Signal transmission between gap-junctionally coupled passive cables is most effective at an optimal diameter

Extracellular Perinexal Separation Is a Principal Determinant of Cardiac Conduction

BACKGROUND

Cardiac conduction is understood to occur through gap junctions. Recent evidence supports ephaptic coupling as another mechanism of electrical communication in the heart. Conduction via gap junctions predicts a direct relationship between conduction velocity (CV) and bulk extracellular resistance. By contrast, ephaptic theory is premised on the existence of a biphasic relationship between CV and the volume of specialized extracellular clefts within intercalated discs such as the perinexus. Our objective was to determine the relationship between ventricular CV and structural changes to micro- and nanoscale extracellular spaces.

METHODS

Conduction and Cx43 (connexin43) protein expression were quantified from optically mapped guinea pig whole-heart preparations perfused with the osmotic agents albumin, mannitol, dextran 70 kDa, or dextran 2 MDa. Peak sodium current was quantified in isolated guinea pig ventricular myocytes. Extracellular resistance was quantified by impedance spectroscopy. Intercellular communication was assessed in a heterologous expression system with fluorescence recovery after photobleaching. Perinexal width was quantified from transmission electron micrographs.

RESULTS

CV primarily in the transverse direction of propagation was significantly reduced by mannitol and increased by albumin and both dextrans. The combination of albumin and dextran 70 kDa decreased CV relative to albumin alone. Extracellular resistance was reduced by mannitol, unchanged by albumin, and increased by both dextrans. Cx43 expression and conductance and peak sodium currents were not significantly altered by the osmotic agents. In response to osmotic agents, perinexal width, in order of narrowest to widest, was albumin with dextran 70 kDa; albumin or dextran 2 MDa; dextran 70 kDa or no osmotic agent, and mannitol. When compared in the same order, CV was biphasically related to perinexal width.

CONCLUSIONS

Cardiac conduction does not correlate with extracellular resistance but is biphasically related to perinexal separation, providing evidence that the relationship between CV and extracellular volume is determined by ephaptic mechanisms under conditions of normal gap junctional coupling.

On the Diverse Functions of Electrical Synapses

Electrical synapses are the neurophysiological product of gap junctional pores between neurons that allow bidirectional flow of current between neurons. They are expressed throughout the mammalian nervous system, including cortex, hippocampus, thalamus, retina, cerebellum, and inferior olive. Classically, the function of electrical synapses has been associated with synchrony, logically following that continuous conductance provided by gap junctions facilitates the reduction of voltage differences between coupled neurons. Indeed, electrical synapses promote synchrony at many anatomical and frequency ranges across the brain. However, a growing body of literature shows there is greater complexity to the computational function of electrical synapses. The paired membranes that embed electrical synapses act as low-pass filters, and as such, electrical synapses can preferentially transfer spike after hyperpolarizations, effectively providing spike-dependent inhibition. Other functions include driving asynchronous firing, improving signal to noise ratio, aiding in discrimination of dissimilar inputs, or dampening signals by shunting current. The diverse ways by which electrical synapses contribute to neuronal integration merits furthers study. Here we review how functions of electrical synapses vary across circuits and brain regions and depend critically on the context of the neurons and brain circuits involved. Computational modeling of electrical synapses embedded in multi-cellular models and experiments utilizing optical control and measurement of cellular activity will be essential in determining the specific roles performed by electrical synapses in varying contexts.

Intrinsic Sources and Functional Impacts of Asymmetry at Electrical Synapses

Electrical synapses couple inhibitory neurons across the brain, underlying a variety of functions that are modifiable by activity. Despite recent advances, many functions and contributions of electrical synapses within neural circuitry remain underappreciated. Among these are the sources and impacts of electrical synapse asymmetry. Using multi-compartmental models of neurons coupled through dendritic electrical synapses, we investigated intrinsic factors that contribute to effective synaptic asymmetry and that result in modulation of spike timing and synchrony between coupled cells. We show that electrical synapse location along a dendrite, input resistance, internal dendritic resistance, or directional conduction of the electrical synapse itself each alter asymmetry as measured by coupling between cell somas. Conversely, we note that asymmetrical gap junction (GJ) conductance can be masked by each of these properties. Furthermore, we show that asymmetry modulates spike timing and latency of coupled cells by up to tens of milliseconds, depending on direction of conduction or dendritic location of the electrical synapse. Coordination of rhythmic activity between two cells also depends on asymmetry. These simulations illustrate that causes of asymmetry are diverse, may not be apparent in somatic measurements of electrical coupling, influence dendritic processing, and produce a variety of outcomes on spiking and synchrony of coupled cells. Our findings highlight aspects of electrical synapses that should always be included in experimental demonstrations of coupling, and when assembling simulated networks containing electrical synapses.

A Single Differential Equation Description of Membrane Properties Underlying the Action Potential and the Axon Electric Field

In a succession of articles published over 65 years ago, Sir Alan Lloyd Hodgkin and Sir Andrew Fielding Huxley established what now forms our physical understanding of excitation in nerve, and how the axon conducts the action potential. They uniquely quantified the movement of ions in the nerve cell during the action potential, and demonstrated that the action potential is the result of a depolarizing event across the cell membrane. They confirmed that a complete depolarization event is followed by an abrupt increase in voltage that propagates longitudinally along the axon, accompanied by considerable increases in membrane conductance. In an elegant theoretical framework, they rigorously described fundamental properties of the Na⁺ and K⁺ conductances intrinsic to the action potential. Notwithstanding the elegance of Hodgkin and Huxley's incisive and explicative series of discoveries, their model is mathematically complex, relies on no small number of stochastic factors, and has no analytical solution. Solving for the membrane action potential and the ionic currents requires integrations approximated using numerical methods. In this article I present an analytical formalism of the nerve action potential, V_m and that of the accompanying cell membrane electric field, E_m . To conclude, I present a novel description of V_m in terms of a single, nonlinear differential equation. This is an original stand-alone article: the major contribution is the latter, and how this description coincides with the cell membrane electric field. This work has necessitated unifying information from two preceding papers [1,2], each being concerned with the development of closed-form descriptions of the nerve action potential, V_m .

Functional contributions of electrical synapses in sensory and motor networks

Intercellular interactions in the nervous system are mediated by two types of dedicated structural arrangements: electrical and chemical synapses. Several characteristics distinguish these two mechanisms of communication, such as speed, reliability and the fact that electrical synapses are, potentially, bidirectional. Given these properties, electrical synapses can subserve, in addition to synchrony, three main interrelated network functions: signal amplification, noise reduction and/or coincidence detection. Specific network motifs in sensory and motor systems of invertebrates and vertebrates illustrate how signal transmission through electrical junctions contributes to a complex processing of information.

Subthreshold somatic voltage in neocortical pyramidal cells can control whether spikes propagate from the axonal plexus to axon terminals: a model study

There is suggestive evidence that pyramidal cell axons in neocortex may be coupled by gap junctions into an "axonal plexus" capable of generating very fast oscillations (VFOs) with frequencies exceeding 80 Hz. It is not obvious, however, how a pyramidal cell in such a network could control its output when action potentials are free to propagate from the axons of other pyramidal cells into its own axon. We address this problem by means of simulations based on three-dimensional reconstructions of pyramidal cells from rat somatosensory cortex. We show that somatic depolarization enables propagation via gap junctions into the initial segment and main axon, while somatic hyperpolarization disables it. We show further that somatic voltage cannot effectively control action potential propagation through gap junctions on minor collaterals; action potentials may therefore propagate freely from such collaterals regardless of somatic voltage. In previous work, VFOs are all but abolished during the hyperpolarization phase of slow oscillations induced by anesthesia in vivo. This finding constrains the density of gap junctions on collaterals in our model and suggests that axonal sprouting due to cortical lesions may result in abnormally high gap junction density on collaterals, leading in turn to excessive VFO activity and hence to epilepsy via kindling.

A novel role of dendritic gap junction and mechanisms underlying its interaction with thalamocortical conductance in fast spiking inhibitory neurons

BACKGROUND

Little is known about the roles of dendritic gap junctions (GJs) of inhibitory interneurons in modulating temporal properties of sensory induced responses in sensory cortices. Electrophysiological dual patch-clamp recording and computational simulation methods were used in combination to examine a novel role of GJs in sensory mediated feed-forward inhibitory responses in barrel cortex layer IV and its underlying mechanisms.

RESULTS

Under physiological conditions, excitatory post-junctional potentials (EPJPs) interact with thalamocortical (TC) inputs within an unprecedented few milliseconds (i.e. over 200 Hz) to enhance the firing probability and synchrony of coupled fast-spiking (FS) cells. Dendritic GJ coupling allows fourfold increase in synchrony and a significant enhancement in spike transmission efficacy in excitatory spiny stellate cells. The model revealed the following novel mechanisms: 1) rapid capacitive current (Icap) underlies the activation of voltage-gated sodium channels; 2) there was less than 2 milliseconds in which the Icap underlying TC input and EPJP was coupled effectively; 3) cells with dendritic GJs had larger input conductance and smaller membrane response to weaker inputs; 4) synchrony in inhibitory networks by GJ coupling leads to reduced sporadic lateral inhibition and increased TC transmission efficacy.

CONCLUSION

Dendritic GJs of neocortical inhibitory networks can have very powerful effects in modulating the strength and the temporal properties of sensory induced feed-forward inhibitory and excitatory responses at a very high frequency band (>200 Hz). Rapid capacitive currents are identified as main mechanisms underlying interaction between two transient synaptic conductances.

Membrane capacitance measurements revisited: dependence of capacitance value on measurement method in nonisopotential neurons

During growth or degeneration neuronal surface area can change dramatically. Measurements of membrane protein concentration, as in ion channel or ionic conductance density, are often normalized by membrane capacitance, which is proportional to the surface area, to express changes independently from cell surface variations. Several electrophysiological protocols are used to measure cell capacitance, all based on the assumption of membrane isopotentiality. Yet, most neurons violate this assumption because of their complex anatomical structure, raising the question of which protocol yields measurements that are closest to the actual total membrane capacitance. We measured the capacitance of identified neurons from crab stomatogastric ganglia using three different protocols: the current-clamp step, the voltage-clamp step, and the voltage-clamp ramp protocols. We observed that the current-clamp protocol produced significantly higher capacitance values than those of either voltage-clamp protocol. Computational models of various anatomical complexities suggest that the current-clamp protocol can yield accurate capacitance estimates. In contrast, the voltage-clamp protocol estimates rapidly deteriorate as isopotentiality is reduced. We provide a mathematical description of these results by analyzing a simple two-compartment model neuron to facilitate an intuitive understanding of these methods. Together, the experiments, modeling, and mathematical analysis indicate that accurate total membrane capacitance measurements cannot be obtained with voltage-clamp protocols in nonisopotential neurons. Furthermore, although current-clamp steps can theoretically yield accurate measurements, experimentalists should be aware of limitations imposed by step duration and numerical errors during fitting procedures to obtain the membrane time constant.

Summation of excitatory postsynaptic potentials in electrically-coupled neurones

Dendritic electrical coupling increases the number of effective synaptic inputs onto neurones by allowing the direct spread of synaptic potentials from one neurone to another. Here we studied the summation of excitatory postsynaptic potentials (EPSPs) produced locally and arriving from the coupled neurone (transjunctional) in pairs of electrically-coupled Retzius neurones of the leech. We combined paired recordings of EPSPs, the production of artificial excitatory postsynaptic potentials (APSPs) in neurone pairs with different coupling coefficients and simulations of EPSPs produced in the coupled dendrites. Summation of the EPSPs produced in the dendrites was always linear, suggesting that synchronous EPSPs are produced at two or more different pairs of coupled dendrites and not in both sides of any one gap junction. The different spatio-temporal relationships explored between pairs of EPSPs or APSPs produced three main effects. (1) Synchronous pairs of EPSPs or APSPs exhibited an elongation of their decay phase compared to single EPSPs. (2) Asymmetries in the amplitudes between the pair of EPSPs added a "hump" to the smallest EPSP. (3) Modelling the inputs near the electrical synapse or anticipating the production of the transjunctional APSP increased the amplitude of the compound EPSP. The magnitude of all these changes depended on the coupling coefficient of the neurones. We also show that the hump improves the passive conduction of EPSPs by adding low frequency components. The diverse effects of summation of local and alien EPSPs shown here endow electrically-coupled neurones with a wider repertoire of adjustable integrative possibilities.

Sustained rhythmic activity in gap-junctionally coupled networks of model neurons depends on the diameter of coupled dendrites

Gap junctions are known to be important for many network functions such as synchronization of activity and the generation of waves and oscillations. Gap junctions have also been proposed to be essential for the generation of early embryonic activity. We have previously shown that the amplitude of electrical signals propagating across gap-junctionally coupled passive cables is maximized at a unique diameter. This suggests that threshold-dependent signals may propagate through gap junctions for a finite range of diameters around this optimal value. Here we examine the diameter dependence of action potential propagation across model networks of dendro-dendritically coupled neurons. The neurons in these models have passive soma and dendrites and an action potential-generating axon. We show that propagation of action potentials across gap junctions occurs only over a finite range of dendritic diameters and that propagation delay depends on this diameter. Additionally, in networks of gap-junctionally coupled neurons, rhythmic activity can emerge when closed loops (re-entrant paths) occur but again only for a finite range of dendrite diameters. The frequency of such rhythmic activity depends on the length of the path and the dendrite diameter. For large networks of randomly coupled neurons, we find that the re-entrant paths that underlie rhythmic activity also depend on dendrite diameter. These results underline the potential importance of dendrite diameter as a determinant of network activity in gap-junctionally coupled networks, such as network rhythms that are observed during early nervous system development.

Nonlinear, binocular interactions underlying flow field selectivity of a motion-sensitive neuron

Neurons in many species have large receptive fields that are selective for specific optic flow fields. Here, we studied the neural mechanisms underlying flow field selectivity in lobula plate tangential cells (LPTCs) of the blowfly. Among these cells, the H2 cell responds preferentially to visual stimuli approximating rotational optic flow. Through double recordings from H2 and many other LPTCs, we characterized a bidirectional commissural pathway that allows visual information to be shared between the hemispheres. This pathway is mediated by axo-axonal electrical coupling of H2 and the horizontal system equatorial (HSE) cell located in the opposite hemisphere. Using single-cell ablations, we found that this pathway is sufficient to allow H2 to amplify and attenuate dendritic input during binocular visual stimuli. This is accomplished through a modulation of H2's membrane potential by input from the contralateral HSE cell, which scales the firing rate of H2 during visual stimulation but is not sufficient to induce action potentials.