVITY OF A CONTIGUOUS ONE

EFFECTS EVOKED IN AN AXON BY THE ACTIVITY OF A CONTIGUOUS ONE