A stimulus dependent spike threshold is an optimal neural coder

Douglas L Jones, Erik C. Johnson, Rama Ratnam

Research output: Contribution to journalArticle

Abstract

A neural code based on sequences of spikes can consume a significant portion of the brain's energy budget. Thus, energy considerations would dictate that spiking activity be kept as low as possible. However, a high spike-rate improves the coding and representation of signals in spike trains, particularly in sensory systems. These are competing demands, and selective pressure has presumably worked to optimize coding by apportioning a minimum number of spikes so as to maximize coding fidelity. The mechanisms by which a neuron generates spikes while maintaining a fidelity criterion are not known. Here, we show that a signal-dependent neural threshold, similar to a dynamic or adapting threshold, optimizes the trade-off between spike generation (encoding) and fidelity (decoding). The threshold mimics a post-synaptic membrane (a low-pass filter) and serves as an internal decoder. Further, it sets the average firing rate (the energy constraint). The decoding process provides an internal copy of the coding error to the spike-generator which emits a spike when the error equals or exceeds a spike threshold. When optimized, the trade-off leads to a deterministic spike firing-rule that generates optimally timed spikes so as to maximize fidelity. The optimal coder is derived in closed-form in the limit of high spike-rates, when the signal can be approximated as a piece-wise constant signal. The predicted spike-times are close to those obtained experimentally in the primary electrosensory afferent neurons of weakly electric fish (Apteronotus leptorhynchus) and pyramidal neurons from the somatosensory cortex of the rat. We suggest that KCNQ/Kv7 channels (underlying the M-current) are good candidates for the decoder. They are widely coupled to metabolic processes and do not inactivate. We conclude that the neural threshold is optimized to generate an energy-efficient and high-fidelity neural code.

Original languageEnglish (US)
Article number61
JournalFrontiers in Computational Neuroscience
Volume9
Issue numberJUNE
DOIs
StatePublished - Jun 2 2015

Fingerprint

Electric Fish
Afferent Neurons
Synaptic Membranes
Somatosensory Cortex
Pyramidal Cells
Budgets
Neurons
Brain

Keywords

  • Coding fidelity
  • Dynamic threshold
  • Energy-efficient coding
  • Neural coding
  • Source coding
  • Spike-threshold
  • Spike-timing

ASJC Scopus subject areas

  • Neuroscience (miscellaneous)
  • Cellular and Molecular Neuroscience

Cite this

A stimulus dependent spike threshold is an optimal neural coder. / Jones, Douglas L; Johnson, Erik C.; Ratnam, Rama.

In: Frontiers in Computational Neuroscience, Vol. 9, No. JUNE, 61, 02.06.2015.

Research output: Contribution to journalArticle

@article{b9f65fc21e504e8ba8741f5b81fd8e4f,
title = "A stimulus dependent spike threshold is an optimal neural coder",
abstract = "A neural code based on sequences of spikes can consume a significant portion of the brain's energy budget. Thus, energy considerations would dictate that spiking activity be kept as low as possible. However, a high spike-rate improves the coding and representation of signals in spike trains, particularly in sensory systems. These are competing demands, and selective pressure has presumably worked to optimize coding by apportioning a minimum number of spikes so as to maximize coding fidelity. The mechanisms by which a neuron generates spikes while maintaining a fidelity criterion are not known. Here, we show that a signal-dependent neural threshold, similar to a dynamic or adapting threshold, optimizes the trade-off between spike generation (encoding) and fidelity (decoding). The threshold mimics a post-synaptic membrane (a low-pass filter) and serves as an internal decoder. Further, it sets the average firing rate (the energy constraint). The decoding process provides an internal copy of the coding error to the spike-generator which emits a spike when the error equals or exceeds a spike threshold. When optimized, the trade-off leads to a deterministic spike firing-rule that generates optimally timed spikes so as to maximize fidelity. The optimal coder is derived in closed-form in the limit of high spike-rates, when the signal can be approximated as a piece-wise constant signal. The predicted spike-times are close to those obtained experimentally in the primary electrosensory afferent neurons of weakly electric fish (Apteronotus leptorhynchus) and pyramidal neurons from the somatosensory cortex of the rat. We suggest that KCNQ/Kv7 channels (underlying the M-current) are good candidates for the decoder. They are widely coupled to metabolic processes and do not inactivate. We conclude that the neural threshold is optimized to generate an energy-efficient and high-fidelity neural code.",
keywords = "Coding fidelity, Dynamic threshold, Energy-efficient coding, Neural coding, Source coding, Spike-threshold, Spike-timing",
author = "Jones, {Douglas L} and Johnson, {Erik C.} and Rama Ratnam",
year = "2015",
month = "6",
day = "2",
doi = "10.3389/fncom.2015.00061",
language = "English (US)",
volume = "9",
journal = "Frontiers in Computational Neuroscience",
issn = "1662-5188",
publisher = "Frontiers Research Foundation",
number = "JUNE",

}

TY - JOUR

T1 - A stimulus dependent spike threshold is an optimal neural coder

AU - Jones, Douglas L

AU - Johnson, Erik C.

AU - Ratnam, Rama

PY - 2015/6/2

Y1 - 2015/6/2

N2 - A neural code based on sequences of spikes can consume a significant portion of the brain's energy budget. Thus, energy considerations would dictate that spiking activity be kept as low as possible. However, a high spike-rate improves the coding and representation of signals in spike trains, particularly in sensory systems. These are competing demands, and selective pressure has presumably worked to optimize coding by apportioning a minimum number of spikes so as to maximize coding fidelity. The mechanisms by which a neuron generates spikes while maintaining a fidelity criterion are not known. Here, we show that a signal-dependent neural threshold, similar to a dynamic or adapting threshold, optimizes the trade-off between spike generation (encoding) and fidelity (decoding). The threshold mimics a post-synaptic membrane (a low-pass filter) and serves as an internal decoder. Further, it sets the average firing rate (the energy constraint). The decoding process provides an internal copy of the coding error to the spike-generator which emits a spike when the error equals or exceeds a spike threshold. When optimized, the trade-off leads to a deterministic spike firing-rule that generates optimally timed spikes so as to maximize fidelity. The optimal coder is derived in closed-form in the limit of high spike-rates, when the signal can be approximated as a piece-wise constant signal. The predicted spike-times are close to those obtained experimentally in the primary electrosensory afferent neurons of weakly electric fish (Apteronotus leptorhynchus) and pyramidal neurons from the somatosensory cortex of the rat. We suggest that KCNQ/Kv7 channels (underlying the M-current) are good candidates for the decoder. They are widely coupled to metabolic processes and do not inactivate. We conclude that the neural threshold is optimized to generate an energy-efficient and high-fidelity neural code.

AB - A neural code based on sequences of spikes can consume a significant portion of the brain's energy budget. Thus, energy considerations would dictate that spiking activity be kept as low as possible. However, a high spike-rate improves the coding and representation of signals in spike trains, particularly in sensory systems. These are competing demands, and selective pressure has presumably worked to optimize coding by apportioning a minimum number of spikes so as to maximize coding fidelity. The mechanisms by which a neuron generates spikes while maintaining a fidelity criterion are not known. Here, we show that a signal-dependent neural threshold, similar to a dynamic or adapting threshold, optimizes the trade-off between spike generation (encoding) and fidelity (decoding). The threshold mimics a post-synaptic membrane (a low-pass filter) and serves as an internal decoder. Further, it sets the average firing rate (the energy constraint). The decoding process provides an internal copy of the coding error to the spike-generator which emits a spike when the error equals or exceeds a spike threshold. When optimized, the trade-off leads to a deterministic spike firing-rule that generates optimally timed spikes so as to maximize fidelity. The optimal coder is derived in closed-form in the limit of high spike-rates, when the signal can be approximated as a piece-wise constant signal. The predicted spike-times are close to those obtained experimentally in the primary electrosensory afferent neurons of weakly electric fish (Apteronotus leptorhynchus) and pyramidal neurons from the somatosensory cortex of the rat. We suggest that KCNQ/Kv7 channels (underlying the M-current) are good candidates for the decoder. They are widely coupled to metabolic processes and do not inactivate. We conclude that the neural threshold is optimized to generate an energy-efficient and high-fidelity neural code.

KW - Coding fidelity

KW - Dynamic threshold

KW - Energy-efficient coding

KW - Neural coding

KW - Source coding

KW - Spike-threshold

KW - Spike-timing

UR - http://www.scopus.com/inward/record.url?scp=84930679818&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84930679818&partnerID=8YFLogxK

U2 - 10.3389/fncom.2015.00061

DO - 10.3389/fncom.2015.00061

M3 - Article

AN - SCOPUS:84930679818

VL - 9

JO - Frontiers in Computational Neuroscience

JF - Frontiers in Computational Neuroscience

SN - 1662-5188

IS - JUNE

M1 - 61

ER -