Theoretical Analysis of Coupled Modified Hindmarsh-rose Model Under Transcranial Magnetic-acoustic Electrical Stimulation

Transcranial magnetic-acoustic electrical stimulation (TMAES) is a new technology with ultrasonic waves and a static magnetic field to generate an electric current in nerve tissues to modulate neuronal firing activities. The existing neuron models only simulate a single neuron, and there are few studies on coupled neurons models about TMAES. Most of the neurons in the cerebral cortex are not isolated but are coupled to each other. It is necessary to study the information transmission of coupled neurons. The types of neuron coupled synapses include electrical synapse and chemical synapse. A neuron model without considering chemical synapses is not comprehensive. Here, we modified the Hindmarsh-Rose (HR) model to simulate the smallest nervous system—two neurons coupled electrical synapses and chemical synapses under TMAES. And the environmental variables describing the synaptic coupling between two neurons and the nonlinearity of the nervous system are also taken into account. The firing behavior of the nervous system can be modulated by changing the intensity or the modulation frequency. The results show that within a certain range of parameters, the discharge frequency of coupled neurons could be increased by altering the modulation frequency, and intensity of stimulation, modulating the excitability of neurons, reducing the response time of chemical postsynaptic neurons, and accelerating the information transferring. Moreover, the discharge frequency of neurons was selective to stimulus parameters. These results demonstrate the possible theoretical regulatory mechanism of the neurons' firing frequency characteristics by TMAES. The study establishes the foundation for large-scale neural network modeling and can be taken as the theoretical basis for TMAES experimental and clinical application.

The hyperpolarization-activated current shifts the dynamic range of a voltage-dependent electrical synapse

Like their chemical counterparts, electrical synapses show complex dynamics such as rectification and voltage dependence that interact with other electrical processes in neurons. The consequences arising from these interactions for the electrical behavior of the synapse, and the dynamics they create, remain largely unexplored. Using a voltage-dependent electrical synapse between a descending modulatory projection neuron (MCN1) and a motor neuron (LG) in the crustacean stomatogastric ganglion, we find that the influence of the hyperpolarization-activated inward current (Ih) is critical to the function of the electrical synapse. When we blocked Ih with CsCl, the voltage dependence of the electrical synapse shifted by 18.7 mV to more hyperpolarized voltages, placing the dynamic range of the electrical synapse outside of the range of voltages used by the LG motor neuron (-60.2 mV to -44.9 mV). With dual electrode current- and voltage-clamp recordings, we demonstrate that this voltage shift is due to a sustained effect of Ih on the presynaptic MCN1 axon terminal membrane potential. Ih-induced depolarization of the axon terminal membrane potential increased the electrical postsynaptic potentials and currents. With Ih present, the axon terminal resting membrane potential depolarized, shifting the dynamic range of the electrical synapse towards the functional range of the motor neuron. We thus demonstrate that the function of an electrical synapse is critically influenced by a voltage-dependent ionic current (Ih).

Hamiltonian energy and coexistence of hidden firing patterns from bidirectional coupling between two different neurons

In this paper, bidirectional-coupled neurons through an asymmetric electrical synapse are investigated. These coupled neurons involve 2D Hindmarsh–Rose (HR) and 2D FitzHugh–Nagumo (FN) neurons. The equilibria of the coupled neurons model are investigated, and their stabilities have revealed that, for some values of the electrical synaptic weight, the model under consideration can display either self-excited or hidden firing patterns. In addition, the hidden coexistence of chaotic bursting with periodic spiking, chaotic spiking with period spiking, chaotic bursting with a resting pattern, and the coexistence of chaotic spiking with a resting pattern are also found for some sets of electrical synaptic coupling. For all the investigated phenomena, the Hamiltonian energy of the model is computed. It enables the estimation of the amount of energy released during the transition between the various electrical activities. Pspice simulations are carried out based on the analog circuit of the coupled neurons to support our numerical results. Finally, an STM32F407ZE microcontroller development board is exploited for the digital implementation of the proposed coupled neurons model.

GABABR Modulation of Electrical Synapses and Plasticity in the Thalamic Reticular Nucleus

Two distinct types of neuronal activity result in long-term depression (LTD) of electrical synapses, with overlapping biochemical intracellular signaling pathways that link activity to synaptic strength, in electrically coupled neurons of the thalamic reticular nucleus (TRN). Because components of both signaling pathways can also be modulated by GABAB receptor activity, here we examined the impact of GABAB receptor activation on the two established inductors of LTD in electrical synapses. Recording from patched pairs of coupled rat neurons in vitro, we show that GABAB receptor inactivation itself induces a modest depression of electrical synapses and occludes LTD induction by either paired bursting or metabotropic glutamate receptor (mGluR) activation. GABAB activation also occludes LTD from either paired bursting or mGluR activation. Together, these results indicate that afferent sources of GABA, such as those from the forebrain or substantia nigra to the reticular nucleus, gate the induction of LTD from either neuronal activity or afferent glutamatergic receptor activation. These results add to a growing body of evidence that the regulation of thalamocortical transmission and sensory attention by TRN is modulated and controlled by other brain regions. Significance: We show that electrical synapse plasticity is gated by GABAB receptors in the thalamic reticular nucleus. This effect is a novel way for afferent GABAergic input from the basal ganglia to modulate thalamocortical relay and is a possible mediator of intra-TRN inhibitory effects.

Extensive GJD2 Expression in the Song Motor Pathway Reveals the Extent of Electrical Synapses in the Songbird Brain

Birdsong is a precisely timed animal behavior. The connectivity of song premotor neural networks has been proposed to underlie the temporal patterns of neuronal activity that control vo-cal muscle movements during singing. Although the connectivity of premotor nuclei via chemical synapses has been characterized, electrical synapses and their molecular identity remain unex-plored. We show with in situ hybridizations that GJD2 mRNA, coding for the major channel-form-ing electrical synapse protein in mammals, connexin 36, is expressed in the two nuclei that control song production, HVC and RA from canaries and zebra finches. In canaries’ HVC, GJD2 mRNA is extensively expressed in GABAergic and only a fraction of glutamatergic cells. By contrast, in RA, GJD2 mRNA expression is widespread in glutamatergic and GABAergic neurons. Remarkably, GJD2 expression is similar in song nuclei and their respective embedding brain regions, revealing the widespread expression of GJD2 in the avian brain. Inspection of a single-cell sequencing data-base from zebra and Bengalese finches generalizes the distributions of electrical synapses across cell types and song nuclei that we found in HVC and RA from canaries, reveals a differential GJD2 mRNA expression in HVC glutamatergic subtypes and its transient increase along the neurogenic lineage. We propose that songbirds are a suitable model to investigate the contribution of electrical synapses to motor skill learning and production.

Neuron dynamics and synchronous transition of symmetrical electrically coupled Sherman

Based on the study of the synchronization of two electric synapse-coupled Sherman neuron systems, this paper analyzes the rich discharge behavior of Sherman neurons through the peak-to-peak interval bifurcation diagram, which determines the parameter values for the study of the electrical synapse coupling Sherman neuron system synchronization. By using the synchronization difference and the correlation coefficient value, this paper analyzes the synchronous transition process of the two electrical synapse-coupled Sherman neuron systems with the change of coupling intensity and studies the bifurcation behavior of neurons in the two electrical synapse-coupled Sherman neuron systems. The experimental results show the transition process of two electrical synapse-coupled Sherman neurons from nonsynchronized, peak-independent cluster synchronization to fully synchronized. In addition, we study the synchronization process of the ring-connected electrical synapse-coupled Sherman neuron system. The experimental results show that the two electrical synapse-coupled Sherman neuron systems show a similar synchronous transition process.

Polarity Reversal Effect of a Memristor From the Circuit Point of View and Insights Into the Memristor Fuse

As the memristor device is asymmetrical in nature, it is not a bilateral element like the resistor in terms of circuit functionality. Thus, it causes hindrance in some memristor-based applications such as in cellular nonlinear network neighborhood connections and in some application areas where its orientation is essentially expected to act as a bilateral circuit element reliable for bidirectional communication, for example, in signal and image processing or in electrical synapse devices. We introduce a memristor-based network for each purpose where we replace the conventional series resistances by memristors. The memristor asymmetry is described from the circuit point of view allowing us to observe its interaction within the network. Moreover, a memristor fuse is proposed in order to achieve the memristive effect with symmetry, which is formed basically by connecting two memristors antiserially. We, therefore, analyze the memristor fuse from its basic principle along with the theoretical analysis and then observe the response from the circuit point of view.

Electrical synapse asymmetry results from, and masks, neuronal heterogeneity

Electrical synapses couple inhibitory neurons across the brain, underlying a variety of functions that are modifiable by activity. Despite recent advances, many basic functions and contributions of electrical synapses within neural circuitry remain underappreciated. Among these is the source and impact of electrical synapse asymmetry. Using multi-compartmental models of neurons coupled through dendritic electrical synapses, we investigated intrinsic factors that contribute to synaptic asymmetry and that result in modulation of spike time 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, true synapse asymmetry can be masked by each of these properties. Furthermore, we show that asymmetry alters the spiking timing and latency of coupled cells by up to tens of milliseconds, depending on direction of conduction or dendritic location of the electrical synapse. These simulations illustrate that causes of asymmetry are multifactorial, may not be apparent in somatic measurements of electrical coupling, influence dendritic processing, and produce a variety of outcomes on spike timing of coupled cells. Our findings highlight aspects of electrical synapses that should be considered in experimental demonstrations of coupling, and when assembling networks containing electrical synapses.

cAMP controls a trafficking mechanism that directs the neuron specificity and subcellular placement of electrical synapses

Electrical synapses are established between specific neurons and within distinct subcellular compartments, but the mechanisms that direct gap junction assembly in the nervous system are largely unknown. Here we show that a transcriptional program tunes cAMP signaling to direct the neuron-specific assembly and placement of electrical synapses in the C. elegans motor circuit. For these studies, we use live cell imaging to visualize electrical synapses in vivo and a novel optogenetic assay to confirm that they are functional. In VA motor neurons, the UNC-4 transcription factor blocks expression of cAMP antagonists that promote gap junction miswiring. In unc-4 mutants, VA electrical synapses are established with an alternative synaptic partner and are repositioned from the VA axon to soma. We show that cAMP counters these effects by driving gap junction trafficking into the VA axon for electrical synapse assembly. Thus, our experiments in an intact nervous system establish that cAMP regulates gap junction trafficking for the biogenesis of electrical synapses.

Identification and classification of innexin gene transcripts in the central nervous system of the terrestrial slug Limax valentianus

Intercellular gap junction channels and single-membrane channels have been reported to regulate electrical synapse and the brain function. Innexin is known as a gap junction-related protein in invertebrates and is involved in the formation of intercellular gap junction channels and single-cell membrane channels. Multiple isoforms of innexin protein in each species enable the precise regulation of channel function. In molluscan species, sequence information of innexins is still limited and the sequences of multiple innexin isoforms have not been classified. This study examined the innexin transcripts expressed in the central nervous system of the terrestrial slug Limax valentianus and identified 16 transcripts of 12 innexin isoforms, including the splicing variants. We performed phylogenetic analysis and classified the isoforms with other molluscan innexin sequences. Next, the phosphorylation, N-glycosylation, and S-nitrosylation sites were predicted to characterize the innexin isoforms. Further, we identified 16 circular RNA sequences of nine innexin isoforms in the central nervous system of Limax. The identification and classification of molluscan innexin isoforms provided novel insights for understanding the regulatory mechanism of innexin in this phylum.