Center for Theoretical Neuroscience, Columbia University, New York, New York, United States of America.
PLoS Comput Biol. 2011 Jan 20;7(1):e1001056. doi: 10.1371/journal.pcbi.1001056.
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.
神经元将随时间变化的输入转换为随时间依赖的速率随机发射的动作电位。从电流输入到输出点火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，其中通过依次将线性时变滤波器和静态非线性变换应用于输入来估计输出点火率。这些简化模型忽略了动作电位产生的生物物理细节。对于具有生物物理意义的更现实的尖峰神经元模型，输入输出映射在多大程度上可以简化为简单的线性非线性级联，这在很大程度上还不清楚。在这里，我们研究了在背景突触活动存在下，漏积分和放电 (LIF)、指数积分和放电 (EIF) 和基于电导的 Wang-Buzsáki 模型的这个问题。我们利用这些模型的可用解析结果以无参数的形式确定相应的线性滤波器和静态非线性。我们表明，所得到的函数与使用标准反向相关分析确定的线性滤波器和静态非线性相同。然后，我们定量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，在大多数参数空间中，LN 级联为尖峰神经元的点火率提供了准确的估计。对于 EIF 和 Wang-Buzsáki 模型，我们表明 LN 级联可以简化为一个点火率模型，我们通过解析确定其时间尺度。最后，我们引入了一个自适应时间尺度率模型，其中线性滤波器的时间尺度取决于瞬时点火率。该模型可实现对瞬时点火率的高度准确估计。
