Computational Convergence of the Path Integral for Real Dendritic Morphologies

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...

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Bibliographic Details
Published in:	Journal of mathematical neuroscience Vol. 2; no. 1; p. 11
Main Authors:	Caudron, Quentin, Donnelly, Simon R, Brand, Samuel PC, Timofeeva, Yulia
Format:	Journal Article
Language:	English
Published:	Berlin/Heidelberg Springer Berlin Heidelberg 22-11-2012 BioMed Central Ltd Springer
Subjects:	Applications of Mathematics Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Neurosciences Dendrites Sum-over-trips Dendritic computation Path integral Morphology
Online Access:	Get full text
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Summary:	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.
Bibliography:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23
ISSN:	2190-8567 2190-8567
DOI:	10.1186/2190-8567-2-11