Nykamp D Q, Tranchina D
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA.
Neural Comput. 2001 Mar;13(3):511-46. doi: 10.1162/089976601300014448.
A previously developed method for efficiently simulating complex networks of integrate-and-fire neurons was specialized to the case in which the neurons have fast unitary postsynaptic conductances. However, inhibitory synaptic conductances are often slower than excitatory ones for cortical neurons, and this difference can have a profound effect on network dynamics that cannot be captured with neurons that have only fast synapses. We thus extend the model to include slow inhibitory synapses. In this model, neurons are grouped into large populations of similar neurons. For each population, we calculate the evolution of a probability density function (PDF), which describes the distribution of neurons over state-space. The population firing rate is given by the flux of probability across the threshold voltage for firing an action potential. In the case of fast synaptic conductances, the PDF was one-dimensional, as the state of a neuron was completely determined by its transmembrane voltage. An exact extension to slow inhibitory synapses increases the dimension of the PDF to two or three, as the state of a neuron now includes the state of its inhibitory synaptic conductance. However, by assuming that the expected value of a neuron's inhibitory conductance is independent of its voltage, we derive a reduction to a one-dimensional PDF and avoid increasing the computational complexity of the problem. We demonstrate that although this assumption is not strictly valid, the results of the reduced model are surprisingly accurate.
一种先前开发的用于有效模拟积分发放神经元复杂网络的方法专门应用于神经元具有快速单位突触后电导的情况。然而，对于皮层神经元，抑制性突触电导通常比兴奋性突触电导慢，这种差异会对网络动力学产生深远影响，而仅具有快速突触的神经元无法捕捉到这种影响。因此，我们将该模型扩展到包含慢速抑制性突触的情况。在这个模型中，神经元被分组为大量相似的神经元群体。对于每个群体，我们计算概率密度函数（PDF）的演化，该函数描述了神经元在状态空间中的分布。群体发放率由跨越动作电位发放阈值电压的概率通量给出。在快速突触电导的情况下，PDF是一维的，因为神经元的状态完全由其跨膜电压决定。对慢速抑制性突触的精确扩展会将PDF 的维度增加到二维或三维，因为神经元的状态现在包括其抑制性突触电导的状态。然而，通过假设神经元抑制性电导的期望值与其电压无关，我们推导出将其简化为一维PDF的方法，并避免增加问题的计算复杂性。我们证明，尽管这个假设并不严格成立，但简化模型的结果却出奇地准确。
