The biophysical properties of dendritic spines play a critical role in neuronal integration but are still poorly understood, due to experimental difficulties in accessing them. Spine biophysics has been traditionally explored using theoretical models based on cable theory. However, cable theory generally assumes that concentration changes associated with ionic currents are negligible and, therefore, ignores electrodiffusion, i.e. the interaction between electric fields and ionic diffusion. This assumption, while true for large neuronal compartments, could be incorrect when applied to femto-liter size structures such as dendritic spines. To extend cable theory and explore electrodiffusion effects, we use here the Poisson (P) and Nernst-Planck (NP) equations, which relate electric field to charge and Fick’s law of diffusion, to model ion concentration dynamics in spines receiving excitatory synaptic potentials (EPSPs). We use experimentally measured voltage transients from spines with nanoelectrodes to explore these dynamics with realistic parameters. We find that (i) passive diffusion and electrodiffusion jointly affect the dynamics of spine EPSPs; (ii) spine geometry plays a key role in shaping EPSPs; and, (iii) the spine-neck resistance dynamically decreases during EPSPs, leading to short-term synaptic facilitation. Our formulation, which complements and extends cable theory, can be easily adapted to model ionic biophysics in other nanoscale bio-compartments.

中文翻译：

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树突棘突触电位的电扩散模型。

树突棘的生物物理特性在神经元整合中起着至关重要的作用，但由于实验上难以获得，因此人们对其了解甚少。传统上已经使用基于电缆理论的理论模型来探索脊柱生物物理学。然而，电缆理论通常假设与离子电流相关的浓度变化可忽略不计，因此忽略了电扩散，即电场与离子扩散之间的相互作用。这种假设虽然适用于大型神经元区室，但当应用于毫微微升大小的结构（例如树突棘）时，可能会不正确。为了扩展电缆理论并探索电扩散效应，我们在此处使用Poisson（P）和Nernst-Planck（NP）方程（它们将电场与电荷和菲克扩散定律相关联）来模拟接收兴奋性突触电位的棘中的离子浓度动态（ EPSPs）。我们使用实验测量的来自带有纳米电极的刺的电压瞬变来探索具有实际参数的动力学。我们发现（i）被动扩散和电扩散共同影响脊柱EPSP的动力学；（ii）脊柱几何形状在塑造EPSP方面起关键作用；（iii）在EPSP期间脊椎颈部阻力动态降低，导致短期的突触促进。我们的公式补充并扩展了电缆理论，可以轻松地应用于其他纳米级生物隔间中的离子生物物理建模。