Brunel N, Sergi S
LPS, Ecole Normale Supérieure, 24 rue Lhomond, Paris Cedex 05, 75231, France.
J Theor Biol. 1998 Nov 7;195(1):87-95. doi: 10.1006/jtbi.1998.0782.
We consider a model of an integrate-and-fire neuron with synaptic current dynamics, in which the synaptic time constant tau' is much smaller than the membrane time constant tau. We calculate analytically the firing frequency of such a neuron for inputs described by a random Gaussian process. We find that the first order correction to the frequency due to tau' is proportional to the square root of the ratio between these time constants radicaltau'/tau. This implies that the correction is important even when the synaptic time constant is small compared with that of the potential. The frequency of a neuron with tau'>0 can be reduced to that of the basic IF neuron (corresponding to tau'=1) using an "effective" threshold which has a linear dependence on radical tau'/tau. Numerical simulations show a very good agreement with the analytical result, and permit an extrapolation of the "effective" threshold to higher orders in radical tau'/tau. The obtained frequency agrees with simulation data for a wide range of parameters.
我们考虑一个具有突触电流动力学的积分发放神经元模型，其中突触时间常数τ'远小于膜时间常数τ。我们对由随机高斯过程描述的输入，解析计算了这种神经元的发放频率。我们发现，由于τ'导致的频率一阶修正与这些时间常数之比的平方根√(τ'/τ)成正比。这意味着即使突触时间常数与电位时间常数相比很小时，该修正也很重要。对于τ'>0的神经元，使用对√(τ'/τ)具有线性依赖关系的“有效”阈值，其频率可以降低到基本积分发放神经元（对应于τ'=1）的频率。数值模拟与解析结果显示出非常好的一致性，并允许将“有效”阈值外推到√(τ'/τ)的更高阶。所得到的频率在很宽的参数范围内与模拟数据相符。
