Istituto Superiore di Sanità, Roma, Italy.
DITEN, University of Genoa, Genova, Italy.
PLoS Comput Biol. 2019 Oct 8;15(10):e1007404. doi: 10.1371/journal.pcbi.1007404. eCollection 2019 Oct.
Message passing between components of a distributed physical system is non-instantaneous and contributes to determine the time scales of the emerging collective dynamics. In biological neuron networks this is due in part to local synaptic filtering of exchanged spikes, and in part to the distribution of the axonal transmission delays. How differently these two kinds of communication protocols affect the network dynamics is still an open issue due to the difficulties in dealing with the non-Markovian nature of synaptic transmission. Here, we develop a mean-field dimensional reduction yielding to an effective Markovian dynamics of the population density of the neuronal membrane potential, valid under the hypothesis of small fluctuations of the synaptic current. Within this limit, the resulting theory allows us to prove the formal equivalence between the two transmission mechanisms, holding for any synaptic time scale, integrate-and-fire neuron model, spike emission regimes and for different network states even when the neuron number is finite. The equivalence holds even for larger fluctuations of the synaptic input, if white noise currents are incorporated to model other possible biological features such as ionic channel stochasticity.
分布式物理系统组件之间的消息传递不是即时的，这有助于确定涌现的集体动力学的时间尺度。在生物神经元网络中，这部分是由于局部突触对交换尖峰的滤波，部分是由于轴突传输延迟的分布。由于突触传递的非马尔可夫性质在处理上存在困难，这两种通信协议如何不同地影响网络动力学仍然是一个悬而未决的问题。在这里，我们提出了一种平均场降维方法，得到了神经元膜电位的种群密度的有效马尔可夫动力学，这在突触电流小波动的假设下是有效的。在这个限制下，所得到的理论允许我们证明这两种传输机制之间的形式等价性，适用于任何突触时间尺度、积分-点火神经元模型、尖峰发射模式以及不同的网络状态，即使神经元数量是有限的。即使对于突触输入的较大波动，如果包含白噪声电流来模拟其他可能的生物特征，如离子通道随机性，这种等价性仍然成立。
