Burst firing transitions in two-compartment pyramidal neuron induced by the perturbation of membrane capacitance

Responses in fast-spiking interneuron firing rates to parameter variations associated with degradation of perineuronal nets

The perineuronal nets (PNNs) are sugar coated protein structures that encapsulate certain neurons in the brain, such as parvalbumin positive (PV) inhibitory neurons. As PNNs are theorized to act as a barrier to ion transport, they may effectively increase the membrane charge-separation distance, thereby affecting the membrane capacitance. Tewari et al. (2018) found that degradation of PNNs induced a 25%-50% increase in membrane capacitance [Formula: see text] and a reduction in the firing rates of PV-cells. In the current work, we explore how changes in [Formula: see text] affects the firing rate in a selection of computational neuron models, ranging in complexity from a single compartment Hodgkin-Huxley model to morphologically detailed PV-neuron models. In all models, an increased [Formula: see text] lead to reduced firing, but the experimentally reported increase in [Formula: see text] was not alone sufficient to explain the experimentally reported reduction in firing rate. We therefore hypothesized that PNN degradation in the experiments affected not only [Formula: see text], but also ionic reversal potentials and ion channel conductances. In simulations, we explored how various model parameters affected the firing rate of the model neurons, and identified which parameter variations in addition to [Formula: see text] that are most likely candidates for explaining the experimentally reported reduction in firing rate.

The role of relative membrane capacitance and time delay in cerebellar Purkinje cells

The membrane capacitance of a neuron can influence the synaptic efficacy and the speed of electrical signal propagation. Exploring the role of membrane capacitance will help facilitate a deeper understanding of the electrical properties of neurons. Thus, in this paper, we investigated the neuronal firing behaviors of a two-compartment model in Purkinje cells. We evaluated the influence of membrane capacitance under two different circumstances: in the absence of time delay and in the presence of time delay. Firstly, we separately studied the influence of somatic membrane capacitance Cs and dendritic membrane capacitance Cd on neuronal firing patterns. Through numerical simulation, we observed that they had two different types of period-adding scenarios, i.e. with and without chaotic bursting. Secondly, our results indicated that when the time delay was included in the model, periodic motions were more inclined to be destroyed, while at the same time, corresponding new chaotic motions were induced. These findings suggested that membrane capacitance and time delay play a pivotal functional role in modulating dynamical firing properties of neurons, especially aspects which lead to behaviors which result in changes to bursting patterns.

Effects of frequency-dependent membrane capacitance on neural excitability

OBJECTIVE

Models of excitable cells consider the membrane specific capacitance as a ubiquitous and constant parameter. However, experimental measurements show that the membrane capacitance declines with increasing frequency, i.e., exhibits dispersion. We quantified the effects of frequency-dependent membrane capacitance, c(f), on the excitability of cells and nerve fibers across the frequency range from dc to hundreds of kilohertz.

APPROACH

We implemented a model of c(f) using linear circuit elements, and incorporated it into several models of neurons with different channel kinetics: the Hodgkin-Huxley model of an unmyelinated axon, the McIntyre-Richardson-Grill (MRG) of a mammalian myelinated axon, and a model of a cortical neuron from prefrontal cortex (PFC). We calculated thresholds for excitation and kHz frequency conduction block, the conduction velocity, recovery cycle, strength-distance relationship and firing rate.

MAIN RESULTS

The impact of c(f) on activation thresholds depended on the stimulation waveform and channel kinetics. We observed no effect using rectangular pulse stimulation, and a reduction for frequencies of 10 kHz and above using sinusoidal signals only for the MRG model. c(f) had minimal impact on the recovery cycle and the strength-distance relationship, whereas the conduction velocity increased by up to 7.9% and 1.7% for myelinated and unmyelinated fibers, respectively. Block thresholds declined moderately when incorporating c(f), the effect was greater at higher frequencies, and the maximum reduction was 11.5%. Finally, c(f) marginally altered the firing pattern of a model of a PFC cell, reducing the median interspike interval by less than 2%.

SIGNIFICANCE

This is the first comprehensive analysis of the effects of dispersive capacitance on neural excitability, and as the interest on stimulation with kHz signals gains more attention, it defines the regions over which frequency-dependent membrane capacitance, c(f), should be considered.

Control of bursting behavior in neurons by autaptic modulation

Firing properties of biological neurons have long been recognized to be determined by extrinsic synaptic afferents that neurons receive and intrinsic ionic mechanisms that neurons possess, however, previous researches have also demonstrated that firing behavior of single neurons can be modulated by the neurons themselves, realized by the autapses. Thus in this investigation, we argued that how autaptic modulations shape the bursting behavior of biological neurons. We considered the issue from the following two aspects: autaptic-excitation and -inhibition. Our results suggested that for autaptic-excitation, under the condition of relatively weak stimulus, regular bursting was more incline to occur when the autaptic strength was weak, while regular spiking was more likely to appear when the autaptic strength was strong. However, larger stimulus would diminish the portion of bursting, but increase the portion of spiking. For autaptic-inhibition, under relatively weak stimulus, a wide range of regular bursting emerges when the autaptic strength was small, but when stronger stimulus were applied, the range of regular bursting shrinked into a small region. Meanwhile, we observed that synaptic delays have no obvious effects in the case of autaptic-excitation, while a subtle effect of synaptic delays was observed in the case of autaptic-inhibition. These results showed that bursting behavior of neurons could be controlled and modulated by the autaptic mechanisms that biological neurons intrinsically possess, and the final results may further promote the understanding in the generation of various neuronal firing patterns.

Dynamical properties of firing patterns in ELL pyramidal neuron under external electric field stimulus

Pyramidal neurons in the electrosensory lateral line lobe (ELL) of weakly electric fish activate in an environment of time-varying electric fields, which are generated by the fish itself, while how these pyramidal neurons would behave or what kinds of firing patterns these neurons would produce under different electric fields is still unclear. In this research, the firing behaviors of ELL pyramidal neuron under DC and AC electric field stimulus are investigated in a two-compartment neuron model. By means of numerical simulations we show that firing patterns of the model ELL pyramidal neuron are much diverse under different values of DC electric field, and neuronal spike frequency exhibits a monotone decreasing trend with the linearly increased DC fields, moreover, the transition mode between these firing patterns with the variation of DC electric fields demonstrates an explicit periodic route. While for AC electric fields, neuronal firing frequency periodically transforms with the increase of AC frequency, particularly, a special transition pattern (from multi-period bursting to spiking) repeatedly appears with the change of AC frequency. Our simulation results indicate that ELL pyramidal neurons fire dynamically under the time-varying electric fields, the diversity of firing patterns and their periodic transition modes may imply the potential roles of these dynamical firings in the coding strategy of sensory information processing.