Capturing the response behavior of spiking neuron models with rate-based models facilitates the investigation of neuronal networks using powerful methods for rate-based network dynamics. To this end, we investigate the responses of two widely used neuron model types, the Izhikevich and augmented multi-adapative threshold (AMAT) models, to a range of spiking inputs ranging from step responses to natural spike data. We find (i) that linear-nonlinear firing rate models fitted to test data can be used to describe the firing-rate responses of AMAT and Izhikevich spiking neuron models in many cases; (ii) that firing-rate responses are generally too complex to be captured by first-order low-pass filters but require bandpass filters instead; (iii) that linear-nonlinear models capture the response of AMAT models better than of Izhikevich models; (iv) that the wide range of response types evoked by current-injection experiments collapses to few response types when neurons are driven by stationary or sinusoidally modulated Poisson input; and (v) that AMAT and Izhikevich models show different responses to spike input despite identical responses to current injections. Together, these findings suggest that rate-based models of network dynamics may capture a wider range of neuronal response properties by incorporating second-order bandpass filters fitted to responses of spiking model neurons. These models may contribute to bringing rate-based network modeling closer to the reality of biological neuronal networks.

中文翻译：

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具有大量尖峰行为的神经元的射速模型。

使用基于速率的模型捕获尖峰神经元模型的响应行为有助于使用强大的基于速率的网络动力学方法研究神经元网络。为此，我们研究了两种广泛使用的神经元模型类型（Izhikevich模型和增强型多自适应阈值（AMAT）模型）对一系列阶跃输入（从阶跃响应到自然峰值数据）的响应。我们发现（i）在许多情况下，可以使用拟合测试数据的线性-非线性激发速率模型来描述AMAT和Izhikevich激发神经元模型的激发速率响应；（ii）发射速率响应通常太复杂而无法被一阶低通滤波器捕获，但需要带通滤波器；（iii）线性非线性模型比Izhikevich模型更好地捕获了AMAT模型的响应；（iv）当神经元由平稳或正弦调制的泊松输入驱动时，电流注入实验引起的各种反应类型崩溃为很少的反应类型；（v）尽管对当前注入的响应相同，但AMAT和Izhikevich模型对尖峰输入的响应不同。总之，这些发现表明，通过结合适合于尖峰模型神经元响应的二阶带通滤波器，基于速率的网络动力学模型可以捕获更广泛的神经元响应特性。这些模型可能有助于使基于速率的网络建模更接近于生物神经元网络的现实。（v）尽管对当前注入的响应相同，但AMAT和Izhikevich模型对尖峰输入的响应不同。总之，这些发现表明，通过结合适合于尖峰模型神经元响应的二阶带通滤波器，基于速率的网络动力学模型可以捕获更广泛的神经元响应特性。这些模型可能有助于使基于速率的网络建模更接近于生物神经元网络的现实。（v）尽管对当前注入的响应相同，但AMAT和Izhikevich模型对尖峰输入的响应不同。总之，这些发现表明，通过结合适合于尖峰模型神经元响应的二阶带通滤波器，基于速率的网络动力学模型可以捕获更广泛的神经元响应特性。这些模型可能有助于使基于速率的网络建模更接近于生物神经元网络的现实。