Schmutz Valentin, Gerstner Wulfram, Schwalger Tilo
Brain Mind Institute, École Polytechnique Féderale de Lausanne (EPFL), Lausanne, Switzerland.
Bernstein Center for Computational Neuroscience, Institut für Mathematik, Technische Universität Berlin, Berlin, Germany.
J Math Neurosci. 2020 Apr 6;10(1):5. doi: 10.1186/s13408-020-00082-z.
Coarse-graining microscopic models of biological neural networks to obtain mesoscopic models of neural activities is an essential step towards multi-scale models of the brain. Here, we extend a recent theory for mesoscopic population dynamics with static synapses to the case of dynamic synapses exhibiting short-term plasticity (STP). The extended theory offers an approximate mean-field dynamics for the synaptic input currents arising from populations of spiking neurons and synapses undergoing Tsodyks-Markram STP. The approximate mean-field dynamics accounts for both finite number of synapses and correlation between the two synaptic variables of the model (utilization and available resources) and its numerical implementation is simple. Comparisons with Monte Carlo simulations of the microscopic model show that in both feedforward and recurrent networks, the mesoscopic mean-field model accurately reproduces the first- and second-order statistics of the total synaptic input into a postsynaptic neuron and accounts for stochastic switches between Up and Down states and for population spikes. The extended mesoscopic population theory of spiking neural networks with STP may be useful for a systematic reduction of detailed biophysical models of cortical microcircuits to numerically efficient and mathematically tractable mean-field models.
将生物神经网络的微观模型进行粗粒化以获得神经活动的介观模型，是迈向大脑多尺度模型的关键一步。在此，我们将近期关于具有静态突触的介观群体动力学理论扩展到表现出短期可塑性（STP）的动态突触情形。扩展后的理论为源自发放神经元群体和经历Tsodyks - Markram STP的突触的突触输入电流提供了一种近似的平均场动力学。该近似平均场动力学考虑了突触数量有限以及模型的两个突触变量（利用率和可用资源）之间的相关性，并且其数值实现简单。与微观模型的蒙特卡罗模拟结果比较表明，在前馈和循环网络中，介观平均场模型都能准确再现输入到突触后神经元的总突触输入的一阶和二阶统计特性，并解释了上状态和下状态之间的随机切换以及群体发放。具有STP的发放神经网络的扩展介观群体理论可能有助于将皮质微电路的详细生物物理模型系统地简化为数值高效且数学上易于处理的平均场模型。
