Physical model of electrical synapses in a neural network

A theoretical model of electrical synapses is proposed, in which connexons play the role of nails that hold unmyelinated areas of neurons at a distance of about 3.5 nm, and the electrical connection between them is provided by charging the membrane of an inactive neuron with currents generated in the intercellular electrolyte (saline) by the action potential in the active neuron. This mechanism is similar to the salutatory conduction of the action potential between the nodes of Ranvier in myelinated axons and the ephaptic coupling of sufficiently close spaced neurons.

Modelling the effect of ephaptic coupling on spike propagation in peripheral nerve fibres

Experimental and theoretical studies have shown that ephaptic coupling leads to the synchronisation and slowing down of spikes propagating along the axons within peripheral nerve bundles. However, the main focus thus far has been on a small number of identical axons, whereas realistic peripheral nerve bundles contain numerous axons with different diameters. Here, we present a computationally efficient spike propagation model, which captures the essential features of propagating spikes and their ephaptic interaction, and facilitates the theoretical investigation of spike volleys in large, heterogeneous fibre bundles. The spike propagation model describes an action potential, or spike, by its position on the axon, and its velocity. The velocity is primarily defined by intrinsic features of the axons, such as diameter and myelination status, but it is also modulated by changes in the extracellular potential. These changes are due to transmembrane currents that occur during the generation of action potentials. The resulting change in the velocity is appropriately described by a linearised coupling function, which is calibrated with a biophysical model. We first lay out the theoretical basis to describe how the spike in an active axon changes the membrane potential of a passive axon. These insights are then incorporated into the spike propagation model, which is calibrated with a biophysically realistic model based on Hodgkin-Huxley dynamics. The fully calibrated model is then applied to fibre bundles with a large number of axons and different types of axon diameter distributions. One key insight of this study is that the heterogeneity of the axonal diameters has a dispersive effect, and that with increasing level of heterogeneity the ephaptic coupling strength has to increase to achieve full synchronisation between spikes. Another result of this study is that in the absence of full synchronisation, a subset of spikes on axons with similar diameter can form synchronised clusters. These findings may help interpret the results of noninvasive experiments on the electrophysiology of peripheral nerves.

Using ephaptic coupling to estimate the synaptic cleft resistivity of the calyx of Held synapse

At synapses, the pre- and postsynaptic cells get so close that currents entering the cleft do not flow exclusively along its conductance, gcl. A prominent example is found in the calyx of Held synapse in the medial nucleus of the trapezoid body (MNTB), where the presynaptic action potential can be recorded in the postsynaptic cell in the form of a prespike. Here, we developed a theoretical framework for ephaptic coupling via the synaptic cleft, and we tested its predictions using the MNTB prespike recorded in voltage-clamp. The shape of the prespike is predicted to resemble either the first or the second derivative of the inverted presynaptic action potential if cleft currents dissipate either mostly capacitively or resistively, respectively. We found that the resistive dissipation scenario provided a better description of the prespike shape. Its size is predicted to scale with the fourth power of the radius of the synapse, explaining why intracellularly recorded prespikes are uncommon in the central nervous system. We show that presynaptic calcium currents also contribute to the prespike shape. This calcium prespike resembled the first derivative of the inverted calcium current, again as predicted by the resistive dissipation scenario. Using this calcium prespike, we obtained an estimate for gcl of ~1 μS. We demonstrate that, for a circular synapse geometry, such as in conventional boutons or the immature calyx of Held, gcl is scale-invariant and only defined by extracellular resistivity, which was ~75 Ωcm, and by cleft height. During development the calyx of Held develops fenestrations. We show that these fenestrations effectively minimize the cleft potentials generated by the adult action potential, which might otherwise interfere with calcium channel opening. We thus provide a quantitative account of the dissipation of currents by the synaptic cleft, which can be readily extrapolated to conventional, bouton-like synapses.

The Electromagnetic Will

The conscious electromagnetic information (cemi) field theory proposes that the seat of consciousness is the brain’s electromagnetic (EM) field that integrates information from trillions of firing neurons. What we call free will is its output. The cemi theory also proposes that the brain has two streams. Most actions are initiated by the first non-conscious stream that is composed of neurons that are insulated from EM field influences. These non-conscious involuntary actions are thereby invisible to our EM field-located thoughts. The theory also proposes that voluntary actions are driven by neurons that receive EM field inputs and are thereby visible to our EM field-located thoughts. I review the extensive evidence for EM field/ephaptic coupling between neurons and the increasing evidence that EM fields in the brain are a cause of behaviour. I conclude by arguing that though this EM field-driven will is not free, in the sense of being acausal, it nevertheless corresponds to the very real experience of our conscious mind being in control of our voluntary actions. Will is not an illusion. It is our experience of control by our EM field-located mind. It is an immaterial, yet physical, will.

Ephaptic Coupling in Hybrid Neuronal Model

In recent decades, there has been growing interest in the impact of electric fields generated in the brain. Transmembrane ionic currents originate electric fields in the extracellular space and are capable of affecting nearby neurons, a phenomenon called ephaptic neuronal communication. In the present work, the Quadratic Integrate-and-Trigger model (QIF-E) underwent an adjustment/improvement to include the ephaptic coupling behavior between neurons and their results are compared to the empirical results. In this way, the analysis tools are employed according to the neuronal activity regime: (i) for the subthreshold regime, the circular statistic is used to describe the phase differences between the input stimulus signal and the modeled membrane response; (ii) in the suprathreshold regime, the Population Vector and the Spike Field Coherence are employed to estimate phase preferences and the coupling intensity between the input stimulus and the Action Potentials. The results observed are i) in the subthreshold regime the values of the phase differences change with distinct frequencies of an input stimulus; ii) in the supra-threshold regime the preferential phase of Action Potentials changes for different frequencies. In addition, we explore other parameters of the model, such as noise and membrane characteristic-time, in order to understand different types of neurons and extracellular environment related to ephaptic communication. Such results are consistent with results observed in empirical experiments based on ephaptic coupling behavior. In addition, the QIF-E model allows further studies on the physiological importance of ephaptic coupling in the brain, and its simplicity can open a door to simulating ephaptic coupling in neuron networks and evaluating the impact of ephaptic communication in such scenarios.

Using ephaptic coupling to estimate the synaptic cleft resistivity of the calyx of Held synapse.

At synapses, the pre- and postsynaptic cell get so close that currents entering the cleft do not flow exclusively along its conductance, gcl. A prominent example is found in the calyx of Held synapse in the medial nucleus of the trapezoid body, where the presynaptic action potential can be recorded in the postsynaptic cell in the form of a prespike. Here, we developed a theoretical framework for ephaptic coupling via the synaptic cleft. We found that the capacitive component of the prespike recorded in voltage clamp is closely approximated by the second time derivative of the presynaptic action potential. Its size scales with the fourth power of the radius of the synapse, explaining why intracellularly recorded prespikes are uncommon in the CNS. We show that presynaptic calcium currents can contribute to the prespike and that their contribution is closely approximated by the scaled first derivative of these currents. We confirmed these predictions in juvenile rat brainstem slices, and used the presynaptic calcium currents to obtain an estimate for gcl of ~1 μS. We demonstrate that for a typical synapse geometry, gcl is scale-invariant and only defined by extracellular resistivity, which was ~75 Ωcm, and by cleft height. During development the calyx of Held develops fenestrations. These fenestrations effectively minimize the cleft potentials generated by the adult action potential, which would otherwise interfere with calcium channel opening. We thus provide a quantitative account of the dissipation of currents by the synaptic cleft, which can be readily extrapolated to conventional, bouton-like synapses.

The Ups and Downs of Mechanism Realism: Functions, Levels, and Crosscutting Hierarchies

Mechanism realists assert the existence of mechanisms as objective structures in the world, but their exact metaphysical commitments are unclear. We introduce Local Hierarchy Realism (LHR) as a substantive and plausible form of mechanism realism. The limits of LHR reveal a deep tension between two aspects of mechanists’ explanatory strategy. Functional decomposition identifies locally relevant entities and activities, while these same entities and activities are also embedded in a nested hierarchy of levels. In principle, a functional decomposition may identify entities engaging in causal interactions that crosscut the hierarchical structure of composition relations, violating the mechanist’s injunction against interlevel causation. We argue that this possibility is realized in the example of ephaptic coupling, a subsidiary process of neural computation that crosscuts the hierarchy derived from synaptic transmission. These considerations undermine the plausibility of LHR as a general view, yet LHR has the advantages that (i) its metaphysical implications are precisely stateable; (ii) the structure it identifies is not reducible to mere aggregate causation; and (iii) it clearly satisfies intuitive and informal definitions of mechanism. We conclude by assessing the prospects for a form of mechanism realism weaker than LHR that nevertheless satisfies all three of these requirements.

The conduction velocity-potassium relationship in the heart is modulated by sodium and calcium

The relationship between cardiac conduction velocity (CV) and extracellular potassium (K+) is biphasic, with modest hyperkalemia increasing CV and severe hyperkalemia slowing CV. Recent studies from our group suggest that elevating extracellular sodium (Na+) and calcium (Ca2+) can enhance CV by an extracellular pathway parallel to gap junctional coupling (GJC) called ephaptic coupling that can occur in the gap junction adjacent perinexus. However, it remains unknown whether these same interventions modulate CV as a function of K+. We hypothesize that Na+, Ca2+, and GJC can attenuate conduction slowing consequent to severe hyperkalemia. Elevating Ca2+ from 1.25 to 2.00 mM significantly narrowed perinexal width measured by transmission electron microscopy. Optically mapped, Langendorff-perfused guinea pig hearts perfused with increasing K+ revealed the expected biphasic CV-K+ relationship during perfusion with different Na+ and Ca2+ concentrations. Neither elevating Na+ nor Ca2+ alone consistently modulated the positive slope of CV-K+ or conduction slowing at 10-mM K+; however, combined Na+ and Ca2+ elevation significantly mitigated conduction slowing at 10-mM K+. Pharmacologic GJC inhibition with 30-μM carbenoxolone slowed CV without changing the shape of CV-K+ curves. A computational model of CV predicted that elevating Na+ and narrowing clefts between myocytes, as occur with perinexal narrowing, reduces the positive and negative slopes of the CV-K+ relationship but do not support a primary role of GJC or sodium channel conductance. These data demonstrate that combinatorial effects of Na+ and Ca2+ differentially modulate conduction during hyperkalemia, and enhancing determinants of ephaptic coupling may attenuate conduction changes in a variety of physiologic conditions.