Aspart Florian, Ladenbauer Josef, Obermayer Klaus
Department of Software Engineering and Theoretical Computer Science, Technische Universität Berlin, Berlin, Germany.
Bernstein Center for Computational Neuroscience Berlin, Berlin, Germany.
PLoS Comput Biol. 2016 Nov 28;12(11):e1005206. doi: 10.1371/journal.pcbi.1005206. eCollection 2016 Nov.
Transcranial brain stimulation and evidence of ephaptic coupling have recently sparked strong interests in understanding the effects of weak electric fields on the dynamics of brain networks and of coupled populations of neurons. The collective dynamics of large neuronal populations can be efficiently studied using single-compartment (point) model neurons of the integrate-and-fire (IF) type as their elements. These models, however, lack the dendritic morphology required to biophysically describe the effect of an extracellular electric field on the neuronal membrane voltage. Here, we extend the IF point neuron models to accurately reflect morphology dependent electric field effects extracted from a canonical spatial "ball-and-stick" (BS) neuron model. Even in the absence of an extracellular field, neuronal morphology by itself strongly affects the cellular response properties. We, therefore, derive additional components for leaky and nonlinear IF neuron models to reproduce the subthreshold voltage and spiking dynamics of the BS model exposed to both fluctuating somatic and dendritic inputs and an extracellular electric field. We show that an oscillatory electric field causes spike rate resonance, or equivalently, pronounced spike to field coherence. Its resonance frequency depends on the location of the synaptic background inputs. For somatic inputs the resonance appears in the beta and gamma frequency range, whereas for distal dendritic inputs it is shifted to even higher frequencies. Irrespective of an external electric field, the presence of a dendritic cable attenuates the subthreshold response at the soma to slowly-varying somatic inputs while implementing a low-pass filter for distal dendritic inputs. Our point neuron model extension is straightforward to implement and is computationally much more efficient compared to the original BS model. It is well suited for studying the dynamics of large populations of neurons with heterogeneous dendritic morphology with (and without) the influence of weak external electric fields.
经颅脑刺激和电突触耦合的证据最近引发了人们对理解弱电场对脑网络动力学以及耦合神经元群体影响的浓厚兴趣。使用积分发放（IF）类型的单室（点）模型神经元作为元素，可以有效地研究大型神经元群体的集体动力学。然而，这些模型缺乏从生物物理角度描述细胞外电场对神经元膜电压影响所需的树突形态。在这里，我们扩展了IF点神经元模型，以准确反映从典型空间“球棒”（BS）神经元模型中提取的依赖形态的电场效应。即使在没有细胞外场的情况下，神经元形态本身也会强烈影响细胞的反应特性。因此，我们为漏电和非线性IF神经元模型推导了额外的组件，以重现暴露于波动的体细胞和树突输入以及细胞外电场的BS模型的阈下电压和放电动力学。我们表明，振荡电场会导致放电率共振，或者等效地，导致明显的放电与场的相干性。其共振频率取决于突触背景输入的位置。对于体细胞输入，共振出现在β和γ频率范围内，而对于远端树突输入，共振频率会转移到更高的频率。无论是否存在外部电场，树突电缆的存在都会减弱体细胞对缓慢变化的体细胞输入的阈下反应，同时为远端树突输入实现低通滤波器。我们的点神经元模型扩展易于实现，并且与原始BS模型相比计算效率更高。它非常适合研究具有异质树突形态的大量神经元在（有或没有）弱外部电场影响下的动力学。
