Departamento de Física Teórica. Universidad Autónoma de Madrid, Cantoblanco 28049, Madrid, Spain.
Neural Comput. 2008 Jul;20(7):1651-705. doi: 10.1162/neco.2008.03-07-497.
Spike correlations between neurons are ubiquitous in the cortex, but their role is not understood. Here we describe the firing response of a leaky integrate-and-fire neuron (LIF) when it receives a temporarily correlated input generated by presynaptic correlated neuronal populations. Input correlations are characterized in terms of the firing rates, Fano factors, correlation coefficients, and correlation timescale of the neurons driving the target neuron. We show that the sum of the presynaptic spike trains cannot be well described by a Poisson process. In fact, the total input current has a nontrivial two-point correlation function described by two main parameters: the correlation timescale (how precise the input correlations are in time) and the correlation magnitude (how strong they are). Therefore, the total current generated by the input spike trains is not well described by a white noise gaussian process. Instead, we model the total current as a colored gaussian process with the same mean and two-point correlation function, leading to the formulation of the problem in terms of a Fokker-Planck equation. Solutions of the output firing rate are found in the limit of short and long correlation timescales. The solutions described here expand and improve on our previous results (Moreno, de la Rocha, Renart, & Parga, 2002) by presenting new analytical expressions for the output firing rate for general IF neurons, extending the validity of the results for arbitrarily large correlation magnitude, and by describing the differential effect of correlations on the mean-driven or noise-dominated firing regimes. Also the details of this novel formalism are given here for the first time. We employ numerical simulations to confirm the analytical solutions and study the firing response to sudden changes in the input correlations. We expect this formalism to be useful for the study of correlations in neuronal networks and their role in neural processing and information transmission.
神经元之间的尖峰相关在皮质中普遍存在，但它们的作用尚不清楚。在这里，我们描述了当一个漏失积分点火神经元（LIF）接收到由前突触相关神经元群体产生的暂时相关输入时的点火响应。输入相关是通过驱动目标神经元的神经元的点火率、Fano 因子、相关系数和相关时间尺度来描述的。我们表明，脉冲序列的总和不能很好地用泊松过程来描述。事实上，总输入电流具有非平凡的两点相关函数，由两个主要参数描述：相关时间尺度（输入相关在时间上的精度）和相关幅度（它们的强度）。因此，由输入脉冲序列产生的总电流不能很好地用白噪声高斯过程来描述。相反，我们将总电流建模为具有相同均值和两点相关函数的色高斯过程，从而将问题表述为福克-普朗克方程。在短和长相关时间尺度的极限下找到了输出点火率的解。这里描述的解扩展并改进了我们之前的结果（Moreno、de la Rocha、Renart 和 Parga，2002），通过为一般 IF 神经元提出输出点火率的新解析表达式，将结果的有效性扩展到任意大的相关幅度，并描述相关性对均值驱动或噪声主导点火状态的微分效应。这里也是首次给出这个新形式主义的细节。我们采用数值模拟来验证解析解，并研究对输入相关性突然变化的点火响应。我们期望这个形式主义对于研究神经元网络中的相关性及其在神经处理和信息传输中的作用是有用的。
