Firing patterns and bifurcation analysis of Purkinje cell dendrite model

This paper mainly studied firing patterns and related bifurcations in the Purkinje cell dendrite model. Based on the methods of equivalent potentials and time scale analysis, the initial six-dimensional (6D) dendrite model is reduced to a 3D form to facilitate the calculation. We numerically show that the dendrite model could exhibit period-adding bifurcation and four bursting patterns for several vital parameters. Then the bifurcation mechanisms and transition of these four bursting patterns are discussed by phase plane analysis, and two-parameter bifurcation analysis of the fast subsystem, respectively. Moreover, we computed the first Lyapunov coefficient to determine the stability of Hopf bifurcation. Ultimately, we analyzed the codimension-two bifurcation of the whole system and gave a detailed theoretical derivation of the Bogdanov–Takens bifurcation.

Muscarinic acetylcholine receptors modulate HCN channel properties in vestibular ganglion neurons

Vestibular efferent neurons play an important role in shaping vestibular afferent excitability and accordingly, on the information encoded by their spike patterns. Efferent-modulation is linked to muscarinic signaling cascades that affect ion channel conductances, most notably low-voltage gated potassium channels such as KCNQ. Here we tested and found that muscarinic signaling cascades also modulate hyperpolarization-activated cyclic-nucleotide gated channels (HCN). HCN channels play a key role in controlling spike-timing regularity and a non-chemical form of transmission between type I hair cells and vestibular afferents. The impact of cholinergic efferent input on HCN channels was assessed using voltage-clamp methods, which measure currents in the disassociated cell bodies of vestibular ganglion neurons (VGN). Membrane properties in VGN were characterized before and after administration of the muscarinic acetylcholine receptor (mAChR) agonist Oxotremorine-M (Oxo-M). We found that Oxo-M shifted the voltage-activation range of HCN channels in the positive direction by 4.1 +/- 1.1 mV, which more than doubled the available current when held near rest at -60 mV (a 184 +/- 90.1% increase, n=19). This effect was not blocked by pre-treating the cells with a KCNQ channel blocker, linopirdine, which suggests that this effect is not dependent on KCNQ currents. We also found that HCN channel properties in the baseline condition and sensitivity to mAChR activation depended on cell size and firing patterns. Large-bodied neurons with onset firing patterns had the most depolarized activation range and least sensitivity to mAChR activation. Together, our results highlight the complex and dynamic regulation of HCN channels in VGN.

Oscillations of pause-burst neurons in the STN correlate with the severity of motor signs in Parkinson's disease

Background. Oscillatory activity in the subthalamic nucleus (STN) in Parkinson's disease (PD) is under extensive study. While rhythmic features of local field potentials are implicated in the manifestation of PD motor signs, less is known about single unit activity (SUA). SUA parameters inside the STN show significant heterogeneity, and various firing patterns may contribute unequally to PD pathophysiology. Objectives. We searched for correlations between SUA parameters and PD motor signs, taking neuronal activity patterns into account. Methods. 829 spike trains for STN SUA were recorded during 25 DBS surgeries. We have isolated three firing patterns (tonic, irregular burst and pause-burst) and, using mixed linear models, examined several ISI parameters and burst descriptors (for the last two patterns) for their correlation with the UPDRS 3 score and bradykinesia and rigidity scores on the contralateral body side. Results. The predominance of pause-burst as opposed to tonic activity was associated with an increase in UPDRS 3 score. Oscillation scores in the alpha range correlated with bradykinesia and rigidity scores, and oscillation scores in the beta range correlated with bradykinesia score only for pause-burst neurons, while other patterns showed no correlation with PD motor signs. There was also significant negative correlation between bradykinesia score and theta oscillations for pause-burst pattern. Conclusions. Pause-burst pattern and rhythmic neurons oscillating in the alpha range may affect motor processing in the basal ganglia more prominently than other activity patterns, probably reflecting progressive switching from tonic to burst to rhythmic activity in the parkinsonian state.

Locus Coeruleus Optogenetic Modulation: Lessons Learned from Temporal Patterns

After reviewing seminal studies using optogenetics to interrogate the functional role of the locus coeruleus in behavior, we conclude that differences in firing rates and firing patterns of locus coeruleus neurons contribute to locus coeruleus nucleus heterogeneity by recruiting different output circuitry, and differentially modifying behavior. The outcomes initiated by different optogenetic input activation patterns and frequencies can have opposite consequences for behavior, activate different neurons in the same target structure, be supported by distinct adrenoceptors and vary with behavioral state.

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.

Firing Activities in Fractional-Order Hindmarsh-Rose Neuron with Multistable Memristor as Autapse

Compared with integer order neurons, fractional-order neuron model can more accurately describe the firing behavior of biological neurons. Considering the fact that memristors have the characteristics similar to biological synapses, a fractional-order multistable memristor is firstly proposed in this study. It is verified that the fractional-order memristor has multiple local active regions and multiple stable hysteresis loops, and the influence of fractional order on its nonvolatility is also revealed. Then by considering the fractional-order memristor as an autapse of HR neuron model, a fractional-order memristive neuron model is developed. The effects of the initial value, external excitation current, coupling strength and fractional order on the firing behavior are discussed by time series, phase diagrams, Lyapunov exponents and inter spike interval (ISI) bifurcation diagrams. Three coexisting firing patterns, including irregulate A-periodic bursting, A-periodic bursting and chaotic bursting, dependent on the memristor initial values are observed. It is also revealed that the fractional order can not only induce the transition of firing patterns, but also change the firing frequency of the neuron. Finally, a neuron circuit with variable fractional order is designed to verify the numerical simulations.

Diverse Dynamic Behaviors and Firing Activities of the Modified Fractional-Order Hindmarsh–Rose Neuronal Model Induced by Fractional-Order

It is important to investigate the firing activities of neurons, and previous experimental works have shown that fractional-order neuronal models depict the firing rate of neurons more verifiably. In this study, a modified fractional-order Hindmarsh–Rose neuronal model is proposed, and the dynamics and firing activities are investigated. Some novel phenomenon can be found. First, by analyzing numerically and theoretically, the Hopf bifurcation is found to occur when the external direct current stimulus is chosen appropriately. The effects of fractional-order on the bifurcation are also studied. Second, when injecting a direct current stimulus, compared with the integer-order model, the system has more varying dynamic behaviors and firing pattern transitions. Under different external current stimulus, periodic firing patterns and chaotic firing patterns occur when fractional-order changes, but the regions of chaotic firing patterns are different. In other words, the transition mode of periodic firing and chaotic firing induced by fractional-order is different under different external current stimulus. The two-dimensional colored diagram of firing patterns is also investigated. Finally, when injecting periodic current stimulus, regular/irregular bursting, multiple spiking, regular\irregular square wave bursting, and mixed firing mods are found by setting the appropriate fractional-order, amplitude, and frequency of the external current stimulus. Some firing patterns cannot be found in integer-order models. When the amplitude is chosen at appropriate values, the region of frequency when the system displays the mixed firing modes decreases with increasing fractional-order.