Department of Neurology, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Tainan, Taiwan 70403.
Innovation Centre of Medical Devices and Technology, National Cheng Kung University Hospital, College of Medicine, National Cheng Kung University, Tainan, Taiwan 70403.
eNeuro. 2019 Jan 17;5(6). doi: 10.1523/ENEURO.0002-18.2018. eCollection 2018 Nov-Dec.
When incorporating more realistic synaptic dynamics, the computational efficiency of population density methods (PDMs) declines sharply due to the increase in the dimension of master equations. To avoid such a decline, we develop an efficient PDM, termed colored-synapse PDM (csPDM), in which the dimension of the master equations does not depend on the number of synapse-associated state variables in the underlying network model. Our goal is to allow the PDM to incorporate realistic synaptic dynamics that possesses not only finite relaxation time but also short-term plasticity (STP). The model equations of csPDM are derived based on the diffusion approximation on synaptic dynamics and probability density function methods for Langevin equations with colored noise. Numerical examples, given by simulations of the population dynamics of uncoupled exponential integrate-and-fire (EIF) neurons, show good agreement between the results of csPDM and Monte Carlo simulations (MCSs). Compared to the original full-dimensional PDM (fdPDM), the csPDM reveals more excellent computational efficiency because of the lower dimension of the master equations. In addition, it permits network dynamics to possess the short-term plastic characteristics inherited from plastic synapses. The novel csPDM has potential applicability to any spiking neuron models because of no assumptions on neuronal dynamics, and, more importantly, this is the first report of PDM to successfully encompass short-term facilitation/depression properties.
当纳入更现实的突触动力学时，由于主方程维度的增加，种群密度方法 (PDM) 的计算效率急剧下降。为了避免这种下降，我们开发了一种有效的 PDM，称为有色突触 PDM（csPDM），其中主方程的维度不依赖于基础网络模型中与突触相关的状态变量的数量。我们的目标是允许 PDM 纳入具有有限弛豫时间和短期可塑性 (STP) 的现实突触动力学。csPDM 的模型方程是基于突触动力学的扩散近似和带有有色噪声的 Langevin 方程的概率密度函数方法推导出来的。通过对未耦合指数积分和放电 (EIF) 神经元群体动力学的模拟给出的数值示例，csPDM 的结果与蒙特卡罗模拟 (MCS) 之间显示出很好的一致性。与原始全维 PDM（fdPDM）相比，由于主方程的维度较低，csPDM 显示出更高的计算效率。此外，它允许网络动力学具有从可塑性突触继承的短期塑性特征。由于对神经元动力学没有任何假设，新的 csPDM 具有潜在的适用性，可以应用于任何尖峰神经元模型，更重要的是，这是首次报道 PDM 成功地包含了短期易化/压抑特性。
