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Computational convergence of the path integral for real dendritic morphologies
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Caudron, Quentin, Donnelly, Simon R., Brand, Samuel and Timofeeva, Yulia (2012) Computational convergence of the path integral for real dendritic morphologies. The Journal of Mathematical Neuroscience, Volume 2 (Number 1). doi:10.1186/2190-8567-2-11 ISSN 2190-8567.
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Official URL: http://dx.doi.org/10.1186/2190-8567-2-11
Abstract
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.
Item Type: | Journal Article | ||||
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Subjects: | Q Science > QH Natural history > QH301 Biology R Medicine > RC Internal medicine > RC0321 Neuroscience. Biological psychiatry. Neuropsychiatry |
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Divisions: | Faculty of Science, Engineering and Medicine > Research Centres > Centre for Complexity Science Faculty of Science, Engineering and Medicine > Science > Computer Science Faculty of Science, Engineering and Medicine > Science > Mathematics |
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Library of Congress Subject Headings (LCSH): | Dendrites, Neurons, Morphology, Cells -- Morphology, Algorithms, Computational biology | ||||
Journal or Publication Title: | The Journal of Mathematical Neuroscience | ||||
Publisher: | SpringerOpen | ||||
ISSN: | 2190-8567 | ||||
Official Date: | 22 November 2012 | ||||
Dates: |
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Volume: | Volume 2 | ||||
Number: | Number 1 | ||||
DOI: | 10.1186/2190-8567-2-11 | ||||
Status: | Peer Reviewed | ||||
Publication Status: | Published | ||||
Access rights to Published version: | Open Access (Creative Commons) | ||||
Date of first compliant deposit: | 6 June 2016 | ||||
Date of first compliant Open Access: | 6 June 2016 | ||||
Funder: | Engineering and Physical Sciences Research Council (EPSRC), Medical Research Council (Great Britain) (MRC), Biotechnology and Biological Sciences Research Council (Great Britain) (BBSRC), Research Councils UK (RCUK) | ||||
Grant number: | EP/E501311 (EPSRC) ; BB/H011900 (BBSRC) ; |
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