Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany.
PLoS Comput Biol. 2010 May 27;6(5):e1000794. doi: 10.1371/journal.pcbi.1000794.
Many neurons have epochs in which they fire action potentials in an approximately periodic fashion. To see what effects noise of relatively small amplitude has on such repetitive activity we recently examined the response of the Hodgkin-Huxley (HH) space-clamped system to such noise as the mean and variance of the applied current vary, near the bifurcation to periodic firing. This article is concerned with a more realistic neuron model which includes spatial extent. Employing the Hodgkin-Huxley partial differential equation system, the deterministic component of the input current is restricted to a small segment whereas the stochastic component extends over a region which may or may not overlap the deterministic component. For mean values below, near and above the critical values for repetitive spiking, the effects of weak noise of increasing strength is ascertained by simulation. As in the point model, small amplitude noise near the critical value dampens the spiking activity and leads to a minimum as noise level increases. This was the case for both additive noise and conductance-based noise. Uniform noise along the whole neuron is only marginally more effective in silencing the cell than noise which occurs near the region of excitation. In fact it is found that if signal and noise overlap in spatial extent, then weak noise may inhibit spiking. If, however, signal and noise are applied on disjoint intervals, then the noise has no effect on the spiking activity, no matter how large its region of application, though the trajectories are naturally altered slightly by noise. Such effects could not be discerned in a point model and are important for real neuron behavior. Interference with the spike train does nevertheless occur when the noise amplitude is larger, even when noise and signal do not overlap, being due to the instigation of secondary noise-induced wave phenomena rather than switching the system from one attractor (firing regularly) to another (a stable point).
许多神经元都有一段时间，在此期间它们以近似周期性的方式发射动作电位。为了了解相对较小幅度的噪声对这种重复活动有什么影响，我们最近研究了 Hodgkin-Huxley（HH）空间钳位系统对这种噪声的反应，即当施加电流的平均值和方差在周期性发射的分岔附近变化时。本文关注的是一个更现实的神经元模型，该模型包括空间范围。采用 Hodgkin-Huxley 偏微分方程组，将输入电流的确定性分量限制在一小段，而随机分量则扩展到可能与确定性分量重叠或不重叠的区域。对于低于、接近和高于重复尖峰的临界值的平均值，通过模拟确定了随噪声强度增加的弱噪声的影响。与点模型一样，接近临界值的小幅度噪声会抑制尖峰活动，并随着噪声水平的增加导致最小值。对于加性噪声和基于电导的噪声都是如此。在整个神经元上施加均匀噪声，其抑制细胞的效果仅比在兴奋区域附近发生的噪声略好。事实上，发现如果信号和噪声在空间上重叠，则弱噪声可能会抑制尖峰。然而，如果信号和噪声应用于不重叠的间隔，则噪声对尖峰活动没有影响，无论其应用区域有多大，尽管噪声会自然略微改变轨迹。在点模型中无法发现这种效应，对于真实神经元行为很重要。即使当噪声和信号不重叠时，当噪声幅度较大时，仍然会对尖峰序列产生干扰，这是由于引发了二次噪声诱导的波现象，而不是将系统从一个吸引子（有规律地发射）切换到另一个吸引子（一个稳定点）。
