Data_Sheet_1_Complex Dynamics in Simplified Neuronal Models: Reproducing Golgi Cell Electroresponsiveness.docx

Brain neurons exhibit complex electroresponsive properties – including intrinsic subthreshold oscillations and pacemaking, resonance and phase-reset – which are thought to play a critical role in controlling neural network dynamics. Although these properties emerge from detailed representations of molecular-level mechanisms in “realistic” models, they cannot usually be generated by simplified neuronal models (although these may show spike-frequency adaptation and bursting). We report here that this whole set of properties can be generated by the extended generalized leaky integrate-and-fire (E-GLIF) neuron model. E-GLIF derives from the GLIF model family and is therefore mono-compartmental, keeps the limited computational load typical of a linear low-dimensional system, admits analytical solutions and can be tuned through gradient-descent algorithms. Importantly, E-GLIF is designed to maintain a correspondence between model parameters and neuronal membrane mechanisms through a minimum set of equations. In order to test its potential, E-GLIF was used to model a specific neuron showing rich and complex electroresponsiveness, the cerebellar Golgi cell, and was validated against experimental electrophysiological data recorded from Golgi cells in acute cerebellar slices. During simulations, E-GLIF was activated by stimulus patterns, including current steps and synaptic inputs, identical to those used for the experiments. The results demonstrate that E-GLIF can reproduce the whole set of complex neuronal dynamics typical of these neurons – including intensity-frequency curves, spike-frequency adaptation, post-inhibitory rebound bursting, spontaneous subthreshold oscillations, resonance, and phase-reset – providing a new effective tool to investigate brain dynamics in large-scale simulations.

脑神经元展现出复杂的电响应特性——包括内在阈下振荡（intrinsic subthreshold oscillations）、起搏活动（pacemaking）、谐振（resonance）与相位重置（phase-reset）——这类特性被认为在调控神经网络动态过程中发挥关键作用。尽管这类特性可在整合了分子层面机制细节的“写实”模型中复现，但简化神经元模型通常无法生成此类特性（尽管简化模型可表现出锋电位频率适应（spike-frequency adaptation）与爆发式放电（bursting）行为）。本文报道，整套此类特性均可通过扩展型广义漏泄积分-发放（Extended Generalized Leaky Integrate-and-Fire, E-GLIF）神经元模型复现。该模型隶属于广义漏泄积分-发放（Generalized Leaky Integrate-and-Fire, GLIF）模型家族，因此属于单室模型，保有线性低维系统典型的低计算负载特性，支持解析解求解，并可通过梯度下降算法进行参数调优。尤为重要的是，E-GLIF的设计初衷是通过最简方程集，实现模型参数与神经元膜机制之间的对应关联。为验证其应用潜力，研究人员使用E-GLIF对一类具备丰富复杂电响应特性的特定神经元——小脑高尔基细胞（cerebellar Golgi cell）——进行建模，并以急性小脑脑片高尔基细胞的实验电生理数据作为验证基准。仿真过程中，向E-GLIF施加的刺激范式——包括电流阶跃（current steps）与突触输入（synaptic inputs）——与实验中所用范式完全一致。实验结果表明，E-GLIF可复现该类神经元典型的全套复杂神经动态特性——包括强度-频率曲线、锋电位频率适应、抑制后回弹爆发（post-inhibitory rebound bursting）、自发阈下振荡、谐振与相位重置——为大规模仿真中研究脑动态过程提供了一款高效的新型工具。