[论文解读] Extending integrate-and-fire model neurons to account for input filtering and the effects of weak electric fields mediated by the dendrite

Florian Aspart, Josef Ladenbauer+1 more|arXiv (Cornell University)|Mar 15, 2016

Neural dynamics and brain function被引用 2

一句话总结

本文通过从球体-轴突神经元模型推导出的解析方法，将脉冲发放（IF）点神经元模型扩展为包含树突输入滤波和弱电场效应的模型。所得到的扩展IF模型能精确再现振荡电场下β/γ频段的亚阈值膜电位动力学与放电率共振，从而实现对形态学和电场效应的高效群体水平研究。

ABSTRACT

The collective dynamics of neuronal populations can be efficiently studied using single-compartment (point) model neurons of the integrate-and-fire (IF) type. Existing point neuron models are intrinsically not able to appropriately reproduce (i) the effects of dendrites on synaptic input integration or (ii) the modulation of neuronal activity due to an electric field, which strongly depends on the dendritic morphology. Weak electric fields, as generated endogenously or through transcranial electrical stimulation, have recently gained increased attention because of their ability to modulate ongoing neuronal activity. However, the underlying mechanisms are not well understood. Here, we extend the popular spiking point neuron model class to accurately reflect input filtering and weak electric field effects as present in a canonical spatially extended ball-and-stick (BS) neuron model. We analytically derive additional components for two major types of IF point neuron models to exactly reproduce the subthreshold somatic voltage dynamics of the BS model with arbitrary morphology exposed to an oscillating electric field. Also the spiking dynamics for suprathreshold fluctuating inputs is well reproduced by the extended point models. Through this approach we further show that the presence of a dendritic cable (i) attenuates the somatic subthreshold response to slowly-varying inputs and (ii) mediates spike rate resonance, or equivalently, pronounced spike to field coherence, in the beta and gamma frequency range due to an oscillatory weak electric field. Our point neuron model extension is simple to implement and well suited for studying the dynamics of populations with heterogeneous neuronal morphology and the effects of weak electric fields on population activity.

研究动机与目标

• 解决标准IF模型在捕捉突触输入树突滤波方面的局限性。
• 纳入弱电场对神经元活动的影响，特别是通过树突形态介导的作用。
• 开发一种计算高效的点神经元扩展模型，以在振荡电场下保持空间扩展神经元的动力学特性。
• 实现能够考虑神经元形态异质性与外部场调制的群体水平模拟。
• 通过标准IF模型的最小扩展，重现β与γ频段的放电率共振与场相干性。

提出的方法

• 推导IF模型中额外膜电位分量的解析表达式，以匹配具有任意树突形态的球体-轴突神经元的亚阈值动力学。
• 通过频率依赖的滤波项将振荡外部电场的影响纳入扩展IF模型。
• 利用球体-轴突模型的电缆方程解来指导扩展IF模型亚阈值动力学的结构设计。
• 在随机输入下，针对亚阈值响应与阈上放电，将扩展模型与完整空间模型进行验证。
• 确保扩展模型保留原始空间模型中观察到的放电时间与放电率共振特性。
• 以保持大规模群体模拟计算效率的方式实现扩展模型。

实验结果

研究问题

• RQ1 如何扩展IF点神经元模型，以精确捕捉突触输入的树突滤波？
• RQ2 弱振荡电场对具有被动树突的神经元亚阈值膜电位动力学有何影响？
• RQ3 IF模型的最小扩展是否能重现由弱电场调制引起的β与γ频段放电率共振？
• RQ4 在电场存在下，树突形态如何影响神经元对缓慢变化输入的胞体响应？
• RQ5 扩展IF模型在电场刺激下，能在多大程度上保持空间扩展神经元模型中观察到的放电-场相干性？

主要发现

• 在任意树突形态与振荡电场下，扩展IF模型能精确再现球体-轴突模型的亚阈值胞体膜电位动力学。
• 树突电缆的存在会衰减胞体对缓慢变化输入的响应，与被动电缆理论一致。
• 当暴露于振荡弱电场时，该模型在β与γ频段表现出放电率共振，表明放电活动具有频率选择性放大特性。
• 扩展模型捕捉到明显的β与γ频段放电-场相干性，反映出网络对弱电场刺激的同步响应。
• 在阈上随机输入下，扩展IF模型保持了精确的放电动力学，支持可靠的群体水平模拟。
• 该解析扩展实现简单，同时保持了标准IF模型的计算效率，并整合了具有生物学意义的树突与电场效应。