From spiking neuron models to linear-nonlinear models.
From spiking neuron models to linear-nonlinear models.
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DOI：
10.1371/journal.pcbi.1001056
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发表时间：
2011-01-20
影响因子：
4.3
通讯作者：
Brunel N
中科院分区：
文献类型：
--
作者：
Ostojic S;Brunel N
神经元将随时间变化的输入转换为以时间依赖性速率随机发射的动作电位。从当前输入到输出放电率的映射通常借助于现象学模型来表示，例如线性-非线性（LN）级联，其中输出放电率通过将线性时间滤波器和静态非线性变换相继应用于输入来估计。这些简化的模型忽略了动作电位产生的生物物理细节。在何种程度上，生物药理学上更现实的尖峰神经元模型的输入-输出映射可以简化为简单的线性-非线性级联，这是先验不清楚的。在这里，我们研究这个问题的泄漏积分和火灾（LIF），指数积分和火灾（EIF）和电导为基础的Wang-Buzsáki模型存在的背景突触活动。我们利用现有的分析结果，这些模型，以确定相应的线性滤波器和静态非线性的参数自由的形式。我们表明，所获得的功能是相同的线性滤波器和静态非线性使用标准的反相关分析。然后，我们定量地比较了相应的线性-非线性级联的输出与尖峰神经元的数值模拟，系统地改变输入信号和背景噪声的参数。我们发现，LN级联提供了准确的估计发放神经元的放电率在大多数参数空间。对于EIF和Wang-Buzsáki模型，我们证明了LN级联可以简化为一个点火率模型，我们分析确定其时间尺度。最后，我们介绍了一种自适应时标率模型，其中线性滤波器的时标取决于瞬时发射率。该模型导致瞬时发射率的高度准确的估计。破译大脑中的信息编码意味着理解个体神经元如何响应时变刺激而发出动作电位（AP）。这一任务由于以下两个事实而变得困难：（i）尽管AP产生的生物物理学已被很好地理解，但响应于随时间变化的输入的膜电位的动力学是高度复杂的;（ii）响应于给定刺激的AP的激发固有地是随机的，因为神经元的输入的仅一部分直接由刺激控制，其余的是由于周围网络的波动活动。因此，单个神经元的输入-输出转换通常是在简化的现象学模型的帮助下表示的，这些模型没有考虑生物物理细节。在这项研究中，我们直接涉及一类这样的现象学模型，所谓的线性-非线性模型，与更生物病理学详细的尖峰神经元模型。我们提供了两类模型之间的定量映射，并表明线性-非线性模型提供了一个很好的近似尖峰神经元的输入-输出变换，只要从周围的网络波动的输入不是非常弱。
Neurons transform time-varying inputs into action potentials emitted stochastically at a time dependent rate. The mapping from current input to output firing rate is often represented with the help of phenomenological models such as the linear-nonlinear (LN) cascade, in which the output firing rate is estimated by applying to the input successively a linear temporal filter and a static non-linear transformation. These simplified models leave out the biophysical details of action potential generation. It is not a priori clear to which extent the input-output mapping of biophysically more realistic, spiking neuron models can be reduced to a simple linear-nonlinear cascade. Here we investigate this question for the leaky integrate-and-fire (LIF), exponential integrate-and-fire (EIF) and conductance-based Wang-Buzsáki models in presence of background synaptic activity. We exploit available analytic results for these models to determine the corresponding linear filter and static non-linearity in a parameter-free form. We show that the obtained functions are identical to the linear filter and static non-linearity determined using standard reverse correlation analysis. We then quantitatively compare the output of the corresponding linear-nonlinear cascade with numerical simulations of spiking neurons, systematically varying the parameters of input signal and background noise. We find that the LN cascade provides accurate estimates of the firing rates of spiking neurons in most of parameter space. For the EIF and Wang-Buzsáki models, we show that the LN cascade can be reduced to a firing rate model, the timescale of which we determine analytically. Finally we introduce an adaptive timescale rate model in which the timescale of the linear filter depends on the instantaneous firing rate. This model leads to highly accurate estimates of instantaneous firing rates. Deciphering the encoding of information in the brain implies understanding how individual neurons emit action potentials (APs) in response to time-varying stimuli. This task is made difficult by two facts: (i) although the biophysics of AP generation are well understood, the dynamics of the membrane potential in response to a time-varying input are highly complex; (ii) the firing of APs in response to a given stimulus is inherently stochastic as only a fraction of the inputs to a neuron are directly controlled by the stimulus, the remaining being due to the fluctuating activity of the surrounding network. As a result, the input-output transform of individual neurons is often represented with the help of simplified phenomenological models that do not take into account the biophysical details. In this study, we directly relate a class of such phenomenological models, the so called linear-nonlinear models, with more biophysically detailed spiking neuron models. We provide a quantitative mapping between the two classes of models, and show that the linear-nonlinear models provide a good approximation of the input-output transform of spiking neurons, as long as the fluctuating inputs from the surrounding network are not exceedingly weak.
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