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Low-rate firing limit for neurons with axon, soma and dendrites driven by spatially distributed stochastic synapses

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Gowers, Robert, Timofeeva, Yulia and Richardson, Magnus J. E. (2020) Low-rate firing limit for neurons with axon, soma and dendrites driven by spatially distributed stochastic synapses. PLOS Computational Biology, 16 (4). e1007175. doi:10.1371/journal.pcbi.1007175 ISSN 1553-7358.

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Official URL: https://doi.org/10.1371/journal.pcbi.1007175

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Abstract

Analytical forms for neuronal firing rates are important theoretical tools for the analysis of network states. Since the 1960s, the majority of approaches have treated neurons as being electrically compact and therefore isopotential. These approaches have yielded considerable insight into how single-cell properties affect network activity; however, many neuronal classes, such as cortical pyramidal cells, are electrically extended objects. Calculation of the complex flow of electrical activity driven by stochastic spatio-temporal synaptic input streams in these structures has presented a significant analytical challenge. Here we demonstrate that an extension of the level-crossing method of Rice, previously used for compact cells, provides a general framework for approximating the firing rate of neurons with spatial structure. Even for simple models, the analytical approximations derived demonstrate a surprising richness including: independence of the firing rate to the electrotonic length for certain models, but with a form distinct to the point-like leaky integrate-and-fire model; a non-monotonic dependence of the firing rate on the number of dendrites receiving synaptic drive; a significant effect of the axonal and somatic load on the firing rate; and the role that the trigger position on the axon for spike initiation has on firing properties. The approach necessitates only calculating the mean and variances of the non-thresholded voltage and its rate of change in neuronal structures subject to spatio-temporal synaptic fluctuations. The combination of simplicity and generality promises a framework that can be built upon to incorporate increasing levels of biophysical detail and extend beyond the low-rate firing limit treated in this paper.

Item Type: Journal Article
Subjects: Q Science > QP Physiology
Divisions: Faculty of Science, Engineering and Medicine > Science > Mathematics
SWORD Depositor: Library Publications Router
Library of Congress Subject Headings (LCSH): Neurons, Neurons -- Mathematical models, Axons, Dendrites, Neural networks (Neurobiology)
Journal or Publication Title: PLOS Computational Biology
Publisher: Public Library of Science
ISSN: 1553-7358
Official Date: 2020
Dates:
DateEvent
2020Published
20 April 2020Available
27 January 2020Accepted
Volume: 16
Number: 4
Article Number: e1007175
DOI: 10.1371/journal.pcbi.1007175
Status: Peer Reviewed
Publication Status: Published
Reuse Statement (publisher, data, author rights):
Access rights to Published version: Open Access (Creative Commons)
Date of first compliant deposit: 29 May 2020
Date of first compliant Open Access: 1 June 2020
RIOXX Funder/Project Grant:
Project/Grant IDRIOXX Funder NameFunder ID
EP/L015374/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
Is Part Of: 1
Contributors:
ContributionNameContributor ID
UNSPECIFIEDBerry, HuguesUNSPECIFIED

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