Department of Theoretical Physics and Center for Biophysics, Saarland University, Saarbrücken, Germany.
Department of Theoretical Physics and Center for Biophysics, Saarland University, Saarbrücken, Germany.
Biophys J. 2018 Nov 20;115(10):2014-2025. doi: 10.1016/j.bpj.2018.09.029. Epub 2018 Oct 4.
We present a coarse-grained model for stochastic transport of noninteracting chemical signals inside neuronal dendrites and show how first-passage properties depend on the key structural factors affected by neurodegenerative disorders or aging: the extent of the tree, the topological bias induced by segmental decrease of dendrite diameter, and the trapping probabilities in biochemical cages and growth cones. We derive an exact expression for the distribution of first-passage times, which follows a universal exponential decay in the long-time limit. The asymptotic mean first-passage time exhibits a crossover from power-law to exponential scaling upon reducing the topological bias. We calibrate the coarse-grained model parameters and obtain the variation range of the mean first-passage time when the geometrical characteristics of the dendritic structure evolve during the course of aging or neurodegenerative disease progression (a few disorders for which clear trends for the pathological changes of dendritic structure have been reported in the literature are chosen and studied). We prove the validity of our analytical approach under realistic fluctuations of structural parameters by comparison to the results of Monte Carlo simulations. Moreover, by constructing local structural irregularities, we analyze the resulting influence on transport of chemical signals and formation of heterogeneous density patterns. Because neural functions rely on chemical signal transmission to a large extent, our results open the possibility of establishing a direct link between the disease progression and neural functions.
我们提出了一个用于非相互作用化学信号在神经元树突内随机输运的粗粒化模型，并展示了首次通过特性如何取决于受神经退行性疾病或衰老影响的关键结构因素：树的延伸程度、由树突直径分段减小引起的拓扑偏差，以及生化笼和生长锥中的俘获概率。我们推导出了首次通过时间分布的精确表达式，该表达式在长时间极限下遵循普遍的指数衰减。渐近平均首次通过时间在降低拓扑偏差时表现出从幂律到指数标度的交叉。我们校准了粗粒化模型参数，并获得了在树突结构的几何特征在衰老或神经退行性疾病进展过程中演变时平均首次通过时间的变化范围（选择并研究了文献中报道了树突结构病理性变化的一些明确趋势的几种疾病）。我们通过与蒙特卡罗模拟的结果进行比较，证明了我们的分析方法在结构参数实际波动下的有效性。此外，通过构建局部结构不规则性，我们分析了对化学信号输运和异质密度模式形成的影响。由于神经功能在很大程度上依赖于化学信号的传递，因此我们的结果为在疾病进展和神经功能之间建立直接联系提供了可能性。
