Computational convergence of the path integral for real dendritic morphologies.
Computational convergence of the path integral for real dendritic morphologies.
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DOI：
10.1186/2190-8567-2-11
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发表时间：
2012-11-22
影响因子：
2.3
通讯作者：
Timofeeva Y
中科院分区：
文献类型：
--
作者：
Caudron Q;Donnelly SR;Brand SP;Timofeeva Y
神经元的特征在于生物细胞中独特的形态结构，其核心是树突树。大量的树突状的几何形状，结合细胞膜的异质性，继续挑战科学家在预测神经元的输入输出关系，即使在亚阈值树突状电流的情况下。对于一个给定的树枝状几何形状获得的绿色的功能提供了被动或准主动树突的这种功能关系，并可以通过基于路径积分形式主义的总和过行程的方法来构建。在本文中，我们介绍了一些有效的算法实现的总和超过行程框架，并调查这些算法的收敛性不同的树枝状几何形状。我们证明了trip采样方法的收敛性强烈依赖于树突状形态以及细胞膜的生物物理性质。对于真实的形态，为了保证小的收敛误差的行程数可能变得非常大，并且强烈地影响计算效率。作为替代方案，我们引入了一个高效的矩阵方法，可以应用于任意分支结构。
Neurons are characterised by a morphological structure unique amongst biological cells, the core of which is the dendritic tree. The vast number of dendritic geometries, combined with heterogeneous properties of the cell membrane, continue to challenge scientists in predicting neuronal input-output relationships, even in the case of sub-threshold dendritic currents. The Green’s function obtained for a given dendritic geometry provides this functional relationship for passive or quasi-active dendrites and can be constructed by a sum-over-trips approach based on a path integral formalism. In this paper, we introduce a number of efficient algorithms for realisation of the sum-over-trips framework and investigate the convergence of these algorithms on different dendritic geometries. We demonstrate that the convergence of the trip sampling methods strongly depends on dendritic morphology as well as the biophysical properties of the cell membrane. For real morphologies, the number of trips to guarantee a small convergence error might become very large and strongly affect computational efficiency. As an alternative, we introduce a highly-efficient matrix method which can be applied to arbitrary branching structures.