Neural Noise Can Explain Expansive, Power-Law Nonlinearities in Neural Response Functions

Miller, Kenneth D.; Troyer, Todd W.

doi:10.1152/jn.00425.2001

Cited by 207Visual perception and processing mechanismsNeural dynamics and brain functionstochastic dynamics and bifurcation

Neural Noise Can Explain Expansive, Power-Law Nonlinearities in Neural Response Functions

Miller, Kenneth D., Troyer, Todd W.·2002·Journal of Neurophysiology

DOI 10.1152/jn.00425.2001

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Abstract

Many phenomenological models of the responses of simple cells in primary visual cortex have concluded that a cell's firing rate should be given by its input raised to a power greater than one. This is known as an expansive power-law nonlinearity. However, intracellular recordings have shown that a different nonlinearity, a linear-threshold function, appears to give a good prediction of firing rate from a cell's low-pass-filtered voltage response. Using a model based on a linear-threshold function, Anderson et al. showed that voltage noise was critical to converting voltage responses with contrast-invariant orientation tuning into spiking responses with contrast-invariant tuning. We present two separate results clarifying the connection between noise-smoothed linear-threshold functions and power-law nonlinearities. First, we prove analytically that a power-law nonlinearity is the only input-output function that converts contrast-invariant input tuning into contrast-invariant spike tuning. Second, we examine simulations of a simple model that assumes instantaneous spike rate is given by a linear-threshold function of voltage and voltage responses include significant noise. We show that the resulting average spike rate is well described by an expansive power law of the average voltage (averaged over multiple trials), provided that average voltage remains less than about 1.5 SDs of the noise above threshold. Finally, we use this model to show that the noise levels recorded by Anderson et al. are consistent with the degree to which the orientation tuning of spiking responses is more sharply tuned relative to the orientation tuning of voltage responses. Thus neuronal noise can robustly generate power-law input-output functions of the form frequently postulated for simple cells.

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Synaptically driven fluctuations in Vm smooth the transformation from Vm depolarization to spike output, creating a power-law relationship between the mean Vm and the mean firing rate.
“Synaptically driven fluctuations in the Vm smooth the transformation from Vm depolarization to spike output, creating a power-law relationship between the mean Vm and the mean firing rate13,63.”
From Mechanisms underlying gain modulation in the cortex (2020) · cites this paper as [63]
Vm fluctuations may contribute to contrast-invariant tuning in neurons of the visual cortex of cats and rodents.
“These fluctuations may contribute to contrast-invariant tuning in neurons of the visual cortex of cats and rodents10,13,63,64.”
From Mechanisms underlying gain modulation in the cortex (2020) · cites this paper as [63]

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Authors: Miller, K. D., & Troyer, T. W.
Affiliations: University of California, San Francisco (US)
University of Maryland, College Park (US)
ORCID: Miller, Kenneth D.
Troyer, Todd W.
Venue: Journal of Neurophysiology
Publisher: American Physiological Society
Published: 2002-02-01
Volume: 87
Issue: 2
Pages: 653-659
ISSN: 0022-3077 (ISSN-L)
1522-1598
DOI: 10.1152/jn.00425.2001
OpenAlex: W1961056875
Cited by: 207
References: 35
Citations by year: 2026: 6 · 2025: 10 · 2024: 4 · 2023: 8 · 2022: 10 · 2021: 13 · 2020: 10 · 2019: 3 · 2018: 7 · 2017: 12 · 2016: 13 · 2015: 8 · 2014: 6 · 2013: 9 · 2012: 12
FWCI: 4.51
Type: journal article
Language: en
Open access: closed
Locations: Journal of Neurophysiology (publishedVersion)
PubMed (publishedVersion)
Funders: National Eye Institute (R01EY011001, EY11001)
Topics: Life Sciences › Neuroscience › Cognitive Neuroscience › Visual perception and processing mechanisms
Life Sciences › Neuroscience › Cognitive Neuroscience › Neural dynamics and brain function
Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › stochastic dynamics and bifurcation
Keywords: neural noise, power nonlinearity, input-output function, linear threshold functions, simple cells, primary visual cortex, orientation tuning, contrast invariance, voltage noise, spike frequency
MeSH terms: Action Potentials, Animals, Computer Simulation, Models, Neurological, Neurons, Visual Cortex, Nonlinear Dynamics

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Neural Noise Can Explain Expansive, Power-Law Nonlinearities in Neural Response Functions

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