State-Dependent Effects of Na Channel Noise on Neuronal Burst Generation

Abstract

We explore the effects of stochastic sodium (Na) channel activation on the variability and dynamics of spiking and bursting in a model neuron. The complete model segregates Hodgin-Huxley-type currents into two compartments, and undergoes applied current-dependent bifurcations between regimes of periodic bursting, chaotic bursting, and tonic spiking. Noise is added to simulate variable, finite sizes of the population of Na channels in the fast spiking compartment. During tonic firing, Na channel noise causes variability in interspike intervals (ISIs). The variance, as well as the sensitivity to noise, depend on the model's biophysical complexity. They are smallest in an isolated spiking compartment; increase significantly upon coupling to a passive compartment; and increase again when the second compartment also includes slow-acting currents. In this full model, sufficient noise can convert tonic firing into bursting. During bursting, the actions of Na channel noise are state-dependent. The higher the noise level, the greater the jitter in spike timing within bursts. The noise makes the burst durations of periodic regimes variable, while decreasing burst length duration and variance in a chaotic regime. Na channel noise blurs the sharp transitions of spike time and burst length seen at the bifurcations of the noise-free model. Close to such a bifurcation, the burst behaviors of previously periodic and chaotic regimes become essentially indistinguishable. We discuss biophysical mechanisms, dynamical interpretations and physiological implications. We suggest that noise associated with finite populations of Na channels could evoke very different effects on the intrinsic variability of spiking and bursting discharges, depending on a biological neuron's complexity and applied current-dependent state. We find that simulated channel noise in the model neuron qualitatively replicates the observed variability in burst length and interburst interval in an isolated biological bursting neuron.

Comparison of Langevin and Markov channel noise models for neuronal signal generation

“…Whether these observations apply to other classes of voltage-gated ion channels remains unclear [51]. Because of the limited data from the voltage-gated N a + and delayed rectifier K + channels we have modeled, we address only the differences between Our study indicates that the Langevin model of channel noise is unable to capture the stochastic behaviour of voltage-gated ion channels, although this method has been repeatedly used in the literature [8,52,53,54]. Contrary to popular assumptions [5], the overestimation of information rates by the Langevin model, does not improve in larger area compartments with greater numbers of ion channels; information rate estimates from Markov and Langevin models do not converge even in large compartments.…”

Noise, transient dynamics, and the generation of realistic interspike interval variation in square-wave burster neurons

“…Stochastic ion channel gating has been suggested to be the major source of noise in isolated neurons [31]. Since our derivation of the generative model for isi map signatures does not impose constraints nor require a particular noise mechanism, we chose to model stochastic gating using three different approaches [32].…”

Whole Cell Stochastic Model Reproduces the Irregularities Found in the Membrane Potential of Bursting Neurons

“…6 and 9 of Rowat and Elson 2004), we measured the spike time in burst (STB) of the time series of both models and plotted the bifurcation diagram of the STBs as a function of the external current, as shown in Fig. 7.…”

“…Because most of the works where the stochastic nature of the ion channels was considered relied on the effects of the fluctuations produced by a small population of channels (Rowat and Elson 2004;Schneidman et al 1998;Skaugen and Walloe 1979;White et al 1998), there is another important question about the irregularities reproduced by our stochastic model: How robust are these irregularities to changes in the number of channels considered in the model (surface of the neuronal membrane). To address this question, we ran the stochastic model for many different sizes of the membrane and plotted the ISI bifurcation diagram as a function of the membrane area, as shown in Fig.…”