PLoS Computational Biology
Public Library of Science
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Low-rate firing limit for neurons with axon, soma and dendrites driven by spatially distributed stochastic synapses
Volume: 16, Issue: 4
DOI 10.1371/journal.pcbi.1007175
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Abstract

Neurons are extended cells with multiple branching dendrites, a cell body and an axon. In an active neuronal network, neurons receive vast numbers of incoming synaptic pulses throughout their dendrites and cell body that each exhibit significant variability in amplitude and arrival time. The resulting synaptic input causes voltage fluctuations throughout their structure that evolve in space and time. The dynamics of how these signals are integrated and how they ultimately trigger outgoing spikes have been modelled extensively since the late 1960s. However, until relatively recently the majority of the mathematical formulae describing how fluctuating synaptic drive triggers action potentials have been applicable only for small neurons with the dendritic and axonal structure ignored. This has been largely due to the mathematical complexity of including the effects of spatially distributed synaptic input. Here we show that in a physiologically relevant, low-firing-rate regime, an approximate level-crossing approach can be used to provide an estimate for the neuronal firing rate even when the dendrites and axons are included. We illustrate this approach using basic neuronal morphologies that capture the fundamentals of neuronal structure. Though the models are simple, these preliminary results show that it is possible to obtain useful formulae that capture the effects of spatially distributed synaptic drive. The generality of these results suggests they will provide a mathematical framework for future studies that might require the structure of neurons to be taken into account, such as the effect of electrical fields or multiple synaptic input streams that target distinct spatial domains of cortical pyramidal cells.

https://www.researchpad.co/tools/openurl?pubtype=article&doi=10.1371/journal.pcbi.1007175&title=Low-rate firing limit for neurons with axon, soma and dendrites driven by spatially distributed stochastic synapses&author=Robert P. Gowers,Yulia Timofeeva,Magnus J. E. Richardson,Hugues Berry,&keyword=&subject=Research Article,Biology and Life Sciences,Cell Biology,Cellular Types,Animal Cells,Neurons,Neuronal Dendrites,Biology and Life Sciences,Neuroscience,Cellular Neuroscience,Neurons,Neuronal Dendrites,Biology and Life Sciences,Cell Biology,Cellular Types,Animal Cells,Neurons,Nerve Fibers,Axons,Biology and Life Sciences,Neuroscience,Cellular Neuroscience,Neurons,Nerve Fibers,Axons,Biology and Life Sciences,Cell Biology,Cellular Types,Animal Cells,Neurons,Biology and Life Sciences,Neuroscience,Cellular Neuroscience,Neurons,Biology and Life Sciences,Cell Biology,Cellular Types,Animal Cells,Neurons,Neuronal Dendrites,Dendritic Structure,Biology and Life Sciences,Neuroscience,Cellular Neuroscience,Neurons,Neuronal Dendrites,Dendritic Structure,Biology and Life Sciences,Cell Biology,Cellular Types,Animal Cells,Neurons,Neuronal Dendrites,Neurites,Biology and Life Sciences,Neuroscience,Cellular Neuroscience,Neurons,Neuronal Dendrites,Neurites,Biology and Life Sciences,Physiology,Electrophysiology,Membrane Potential,Action Potentials,Medicine and Health Sciences,Physiology,Electrophysiology,Membrane Potential,Action Potentials,Biology and Life Sciences,Physiology,Electrophysiology,Neurophysiology,Action Potentials,Medicine and Health Sciences,Physiology,Electrophysiology,Neurophysiology,Action Potentials,Biology and Life Sciences,Neuroscience,Neurophysiology,Action Potentials,Biology and Life Sciences,Anatomy,Nervous System,Synapses,Medicine and Health Sciences,Anatomy,Nervous System,Synapses,Biology and Life Sciences,Physiology,Electrophysiology,Neurophysiology,Synapses,Medicine and Health Sciences,Physiology,Electrophysiology,Neurophysiology,Synapses,Biology and Life Sciences,Neuroscience,Neurophysiology,Synapses,Biology and Life Sciences,Cell Biology,Cellular Types,Animal Cells,Neurons,Ganglion Cells,Pyramidal Cells,Biology and Life Sciences,Neuroscience,Cellular Neuroscience,Neurons,Ganglion Cells,Pyramidal Cells,