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Abstract:Neuronal membrane capacitance C (m) is one of the prominent factors in action potential initiation and propagation and then influences the firing patterns of neurons. Exploring the roles that C (m) plays in different firing patterns can facilitate the understanding of how different factors might influence neuronal firing behaviors. However, the impacts of variations in C (m) on neuronal firing patterns have been only partly explored until now. In this study, the influence of C (m) on burst firing behaviors of … Show more
“…The motivation to quantify the impact of c(f) on the firing rate of a pyramidal cell came from the findings of (Wang et al, 2012), who in a two compartment model of a pyramidal cell, observed great variation in the firing patterns of the cell by altering the (constant) capacitance of one or both compartments. In their model they defined quiescent, spiking, and bursting activity, and by introducing an imbalance between somatic and dendritic capacitance, the firing pattern transitioned between these states.…”
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 (HH) 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. 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 prefrontal cortex 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.
“…The motivation to quantify the impact of c(f) on the firing rate of a pyramidal cell came from the findings of (Wang et al, 2012), who in a two compartment model of a pyramidal cell, observed great variation in the firing patterns of the cell by altering the (constant) capacitance of one or both compartments. In their model they defined quiescent, spiking, and bursting activity, and by introducing an imbalance between somatic and dendritic capacitance, the firing pattern transitioned between these states.…”
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 (HH) 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. 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 prefrontal cortex 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.
“…However, altering the time course of the membrane potential dynamics will also alter the complex interplay between various depolarizing and hyperpolarizing membrane currents through active ion channels. Hence, the relationship between and f is not trivial, and will generally depend on the ion channels that a neuron possesses, as well as its input conditions (Szlavik, 2003 ; Wang et al, 2012 ). Fig.…”
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 $$c_\text {m}$$
c
m
and a reduction in the firing rates of PV-cells. In the current work, we explore how changes in $$c_\text {m}$$
c
m
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 $$c_\text {m}$$
c
m
lead to reduced firing, but the experimentally reported increase in $$c_\text {m}$$
c
m
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 $$c_\text {m}$$
c
m
, 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 $$c_\text {m}$$
c
m
that are most likely candidates for explaining the experimentally reported reduction in firing rate.
“…In analyzing the transitions between different firing patterns, the diagram of interspike intervals (ISI) is introduced, which has been widely used to describe the transition modes among various firing behaviors in neurons [32][33][34][35]. The value of ISI is represented as the time difference between adjacent peaks within spike trains, which is illustrated in Fig.…”
Section: Resultsmentioning
confidence: 99%
“…In this study, the method we employed to describe the transition modes between different firing patterns is the ISI diagram, which has been widely used in the field of nonlinear analysis of neuronal systems [32][33][34][35]. Although widely applicable, and easy to be calculated numerically, ISI diagram has still failed to characterize the specific geometric structures of the corresponding bifurcation maps, thus for future considerations, other useful approaches, the phase plane analysis [59-50] and the fast/slow dynamical analysis [51][52][53] can be introduced to study the detailed bifurcation cascades like many other studies.…”
Abstract:Most of the traditional clustering algorithms are poor for clustering more complex structures other than the convex spherical sample space. In the past few years, several spectral clustering algorithms were proposed to cluster arbitrarily shaped data in various real applications. However, spectral clustering relies on the dataset where each cluster is approximately well separated to a certain extent. In the case that the cluster has an obvious inflection point within a non-convex space, the spectral clustering algorithm would mistakenly recognize one cluster to be different clusters. In this paper, we propose a novel spectral clustering algorithm called HSC combined with hierarchical method, which obviates the disadvantage of the spectral clustering by not using the misleading information of the noisy neighboring data points. The simple clustering procedure is applied to eliminate the misleading information, and thus the HSC algorithm could cluster both convex shaped data and arbitrarily shaped data more efficiently and accurately. The experiments on both synthetic data sets and real data sets show that HSC outperforms other popular clustering algorithms. Furthermore, we observed that HSC can also be used for the estimation of the number of clusters.
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