Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions
Fractional cable equation models for anomalous electrodiffusion in nerve cells: infinite domain solutions
复制标题
DOI：
10.1007/s00285-009-0251-1
复制
发表时间：
2009-12-01
影响因子：
1.9
通讯作者：
Wearne, S. L.
中科院分区：
文献类型：
--
作者：
Langlands, T. A. M.;Henry, B. I.;Wearne, S. L.
我们引入分数能斯特-普朗克方程，并推导出分数电缆方程作为宏观模型的离子在神经细胞中的电扩散时，分子扩散是异常亚扩散，由于绑定，拥挤或捕获。反常亚扩散模型取代扩散常数与时间相关的分数阶指数参数化的运营商。得到的解决方案作为无限电缆和半无限电缆与瞬时电流注入的缩放参数的函数。计算响应于α功能突触输入的沿树突的电压衰减沿着。动作电位放电率也是基于简单的集成和火灾版本的模型。我们的研究结果表明，在这些模型中，神经细胞的电紧张性和放电率被异常亚扩散改变。我们建议电生理实验来校准和验证模型。
We introduce fractional Nernst-Planck equations and derive fractional cable equations as macroscopic models for electrodiffusion of ions in nerve cells when molecular diffusion is anomalous subdiffusion due to binding, crowding or trapping. The anomalous subdiffusion is modelled by replacing diffusion constants with time dependent operators parameterized by fractional order exponents. Solutions are obtained as functions of the scaling parameters for infinite cables and semi-infinite cables with instantaneous current injections. Voltage attenuation along dendrites in response to alpha function synaptic inputs is computed. Action potential firing rates are also derived based on simple integrate and fire versions of the models. Our results show that electrotonic properties and firing rates of nerve cells are altered by anomalous subdiffusion in these models. We have suggested electrophysiological experiments to calibrate and validate the models.