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首页> 外文期刊>Journal of Computational Neuroscience >Reduction of stochastic conductance-based neuron models with time-scales separation
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Reduction of stochastic conductance-based neuron models with time-scales separation

机译：时标分离减少基于电导的随机神经元模型

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摘要

We introduce a method for systematically re ducing the dimension of biophysically realistic neuron models with stochastic ion channels exploiting time scales separation. Based on a combination of singular perturbation methods for kinetic Markov schemes with some recent mathematical developments of the averag ing method, the techniques are general and applicable to a large class of models. As an example, we derive and analyze reductions of different stochastic versions of the Hodgkin Huxley (HH) model, leading to distinct reduced models. The bifurcation analysis of one of the reduced models with the number of channels as a para meter provides new insights into some features of noisy discharge patterns, such as the bimodality of interspike intervals distribution. Our analysis of the stochastic HH model shows that, besides being a method to reduce the number of variables of neuronal models, our reduction scheme is a powerful method for gaining understanding on the impact of fluctuations due to finite size effects on the dynamics of slow fast systems. Our analysis of the reduced model reveals that decreasing the number of sodium channels in the HH model leads to a transition in the dynamics reminiscent of the Hopf bifurcation and that this transition accounts for changes in char acteristics of the spike train generated by the model. Finally, we also examine the impact of these results on neuronal coding, notably, reliability of discharge times and spike latency, showing that reducing the number of channels can enhance discharge time reliability in response to weak inputs and that this phenomenon can be accounted for through the analysis of the reduced model.
机译：我们介绍了一种利用时间尺度分离系统地减少具有随机离子通道的生物物理现实神经元模型尺寸的方法。基于动力学马尔可夫方案的奇异摄动方法与平均方法的一些最新数学发展的结合，该技术是通用的，适用于一大类模型。例如，我们推导和分析霍奇金赫x黎（HH）模型的不同随机版本的减少量，从而得出不同的减少量模型。简化模型之一的分叉分析以通道数量作为参数，为嘈杂的放电模式的某些特征提供了新的见解，例如钉间间隔分布的双峰性。我们对随机HH模型的分析表明，除减少神经元模型变量数量的方法外，我们的归约方案是一种有效的方法，可用于了解有限大小效应对慢速快速运动的波动影响。系统。我们对简化模型的分析表明，减少HH模型中钠通道的数量会导致动力学跃迁，使人联想到Hopf分叉，并且这种跃迁说明了模型所产生的尖峰序列的特性变化。最后，我们还检查了这些结果对神经元编码的影响，特别是放电时间和尖峰潜伏期的可靠性，表明减少通道数量可以增强放电时间对弱输入响应的可靠性，并且可以通过以下方法解决这种现象：简化模型的分析。

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