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A quantitative population model of whisker barrels: Re-examining the Wilson-Cowan equations

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Abstract

Beginning from a biologically based integrate and fire model of a rat whisker barrel, we employ semirigorous techniques to reduce the system to a simple set of equations, similar to the Wilson-Cowan equations, while retaining the ability for both qualitative and quantitative comparisons with the biological system. This is made possible through the clarification of three distinct measures of population activity: voltage, firing rate, and a new term called synaptic drive. The model is activated by prerecorded neural activity obtained from thalamic “barreloid” neurons in response to whisker stimuli. Output is produced in the form of population PSTHs, one each corresponding to activity of spiny (excitatory) and smooth (inhibitory) barrel neurons, which is quantitatively comparable to PSTHs from electrophysiologically studied regular-spike and fast-spike neurons. Through further analysis, the model yields novel physiological predictions not readily apparent from the full model or from experimental studies.

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Abbreviations

PW:

Principal Whisker

AW:

Adjacent Whisker

RSU:

Regular-Spike Unit (excitatory/spiny)

FSU:

Fast-Spike Unit (inhibitory/smooth)

TCU:

Thalamocortical Unit

VPM:

Ventral Posterior Medical Nucleus

PSTH:

Peristimulus Histogram

PSP:

Post-Synaptic Potential

CTR:

Conditioned-Test Ratio

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Authors and Affiliations

  1. Department of Mathematics/Statistics and Center for Neuroscience, University of Pittsburgh, 15261, Pittsburgh, PA

    David J. Pinto

  2. Department of Neurobiology, University of Pittsburgh, 15261, Pittsburgh, PA

    Joshua C. Brumberg & Daniel J. Simons

  3. Department of Mathematics/Statistics, University of Pittsburgh, 15261, Pittsburgh, PA

    G. Bard Ermentrout & Roger Traub

Authors
  1. David J. Pinto
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  2. Joshua C. Brumberg
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  3. Daniel J. Simons
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  4. G. Bard Ermentrout
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  5. Roger Traub
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Pinto, D.J., Brumberg, J.C., Simons, D.J. et al. A quantitative population model of whisker barrels: Re-examining the Wilson-Cowan equations. J Comput Neurosci 3, 247–264 (1996). https://doi.org/10.1007/BF00161134

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  • DOI: https://doi.org/10.1007/BF00161134

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